HOT TOPIC
A New Source of THz-FIR Radiation
J. E. Walsh, J. H. Brownell, J. C. Swartz
Department of Physics and Astronomy,
Dartmouth College, Hanover, New Hampshire 03755-3528
M. F. Kimmitt
Department of Physics, Essex University, Colchester, UK
January 7, 1999
Abstract
A new source of tunable coherent radiation which operates in the THz-FIR region of the
spectrum is described. The device is based on the passage of a small diameter, moderate
current but extremely “bright” electron beam over a diffraction grating. The
beam is produced in a modified scanning electron microscope (SEM) and the grating is
mounted in the focal region of the electron beam. Unlike some earlier devices of this type
where the available output power is limited to the incoherent superposition made by
individual electrons as they move over the grating, the present source operates in a
collective mode in which the output power increases as the 4th power of the beam current.
Present performance levels are reviewed and speculations on future developments are
presented.
Introduction
A new variation on an old theme has been used as the basis of a novel source of tunable
coherent radiation. The device, which currently operates in the far infrared region of the
spectrum, makes use of the electron beam in a scanning electron microscope (SEM) which
drives a diffraction grating that is mounted in the e-beam focal region of the SEM [1].
The grating acts as a coupler which converts a part of an electron’s kinetic energy
into radiation. The basic coupling mechanism, which is known almost universally as the
Smith-Purcell [2] effect, was first described by those authors more than four decades ago.
In the original experiments [2] and a number of subsequent investigations, constraints
on the e-beam focus was a limiting factor in setting the strength of the beam-grating
coupling. Although the interference of wavelets scattered from adjacent grating periods
added constructively, the superposition of the responses from individual electrons was
incoherent. In this limit, in a given direction, the beam-grating system is in effect a
source of band-limited spontaneous emission or in this classical regime “shot
noise.” The operating regime in the present device is fundamentally different. The
electron beam current in the SEM is relatively low but the current density is large and
the beam’s “quality” parameters, energy spread and angular collimation, are
excellent. The new device operates in a collective mode and the power available increases
dramatically.
In this respect, the new source is a direct descendent of mm wavelength devices [3]
known variously a orotrons [4,5], ledatrons [6] diffraction generators [7] or
Smith-Purcell free electron lasers [7]. Unlike those devices, however, the present source
uses only the distributed feedback on the grating to achieve threshold.
Grating Coupled Radiation
An electron moving over a conducting surface will create a surface current footprint
and, when the surface has periodic rulings, the induced current will also be modulated. As
the electron passes by, the modulation in effect moves through the envelope of the surface
current. The combined effect produces a pulse which has superimposed on it a set of space
harmonics separated in wave number by integral multiples of the grating constant, kg,
where kg is given by:
and is
the gratingperiod. Components of the modulated surface current with phase velocities that exceed the
speed of light produce a radiative wake.
The wavelength, l, of the emitted radiation is given by:
(2)
and depends on the relative velocity of the electron, b, and
the angle of emission q. The factor n is the order of
the interference. Equation (2) follows from either a Huygens construction or alternatively
from a analysis of the wave-particle kinematics for an electron moving above a diffraction
grating.
The distribution of energy radiated into the nth order by a single electron
moving over a grating of length L, at a height b above the surface, is
given by:
(3)
where g is the relative energy of the electron,
and |ngn|2 is the grating efficiency for nth
order coupling.
and |ngn|2 is the grating efficiency for nth
order coupling.
When multiplied by the number of electrons per second passing over the
grating, Eq. (3) may be recognized as a generalized shot noise formula. The total power is
a result of the incoherent superposition of the individual electron contributions. If the
electron is highly relativistic (b » 1), the peak power
emitted in the shot noise limit can be surprisingly large. Even in the non-relativistic
limit easily observed levels of power are predicted.
grating, Eq. (3) may be recognized as a generalized shot noise formula. The total power is
a result of the incoherent superposition of the individual electron contributions. If the
electron is highly relativistic (b » 1), the peak power
emitted in the shot noise limit can be surprisingly large. Even in the non-relativistic
limit easily observed levels of power are predicted.
Examination of Eq. (3) reveals the critical importance of the “impact
parameter” b. Energy is transferred to the fields on the grating via a
velocity synchronous coupling of the electron with a co-propagating space harmonic
component of the field. At phase velocities below the speed of light, the wave number in
the direction normal to the grating is purely imaginary and the evanescent factor in Eq.
(3) is a direct consequence. The magnitude of b and the velocity of the electron
determine both the effective upper limit to the spectral content of the emitted radiation
and the strength of the beam-grating coupling.
parameter” b. Energy is transferred to the fields on the grating via a
velocity synchronous coupling of the electron with a co-propagating space harmonic
component of the field. At phase velocities below the speed of light, the wave number in
the direction normal to the grating is purely imaginary and the evanescent factor in Eq.
(3) is a direct consequence. The magnitude of b and the velocity of the electron
determine both the effective upper limit to the spectral content of the emitted radiation
and the strength of the beam-grating coupling.
Gain in the device becomes appreciable when feedback that results from the
stored energy in the non-radiative part of the invidual electron wakefields is large
enough to excite collective oscillations on the electron beam. Derivation of the
stimulated emission coefficient is involved but an expression not unlike Eq. (3) results.
The geometric factors that appear in Eq. (3) retain their importance.
stored energy in the non-radiative part of the invidual electron wakefields is large
enough to excite collective oscillations on the electron beam. Derivation of the
stimulated emission coefficient is involved but an expression not unlike Eq. (3) results.
The geometric factors that appear in Eq. (3) retain their importance.
Recent Experiments
In order to explore this interaction and at the same time develop a useful
source of radiation for the far infrared spectral region, the already mentioned slightly
modified SEM has been employed. The voltage levels available in the original apparatus,
10’s of kV, were already sufficient but the sub-µA currents that typify microscope
applications were smaller than desired. Evaluation of Eq. (3) for emission at near normal
angles in the range of several 10’s of kV yields predicted power levels in the
vicinity of 100 pW/sr µA in the FIR spectral range.
source of radiation for the far infrared spectral region, the already mentioned slightly
modified SEM has been employed. The voltage levels available in the original apparatus,
10’s of kV, were already sufficient but the sub-µA currents that typify microscope
applications were smaller than desired. Evaluation of Eq. (3) for emission at near normal
angles in the range of several 10’s of kV yields predicted power levels in the
vicinity of 100 pW/sr µA in the FIR spectral range.
A greater margin for exploring the beam current dependence of the
interaction was obtained by replacing the original internal high voltage power supply with
one that can provide up to 5 mA of total beam current. All of the apertures were removed
to allow high beam current operation. Provision has also made for a new wehnelt electrode
bias system so that the e-beam can be pulsed as well as swept. The SEM is otherwise
unmodified. At low currents, it still functions as originally intended, although with
reduced resolution.
interaction was obtained by replacing the original internal high voltage power supply with
one that can provide up to 5 mA of total beam current. All of the apertures were removed
to allow high beam current operation. Provision has also made for a new wehnelt electrode
bias system so that the e-beam can be pulsed as well as swept. The SEM is otherwise
unmodified. At low currents, it still functions as originally intended, although with
reduced resolution.
Fig. 1: Diagram of the SEM optical system.
A schematic view of the SEM is shown in Fig. 1. Electrons are emitted from
a Tungsten hairpin cathode, focused by the back-biased wehnelt electrode and accelerated
by the anode. The beam is further focused and positioned over the grating with the
SEM’s original electron optical system. The beam diameter over the grating can be
varied between 20 µm and 60 µm with current up to 1.5 mA. The solid angle subtended by
the output window is 0.07 sr.
a Tungsten hairpin cathode, focused by the back-biased wehnelt electrode and accelerated
by the anode. The beam is further focused and positioned over the grating with the
SEM’s original electron optical system. The beam diameter over the grating can be
varied between 20 µm and 60 µm with current up to 1.5 mA. The solid angle subtended by
the output window is 0.07 sr.
Fig. 2: Grating resonator block.
A sketch of the grating block is shown in Fig. 2. The block itself is
mounted on a 10 ґ 10 cm miniature optical bench that also
serves to support a faraday cup that collects the current and an electrode system that can
be used to monitor the beam profile “on-the-fly.’’ Alignment is facilitated
by reducing the beam current and using the SEM in its originally intended operating mode.
At present the grating is mounted opposite the FIR window and only normally emitted
radiation is collected. This has been a convenient initial configuration but it is not an
essential restriction. Examinations of the angular dependence of Eq. (3) with other
parameters fixed reveals that the emission pattern tips forward with increasing beam
energy. At non-relativistic energies the effect is not dramatic but theory suggest that
the shift should be easily observed. Exploitation of the angular tuning of the device may
also be useful in applications.
mounted on a 10 ґ 10 cm miniature optical bench that also
serves to support a faraday cup that collects the current and an electrode system that can
be used to monitor the beam profile “on-the-fly.’’ Alignment is facilitated
by reducing the beam current and using the SEM in its originally intended operating mode.
At present the grating is mounted opposite the FIR window and only normally emitted
radiation is collected. This has been a convenient initial configuration but it is not an
essential restriction. Examinations of the angular dependence of Eq. (3) with other
parameters fixed reveals that the emission pattern tips forward with increasing beam
energy. At non-relativistic energies the effect is not dramatic but theory suggest that
the shift should be easily observed. Exploitation of the angular tuning of the device may
also be useful in applications.
A typical FIR power vs beam current plot is shown on Fig. 3. The FIR power
is sensitive to the beam tune but is very stable given constant beam charateristics. As
expected in the lower current range the observed power varies linearly with beam current
in accord with the predictions of Eq. (3).
is sensitive to the beam tune but is very stable given constant beam charateristics. As
expected in the lower current range the observed power varies linearly with beam current
in accord with the predictions of Eq. (3).
Fig. 3: Detected FIR power vs. beam current. The
solid lines are power law fits to the linear and super linear regimes. The exponents are
indicated. The detected power at threshold is 5 pW.
solid lines are power law fits to the linear and super linear regimes. The exponents are
indicated. The detected power at threshold is 5 pW.
The detected power near threshold on Fig. 3 is approximately 5 pW, which
does not include any correction for total collection efficiency. The latter factor is
between 1% and 10%. As the beam current is increased, a transition is reached after which
the power rises rapidly with beam current. Above this threshold a super linear dependence
(on a log-log plot) is observed. In this regime, in the present apparatus, the power rises
as roughly the fourth power of the beam current. A sharp rate of rise of power with
current is expected but the exact origin of the exponent is still under investigation.
Above the upper power limit shown on Fig. 3, measurements with an InSb detector in single
shot pulsed modes yield detected power levels in the several hundred nW range.
does not include any correction for total collection efficiency. The latter factor is
between 1% and 10%. As the beam current is increased, a transition is reached after which
the power rises rapidly with beam current. Above this threshold a super linear dependence
(on a log-log plot) is observed. In this regime, in the present apparatus, the power rises
as roughly the fourth power of the beam current. A sharp rate of rise of power with
current is expected but the exact origin of the exponent is still under investigation.
Above the upper power limit shown on Fig. 3, measurements with an InSb detector in single
shot pulsed modes yield detected power levels in the several hundred nW range.
The mode quality of the emitted beam is excellent. The transmission
through a polarizer as a function of polarizer angle, shown in Fig. 4, confirms that the
radiation is linearly polarized. Also, the observed spatial mode is smooth and single
peaked with no side lobes evident.
through a polarizer as a function of polarizer angle, shown in Fig. 4, confirms that the
radiation is linearly polarized. Also, the observed spatial mode is smooth and single
peaked with no side lobes evident.
Fig. 4: Transmitted power vs polarizer angle. The
solid line is the square of the cosine of the polarizer angle.
solid line is the square of the cosine of the polarizer angle.
Experimental and Theoretical Challenges
Although numerous details remain unexplored the broad outlines of e-beam
grating coupled radiation theory, in the spontaneous emission or shot noise regime, are
well established. Comparatively less is known about the super linear regime. Geometric
factors such as the diameter and position of the beam relative to the evanescent scale of
the field above the grating undoubtedly retain their importance. It is assumed but not yet
definitively established that other basic gain characteristics are similar to those which
govern any generic traveling wave device. A considerable body of literature in this area
already exists. The way in which these considerations may be adopted to a grating coupled
system for example have been explored by Schдcter and Ron [9].
grating coupled radiation theory, in the spontaneous emission or shot noise regime, are
well established. Comparatively less is known about the super linear regime. Geometric
factors such as the diameter and position of the beam relative to the evanescent scale of
the field above the grating undoubtedly retain their importance. It is assumed but not yet
definitively established that other basic gain characteristics are similar to those which
govern any generic traveling wave device. A considerable body of literature in this area
already exists. The way in which these considerations may be adopted to a grating coupled
system for example have been explored by Schдcter and Ron [9].
Remaining challenges divide into two categories. In the first are
questions pertaining to e-beam optics. The total current in the SEM is modest but the beam
current density is remarkably high. It can easily exceed 100 A/cm2 in the
present system but this is still well below reported limits. The emittance of the beam in
the current apparatus is also low. Typical values are in the range of 0.03p mm mrad. The angular collimation is excellent and the beam can be
described as very “bright.’’ These emittance values (and the energy
spread), although already excellent, do not yet approach theoretically predicted limits or
limits achieved in other electron optical systems. Replacing the tungsten hairpin cathode
with a higher current density emitter such as LaB6 would improve performance
substantially. In a more extreme limit, current densities at the cathode in the range of
(104 – 106) A/cm2 from single tip ZrC field emitters
have been reported [10]. It is also clear from the FIR power vs beam current plot that the
system is not yet saturated. The highest FIR power levels detected to date are in the
µwatt range. This is a useful level of output but the electronic efficiency is clearly
still very low, (10–8 – 10–7) . If, as is the case in
other travelling wave systems, that ultimate saturation occurs near the threshold where in
the phase velocity frame the field amplitude is large enough to turn electrons back,
electronic efficiencies in the 1% range may be reached. Exploring the role of still
further improved electron optics can play in reaching this goal is of critical importance.
questions pertaining to e-beam optics. The total current in the SEM is modest but the beam
current density is remarkably high. It can easily exceed 100 A/cm2 in the
present system but this is still well below reported limits. The emittance of the beam in
the current apparatus is also low. Typical values are in the range of 0.03p mm mrad. The angular collimation is excellent and the beam can be
described as very “bright.’’ These emittance values (and the energy
spread), although already excellent, do not yet approach theoretically predicted limits or
limits achieved in other electron optical systems. Replacing the tungsten hairpin cathode
with a higher current density emitter such as LaB6 would improve performance
substantially. In a more extreme limit, current densities at the cathode in the range of
(104 – 106) A/cm2 from single tip ZrC field emitters
have been reported [10]. It is also clear from the FIR power vs beam current plot that the
system is not yet saturated. The highest FIR power levels detected to date are in the
µwatt range. This is a useful level of output but the electronic efficiency is clearly
still very low, (10–8 – 10–7) . If, as is the case in
other travelling wave systems, that ultimate saturation occurs near the threshold where in
the phase velocity frame the field amplitude is large enough to turn electrons back,
electronic efficiencies in the 1% range may be reached. Exploring the role of still
further improved electron optics can play in reaching this goal is of critical importance.
The other major category of open questions relates to resonator optics.
Although the effect of adding external mirrors to the system have been investigated, to
date their impact on observed performance has been modest. It seems clear that the
dominant feedback is on the grating itself. The grating block, Fig. 2, is apparently
functioning as an open “surface” resonator. Individual electrons create a wake
part of which is radiated in accord with Eqs. (2) and (3). A second part of the wake, the
space harmonic components with phase velocities which fall outside the light cone, are
trapped on the surface. Undoubtedly the trapping is imperfect. Some accidental conversion
to radiation may occur and finite conducivity and other effects will limit the Q of these
surface modes. Never-the-less they certainly appear to provide the energy storage capacity
needed to establish the threshold seen in the power transfer curves. To date the period
and profile of the gratings have been designed with radiative efficiency as the dominant
concern. The structure of the trapped modes and their role in establishing the threshold
is less thoroughly investigated but very much of interest. A speculative suggestion but
one that is intriguing to reflect upon is the potential role that many of the ideas
emerging from “photonic-band-gap’’ research might play in improving grating
resonator design.
Although the effect of adding external mirrors to the system have been investigated, to
date their impact on observed performance has been modest. It seems clear that the
dominant feedback is on the grating itself. The grating block, Fig. 2, is apparently
functioning as an open “surface” resonator. Individual electrons create a wake
part of which is radiated in accord with Eqs. (2) and (3). A second part of the wake, the
space harmonic components with phase velocities which fall outside the light cone, are
trapped on the surface. Undoubtedly the trapping is imperfect. Some accidental conversion
to radiation may occur and finite conducivity and other effects will limit the Q of these
surface modes. Never-the-less they certainly appear to provide the energy storage capacity
needed to establish the threshold seen in the power transfer curves. To date the period
and profile of the gratings have been designed with radiative efficiency as the dominant
concern. The structure of the trapped modes and their role in establishing the threshold
is less thoroughly investigated but very much of interest. A speculative suggestion but
one that is intriguing to reflect upon is the potential role that many of the ideas
emerging from “photonic-band-gap’’ research might play in improving grating
resonator design.
Conclusions
In assessing the future role of grating coupled sources, the fact that they may provide
a convenient laboratory scale source of coherent tunable FIR radiation is of central
importance. The FIR range of the spectrum, that region bounded approximately by the
wavelength that fall between 10 and 1000 µm, has been regarded for many decades as a bit
of an orphan. In comparison with the situation encountered at longer and shorter
wavelength regions, the technology base in this spectral range is limited. This has
inhibited research. It is still the case that much research in the FIR is done with the
traditional thermal source used in conjunction with some version of the Fourier Transform
spectrometer.
Although options were limited, sources that operate in some part of the FIR have of
course been available. Versions of the conventional microwave tube, particularly versions
of the backward wave oscillator, have had their operating range extended into the
submillimeter range of the spectrum. Optically pumped FIR lasers provide discrete but wide
ranging coverage and they have been available for nearly three decades. Solid state
multiplier chains have also played a significant role in providing a source in the longer
wavelength end of the FIR.
The existence of significant research challenges and possible technological
applications, such as long wavelength excitation of bio-molecules, mapping phonon spectra
in mesoscopic structures and applications as a local oscillator in FIR radio telescopes or
atmospheric sounders, have continued to motivate the search for new FIR sources. Although
not itself a new source, recently a significant effort has been expended on adopting the
FIR component of the emission from synchrotrons for FIR spectroscopy. Various conventional
and novel semiconductor laser techniques have had their operating range from the mid
infrared into the short wavelength part of the FIR. Laser mixing has been demonstrated.
The p-type Ge laser has been operated over much of the FIR and finally in a brief summary
the array of FIR sources the ultra wide band short pulse sources must be listed.
To date the device described in this note has been operated over a spectral range which
extends from 200 µm to beyond 1 mm. Operation at longer wavelength is possible but
probably not of particular interest since at longer wavelengths many competing options
exist. Extension to shorter wavelengths is the central goal. Estimates based on
application of the best available electron beam art, and presuming only modest additional
gains from an exploitation of a better understanding of the grating as an open resonator,
support a claim that operation of a grating coupled source should be possible in
wavelength regions as short as the 10—20 µm range. In establishing this claim,
dramatic increase in beam voltage has not been assumed. Increasing electron energy does of
course extend the evanescence length and dramatically raise the power predicted by Eq.
(3). The grating is a potentially interesting coupling structure for highly relativistic
electron beams, but that is a separate story.
Support from ARO Contract DAAH04-95-1-0640, DoD/AF DURIP Contract F49620-97-1-0287, and
Vermont Photonics, Inc., is gratefully acknowledged.
References
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[3] W.W. Salisbury, US Patent 2,634,372, filed October 26, 1949, granted April 7, 1953.
[4] F.S. Rusin and G. Bogomolov, Proc. IEEE 57, 720 (1969).
[5] D.E. Wortman, H. Dropkin and R.P. Leavitt, IEEE Journ. Quant. Elect. QE-17(8), 1341
(1981).
[6] K. Mizuno and S. Ono, The Ledatron, Infrared and Millimeter Waves 1: Sources of
Radiation, ed. K. Button (Academic Press, Inc., 1979), Ch. 5, pp. 213-233.
[7] V.P. Shestapolov, Diffraction Electronics (Kharkhov: 1976).
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[10] W.A. Mackie, T. Xie, M.R. Matthews, B.P. Routh, and P.R. Davis, J. Vac. Sci. and
Technol. B 16, 2057 (1998).
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