A COHERENT, TUNABLE, FIR SOURCE

J.H. Brownell, M.F. Kimmitt, J.C. Swartz and J.E. WalshDepartment of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755-3528

(March 18, 1998)

A tunable coherent source which operates in the THz-FIR region of the spectrum has been developed. Thedevice, termed a grating-coupled oscillator (GCO) usesthe beam in a scanning electron microscope (SEM) and adiffraction grating placed in the e-beara's focal region togenerate the radiation. Distributed feedback is provided.by the grating itself and the e-beam is focused and po-sitioned using the microscope's internal control system.A summary of operating characteristics of the presentdevice and a survey of the scaling relations which willdetermine the spectral coverage is presented. Commentson what will be required in order to develop a very com-pact device are also included.

I. INTRODUCTION

The region of the electromagnetic spectrum whichfalls in the approximate band of wavelengths be-tween 10 and 1000 Am, the so-called far-infrared(FIR) spectral region, is relatively devoid of tunable,coherent, radiation sources. Until quite recently, andrelative to the range of options available at longerand shorter wavelengths, this assertion would be al-most indisputable. However, the challenge presentedby the lack of sources together with the existence ofa broad range of interesting research puzzles and op-portunities has led to a renewed interest in providingaccess to this spectral region. The present note dealswith one promising approach to a means of produc-Lug tunable THz or FIR radiation.

The beam in a scanning electron microscope(SEM) and a diffraction grating mounted in the e-beam focal region has been used to produce coherentradiation {1: over a range of wavelengths that ex-tends from approximately 250 1um out to 1000 Am.Termed a grating-coupled oscillator (GC0), the de-vice is a new variation on an old theme.

Observation of radiation produced by electronsskimming over a diffraction grating was first re-ported by Smith and Purcell [21 in 1953. Even ear-lier, Salisbury had filed a patent application [3] ona device based on the coupling of moving electronsand a diffraction grating although Salisbury appar-ently did not conduct experiments until somewhatlater [4]. Others 15-8 1 have also followed up on theearly work.

The radiation mechanism described in referencewhich has become associated with the authors'

names, was essentially an incoherent or shot noiseprocess. Individual rulings on the grating con-tributed coherently to the passage of a single elec-tron but the contributions of each electron in thebeam added incoherently. This was a consequenceof the fact that in the early experiments, the fo-cus was on short wavelengths, visible, and the sizeof the beam was large relative to the wavelength.The relative beam energy which is also a factor inthe dimensionless coupling parameter was also low.A quantitative discussion of this point is presentedfurther along in the manuscript.

Coherent radiation at mm [9-12] and sub-mm[13,14] wavelengths has been introduced in grating-coupled devices. Termed either Orotrons [9,11-14]or the Ledatron [10), these devices used gratings em-bedded in Fabry-Perot resonators and electron beamtechnology similar to that used in other microwavetubes to produce the radiation. The name Ledatron,introduced by Mizuno [10], was an acronym that waschosen in order to emphasize the dual nature of thesurface modes and the importance of both the boundand radiative space harmonics in the coupling andemission process.

In the present device it is the distributed feedbackon the grating itself that leads to bunching of theelectron beam and the growth of coherent radiation.The beam voltages are modest (10-50 kV) but higherthan those used in any but high-power tubes. Beamcurrent density is high (100 Aicm 2 or greater), butthe total currents are modest (100's AA). The "qual-ity" of the electron beam, energy spread and emit-tance are critical factors. Thus, overall, the "bright-ness" of the beam is very high. The "open" natureof the resonator together with the extremely brightelectron beam are the essential features of the de-vice.

The remainder of the paper is divided as follows:A survey of device performance will be given in Sec-tion II and a summary of basic scaling relations thatgovern device operation is contained in Section III.These sections are followed by brief remarks on pos-sible means by which very compact GCO devicesmight be realized, and by concluding remarks.

537

CathodeWehnelt

Anode and ApertureAlignment Coils

First Lens

Upper Scan CoilsStigmatorLower Scan Coils

Second Lens

PolyethyleneWindow

FIRRadiation

II. SURVEY OF EXPERIMENTAL RESULTS

Given the importance of beam quality and bright-ness, an SEM is the ideal device for exploring thepotential of the GCO. The beam quality is excel-lent and the microscope's own focusing and trans-port elements may be used to shape and positionthe beam. The beam column of the SEM used inthe present experiments is illustrated in Fig. 1. Elec-trons are emitted from a Tungsten "hairpin" cathodeand focussed by a Wehnelt electrode and a series ofmagnetic lenses. The waist of the beam is placedat approximately the midpoint of the grating andat present the lower limit to the waist diameter isapproximately 25 AM. This however is a machine-design imposed but not an absolute limit. The beammay also be swept either in and out along the gratingnormal or across the grating surface. This providesa convenient temporal reference modulation. Oper-ation in fixed spot temporally pulsed mode is alsoan option.

The grating is placed on a miniature "opticalbench" which is mounted on the microscope stage.At present the FIR optical system limits observationto the normal direction and the grating parametersare chosen to optimize normal emission. Designsthat circumvent this limitation are under evaluation.

FIG. 1. Diagram of the SEM optical system.

A typical example of a plot of observed power ver-sus electron beam current is shown in Fig. 2. It hastwo characteristic regions. When the current is rel-atively low and/or the beam diameter is compara-tively large, the observed power increases linearlywith current. This is characteristic of a shot noiseor spontaneous emission process. In this region, adetailed analysis of the emission process has beencarried out [14 The emitted power in Wisr is givenby:

dP Nn2=

2teoF 2 eXP (

—X0/

Ae) (1)

where e is the electron charge, I is the beam current,N is the number of grating periods, n is the orderof emission, is the grating period, and €0 is hepermittivity of free space. Other parameter whichappear in Eq. (1) are:

sin2 83

— cos e)7,8e= 47rini

Eq. (2) is the variation of the emission with polarangle. The symbols fi and 7 are respectively theelectron velocity relative to the speed of light andthe relative electron energy. Angles are measuredwith respect to the electron beam axis and xo is thedistance of the infinitessimally thick beam above thegrating. When observed power is composed withthe prediction of Eq. (1), the measured beam profileis folded together with the evanescent field lengthgiven by Eq. (3). The remaining factor in Eq. (1),

2 - iI Rni , n effect an antenna gain and the notationis that first introduced by van den Berg [16]. Adetailed discussion that is adapted to the conditionsof this experiment may be found in Urata [17].

When evaluated for parameters used in produc-ing Fig. 2 and assuming an interaction length of 5narn, Eq. (1) would predict emitted power levels ofthe order of 100 pW/gA-sr. The effective field ofview of the collection optics is approximately 0.07 Sr.The FIR emission is detected with a silicon compos-ite bolometer placed between 0.5 and 1.0 m distantfrom the grating. Although the loss in the collectionsystem is not accurately known, the theoretical pre-dictions and estimated geometrical factors are con-sistent with the sub-nW power levels observed in therange where P cc I.

The focused beam will support fast and slow spacecharge modes. As the beam plasma frequency is in-creased, those modes become resolved on the scale

F =(1/13 — cos

= 713A47c

(2)

(3)

538

104Beam diameter

I• 24 gm

- o 60 gm

103

102

102103 io4

Beam Current (1A)FIG. 2. Detected power vs. beam current. Fits of the

form y = Ax are shown for the linear and superlinearregimes.

of the free spectral range which is determined bythe beam velocity and the interaction length (i.e.the transit time). When, by increasing the beamcurrent, this regime is reached, it is expected thatcoupling of the "negative energy" slow space chargewave with a co-propagating space harmonic compo-nent could result in a bunching of the beam. In thiscase, growth of the component of the emitted ra-diation will occur. While the details of the theoryin this regime are still under development, such atransition is indeed observed. The transition occurswhen the beam plasma frequency times the transittime exceeds 0.2-0.25. Beyond the transition point,the radiated power grows rapidly as a power of thecurrent exceeding the expected spontaneous emis-sion by 1 to 2 orders of magnitude. The exponentin this power law relation typically ranges from 3 to6 and is sensitive to the operating conditions. Withthe present operating parameters, the system doesnot appear to have reached saturation.

It is clear that the finite length grating is func-tioning as a relatively high quality surface resonatorbut the details are yet to be understood. A sim-ilar caveat applies to the non-linear regime butEq. (1) provides a basis for some interesting esti-mated. Since it is proportional to the product of theelectron charge and the current, it has the charac-teristic form of a shot noise formula. If it is mul-tiplied and divided by a spectral interval, d.), andthe product el. factored out, what remains is a "ra-diation resistance" . The spectral width of the spon-taneous emission "Smith-Purcell line" has been de-duced from both grating spectrometer and Fouriertransform interferometer measurements. In eithercase the spectral width is about .1v 1cm-1 . Con-verting this to an angular frequency, d, and usinga beam current of 100 pA, the factors

3.2pW/9. (4)

Thus the measured power near the upper limit ofthe spontaneous emission regime indicates that theradiation resistance lies between 1 and 10 kn. Theinteraction length and the exact value of the beamprofile - evanescent wave overlap are not determinedprecisely. However the 1-10 Icf/ range for a radi-ation resistance is also consistant with an indepen-dent evaluation of Eq. (1) (after factoring out a andevaluating c/f/fd,w).

A bunched beam with 100 p,A rms current wouldbe expected to generate between 10 and 100 kr,W.A beam with approximately one order of magnitudegreater current (=-- 1 mA) would produce power lev-els in the mW range.

These arguments are qualitative but they are alsobased on fundamental constraints. The estimatesprobably represent reasonable upper limits to whatcan be expected from SEM electron optical systembased e-beam technology.

III. SCALING OF GC0 DESIGNCONSTRAINTS

A discussion of the constraints governing GC0 op-eration is facilitated by first examining the disper-sion plane associated with the electromagnetic fieldsabove a grating. A schematic dispersion plane is il-lustrated in Fig. 3. The vertical axis is the angularfrequency measured in units of 2r times the speed oflight divided by the grating period. The horizontalaxis is the wave number along the grating in a direc-tion perpendicular to the rulings. Again, the unitsare normalized.

The plane is divided into two principal regions,"fast" and "slow" . These designations are relative to

2 3 k11t/2/c

FIG. 3. Schematic of GC0 dispersion plane.

539

(6)

(7)

the speed of light, the lines with slope ±1 on the dia-gram. Each Fourier component of the field above thegrating will contain a complete set of space harmonicwhose axial wave numbers differ by 27r/t. Spaceharmonics with phase velocities that fall within the"light cone" , the region labeled fast, satisfy radia-tive boundary conditions. The points in the fastregion represent components of either incident andscattered waves or an outgoing wave generated bythe beam.

Points on the plane which fall outside the lightcone have phase velocities less than the speed oflight. Space harmonic components in this region arenon-radiative but they do serve as a coupling mech-anism for the electron beam. A "beam line" is alsoshown on the figure. Along this line the relation

= k H z; (5)

is satisifed (;.; is the angular frequency, k it is the ax-ial wave number in dimensional units, and v is thevelocity of the beam. In the current discussion onlywaves which have at least one space harmonic com-ponent in this light cone are of interest. Thus, thedarker shaded areas, marked bound, may be ignored.The wavenumber which appears in Eq. (5) may bebroken down into two components

kii = ko 2rin1i

where

t

ko = (4k) cos 9

is the axial component of the wavenumber along thegrating that would be associated with an outgoingradiative wave. Combining Eqs. (5 — 7) and choosingIn! = 1 yields

— =c 1 1 — cos 9

2r/i (8)

Or

(9)A = (1/ — cos9)

which is the well-known relation discussed by Smithand Purcell in Ref. [2]. It can also be deduced usingthe Huygens construction.

The choice int = 1 is not necessarily the dominantmode. It is interesting to note that if, for instance,the depth of the grating is chosen in order to opti-mize the spontaneous emission for n = 3 that modewill also dominate above threshhold (Fig. 4). Smallvariations in voltage will also lead to inj = 1 and

= 3 operating simultaneously (Figs. 5 and 6).The potential for operation on higher-order modesof the grating provides an important degree of free-dom for grating design.

Another important constraint is related to theevanescent scale length of the slow space harmonics.Outside the light cone, the square of the perpendic-ular component of the total wavenumber is less than

10

10 20 30 40Wavenumber (1/cm)

FIG. 4. Power spectrum of GC0 operating at ini = 3.

5

3

2

0

Mirror displacement (cm)FIG. 5. Interferogram of GC° radiation while oper-

ating simultaneously at ini = 1 and ini = 3.

12

10-

s -

6 -

4-

2-

10 20 30 40Wavenumber (1/cm.)

FIG. 6. Power spectrum inferred from the interfero-gram in Fig. 5.

540

(eomc3/e)70e2N

Finally, if re-written in terms of wavelength, the re-suit

JA!> 1 (21)

(14)

or

(15)

zero and the wavenumber itself is pure imaginaryand has a magnitude

IkL l _w2/c (10)

Since energy transfer is through the nearly-.synchronous co-propagating space harmonic the re-lation k il w/v can be used to infer that

Ik iJ =wiry

where -y = 1/V1 - 02 . Thus,

I kl I = 2r/7,3A

or

1k11-1 = A,

the evanescent scale length introduced in Section II.In general, good coupling will require the beam di-ameter to be

also follows.Threshhold occurs when the beam plasma fre-

quency cob times the transit time of a beam electronthrough the interaction length exceeds about 0.25.Operation well above threshhold will require

cubL > 1 (19)3/2v

(where the factor 3/2

has been included since thebunching is longitudinal; it has, of course, a negligi-ble numerical effect for non-relativistic beams).

With the aid of the usual expression for the beamplasma frequency and multiplying and dividing byadditional factor of beam velocity yields the con-straint

JL2

(€0mc3/e)(70)3 > 1(20)

where J is the beam current density. If the relationbetween the interaction length and the evanescentscale are invoked, the constraint becomes

Using the values associated with a 25 kV beam givesthe relation

A > 20d (16)

Good coupling at 300 pm (1 THz) would be achievedwith a beam parameter of the order of 15 pm. Thisis consistent with data obtained in the proof-of-principle experiments. Experiments designed to testthe lower limits of d are currently in progress. Muchsmaller values of d are achievable and operation wellabove 1 THz may be expected. Further extension ofthe evanescence scale length may also be achievedby increasing the beam voltage.

A final pair of scaling relations follow if it maybe assumed that the depth of field of the beam fo-cus is emittance dominated and that this limits theeffective interaction length. In this case the interac-tion length L is related to the beam diameter by theexpression

-y 3d2 (17)EN

where eN is the normalized emittance. Since d andA, are comparable, the relation

"i32L Äe (18)

EN

[(6077/C3/e)e2N 11/4> 2r (22)(70)3J .1

is obtained. Evaluating this last expression usingtypical parameters for the present electron opticalsystem indicates that we are operating near thelower wavelength limit of that apparatus.

Iv. TOWARD A COMPACT GCO

The GC0 described in the preceding sections isalready compact by some standards. As is evidentfrom the scaling relations discussed in Section III, in-crease of beam energy as well as a decrease of beamemitta.nce can be used to lower the limiting wave-length. Increasing the beam energy is, of course,the route taken in relativistic electron-beam-driven,free-electron lasers (FEL). The present GC() is al-ready far smaller than these devices. The GCO'soutput power is much smaller than the levels pro-duced by a relativistic beam-driven FEL. However,it is already sufficient for application in spectroscopyor as a local oscillator.

Straightforward engineering and elimination ofthe non-essential features of the SEM would leadimmediately to a much smaller device. It is also in-teresting to speculate on more dramatic options.

541

The beam voltage required for GC0 operationprobably need never exceed 50 kV and in the presentdevice, THz operation is achieved with only 20 kVof beam voltage. This range is well within the scopeof modern dc--dc converter-based power supply tech-nology. The beam currents required are also modestand well within the scope of current converter-basedpower supplies. These supplies can now be obtainedin very compact packages.

A second major reduction in size might be ob-tained if modern field emission cathode technologywere employed. The primary motivation for muchwork on the field emission cathode is for use in fiatpanel displays. However, use in microwave tubes hasalso been a factor. The GC0 is an ideal place to usethis technique. A ribbon beam a micron thick andabout a millimeter wide propagating a distance nomore than a few centimeters would be ideal. Powerconsumption and heat load would be reduced dra-matically.

The GCO is also a linear device and standard en-.eru recovery technology is probably applicable. Im-plementation of energy recovery would improve ter-minal efficiency. If done in a way such as to alsoreduce beam intercept at high voltages the already-modest x-ray production could be further reduced.

Finally, although the grating is a simple and re-liable means of converting electron beam kineticenergy to coherent radiation, other photonic bandgap structures might be employed. The presentGCO uses only the distributed feedback on the grat-ing. More complex structures, particularly ones withwell-defined high-quality factor modes, may offer sig-nificant advantages.

V. CONCLUSIONS

A potentially very useful THz-FIR source hasbeen developed. Based on a novel variation of anold theme, the device is simple and versatile. Poweroutput levels and tuning range are already of interestin some applications and fundamental scaling argu-ments support the claim that considerable extensionof the tuning range and output power is possible. Ifoperated near the limit of established electron beamoptical art it will be possible to access the challeng-ing 10-1000 pm wavelength range.

Support from ..kR0 Contract DAAH04-95-1-0640,DoD/AF DUMP Contract F49620-97-1-0287, andVermont Photonics. Inc., is gratefully acknowledged.

[1] J. Urata, M. Goldstein, M.F. Kimmitt, A. Naumov,C. Platt and J.E. Walsh, Phys. Rev. Lett. 80, 516(1998).

[2] S.J. Smith and E.M. Purcell, Phys. Rev. 92, 1069(1953).

{3] W.W. Salisbury, US Patent 2,634,372, filed October26, 1949, granted April 7, 1953.

[4] J.P. Bachheimer, Phys.Rev. B 6, 2985 (1972).[5) W.W. Salisbury, Science 154, 386 (1966).[6] E.L. Burdette and G. Hughes, Phys. Rev. A 14,

1766 (1976).[7] A. Gover, P. Dvorkis and U. Elisha, J. Opt. Soc.

Am. B 1, 723 (1984).[8] I. Shih, D.B. Chang, J.E. Drummond, K.L. Dubbs,

D.L. Masters, R.M. Prohaska and W.W. Salisbury,J. Opt. Soc. Am. B 7, 351 (1990).

[9] F.S. Rusin and G. Bogomolov, Proc. IEEE 57, 720(1969).

[101 K. Mizuno and S. Ono, The Ledatron, Infrared andMillimeter Waves 1: Sources of Radiation, ed. K.Button (Academic Press, Inc., 1979), Ch. 5, pp. 213-233.

[11]D.E. Wortman, H. Dropkin and R.P. Leavitt, IEEEJourn. Quant. Elect. QE-17(8), 1341 (1981).

[12]V.P. Shestapolov, Diffraction Electronics(Kharkhov: 1976).

[13] E.J. Price, Appl. Phys. Lett. 61, 252 (1992).[14] J.H. Killoran, IEEE Trans. Pl. Sci. 22, 530 (1994).[15] M. Goldstein, J.E. Walsh, M.F. Kimmitt, J. Urata

and C.L. Platt, Appl. Phys. Lett. 71, 452 (1997)and A Far-Infrared Smith-Purcell Micro-Radiator,Ph.D. thesis, 1994, available from Departmentof Physics and Astronomy, Dartmouth College,Hanover, NH 03755.

[16] P.M. van den Berg, J. Opt. Soc. 63, 1588 (1973).[17] J. Urata, Spontaneous and Stimulated Smith-

Purcell Radiation Experiments in the Far-Infrared,Ph.D. thesis, 1997, pp. 19-20, available from Depart--ment of Physics and Astronomy, Dartmouth Col-lege, Hanover, NH 03755.

542