Hi Sapo and everybody!
And thanks to your interest at my bottle in the ocean...

The advantage I hope to get from creating all WDM carriers at once is that their phases are related. This means that from a few reference (=unmodulated) subcarriers, the receiver can infer phase references for all the subcarriers containing the transmitted information, thus making coherent detection easier.

In fact, re-creating the subcarriers at the receiver and using them to demodulate the unseparated (unfiltered) signal still containing all modulated frequencies could be easier than splitting the signal in all subcarriers and demodulating, since the filters on the unmodulated carriers don't need to be fast.

Fourier transform: the methods I know would be pretty difficult for WDM. Carriers are some 100GHz apart and carry some 10Gb/s data, so this is too fast for digital signal processing as well as for Fourier transform spectroscopy. Maybe I miss something.

I wish I typed fast! Look, this topic is really old...

In fact, I was coming back because of this paper:
www.sciencedaily.com/releases/2007/11/071101084950.htm

Basically, they tune the repetition frequency of a pulse laser to match the mechanical resonance of a virus and kill it selectively, if I got the picture properly.

If these repetition frequencies fall in a reasonable range for microring lasers, it could be a nice use! Build a chip with some microring lasers adjusted for the resonant frequencies of virus A, virus B... Choose the output you like, put it in a laser amplifier and banzai!

This would make a compact, portable, durable source - better than femtosecond lasers, which I imagine like optics lab experiments, with oversensitive adjustments everywhere.

Golly, where did the OP go?

Enthalpy, I was mostly serious in my reply, but the part about FFTs on-chip at high speed really shouldn't be that hard, considering how quickly we're finding new uses for qubits, eh?

Killing bacteria: I got it wrong. The proposed method has nothing to do with a mechanical resonance, so forget the microring laser for that application.

FFT: I wasn't sure it was a joke, hence the neutral response.

Exhuming this discussion because of the guys who produced some nW of THz power by letting two quantum-cascade infrared laser beat in a nonlinear crystal. My highly subjective and unfair intuition tells me that the ring laser driving a nonlinear element is way better for it.

For the nonlinear element, I was just considering a kind of tunnel-effect element. It could be more efficient than a nonlinear crystal, especially a low power levels.

Imagine: stack a metal, then 1nm insulator or little more, and metal again - similar stacks compose Flash memories nowadays, which rely on tunneling through the insulator. Put a limited voltage across so that a reasonable current flows.

Let the laser pulse run within the insulator. I know it's thinner than half a wevelength, but only the width must be more than that. Frequently done on microwaves guides. Sure, you need a good taper or several transition from a normal thickness to 1nm - call it an impedance matching if that's your vocabulary.

Light with 1mW (peak) power in a 1µm*1nm guide with e=2.5 creates a voltage swing of 25mV peak between the electrodes. While this is less than the 1V to 3V DC polarization, the very nonlinear nature of the tunnel effect will increase the tunnel current a lot where electric fields add up, and decrease it less where they subtract. This means, the polarized tunnel stack is a rectifier, fast enough to react to light frequency, and more current will flow when the light pulse passes through. Rectifying efficiency also looks good: just think of a 3V so-called Zener diode (in fact a tunnel diode), it's already quite nonlinear at 50mV peak-to-peak.

People who prefer to think of quanta should consider a light photon being absorbed by the insulator whose bandgap is much wider than tha photon energy, so the created electron-hole pair is virtual, but materializes at the electrodes because these are near enough and have different potentials, so that the energies of the electron and the hole become real.

The current peak induced by the light pulse is used in an antenna to make THz waves (or carried away for further processing) at a frequency determined by the ring length, maybe including some refinements suggested before. Also, some suitable "circuitry" (that is, form and layout of electrodes, as is done in microwaves but microscopic) is needed immediately at the Tunnel stack to provide a low impedance a light frequency and a coupling impedance at THz.

The tunnel effect rectifier can be built another way: by field emission.

Take the "usual" (hum, still a research subject) field emission cathode corrugated at atomic scale, for instance by diamond epitaxy or using nanotubes - or whatever you prefer, as all solutions are still bad. Put the usual polarization voltage on it.

Then, send the light pulses on this field emission cathode. Because the emitted current relies on tunnel effect, it is highly sensitive to added electric fields (from the light), and reacts nonlinearly to them.

Again, you get current peaks as the light pulses arrive, and the laser loop length defines the THz frequency of the current, to be used in an antenna.

What is less obvious with feld emission :
- You need electron transit times smaller than a quarter THz period (not a quarter light period, I believe), needing electrodes very close toanother.
- Unless the cathode is very small, light must impinge almost tangentially on it, so that the THz radiation can sum additively in some direction. Or you need an antenna network that compensates for the phase.

So my guess is that the 1nm tunnel diode is better, as carriers transit time is zero in it.

But it can be worth investing a few neurons on it. Anyway, I like the idea that the field emission cathode is sensitive to photon energies lower than the extraction potential. IR detector?

However, we might completely avoid any rectifier, and use the light emitter as a THz generator. Look:

- Take an almost standard laser diode, but without its end mirrors. Better said, put antireflective coatings, or impedance matchers, at both ends. Do it well enough that the diode can't lase alone.

- Put this diode in a resonant ring (here we are) that reinjects the light in the diode, and whose length defines the THz pulse repetition rate.

- Convince the diode to work in a pulsed mode, for instance with a saturatable absorber. Throwing together the microelectronic equivalent of a dye cell should be easy, for instance with a limited amount of deep-level dopant somewhere in the optical path.

- After the diode emits a light pulse, the carrier concentration drops in the semiconductor, and so does the direct voltage across the diode, so one gets the THz power directly at the diode electrodes.

Again, the diode electrodes must be designed properly to make use of the current pulse. As the diode is probably longer than the THz wavelength, the radio power should be collected at the light emitting end of the diode, either as a radiowave, or maybe as a current in a cable - cables are probably bad at such frequencies.

I like this one. It looks simple, rather efficient, and uses existing technology.

Some more ramblings about the laser diode in a ring:

- Several diodes can be coupled through the light guide and build an antenna array. Classical phasing methods apply.

- What I suggested some time ago with several coupled rings etc still apply.

- A ring is better than a stripe plus mirrors, as it concentrates THz power at one single diode end.

- Several optical paths may have one laser diode each. Switching the power supplied to each diode selects the path. This allows electronic beam steering, frequency adjustment etc (like in a trumpet, you know? Fine, I could bring a bit of civilization in this discussion).

Estimating the available THz power:

Take a 1mW diode from a CD burner - if that isn't common technology! It draws maybe 2mA DC. Use it at 2mA peak (fine, its life is longer) and 30% cycle ratio. If the carrier concentration drops by a factor of 2.7 after lasing, the direct voltage drops by 25mV. Matching all impedances carefully leaves 10mV peak and 1mA peak available, or 5mVpp and 0.5mApp, which make about 1µW THz power.

This looks simpler and more efficient than the pair of quantum cascade lasers, I mean.

But if you take a powerful laser diode, say a 5W model used to pump Yag lasers, you get continuous 5mW THz power. Not bad !

DVD writers have laser diodes with 50mW optical power. Better than 1mW: it would rather make 50µW THz power.

However, the THz power won't be that easy to extract from the semiconductor. The junction has an important capacitance, and the semiconductor electrodes have a series resistance. Their combination gives a time constant that limits the speed or frequency.

As some diode lasers are modulated at 100Gb/s (maybe more meanwhile), their time constant allows to extract 50GHz with little losses, but losses may be big at 1THz or 10THz.

This is what I liked about the metallic tunnel junction: it is damned fast. The tunnel effect itself of course, and the electrodes as well with their tiny resistance.

As for field emission, the electron transit time can barely be kept small enough. Taking a voltage drop of 100V, the electrons have a speed of 5.6Mm/s maximum or 3.8Mm/s average. Over a quarter period of only 1THz, they would drift only 0.9µm, which should be the electrode spacing. So we're back to micromachining processes.

The good news is that with about 100V over 1µm, any cathode creates field emission.

Then, the fast light-to-current converter would look much like the metal-insulator-metal Tunnel junction, with 1µm vacuum replacing 1nm ceramic.

One may prefer to use a photocurrent rather than light-enhanced field emission, with the same buildup. It needs photons with a higher energy, but at least the electrical effect is strong.

Inducing the photocurrent in an insulator rather than at a photocathode would ease manufacturing, but remember the electrodes must be metallic. With 10V across 100nm (for 3THz then), it already needs good semiconductor manufacturing practices.

Here a nice paper:
http://www.ofcnfoec.org/materials/PDP13.pdf

In 2003, they modelocked a laser diode at 240GHz, converted the light pulses to radiowaves with a photodiode ("not optimized for 240GHz": sure!), detected the radiowaves with a Schottky diode and transmitted data.

Meaning that THz isn't very far, the photodiode being the limiting element... Or a component with equivalent function, for instance the tunnel diode with metal electrodes - or picking the RF power at the laser diode's electrodes where possible.

In the laser diode, time constants aren't a limit.

In fact, the junction capacitance is discharged directly by the stimulated emission, which doesn't act through the access resistance. So the voltage drop can be extremely fast - it only means that the light pulse can be short and intense, which is nothing original.

The effect of the junction capacitance is already accounted for, as soon as I wrote that the direct voltage drops by 25mV - this corresponds to the charge drop across the junction.

Now, the access resistance loses power because it is in series with the useful circuit - for instance, the antennas network, or the propagation line.

Putting sort of figures:

With a 50mW diode, the formerly estimated 50µW THZ power available at 5mV peak and hence 20mA peak would need a load (the useful circuit) of only 0.25 ohm.

The diode draws some 100mW at 2V, hence 50mA, and looses hopefully less than 0.2V in its access resistance, which is then under 4 ohm (at least in DC): expect losses.

Now, if we choose rather a load of 4 ohm, we get 5mV peak in it, or 3µW for a 50mW diode instead of the full 50µW. Pity, but still very exciting. And a 5W laser diode would emit 0.3mW CW, nice!

4 ohm is uneasy but common at high frequencies, for instance at power amplifiers. The thin insulator of an integrated circuit achieves it readily. And it's just 18 halfwave dipoles in parallel, if they were independent.

Optimizing further the access resistance would be more important to producing THz power than to laserlight. A long narrow form could be better.

In case the high-power laser diode is longer than the microring laser tailored to the light repetition rate (the THz frequency), one can use the diode as a laser amplifier and produce the driving pulses separately - this is existing technology.

I've had a look at conduction losses in propagation lines at these frequencies, and they're bad.

Data comes from the Handbook of Chemistry and Physics, which has a table titled "Optical Properties of Metals" giving the complex refractive index for many metals, beginning at 40meV or 9.7THz.

To put it short: at 9.7THz and 30.2THz (=10µm = 300K), the usual formula for the Kelvin effect applies with just 10-20% error. That is: 9.38mm skin depth for Cu at 50Hz, 11.5mm for Al, decreases with the square root of frequency; permeability and permittivity would also matter.

At 2eV or 620nm, one would need to take 330 nohm*m to get the measured skin depth; this would be neglecting other absorption mechanisms that may be predominant at optical frequencies.

Now, estimating the efficiency of a dipole antenna in air: at 9.7THz, the conduction losses would equal 9 ohm, and 15 ohm at 30.2THz, but 130 ohm at 620nm, as compared to the 73 ohm radiation (=useful) resistance of the dipole. That is: a good dipole works well at moderate THz frequencies, but rather badly at visible wavelengths.

Antenna configurations that decrease the radiation resistance should be avoided. Patch antennas for instance should have quite a thick dielectric. Uda-Yagi antennas aren't necessarily a good choice; the reflector should be put rather far away from the radiator.

Small improvements would come from a somewhat longer dipole antenna, tuned with thinner ends and a thicker central part. More radiation resistance, less conduction resistance.

Please remember that dielectric antennas exist, especially the cigar antenna. This will be one of the best directional THZ antennas (arrayed if needed), and is easier to integrate than a parabolic reflector. See Kraus for instance.

A funny consequence of metal antennas having some efficiency is that every modelocked laser diode has radiated THz waves (or high GHz) through its feeding lines, and maybe with more power than purposely designs did, but hadn't been observed as this wasn't the intent of the experiment. I enjoy this thought.

As halfwave pieces of metal already shows significant losses, you may expect long propagation lines to be bad. True.

At 10THz, a microstrip line of W=2µm on SiO2 with h=2µm would have a loss resistance of about 800 kohm/m as compared to some 70 ohm wave impedance, meaning that the voltage gets divided by 2.7 in just 87µm distance or 3 wavelengths. It's even worse at 30THz and more so at visible frequencies.

A waveguide is known to be better. As frequency increases and sizes decrease accordingly, losses per m increase as F^1.5; I extrapolate to THz since the skin depth still follows the usual values.

From (optimum but observed) 2.7dB/m at 90GHz with copper and air, I get 3dB/mm at 10THz. Al instead of Cu increases to 3.7dB/mm at 10THz, and I found that permittivity lets conduction losses unchanged when guide sizes decrease as sqrt(permittivity). This makes manufacturing possible and saves thicknesses on an optical chip.

In other words, a waveguide loses 3dB after 820µm at 10GHz and 460µm at 30THz. This is over 10 times better than a microstrip, as usual, but still doesn't allow arbitrary path lengths.

The THz guide with lowest losses is, as for optics, a dielectric guide. Sizes aren't always comfortable but are achievable on a chip: with K=3.9, the 10THz half-wavelength is 3.8µm.

High losses in metal lines are a big concern. They still allow the electrodes of a modelocked laser diode to radiate THz waves, but prohibit the ultrathin microstrip line or waveguide I imagined to convert light pulses in THz by tunnel effect or photoelectric effect.

Adapting the form of a dielectric line looks interesting, if using a nonlinear crystal as well. I will come back to it later, in order to describe first an alternative method that doesn't use light.

An electron beam looks like an interesting means to produce THz waves.

It can be concentrated in tiny spots. We need about 1µm; electronic microscopes achieve far smaller ones.

It can be swept quickly, for instance at 40GHz, like in an oscilloscope. The speed of the sport can be extremely high (as no matter moves with this spot: it's the crossing of a sweeping beam and a surface), for instance 2ps/cm or 15*C on some (baseband) oscilloscopes.

The combination of small spot size and high sweeping speed makes short electric pulses which contain THz power.

Steer an electron beam in X and Y to make a circle. Do it at a speed commonly achieved with electronics; I take 40GHz here. The spot path is fine-tuned to run close to a dielectric line for THz shaped as a ring. With a permittivity of 12 and a speed of about 1e8m/s, this makes a ring of 800µm diameter.

The electron current induces an electric potential in the dielectric line as it swifts by. And as the beam is steered to match the speed of the THz pulse in the line, this effect adds upon time; if losses are very low, for instance with SiO2, coupling eventually becomes high and the power is limited by the electric breakdown of the line.

Now, there are several ways to convert this narrow pulse with 40GHz repetition rate, which already contains some THz power but has many unwanted spectra lines, into a cleaner spectrum THz line - if you prefer to think of time domain: to increase the repetition rate.

Of course, cavities or rings can be used once the power is extracted from the e-Beam/ring device. But I prefer other method, as they allow to increase the THz power by letting many pulses run in the dielectric ring. Each pulse can now reach the maximum field allowed by the dielectric (provided that the dielectric losses are really low); only one pulse at a time gets an energy boost from the electron beam.

One way to add pulses in the race on the dielectric ring is to add one or several dielectric rings which are coupled to the main ring - for instance through fading waves in the THz domain - and whose length differ from the main ring, so that they reinject pulse at positions differing from the fed pulse. The proper ratio of lengths (relative primes etc) makes the shift from GHz to THz. Adding several rings with different lengths helps to equalize the amplitudes of all pulses running in the main ring and get a clean THz spectrum.

A cleaner THz spectrum can also be achieved by increasing the repetition rate in steps: say, from 40GHz to 800GHz in the main ring, and then to 16THz once the power is extracted from the main ring. However, the GHz frequency must still be locked as precisely as before so that its high THz harmonic resonates in a ring or cavity; this needs the GHz frequency to be locked to 1e-4 or better, though the resonators probably aren't that precise, hence an adaptive locking.

Another means of running many pulses in the dielectric line is to add a detour to the line: most of its length is still circular and coupled to the e-beam, but a part moves away and delays the pulse, which then makes several turns before it meets the e-beam again, so that the e-beam adds power to each pulse in turn. Chosing properly the number of THz periods added by the detour optimizes the spectrum. Several detours of different lengths are also possible.

If (big IF) the length of the additional rings, cavities or detours can be varied or switched without introducing THz losses, they are a way to vary the THz frequency - that is, to choose the harmonic of the GHz frequency. But remember we need low losses after some 1000 turns in the ring.

An alternative method to produce THz oscillations from an e-beam swept at some GHz involves a metal THz cavity, still in a ring form, but with a standing THz oscillation instead of a travelling pulse.

In this case, the THz frequency is produced by a periodic form, like holes or fingers in the metal, that let the e-beam hit one part of the cavity or another as the beam sweeps across them. The periodic form, made by semiconductor processes, is small enough to create THz frequencies.

With figures: make a pattern of holes, 1µm in diameter, alternating with 1µm metal. Sweep the e-beam at 60Mm/s across the pattern, you get 30THz oscillation. The beam being deflected by a 40GHz signal, it makes circles of 478µm diameter.

This circumference is less than perfect. It means that the THz will be modulated at 40GHz (=its spectrum will contain unwanted lines) due to the losses in the cavity. It can be further improved by coupled rings, resonators etc as described before.

Semiconductor processes would allow holes of 100nm with a 200nm period, on a ring of 48µm diameter. This would improve the losses and the spectrum. However, it needs an electron beam concentrated to 100nm diameter; microscopes achieve better figures, but it's nothing easy.

The most obvious form for the metal cavity is a waveguide bent to make a ring, with holes drilled at its top at the median radius of the guide, so that the electrons hit aternatively the top or the bottom of the guide. The guide is preferably evacuated, by usual MEMS processes, to avoid electric charge accumulation.

Other cavity forms may well be better, especially if they provide some form of shortcuts between distant parts of the ring - that is, not a ring-shaped guide - thus making the stored energy more uniform and constant, and hence the spectrum cleaner.

It can be simpler to go from 40GHz to 30THz in several steps, each step involving a steered e-beam. This allows a wider beam hence a smaller electron source, and the cavities have smaller losses. The spectrum is also cleaner. Just use the intermediate 1THz signal to deflect the second beam.

I like this one. It looks robust and relatively easy to manufacture. And with 1mA beam (20W dc?) and 50V peak cavity voltage, we get about 25mW THz power.

It looks like very early machines to make high voltages, where rotating mercury jets swept across electrodes to connect a primary winding. Some sirens still work in a similar way.

I tried to check the difficulty of the electron beam: it looks very easy. Independent checks are welcome here as well!

First, concentrating electrons on a 1µm spot needs a ridiculous electron energy in mV. This is confirmed by Jeol for instance, whose microscopes achieve a resolution of 1.2nm with just 30kV acceleration voltage. Put another way: diffraction is not a limit to the resolution of electron beams, but rather spherical aberration.

So I chose 1keV energy (19Mm/s) for no good reason, and a deflection distance of 200mm for a prototype. Deflecting by +-240µm requires 23km/s laterally, and a driving frequency of 40GHz gives some 10ps or 0.2mm to do it, which is achieved by just 2.6V across plates 0.2mm apart as well.

It looks like if amplification is even possible.

Now, if we make two steps and drive the second beam at 1THz instead of 40GHz, the deflection can be /25 but in a time /25 also, so the electric field remains the same.

I like to compare the path of the electron beam to the water jet of a garden hose when you shake quickly the end in circles. Nice picture.

Well, I think I've cracked the jackpot. My e-beam siren can produce many mW of THz power at a precise frequency and its manufacturing processes are relatively easy at today's standards. I enjoy having done it on a (very) open forum.

I have no 1µm drill here at home, so who will be the first to make a prototype?

Marc Schaefer, aka Enthalpy

Bingo and Super-bingo.

Forget about the ring cavity.

Keep the microscopic holes or fingers made by semiconductor processes that interrupt at THz frequency the electron beam whirling at GHz frequency, but now, add a deflecting steady (electro-) magnet to concentrate the e-beam back to a point on the axis.

There, you harvest the THz power at a single point. This brings a cleaner spectrum and more power. Even better, you can now adjust the THz frequency freely.

At the focus (don't focus too much!) I would still put a metal resonant cavity - but if someone believes a dielectric resonator can survive the e-beam, all right. This metal cavity, for instance a cylindrical box with a hole on its top to let the e-beam impact the bottom of the cavity, is better than the former ring:
- The output amplitude isn't heavily modulated at the GHz frequency by the ring's cavity losses;
- Less losses;
- Easier to cool, as only the bottom receives the impact of the beam. It can produce many Watts of THz power. Don't forget to cool the masking wheel as well, then.

To reduce the losses by the metal cavity, sink its external Q-factor by coupling it heavily to the output dielectric line - but not too much, as a high Q couples more power from the beam. Also, aluminium looks like a good choice, but not necessarily the best one even at room temperature.

And if someone wants to try a dielectric resonator, he may drill a hole at its center to let the e-beam through, and catch the beam with a metal part downstream the resonator (a pit may avoid secondary electrons and ease cooling). A metal screen upstream may also protect the dielectric resonator from electrons accidentally off-axis; building it of insulated overlapping metal rings reduces the losses if it's close to the resonator.

If filtering is needed, a separate dielectric resonator does it better than the metal cavity.

Now, as the fingers or holes of the mask (to be hold and cooled at its periphery) are tiny, one may probably need to slowly steer the e-beam actively to them. The simplest way to measure the mean position, width and ellipticity of the beam is to detect the GHz field (including its second harmonic, or at >3 places on a circle) created at the mask.

Silicon may be a good choice for the mask, as it conducts heat well; copper is just another possibility. Use the good old water microchannels if you like them. A deep narrow groove at the beam's path helps spread the heat on more surface.

Maybe I make a drawing some day. Or maybe not.

Now, some thoughts for the electronics engineers.

As you've noticed, the device works as a frequency multiplier (and an amplifier, probably), so you can lock and modulate the frequency and phase directly by the GHz input - as usual, inaccuracies will be multiplied as well. The amplitude is modulated at the electron source: through a grid-cathode voltage if field emission or thermionic emission creates the beam, or by controlling the optical power if photoelectric emission creates it.

The output spectrum will contain many spurious lines spaces at the GHz frequency. The asymmetry of the mask causes them, and can't be much improved at µm sizes. As THz communications and imagery become common, these lines will need to be removed.

As usual, multiplying the frequency in several smaller steps helps filtering these spurious lines out, especially if the center frequency is to be variable. And augmenting the order of the filter is often better than making it more selective.

Also, a resonator centered at the output frequency isn't necessarily the best to dampen the spurious. Tuning a Fabry-Perot or a ring at a harmonic of the input frequency may be better, and several ones tuned on different harmonics even better (think in time domain here: delay and reinject). All built with dielectric lines of course. But this is rather for a fixed output frequency.

The resonator that picks the THz power from the e-beam will be selective if it needs a high Q to be efficient (I more and more guess so). Then, one may actively tune it by adjusting its geometry, for instance with some dielectric screw, or by adjusting a gap at its mid-height - until someone invents a lossless THz varicap, of course... Also, several resonators stacked would allow to work at different frequencies.

Maybe the element that couples the THz power from the beam to the output line can be made aperiodic.

Put a second magnet that lets the beam flow along the axis (if this doesn't work, use driven electrostatic plates like after the gun, but it needs the proper phase). Put a dielectric propagation line along this part of the beam. Choose the electron energy to match the phase velocity in the line; for instance, if you find a lossless medium with K=12 and build a line at 1e8m/s, you need some 30kV. Collect the power at the end.

By the way, such a velocity matching eases a tuned resonator as well, and is easier with a metal cavity.

If some kind of superlattice can slow down the phase velocity, it's welcome. Or try to build a helix with the dielectric line around the beam, as is done with metal in other vacuum tubes. This will allow small acceleration voltages. Nice.

Two or more lines sitting symmetrically around the beam may prevent repelling the electrons.

If efficient coupling needs too much length, try to build a recirculating line. It will be periodic, but allows many frequencies.

Another means to extract the power from the e-beam: an undulator http://en.wikipedia.org/wiki/Undulator

Except that in our case the electrons of the beam are already in packets, so no self-organizing is needed. Easier!

With slow electrons, the period of the magnet pairs must be nearly the distance between the electron packets if one wants to radiate on axis - normally the case as other directions are occupied by the magnets. When changing the frequency, tune the acceleration voltage accordingly, and compensate the power with the beam intensity.

At 30GHz, two poles plus two magnets add their thicknesses to about 100µm, so this is laminated materials. The beam has that little room, so it must be parallel to the axis and near to it.

At the end, divert the electrons to a surrounding anode, and radiate the THz wave directly, or through a dish or lens, or catch it (with a cigar antenna) in a dielectric line. Or maybe the line can run parallel to the beam and the undulator.

One limit is that, with slow electrons, the magnets must be near the beam in terms of wavelengths, and they will waste some radiated power. Clearly, the undulator works better with highly relativistic particles.

If you don't want to radiate, a metal shield is due now around the undulator.

Forget about the undulator in our case.

First, the period of a pole pair is about 3.3µm at 30THz and 30keV=100Mm/s. I knew nobody seriously paid attention.

Such a thickness would already need a small technological effort. Worse, it only allows some 1.5µm clearance for the beam between the poles: much less than a half-wave. And finally: it radiates nothing.

To evaluate it: I take a field of 0.5T peak value, varying as a sine. Then, all in peak values, the electrons feel 8pN and wobble only 250pm. A short dipole antenna of 500pm=5e-5*lambda has a radiation resistance of just 2µohm...

With a beam current of 1mA or some 0.5mA rms, multiplied by 30,000 pairs of poles over 100mm, it will radiate on the axis as a dipole of 2µohm and 15A, or an EIRP of 0.4mW+2dB, but only on a solid angle of some 3e-4sr, which means a total radiated power of 30nW.

So it may work with relativistic electrons, but not here. Putting any hope in it is undue right now.

Just for the length of this message, I would like to imagine a few devices that don't use the micrometer-sized mask or chopper, nor deflect the e-beam back to the axis, but do make use a the e-beam deflected at GHz frequencies so that its impact point moves quickly.

The idea that this impact point can easily move near, at or above the light of speed is simply fascinating.

Imagine a guide of electromagnetic wave, without any holes or fingers or features - smooth, in other words. When properly impacted by the e-beam whose speed is the wave velocity in the guide, it carries an electromagnetic shock wave, whose amplitude and steepness is limited by the guide's losses at the desired frequency - and maybe by the speed of the electrons, but probably not by the beam concentration as 1nm is achievable.

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A robust metal guide is relatively easy to make. A void slot in a metal sheet (thin versus a quarter wavelength) already is a guide - it would be a disk within a hole in a sheet so that the beam impact directly the disk or the sheet. The disk can also overlap the sheet above or beyond, protecting other parts from the beam. Less obvious but well-known, one side of the slot - that is, the disk alone or the hole alone - also acts as a waveguide.

Some favourable features are that one can increase the beam intensity up to the breakdown of the guide, and that the DC return path for the beam can be at points that are electrically cold and hence induce no GHz and THz losses - something a metal ring doesn't offer.

Now, the shockwave contains components at high THz frequencies but runs "slowly" (GHz) around the guide. A means of collecting the high THz is to build many local harvesters around the guide and unite them to add the pulses; one benefit is that they harvest the high THz contents before it is damped in the lossy metal (gold), as high THz don't even survive a full turn. Dielectric guides seem to be good for that task; they could begin at the slot, where overlapping metal parts create a strong and well-oriented field. They should be pulled away early from the lossy metal; if possible, a slot in the dielectric would allow the guides to carry more power before breaking down.

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Of course, a guide made or dielectric instead of lossy metal would be better, provided that one can couple the beam power in the guide without destroying it. Could the answer be as simple as semi-insulating GaAs or lightly-P Si (maybe by a deep acceptor)? As a (commonly used) dielectric guide, they could make a ring, or in whispering mode, a disk. The pulse would be around one gap high, or a few mW.

One funny idea with a dielectric guide is that it may not be limited to THz by the losses in metals. After all, the beam can be concentrated to 1nm and moves at some 2e8m/s, so it can carry components to 5as (5e-18s) or 1.5nm, very deep in the UV. Just find a way to couple the beam energy in the guide. But as losses are lower, you may have several turns for it.

Another funny possibility would be to pump a lasing medium with the beam, directly or not. Propagating the population inversion at the speed of the laser pulse allows to use ultrashort-lived lasing levels in superradiant mode. The beam can bring a high power very locally. This sounds like ultrashort pulses with a high and stable noiseless repetition rate. Again, a whispering mode can be considered.

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Some applications would require the quick beam impact to follow a straight path, and this is less easy as a constant speed is generally desired. When deflecting the beam (this time in one direction only, not in a circle), one may add harmonics to the deflecting signal to compensate more or less the sine waveform.

Then, more exotic applications may appear:
- Far-UV or X-rays lasers (directly in a metal sheet or wire as a lasing medium, on deep levels wavelengths; a thin wire may allow light to escape the attenuating metal)
- Particle accelerator? The electromagnetic pulse has a limited voltage, but can be very steep and thus push the particles, provided speeds match precisely.

A few more words about the very hypothetical X-ray laser pumped by the fast sweeping e-beam. Please take with big caution, as I'm very uneasy with such topics.

I didn't find usable data on emission efficiency, so I used photon absorption curves - but this is quite different, as emission would use an internal transition (say, 2p to 1s) as opposed to absorption which is always to a non-bound energy, since 2p and other levels are full.

Absorption efficiency increases by a factor of 4 when the photon energy suffices to eject a 1s electron. The minimum would be a factor of 2 in order to lase with 100% population inversion. This is a tiny margin, which may well vanish if considering only the useful internal transition.

It also means that the e-beam must blast away a high proportion of 1s electrons. However, the beam will blast all bound electrons the same way, effectively destroying the solid target. One may rotate a cylindrical target to spread the damage. Or unroll a sheet of W, a bit like toilet paper?

Converting first the e-beam to uncoherent X-rays (similar to He-Ne pumping) wouldn't target one electron shell specifically, even if the primary X-rays were monochromatic, because the interesting shell is 1s, which is harder to deplete than the others.

I couldn't see how a rare earth, with its uncomplete shell, could help targeting only the 1s shell. Photons tuned to this transition would just ionize other shells.

In YAG lasers, a few colour centers are hold in place by a transparent solid medium, allowing to reuse the lasing atoms. However, no element (Be, C...) is transparent enough to X-rays to allow such a huge dilution factor of the lasing element (W, Pb, U...). And anyway, such a matrix would itself absorb effectively the pumping electrons or photons and be destroyed.

The only good news is the lifetime of deep transitions. From the "natural width of X-rays lines" of 50eV for W (similar for Pb and U), the lifetime must be around 8e-17s, corresponding to the sweep time of a 25nm e-beam swept at 3e8m/s - this is achievable at least at the surface of the target as long as it is new.

About pumping a laser (a working one, for instance at visible frequencies) by the sweeping e-beam, a funny idea would be to build a laser diode, either straight or in circle if light can be bent enough. At least, we know that a laser diode can be pumped with a current.

In addition to controlling completely the repetition rate (in a straight form), it would allow to use materials and designs with short carrier lifetimes and still lase at a sustainable mean power, and produce short pulses.

Then, the diode light may in turn pump another lasing medium, including at will a Q-switch, as usual. Propagation speeds must be matched if both mediums are side-by-side.

By the way, pumping a laser by a wave propagating at C is already known for nitrogen lasers (pumped by a gas spark), and I guess for fibre lasers (light pumping).

More fun with the laser diode pumped by the e-beam.

Instead of collecting the electrons in an electrode connected to a junction that injects minority carriers which recombine with majority carriers, as this is quite an indirect method...

Stop the electron beam within the semiconductor, where it creates electron-hole pairs ready to lase. ¡Ole!

OK, it's not a very delicate method, but current densities in a laser diode aren't delicate neither, are they?

An acceleration voltage of about 2keV would let the electrons give their energy over 200nm depth centred around 200nm beyond the surface in GaAs - values comfortable for laser diodes. This means that passivation must be thin and must resist charge injection. Passivate with a metal?

A 2keV electron transfers a momentum equivalent to less than 0,14eV to a phosphorus atom, and 0,06eV to Ga or As, insufficient to damage the semiconductor directly. I expect broken chemical bonds to heal spontaneously in a semiconductor. However, the repeated oriented shocks may let atoms flow over time as electromigration does. To be experimented.

Each 2keV electron creates some 500 pairs. This means that, to create the equivalent of 0.1mA injection in a 1µm*1µm spot, the beam intensity is just 0.2µA - so the process is less brutal as it first looks.

If the lasing zone is narrow enough, light should follow the beam impact even in a circle. This would be nice to allow changing the GHz frequency at will: just make a uniform semiconductor sandwich, increase the beam deflection radius proportionally to the frequency, and find a way to extract the light.

If the light isn't willing to take the turns, it may be helped a bit. Apart from some index box or whispering mode, one can also make the central higher-index material, or rather the upper material, thinner at the outer side of the curve so that wave speed will be higher there. A bit like braking the inner caterpillar of a battletank to turn.

That's all for this day and for this class of devices, where the beam hits continuously the target.

I'll be back (hopefully, since I've heard "génère" - as secret services call me - and "anticiper") with more about my Terachopper - you know, where the beam whirling at GHz is chopped by a µm mask to create THz packets in the e-beam.

Do you like the name Terachopper? I prefer it to Siren, for instance.

As it looks, the "photodiode" (semi-insulating GaAs with tiny carrier lifetime and DC polarization) commonly used to create THz pulses from femtosecond light flashes could be used directly as a target for the e-beam.

But far better methods seem to exist. Simple gold halfwave dipoles, overflown at one end by the electron packets, could radiate several mW each and be used in array along the beam. Somewhat better than multiple cavities.

Dielectric guides also look good, especially with faster electrons matched to the slow wave.

See you soon!
Marc

A more detailed insight at the e-beam tells that the nicely chopped packets don't stay separated over the distances I figured before, because of their space charge. Here is what I tried to compute; again, the opinion of somebody knowledgeable for e-beams would be highly appreciated!

The 10mA beam being interrupted half of the 30THz period (16fs+16fs), each packet carries 1.6e-16C or just 1000q. An acceleration voltage of 2kV gives 27Mm/s, or packets 0.45µm long separated by 0.45µm. I take spheres of 0.5µm diameter.

At the surface of the packets, the potential is 0.58V and the field 230kV/m, pushing electrons apart at 4.1e16m/s2. After a flight of 0.2m or 7ns, they would be 1m away if the field stayed constant - in other words, they are mixed up.

The situation isn't that tragic for the beam concentration: one must only concentrate the beam where needed and use it within 3ps or 80µm of the focal point - which will be at some distance from the "lens" (magnet). Sort of field depth in optics.

Less easy with the packet separation! Packets should be used shortly after being chopped. An axial magnetic field may keep the beam collimated, but won't keep the packets separated - or will it?

I fear my computation here is correct. It explains why simple triode or pentode valves don't work at high GHz: there, klystrons and TWT are used (see Wiki), and all have some trick to keep the electron packets tight, or even amplify the clumping of the beam over the path. Looks like if this had been known for some decades.

What can improve this? Little. Accelerating with 20kV instead of 2kV allows 3 times more distance. Defocussing the beam between the chopper and the target also improves a bit: with 500µm electron "disk" diameter instead of 5µm, fields are 1e4 times weaker, allowing for distances 100 times longer or 8mm; but then, some electrons have a longer path than others... And anyway, spreading and concentrating must occur within a tiny distance.

So I'll improve the affected designs with smaller distances.

As compared to the effect of space charge estimated above, the thermal dispersion of the beam is less of a concern.

The electron gun would use field emission as in microscopes, who have similar goals. I expected thermal dispersion to be well under 26meV, but for some reason people observe 100meV or even more - values I had expected from thermionic emission.

The effect on the axial speed is limited. 100meV over 2keV change the speed by 25ppm or 700m/s: this makes 0.1µm after 150ps or 4mm - far less critical than the 80µm space charge allows.

On my devices, where the beam is swept quickly, axial speed dispersion also translates to beam widening - for devices without a chopper as well. A dual chopping mask scheme would improve this dispersion but would lose beam intensity.

The effect on transverse speed is already solved by (electron) optics and collimation, as microscopes have a resolution of 1nm and less.

You thought the X-ray laser was just crap, then what about a gamma laser?
Sweep a positron beam against any material, the impact point moving at C.
Here http://news.bbc.co.uk/2/hi/science/nature/6991030.stm they say every 200th positron builds a pair that lasts for a quarter nanosecond - any spot size under 75mm lasts shorter.
OK, OK, I don't insist.

Remember? I wanted to concentrate the chopped beam back to the axis before extracting power from it - because if built with metal, a smaller extractor has less losses.

One additional difficulty: designs with a direct electron impact tend to roast, vaporize, destroy the target, which must be microscopic at 30THz.

As it looks, direct electron impact designs must spread the beam over a large target. If concentrating the beam back, then the extractor must work through the beam's proximity but let other parts take the beam impact. Very possible, with components like cavities.

Did you notice? We're nearing klystrons, TWT and other existing designs... But original designs still have a chance.

About the cathode:
- It must emit enough current to produce THz power (say, 10mA, excepted when the e-beam creates electron-hole pairs directly in a semiconductor to pump a laser diode)
- And the beam must be focussed later, without loosing much intensity.

Field emission is very fashionable, especially when done with carbon nanotubes. It produces a beam which is well-oriented even before the high voltage accelerates the electrons. This helps concentrating the beam later with a magnetic lens - a bit like a wide laser beam can be well concentrated because it is coherent. It also gives the best uniformity in electron energy.

However, emitting such a current with nanotubes would need several cm2. I'm not enthusiastic about this.

The classical method is thermionic emission, where LaB6 and CeB6 have replaced W (less hot, longer life, electron energy more uniform). This one is less good than field emission to focus the beam.

People who want to concentrate a powerful beam, to energize a Linac or a Fel or other toys, now use a photocathode or an RF gun (where light is pulsed). This corresponds to our needs.

Illuminating with a laser, current densities can be huge. Researchers report some 10GA/m2 = 10mA/µm2. Remembering that the acceleration voltage will put the electrons almost parallel, it's clear that several 10mA can be focussed on a target of less than 1µm2.

I've had a look whether the driving light can be chopped at THz frequency to get a modulated e-beam. The answer is no, because space charge at the cathode evens the current. People use light pulses at 3GHz to 30GHz with difficulty. So: emit a continuous beam, chop it later.

I hoped CeB6 would be a perfect photocathode as well: heat-resistant, low work function, good conductor of heat and electricity - but its measured quantum efficiency is horrible. I guess CeB6 and LaB6's surfaces are heavily contaminated at room temperature. Anyway, people use Mg or an alkali compound. Computations tell permanent 10mA in a few µm2 are achievable without vaporizing the cathode. A work function under 2eV would allow a DVD laser diode, or a pump diode designed for Yag lasers.

Papers about photocathodes with dense current tell little about the cathode itself; they insist much on an RF cavity, superconducting if possible, directly at the cathode. I guess this is necessary to keep the electron bunches separated, not to emit the beam. However, this is how I like to imagine a photocathode setup:

I would concentrate laser light with a lens (or mirror) with very short L/D, centred on the e-beam. Light would come from where the beam goes if using a (centreless) lens. And I would illuminate only two sides of the mirror (or the lens) according to the polarization of the light, so that the interference at the focus has its electric field perpendicular to the cathode's emitting surface, for I figure somehow that it helps the photoemission.

Not really necessary, of course. But funny to try.

No, a way to keep the electron bunches concentrated despite electrons having slightly different speeds. It makes paths longer for the fastest electrons, so that the bunches are concentrated again when arriving at a chopper or at the target.

For that, we may use electrostatic mirrors. You know? They are boxes, with the slit input surface at the same potential as the surroundings, and the bottom (slightly) more negative than the cathode, so that electrons are repelled back. Sure, it works well with 250V or 20kV but badly in a synchrotron.

In the simplest form, a single mirror would let the e-beam make half a turn or nearly. Now, imagine: the fastest electrons go nearer to the repelling electrode, so their way is longer and needs more time. By choosing the right mirror thickness, the fastest electrons exit the mirror later, and all arrive at the same time at the target. Mirrors slightly too thick allow a somewhat higher repelling voltage to adjust the synchronizing effect.

I suppose this effect is already known and desired in the "reflex klystron" and the "carcinotron".

Now, the U-turn may be inconvenient. But with four mirrors, the beam can exit in the same direction in entered: by turning for instance 90° left, 90° right, 90° right and 90° left. The energy doesn't shift the beam's position in this design neither. Other combinations and angles are possible.

Concentric forms may be necessary with my whirling beam.

Near-optic quality is needed for these mirrors to keep the end focal point precise when deflecting the beam. Optical polishing is not needed. Holding all parts, especially the slit input surface, without interrupting the beam, needs some thinking.

Some THz generators need the beam to be focussed, hence synchronized, at several places - for instance at the mask and at the target for my terachopper. Then, speed compensators are to be inserted at several places.

These speed compensators work best with electrostatic deflection, as they make also the impact point independent of the electron's speed. Magnetic deflection looks less adequate here.

Another device with a deflected electron beam: a detector or heterodyne mixer for THz frequencies.

This time, the beam is deflected in one dimension only, and at the incoming THz frequency (frequencies). It is then focussed to a target whose form makes the output current a nonlinear function of the instantaneous deflecting field.

An example of such a target are four 90° sectors with opposing sides connected together, and the output electronics measuring the current difference. Wobbling the beam makes it flatter as a mean, so two sectors receive more current than the two others as a mean value over one (or many) THz period. Optimized forms may give a better nonlinear function; a pure square transfer function is generally preferred.

One nice feature is that this device doesn't need precise flight times from the electrons, as only their direction matters. More specifically, flight times must be matched only to a fraction of the period of the output frequency, which may range from very low to just some GHz in a heterodyne receiver - and this is much easier than matching for a THz frequency.

The sectors can be metallic and collect the beam current, or semiconductor and collect the many pairs created by each stopped electron. In both cases, a micrometre-sized target (made by microelectronics processes) combined with a focussed beam give the detector a high sensitivity to any deflection. Even better, electron lenses may increase the deflection. And as the sensitivity of the following electronic amplifier is limited just by shot noise (= fluctuations in electron number), the device's sensitivity can be very interesting, both as a mixer and as a detector, especially a synchronous one.

Two deflecting electrodes pairs (or coils, less probably) can be built to let first the received signal deflect the beam and then the local oscillator without polluting the input signal. One could even tilt the electrode axis (input signal "Down-Up" and local oscillator "Right-Left") with respect to the target (sectors UpRight+LowLeft-UpLeft-LowRight) so that one single input gives no output, only their product does (electronicians call it "L.O. rejection", mathematicians will see a product instead of the square of a sum); but as the output frequency is much lower than the input, rejection and tilting have limited interest.

Isn't that nice? It remembers a mixing hexode or heptode. Get 6.3V AC to power the laser diode for the photocathode, and it will be perfect. Pity the Noval footprint doesn't work with THz dielectric guides.

As deflecting the beam needs some electric field but very little power, optimizing the electrodes improves sensitivity. Resonant electrodes - especially with a dielectric resonator - would be far better if the input frequency has a narrow range. For a wider range, try to slow down the phase velocity to match the electron velocity.

I'll be back with more figures. Since I hadn't understood properly the interaction between deflection and focussing, some figures are false in my previous posts. Still to be improved, and I'll try do it better for the detector-mixer.

Most of my previous designs in this thread have a flaw with the beam concentration. It is a big limitation for most uses of electron beams that intense beams need a big cathode surface producing a wide beam that is quite difficult to concentrate later.

Microscopes use tiny cathodes at µA currents and reduce the diameter with a diaphragm, losing the intensity down to nA currents. Then, de-magnifying the image of the source makes the spot nm sized. Not usable to create HF power.

Normal valves (triodes, pentodes etc) have a very broad beam and don't use deflection. Not my goal here.

Particle accelerators use nonuniform magnetic fields to concentrate an initially diffuse and intense beam. And with huge light pulsed power and huge GHz electric fields using superconducting cavities, they begin with a very high current density at the photocathode. I feel it too complicated for a component.

So from my previous proposals, please consider all ones needing mA currents and µm concentrations over some distance to be flawed.

The next designs will hopefully make sense about beam concentration, electron speed dispersion, space charge and deflection vs lenses. I'll go back to the previous ones later.

Here is the description with figures for the mixer - synchronous detector. This one has survived the beam concentration issue.

It uses only 20µA beam current, emitted by a single hot nanowire of LaB6 (80nm diameter) with 500V extraction voltage. The paper describing it shows 20µA for 260V at 5µm distance, so the 500V needed elsewhere allow a lower temperature or more distance to the extraction electrode. Alternatively, a single hot pyramid of W covered with ZrO would emit 200µA at 3200V from a similarly small area; focussing would be easier, at the price of a higher voltage.

Electrons pass the extraction electrode at 13,3Mm/s +-300ppm with a typical side speed of +-325km/s or +-24mrd. Typical beam radius there is 285nm.

A first magnifying lens *12 makes an image of D=1µm with a typical convergence of +-2mrd. At 120µm before or after the focus, divergence raises the beam radius by 240nm, and space charge by 280nm, so the beam diameter is 2µm. The beam is deflected there, by the incoming signal before the focus, and by the local oscillator signal after the focus.

A second magnifying lens makes an big image on the target, for instance *10 makes an image of 10µm diameter.

The target is of metal. A photodiode target is useless, as it would amplify the signal as much as the shot noise, which is already stronger (2,5pA/Hz^0,5) than any other noise source, even of an integrated transimpedance amplifier at 10Gb/s. With 10µm spot diameter, the four-sectors target can be made by Mems technology, allowing to integrate a low-capacitance transimpedance amplifier. Other combinations make sense, for instance a passive tuned circuit if building a heterodyne converter to IF; then, an external amplifier is just as good, and a third magnifying lens accommodates a mm-sized target.

With 10µm spot size, the four-sectors target with quadratic response (a previous message) delivers 0.6µA/µm2 of instantaneous deflection, or 0.3µA/µm2 of peak sine deflection. By superimposing a sine deflection of 4µm peak through the local oscillator, the target delivers 3,4µA/µm of rms input signal. This combines with the noise current to give a correlated deflection noise of 735fm/Hz^0,5 at the target or 74fm/Hz^0,5 at the second focus where deflection is made.

I decompose the 120µm available before and after the focus in 44µm to accelerate the electrons to the side and 76µm free flight to the focus. Now, it takes 3.3ps to cross 44µm, which are 10 periods of 3THz, so we put 20 electrode pairs with alternating polarities, and can sum the deflection over 20µm (length is lost between opposing polarities).

A higher acceleration voltage would ease this part. It makes the beam thin over a longer distance, makes electrodes longer and thus farther apart, which again gives more length to deflect the beam. Manufacturing is also easier. It would be necessary at higher frequencies.

Still with 500V supply, 1pm deflection at the second focus takes 2µV over 3µm electrode spacing, so the voltage noise is 147nV/Hz^0,5. As the 20 electrode pairs in parallel may have a wave impedance of 10ohm, a wideband resistive termination would mean a noise of 2.2fW/Hz^0,5 or 300K+57dB.

However, deflecting electrons consumes very little power, and putting 20 electrode pairs has already narrowed the passband, so a better method is to have near the electrodes a resonator that provides the higher voltage. With Q=20, the bandpass remains similar but the noise figure drops to 300K+31dB. With a narrower bandwidth, Q=200 lowers the noise to 300K+11dB. Not bad!

A possible form for a metal resonator (a dielectric one would be welcome) would look like a crimped staple, with half a wavelength unfolded length, but extruded to the 44µm, and with its open ends cut in interleaved zigzag with 4.4µm period. The beam would pass between the bottom and the zigzag. Make with Mems technology, put a bit of structural SiO2 if needed.

And now the 10THz variant of the mixer or synchronous detector. Same general architecture.

The electron source uses thermal field emission by ZrO-covered W, with a brilliance of 5e8A/cm2/sr from supplier data. The extraction voltage is now 3200V giving 33Mm/s, the high emitted current is reduced to 5µA by an aperture, bringing the divergence*image size to 1e-18m2*sr half-angle.

The only lens makes an image of 250nm radius with a beam divergence half-angle of 1.3mrd which gives 150µm length before and after the focus where beam radius is at most 200nm bigger. With less current and more speed, space charge acts little this time.

The beam is deflected by the input signal before the focus, by the local oscillator after the focus, and is then allowed to diverge for 3.8mm before hitting the target with 10µm diameter.

The shot noise is now 1.3pA/Hz^0.5. With the local oscillator swinging the spot by 4µm peak, the sensitivity to a synchronous deflection added by the input signal is 850nA/µm rms (crossing both signals at +45° and -45° vs target would improve the sensitivity a little bit), giving a noise of 1.5pm/Hz^0.5; over the 3.8mm free flight, this amounts to a deflected speed noise of 13mm/s/Hz^0.5.

One now needs 2*44 electrode pairs with a period of 3.4µm and a spacing of 1.5µm, acting on the electrons over 100µm. Noise voltage is then 39nV/Hz^0,5 rms. Tuning with Q=100 (needs care at 10THz), the estimated 1.5 ohm wave impedance translates to 1e-19W/Hz or 300K+14dB.

The deflector can be made wideband if wave speed is reduced to 33Mm/s by a dielectric with huge K (effective index of the line = 9.1 needing reasonable losses over 150µm as well as resistance against accidental beam impacts) or by the form of the line (but metal losses make it difficult). Then, the full 150µm length and 1.5µm gap convert to 26nV/Hz^0.5 or, with a line impedance of 25 ohm, 2.6e-17W/Hz or 300K+38dB.

The lower frequency limit of the wideband version is far away; adjust the 3200V if the slow line is dispersive. The upper limit is set by the gap: sensitivity drops if the half-wave in the line is smaller than the gap.

Noise can be improved by 3dB (narrow band) or 6dB (wideband) with one lens more, giving 150µm+150µm to the deflector for the signal input and another 150µm+150µm to the local oscillator. More focus points would be difficult to use, as phase needs to be coherent. Reducing the current further, allowing longer deflectors, looks easier.

Hey, my 1000th post here!
Marc Schaefer, aka Enthalpy

And this is the broadband 30THz variant. At least, sources exist for this frequency...

It uses an electron speed of 91Mm/s, fast enough to match a dielectric guide made of silicon. A slower material with low losses over 1mm at this frequency would be welcome, provided it survives accidental beam impact.

The corresponding acceleration voltage is 24.7kV which about the maximum for easy X-rays screening. It improves also the brilliance of the source: 39e8A/cm2/sr with the ZrO-covered W hot spike. The beam is screened again to 5µA and corresponding 1.3e-19m2*sr.

A first lens makes an image of 200nm radius; beam divergence keeps the radius under 350nm for 260µm before and after focus or 2*2.9ps deflection time which is completely used for the input signal. Space charge is small this time.

A second lens makes an identical image. This second focal zone is used for deflection by the local oscillator. The beam is then allowed to diverge for full 8.8mm or 96ps, widening to 10µm diameter. Shot noise stays at 1.5pm/Hz^0.5.

Noises are then 16mm/s/Hz^0.5 and 2.7Gm/s2/Hz^0.5 and 16mV/m/Hz^0.5 and 16nV/Hz^0.5 (across the slot) and 6.5e-17W/Hz^0.5 = 300K+42dB with a slotted dielectric guide with 1µm slot for the beam, assuming 100ohm wave impedance, and a potential drop across the whole thickness of the guide 5 times as big as accross the slot - probably pessimistic.

The speed-matched dielectric guide maintains this sensitivity at lower frequencies as well and is essentially very broadband. Sensitivity drops at higher frequencies as the halfwave isn't big compared to the slot.

Crossing the deflections at +45° and -45° vs the target would bring some 3dB more sensitivity on the signal input. The local oscillator input needs just a bit under 1mW in both cases. A more complicated target form would then also allow to mix the input signal with a harmonic of the local oscillator more efficiently, but the mixer will be somewhat sensitive to all harmonics of the LO - a drawback if telecoms develop.

In all setups, some fluorescent paint should be helpful to align all components around the beam, especially the deflectors.

Except for the mixer - detector (and this makes it simpler), all THz components with an electron beam need electrons to arrive in bunches at a target. I have written that mirrors can compensate the different flight times due to speed dispersion: here is more about such mirrors.

The simplest case, detailed here, is when electrons make a U-turn of almost 180°. Electrons come from a surroundings at uniform anodic potential that we may call zero and enter a zone of uniform electric field E.

This sounds simple, but remember that radial components of the electric field would deviate or defocus the beam. In the configuration I imagine, electrons come through a tube which is narrow compared to the way they make in the mirror; then, the tube comprises many sections with a potential step between them, or maybe a single resistive section; the end is the electrode at nearly cathode potential.

A mirror consisting of an anode with a hole and a cathode would be simpler, but I suppose the field curvature at the hole is unbearable. Maybe a short portion of tube protruding from the hole towards the cathode corrects the field enough; this requires a FEM analysis.

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V being the mean speed and dv the individual variation, the time spent in the mirror is (classic):
m*(V+dv) = E*q*(T+dt)

In the free flight region of length X to be compensated, the time is
t+dt = X/(V+dv), or
dt = (X/V)*[-dv/V + (dv/V)^2 -etc]

Putting together: the distance within the mirror must be half as long as outside to compensate the first-order flight time dispersion.

Even with an unfavourable speed of 500V +-0.3V or 31Mm/s +-300ppm, and long legs of 40+40mm free flight and 20+20mm mirror, second-order errors are very small. The uncompensated 80mm would make a spread of +-1ps, but the remaining second order is just 0.3fs, excellent for any THz frequency.

With the same figures, compensating the first-order errors to +-2fs needs a precision of +-2000ppm on the distance within the mirror. This is best done with a somewhat longer mirror and a mirror voltage a bit more negative that the electron gun: the mirror voltage is then adjusted to +-2000ppm precision or +-1V, easy.

Fun: bunches are allowed to spread over many THz periods due to speed differences, and they will still concentrate again at the target. This is even better, as it limits the spreading due to space charge.

------------------------------

Designers will want to tilt slightly the mirror so the target isn't in front of the gun. The effect is less critical than is seems. Remembering that the complete flight time is now constant, the speed dispersion acts through its side component: if the target is 5mm off-axis, +-300ppm speed dispersion result in +-1.5µm precision. More precision requires a higher voltage or a scheme with more mirrors, like 2*45° or 4*45° as described for some time.

[Continued]

With electrons flowing in both directions at the same place, one may wonder about possible collisions. In short: not very critical. Small enough deviation speeds are given by
Vy = (q^2)/(2pi*e0*d*V*m)
where e0 is the permittivity and d the impact parameter.

At unfavourable 500V=2*31Mm/s, a deviation of 0.5µm at 10mm, or 1550m/s, occurs with an impact parameter of 6nm only. Spreading the beam a bit is bettter: with 200µA over D=100µm or 2µA over D=10µm, each electron has 2e-16m3 so the probability of deviating a pair of electrons is about 0.15% over 10mm opposite traffic.

------------------

These mirrors can be curved, for instance spherical or elliptic. I expect them to focus a beam much more precisely than a magnetic or electrostatic lens does. The tube that varies the potential slowly between anode and cathode must now be a cone. The combination with beam deviation remains twisted, resembling optics more than ballistics.

Combining such a compensation mirror with a valve that bunches electrons by modulating their speed (klystron, TWT...) instead of chopping the beam is nothing obvious. I believe the mirror must be on the path between the modulator and the target, and then it compensates also the modulated speed, not just the unwanted spreading. The reflex klystron, which has only a mirror and no uniform-field zone between the cavity and the cavity, doesn't try to compensate the speed.

Now, back to the ring laser diode. Remember, it is pumped directly by the electron beam creating electron-hole pairs in the semiconductor, ¡ole!. The beam whirls in circle at the speed of light, and so does the laser light pulse.

I imagine a thin metal top / ~400nm AlGaAs / ~400nm GaAs / AlGaAs heterostructure that would confine carriers and light in GaAs. However, other materials may have a more useful wavelength.

The beam has an energy of 6keV to stop within the GaAs layer. It takes about 20fs to do so, fine. But hot electrons seem to take some 50ns to thermalize in GaAs, which would be unacceptable. Suggestions:
- Use a ternary semiconductor where ballistic electrons are stopped quickly.
- Dope heavily, maybe both N and P at the same place
- Implant dopant in this zone and don't anneal.

As the light pulse shall also stop within some 20fs, it would be good to inject a Q-switch at this place, and also sink the carrier lifetime to avoid that carriers created in AlGaAs flowing "slowly" to GaAs create a light tail. Heavy doping may help. And anyway, the heterostructure may not be necessary at all, as few pairs are created at the surface.

The good news is that short carrier lifetime and fast thermalization are perfectly compatible, and shortening them is easier than lengthening.

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I imagine a whirling frequency of 100GHz, for which transistors exist. The ring has then 280µm diameter (88Mm/s and index=3.40) and the beam spot only 2µm, so light should bend easily. Anyway, the ring's border is etched vertically and the groove filled with Si3N4; the index contrast provides a complete reflexion.

The (really) many outputs of the ring are not coupled by fading waves through Si3N4 as I previously thought. The border of the ring is simply open (I mean, the semiconductor sandwich isn't cut by Si3N4 there) at each exit, on a width narrower that half a wavelength: this lets a small but controllable amount of light through. Another advantage is that the outputs now are perpendicular to the ring, thanks to the narrow pass which isn't directional.

Each output feeds a laser diode amplifier classically supplied with DC current, which can be made by the same layers as the ring and etched at the same step. The amplifiers broaden towards their outputs, and are long enough to create a strong attenuation if they aren't fed with current. These need reasonable carrier lifetime (>10ps for 100GHz) and can incorporate a Q-switch doping. Obtaining 10mW mean power from each amplifier would be nice.

Then, as you suppose, all amplifier outputs are joined for future uses, for instance illuminating a photoswitch or a photoschottky to create THz waves: 1W optical power as from a usual Ti:sapphire laser, but concentrated at one frequency.

I haven't seen photoschottkys where light and THz propagate in the same direction, but they probably exist.

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The e-beam has only 20µA intensity, as each electron creates 1000 pairs in the GaAs layer. This makes only 2.5 primary electrons per THz half-period: here is an advantage of the light ring over injecting the beam at the starts of the amplifiers and let the start superradiate. The ring accumulates photons over more than half a THz period, thus reducing the shot noise on the output pulses. Also, the random beginning of superradiance would introduce a phase noise that the ring avoids.

The 20µA induce a big ionization current density of 20mA over 3µm2. I haven't seen drawbacks to it, as this current doesn't move. Before lasing, it equates a carrier density of 1,8e15/cm3: nothing tragic.

A mirror isn't really necessary here. With a Schottky (=hot spike) ZrO/W emitter, the speed dispersion of +-0.3V over 6kV allows a free flight of 10mm with electrons arrival within +-5fs : this option is developed here. A mirror would give more room for the fingers, for instance 60mm+25mm+25mm+40mm.

The brilliance of this source allows a beam diameter of 13µm at the deflector, after the lens but 10mm before the ring. This XY deflector needs 22V across 20µm with 230µm length; let it resonate to reduce the power needed, or use more stages. That's less than perfect. A mirror wouldn't improve it.

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The ring having a highly divisible number of outputs (240, 300, 360), the user can choose the output frequency among a dozen ones just by feeding certain amplifiers. This compensates for the fixed whirling frequency, at least for imaging applications for instance.

Other uses are fun as well. Feed some amplifiers according to a PN sequence, make a lidar with very high ranging resolution.

More fun: put one bit of data on each amplifier's power feed, and transmit information at 24Tb/s. Use rather 10GHz whirling frequency so that data has time to modulate the amplifiers. Take the same ring at the receiver to open photoshutters and demultiplex the data to 2400 outputs of 10Gb/s. Hey, if this isn't megalomaniac!

A precision about the mixer-detector:

Its output is at a low frequency and puts little constraint on the dispersion of electrons flight times. But electron speed shall be uniform enough and distance small enough to maintain coherency at THz input frequency between both deflection inputs - that is, between the signal input and the local oscillator input.

By chance, all three design examples I gave before do maintain this coherency with a safety margin of 10 to 50. But this is a constraint designers should be aware of, especially if putting a lens between both deflectors.

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Also, one may be surprised, in the third design, that the first deflector is around a focus and should act through a lens. Optic rules do say that the next focus won't move by the action of this deflector, yes; the trick is that the spot on the target is far beyond the second focus (no image there), and this spot moves as electrons leave the first focus or enter the second focus at the same place but with a different angle.

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About flight-time compensating mirrors: this effect is already known, as expected. Not necessarily for electronic valves, but in mass spectrometers, where they provide a better focus for ions having been deflected electrostatically.

At least, we know it works.

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About thermalization time for hot electrons in GaAs:
please read ps, not ns.

And now, another THz generator that is free of the known design flaws (source brilliance, debunching over flight time, space charge defocussing, target burn...)

It looks powerful (relatively to what exists today...) and flexible. I will take several messages to describe it. Please fasten your seat belts.

This one also uses electron beams with a rather high acceleration voltage (avoiding again a mirror) combined with moderate currents, because primary electrons create many charge carriers in the target, which is a semiconductor photoswitch, ring-formed, on which the electron impacts whirl at GHz speed.

As a nice feature, this ring is a "photo"-switch, but is as well a dielectric waveguide for the THz waves created by the swift drift of the carriers in the strong electric field. This enables to accumulate wave intensity over time, improving the conversion (in-)efficiency from the e-beam to the THz output.

I consider making the ring of silicon. Silicon is known to work in photoswitches; since the created carriers are hot anyway, they should be about as mobile in Si as in GaAs. Si is also a low-loss dielectric for THz guides, and has a good heat conductivity - two advantages over GaAs here. Si should be as intrinsic as possible and have a minute carrier lifetime - maybe gold doping achieves both. I couldn't find enough data about polysilicon, an interesting option. Germanium could be nice to reduce the e-beam power.

The silicon ring would be half-buried in a sapphire substrate to remove the heat. Nice, Silicon-On-Sapphire is known for short carrier lifetime, especially if badly made. And sapphire has low THz losses and index, making a good guide in combination with silicon. I imagine a thinner (poly)silicon layer everywhere to protect sapphire from the e-beams if needed. Alternately, a polysilicon ring could just sit on a golden surface, but THz losses in the metal look a bit too high to my taste.

The ring can have several outputs tied together to harvest pulses at several instants in order to attain the THz frequency. However, it doesn't need a number of outputs as big as the frequency multiplication factor; a smaller number of outputs in fact allows to change the output frequency without hardware changes.

These output guides are built just as the ring is. And at THz wavelengths, fading wave coupling is easy - though a narrow section still can make a controlled small coupling.

To achieve an interesting power, the ring accumulates the currents of many e-beams, each of which is emitted by a sharp hot ("Schottky") ZrO/W cathode, and is steered by an individual electrodes set. This is the nasty side of this design, sorry for that - but a flat LaB6 cathode doesn't have the necessary brilliance to focus that much current on the ring.

A photocathode could maybe have the required brilliance, but would need some 20W mean optic power concentrated on a few µm2, so the cathode would be spinning or of liquid type... Adding that the many e-beams allow to vary the output frequency, reduce peak fields and help choose the output frequency, the choice is clear.

The number of beams is related to the frequency multiplication factor, but it doesn't need to be equal neither. The reason is that the dielectric waveguide is dispersive: longer wavelengths have a higher phase velocity. The user takes advantage of this dispersion by varying somewhat the GHz frequency to choose which THz harmonic has the favourable phase velocity and accumulates amplitude.

As the frequency multiplication factor is big, several close harmonics would be capable of summing up in the ring. This is where several ring outputs and several e-beam impact points help, as they discriminate between close harmonics.

[Continued...]

Marc Schaefer, aka Enthalpy

And now some figures on the ring photoswitch with e-beams. This is an example centred around 3THz output frequency; higher frequency like 10THz are possible with the same component or with a reoptimized one, but the output power is smaller, mainly because created carrier pairs have less time to move.

I take an input frequency of about 30GHz, produced by transistors from the next Chinese grocer's. Then, the silicon ring (index=3.4 in bulk, taken 2.0 in a dielectric guide) has a diameter of 1.59mm, a width and a height of 15µm. This massive ring can absorb 50W at its top with just 60K rise, or rather 100K locally: this is a key to produce appreciable THz power. The ring is polarized with vertical 200V. Silicon is damaged (Implantation? Gold? Nanocrystalline?) to reduce the carrier lifetime to 160fs, then they move 29nm or 1V in the field before recombining.

Contacts must take some 36mA to and from the ring but not create THz losses. Moving the bottom contact to both sides at mid-height (then with 100V) could be nice as THz potentials are minimum there. At the top, I hope some thin zigzags (to match wave speeds) of metal are enough when combined with a few wires, maybe running down to mid-height. This would need a better analysis.

The acceleration voltage is 15kV so that primary electrons brake in <40fs. Silicon atoms then receive 0.6eV kinetic energy at most; if this is too much, the acceleration voltage can be reduced - less practical. Germanium can also be better. All e-beams sum then to 2.1mA (a pair consumes 3.36eV to create, then drifts 1eV+1eV). I take 105 beams and guns of 20µA each to reduce peak loads in the ring and give a cleaner output spectrum. The induced current is huge: 2*9,4A if all carriers did add up, and 36mA taking into account that carriers move 29nm+29nm compared to 15µm thickness.

Even if something (trailing carriers?) made heavy THz losses in the ring, each 20µA e-beam inducing 340µA carrier current and 2.3pC/m would create a step of 22mV p-p in the 102pF/m of the ring; with an estimated wave impedance of 110 ohm, the available THz power would be about 10µW over all beams. But I'm confident that the guide can sum up the waves to 5V p-p (needs losses under 1/cm hopefully made by the output coupling only), and then the ring produces 12mW concentrated at one frequency.

More to come about the e-beams for this ring.

Billions of blistering barnacles in a thundering typhoon! Shipwreck.

The ring photoswitch with e-beams is wreaked havock by space charge again, which brutally defocusses the beams with the above figures.

The ring laser pumped by the e-beam survives to space charge thanks to its single low-intensity beam. It hoped the ring photoswitch would be a quick adaptation.

But the ring photoswitch needs more current, and guns at a bigger distance because it has several of them, then they must be offset, but this needs distance to avoid excessive variations in the electrons' flight time. Fewer guns could be closer to the axis, but more intensity per gun at a longer distance means space charge is more critical.

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Though, probably, limiting the output spectrum to 3THz makes everything much easier. The dielectric guide (the ring) can be wider, accepting a wide spot. The acceleration voltage can be higher as well.

Also, a higher input frequency allows a smaller ring diameter, and then the gun(s) can be nearer.

And here is an improved ring photoswitch with e-beam where space charge has acceptable effects. It is also simplified as it has only one beam.

I've taken GaAs for the ring at 100GHz, D=478µm W=20µm h=20µm for full performance at 3THz. Ge has a less good breakdown field but produces more carrier pairs : to be considered if THz losses of GaAs are too big. Si remains interesting if it survives the high electron energy.

The only e-beam has 150µA at 24kV (shield X-rays) with a ZrO/W schottky gun. Primary electrons stop in less than 80fs. Heat isn't an issue. Each primary electron creates 5600 carrier pairs. Limit their life to 160fs. With 300V polarization, they move some 45nm, inducing about 3,8mA photocurrent locally. Without any resonance, this would make a step of several V as the beam passes by. With resonance over several turns, one may hope to harvest several mW power at a single frequency.

5 outputs would allow some 0.5THz between the output frequencies. The overtone is still to be selected by varying the 100GHz a bit, as the ring is dispersive.

The beam is focussed to D=12µm at the ring. The 5e12A/m2/sr source alllows D=21µm at steering, which is located 15mm before the ring. Space charge widens the beam by about D+7µm at the ring.

Steering is made by two electrode pairs, 300µm long and 30µm apart, with 148V peak. If they're the open ends of 200 ohm lines, each direction needs 27W incident power at 100GHz - sorry for that. Resonating the electrodes would reduce this steering power.

Nabend - Gruetzi!

Falls jemand versuchte, mich am 14.08.08 gegen 21:25 anzurufen: Das war schon die richtige Nummer, er kann wieder versuchen. Weitere Elemente:

- So ein Versuch gefällt den Geheimdiensten meines Landes nicht, also Vorsicht. Das mag den unhöflichen Empfang durch meine Familie erklären, tut mir Leid.

- Ich bin überhaupt nicht sicher, dass ich wieder einen Arbeitgeber haben möchte.

- Diese Erfindungen habe ich hier veröffentlicht, damit sie für alle verfügbar sind, also bitte sich frei bedienen. Lieber für Medizingeräte als für Waffen.

Schönen Gruss! Marc

[OK, I go back to English, just a short interruption]

Dammit, and I was just getting used to Romanian!

Back to English - though I had the nice surprise to be able to read Romanian, it's just one Roman language more.

Just a short description without figures of a small-signal amplifier at THz frequencies.

Once again, with an electron beam, 24kV and 5µA are likely. The target is photoelectric silicon (on sapphire), call it photoswitch as an analogy, which resonates with a high Q - this is important for the gain.

To reduce radiation losses, the target is long and broad at the same time. I hope 2*2 half-waves are enough, but if the <110> directions radiate too much, increase the number of waves (this works because phase speed is lower in silicon). DC and THz fields are vertical.

The beam is steered at the output frequency from one stationary voltage maximum to the next one and back.

The deflector resonates as well. It is also made of silicon (a slotted dielectric guide) with phase speed tune precisely to the electron velocity. Making it resonate improves the gain, even though the electrons aren't stationary; this would apply as well to the previous downmixer/detector.

No mirror here, and the flight length is short, about 10mm. Gain looks possible because deflection is small, about 10µm, and thanks to the Q-factors at input and output. Noise figure looks interesting.

The beam is focussed at steering and allowed to diverge a bit at the target.

Variants:

- Wobble the beam diagonally, or use a non-uniform DC polarization pattern, to make a mixer (possibly with two deflectors) or a doubler instead of an amplifier.

- Build many beams hitting a big target (again long and broad, to reduce the length), and get more THz output power. Hopefully with some gain, though the deflectors have probably less Q-factor : I imagine them a a long and broad surface, but thin, with a slot for each beam. Then, we lose the thickness that improves steering efficiency.

That's all for today, sorry folks: I have little time these days. My mother's sick, maybe because I had this idea 2-3 weeks ago and hadn't published it, so the French secret services may have hoped to steel it - and then, give me worries in order to protect the secret. But now, it isn't secret any more, you morons.