P. Musumeci et al- A THz radiation driven IFEL as a phaselocked prebuncher for a Plasma Beat-Wave...

8/3/2019 P. Musumeci et al- A THz radiation driven IFEL as a phaselocked prebuncher for a Plasma Beat-Wave Accelerator

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A THz radiation driven IFEL as a phaselocked prebuncher for aPlasma Beat-Wave Accelerator

P. Musumeci1, S. Ya. Tochitsky

2, C. E. Clayton

2, C. Joshi

2, C. Pellegrini

1, J.B. Rosenzweig

1

1 Department of Physics, 2 Department of Electrical Engineering, University of California at Los Angeles,405 Hilgard avenue, Los Angeles, CA 90095

Abstract To obtain a high quality electron beam with small energy spread in the laser driven plasma

accelerator, the electrons have to be prebunched at the scale of the plasma wavelength. We study the

feasibility of an experiment where an inverse free electron laser (IFEL) is used to bunch the electron beam

before the injection into a plasma beatwave accelerator. It is suggested to drive the IFEL prebuncher by a

THz seed radiation phase-locked to the electromagnetic beatwave through difference frequency generation

process in a nonlinear crystal. Design and numerical simulations for this experiment are presented.

1. Introduction

In recent years advanced high gradient accelerator experiments have taken place successfully.Proof-of-principle demonstrations using laser or electron driven plasma waves and non-plasma based

structures have shown gradients much higher than conventional accelerators [1]. The focus of the current

research in this field is now shifting from increasing the energy gain in short distances to delivering high

quality electron beams that could be used for different applications.

One of the main characteristics of any usable electron beam is the energy spread. So far all

schemes for high gradient acceleration have shown 100 % energy spread. This is physically due to the

experimental difficulties related to the generation and the injection of an electron beam in the high gradient

accelerating field wave with a typical period of 10-300 m. It is obvious that if the injected electron beamsamples all the phases of the accelerating field, the energy spectrum at the output will be continuous. The

goal of future experiments is to reduce the energy spread by reducing in some way the electron bunch

length, either at the stage of electron generation, or by compressing the bunch length and synchronizing the

electrons to the accelerating structure.

Injection of prebunched electrons that are synchronized to the high gradient electric field wave iscommonly called phase locking. The experimental challenges in acceleration of phase-locked electrons

have been individuated and studied [2]. Recently some positive experimental results in this field have been

reported. At Brookhaven National Lab, by use of the Inverse Free Electron Laser (IFEL) interaction

microbunching of the electron beam on the optical scale has been demonstrated [3]. Later, in the frame of

STELLA collaboration, the timed injection of these microbunches in an IFEL accelerator has been

successfully realized [4].

At the Neptune Laboratory at UCLA, there is an ongoing experiment on Plasma Beat Wave

Accelerator (PBWA) of electrons [1]. The experiment uses two lines of a CO 2 laser (10.6 and 10.3 m) toexcite a relativistic plasma beat wave with acceleration gradient ~3 GeV/m. The plasma wavelength is 340

m, requiring a bunch length of about 50-60 m. In phase I of the experiment, currently underway, a long

(>340 m) electron bunch will be injected in the plasma structure and accelerated up to 100 MeV. Then in phase II, prebunched phase-locked electrons will be injected to achieve small energy spread. Several

methods for phase-locked injection have been considered including FIR driven IFEL [2]. It was recognizedthat the main drawback of such a scheme is the need of a high-power (>100 MW) seed radiation at the

wavelength of 340 m. All feasible solutions of this issue were based on an FEL source that seriouslycomplicates the experiment. For example, a classical FEL oscillator-amplifier scheme was suggested by

Lampel et al for a 1 m driven PBWA [5].In this paper we address the challenge of generating such micro-bunches with characteristic length

shorter than the plasma beat wavelength, phase locked with the accelerating structure. It is suggested to use

the IFEL interaction between the relativistic electrons from the Neptune photoinjector and a high power

electromagnetic beat-wave. We propose to generate 100 MW of 1 THz radiation by difference frequency

generation (DFG) in a nonlinear crystal, mixing the two CO2 lines. Co-propagating the radiation with the


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electron beam inside a short undulator achieves the bunching at the required wavelength. Moreover,

because the electromagnetic radiation is generated from the same laser that excites the relativistic plasma

wave, phase-locking is achieved. In the first part of the paper we illustrate the scheme, then after a study of

the microbunching dynamics we present the simulation results and discuss the optimization of the

experiment. In the last section we focus on possible design of GaAs nonlinear mixer for generating the

required power of THz electromagnetic wave.

2. Inverse Free Electron Laser interaction as an efficientprebuncher at Neptune Laboratory

The Neptune Laboratory at UCLA is an advanced accelerator laboratory dedicated to the study of laser

plasma acceleration and high brightness electron beam. There are two main components at the laboratory:

the most powerful in the world, TW-class CO2 laser system and a state-of-the-art photoinjector. A two

wavelength 1 TW CO2 laser is used to drive the plasma beat-wave structure. A standard master oscillator-

power amplifier approach is used to amplify 100 ps pulses up to 100 J as presented elsewhere [6]. The

electron source for the Neptune Linac is a 1.6 cell S-band RF gun driven by 266 nm photocathode laser

followed by a plane-wave transformer (PWT) linac section. The electrons are accelerated inside the PWT

up to 12 MeV with a small energy spread (0.5%). An emittance compensation solenoid and quadrupoles for

transporting and focusing the electrons are important components of the system. Small transverse emittance

(6 mm-mrad) and 100 m rms spot sizes at the interaction point are obtained. There is also a magneticchicane for manipulations on the electron longitudinal phase space [7].

In Fig.1 we show proposed solution for the PBWA phase II experiment on injecting an electron beam

prebunched on the scale of the plasma wavelength and phase locked with the accelerating structure. As

shown in the picture, using a salt (NaCl) beamsplitter, a small fraction (~4 %) of the high power CO2 laser

is split and then sent into a non-linear crystal. Here, by difference frequency mixing, as discussed in the last

section of this paper, we should generate up to 100 MW of 1 THz radiation. This 340 m wave originatesfrom the mixing of the same two wavelengths that drive the plasma beat wave, so that it has a well-defined

phase relationship with the accelerating structure. Absolute phase can then be adjusted using a delay line.

The THz beam is made collinear with the electron beam and is sent through a planar undulator using a

mirror with a hole. This off-axis parabolic mirror has also the function of focusing the radiation to a spot

size of 7 mm located at the end of a 0.5 m long undulator. The electron beam coming from the linac is

microbunched on the scale of 340 m by the IFEL interaction going through the undulator magnetic field,then it is focused with the final focus triplet at the interaction point (IP) and finally it is accelerated by the

relativistc plasma beatwave excited by the main fraction of the TW CO2 laser beam. The distance betweenthe end of the undulator and the IP is less than 1 m. Note that for the 10 m STELLA experiment wheretolerances are tighter because of the shorter wavelength, the IFEL accelerator was located 2.3 m

downstream of the IFEL prebuncher [4].

Fig.1: Experimental layout for THZ Inverse Free Electron Laser microbunching.


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3. IFEL Bunching dynamics and simulation resultsIn an IFEL [8], relativistic particles are moving through an undulator magnet; an electromagnetic wave

is propagating parallel to the beam. The undulator magnet produces a non zero transverse velocity

(wiggling motion) in a direction parallel to the electric vector of the wave, so that energy can be transferred

between the particle and the wave. The Inverse Free Electron Laser dynamics is usually described in terms

of the energy of the electron () and the phase of the coupling between the wiggling motion and the

electromagnetic wave (). The equations of the motion for a single electron moving in a plane linearlypolarized electromagnetic wave in a planar undulator magnetic field, are:

)sin(2

)(2

0

KJJK

mc

eE

z=

2/1

2

22

)cos()(22

1

1

+++

+=

KJJKKKK

kkk

z

ll

w

where kw is the undulator wave number, K is the undulator dimensionless parameter (eB/ mckw), Kl is the

radiation dimensionless parameter (eE0/mck) and JJ is the Bessel factor due to the planar geometry. The

IFEL acts as a longitudinal lens and microbunches the electrons on the scale of the electromagnetic

wavelength.

Fig.2: Rms microbunch length as a function of normalized distance for a harmonic oscillator and an IFEL.

To understand a fundamental limitation of an IFEL-microbuncher it is instructive to study the

difference between the IFEL longitudinal lens compression and an ideal case of a harmonic oscillator type

of interaction (Fig.2). In the ideal case, the electron density evolves under linear transformation and the

minimum bunch length is obtained after 1/4 of the synchrotron period with a final bunch length thatdepends only upon the initial energy spread. In the IFEL case, the equations are not linear and the

corrections to the linear motion (expansion of the sine term in the equation for) are important. The IFELreaches optimum bunching 50% later than the harmonic oscillator (at 3/8 of the calculated synchrotron

period) and the minimum microbunch length is set now by the aberrations, or non-linearities of the

potential (Fig.2). They cause an effective emittance growth, or diluition in the longitudinal phase space.

This is the limit of the IFEL as a longitudinal lens. Nevertheless, bunch lengths on the order of 1/10 the

wavelength can easily be obtained, and that is well within the goals for the Phase II of PBWA.

At the Neptune Laboratory, in order to achieve efficient microbunching in the small experimental

area available, we need to optimize parameters of the THz IFEL. We considered here a planar permanent

magnet undulator. The requirement that the undulator should geometrically match the THz beam

propagating in free space with the electron beam limits the minimum gap or the maximum achievable

0.0 0.5 1.0 1.5 2.0

0.00

0.05

0.10

0.15

0.20

0.25

0.30

bunchlength(fractionofwavelength)

Distance (normalized units)

Full IFEL equations

Harmonic oscillator approximation


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magnetic field. The undulator length sets the duration of the IFEL interaction. Obviously the choice of the

undulator length depends strongly on the available electromagnetic power. For 100 MW of THz radiation

and a magnetic field of 0.6 T, we achieve maximum bunching through the Inverse Free Electron Laser

interaction after ~0.5m. As it is shown in the Fig.3, having more electromagnetic power or a longer

undulator doesnt significantly increase the performance of the system. The IFEL buncher efficiency

reaches the limit mentioned above, considering the effects of the non-linearities and the longitudinal

emittance dilution.

05010 0

15 020 0

25 030 0

35 0

40 0

0

20

40

60

80

10 0

12 0

14 0

16 0

0. 30. 4

0. 50. 6 0. 7

0. 80. 9

1. 0

Microbunchlength()

Undulat

orlength

(m)

FIRrad

iationpower(M

W)

Fig.3: Electron microbunch length versus electromagnetic power and undulator length.

We note that the undulator requirements to get optimum bunching having 100 MW of FIR

radiation available to drive the IFEL are not very demanding from the magnet construction point of view

(Table1). A planar permanent magnet undulator with the Halbach scheme will easily produce these

characteristics.

Table 1: Undulator parameters

Magnetic field 0.6 T

Undulator wavelength 6 cm

Magnet gap 2 cm

K parameter 3.1

Undulator length 0.54 m

Our preliminary calculations are well confirmed by full 3D simulations. The results are shown in

Fig. 4. The simulations are performed using TREDI [9], a 3d Lienerd-Wiechert based, 4 th order Runge

Kutta, Lorentz solver code to track the electrons through the undulator magnetic field and the laser field.

The input electron beam has the parameters typically running at Neptune laboratory, 4 ps (rms) long,

emittance 6 mm-mrad, charge 300 pC. The radiation is assumed to be a 100 MW THz wave, focused in

vacuum to 7 mm focal spot.

Fig.4 shows a snapshot of the electron longitudinal phase space at the end of the undulator. The

longitudinal microbunching on the scale of the plasma wavelength is evident within the 4 ps (rms) long

beam envelope. Fig.4b presents the phase histogram over the 340 m wavelength. The microbunches have

a width of ~30 m - much smaller than the plasma wavelength - which should allow us to load electronsinto the best accelerating fields, giving a relatively monochromatic output spectrum. Obviously because the


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200 400 600 800 1000

0.98

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

Relativeundulatorlength

Charge (pC)0 20 40 60 80 100 120 140 160

1.00

1.05

1.10

1.15

1.20

1.25

Relativeundulatorlength

Spectral width (GHz)

Fig. 4: Simulation results for THz IFEL microbunching.

THz IFEL driving radiation is locked in phase with the plasma beatwave, all these microbunches are

phaselocked with the accelerating structure.We also analyzed the relevance of diffraction, spectral bandwidth and space charge, that are

usually not included in the simple analytic treatment of the IFEL interaction, but that are potentially critical

for the IFEL interaction.

It is important to take into account effect of the diffraction of the long wavelength (340 m)electromagnetic radiation. Including diffraction effects in the analysis is necessary any time the radiation

Raleigh range is shorter than the undulator length [10]. Slow variation of electric field amplitude and phase

along the undulator effectively change the resonant condition along the undulator. With a 7 mm spot size,the Raleigh range for THz radiation is 50 cm, so that in our case this effect is not very important. If less

FIR power is available, a guiding system rather than tighter focusing should be implemented to avoid this

diffraction effect.

As was reported by Corkum et al. [11], significant broadening of the 10 m radiation in the bulkof nonlinear material could be observed due to high non-linearity. This, of course, could result in broader

than Fourier transformed limited bandwidth of THz radiation. We simulated the effects of spectral

sidebands to the bunching process. As it is shown in Fig.5a, the bunching efficiency starts to decrease when

the spectrum becomes larger than 100 GHz FWHM. This frequency interval is more than 10 times greater

than the Fourier limited spectral width for 100 ps pulses. Estimations have shown that at pump intensity ~3

GW/cm2 one should not expect spectral broadening above 50 GHz. More detailed study of this issue is

required.

Another question is what happens when we increase the number of electrons in the microbunches.

The longitudinal space charge fields counters the IFEL bunching force, so that the IFEL interaction has to

stay on for a longer period of time to get to the optimum bunching point. No significant effect is seen for

charge up to 300 pC (Fig.5b).

Fig. 5: Undulator length for the optimum bunching as a function of (a) thespectral width of radiation and

(b) the electron beam charge.

Optimization of the system in our case means getting more electrons with a smaller phase spread in order to

have better energy spread after acceleration in the PBWA. Further improvement in this respect (excluding

0 1.57 3.14 4.71 6.280

0.1

0.2Histogram of phase distribution

phase

%

0.002 0 0.0020.05

0

0.05

0.1Bunching in IFEL

z (m)

deltap/p


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adiabatic capture or undulator tapering from the consideration) is possible with additional modulation of

the e-beam injected in the IFEL structure. Here we briefly consider several options. One approach is to

have pre-bunched electrons generated at the cathode with a modulated UV laser as described in [2].

Another possibility is to utilize the Neptune magnetic chicane in order to pre-compress the electron beam.

In this case the problem of the jitter of the RF clock with respect to the laser beatwave clock has to be

addressed. The results of the simulations for these options are shown in Fig.6.

Fig. 6: Phase distribution for: a) electrons prebunched at the photocathode through UV driving lasermodulation. b) electron beam precompressed in the magnetic chicane.

4. THZ radiation sourceThe key element of a laser-driven IFEL prebuncher is a high-power source of optical radiation. We

propose to use difference frequency mixing process in a nonlinear crystal to produce high-power driving

THz radiation (>100 MW) for the IFEL buncher. It is known that low DFG efficiency is a serious problem

for the FIR spectral range. The highest FIR power generated by now using this method is a few kW [12].

At the same time 100 ps, two-wavelength CO2 laser pulses from the Neptune Lab system are naturally very

well suited for producing high-power FIR radiation. Nonlinear frequency conversion efficiency increases

significantly for short pulses: first owing to the power increase and second, this power can be coupled into

a crystal because of the higher surface damage threshold for shorter pulses.

Three methods to generate high-power 340 m radiation by CO2 laser difference frequency mixing in anonlinear crystal have been considered. They are: standard birefringent phase matching, quasi-phasematching with periodic structures, and noncollinear phase matching in isotropic materials.

FIR generation by difference frequency mixing is possible in the birefringent materials ZnGeP 2,

AgGaSe2 and Te, which are transparent for both MIR (10 m) and FIR (340 m) radiation. Collinear phase-matched DFG has been reported in ZnGeP2 [13,14]. Our calculations have shown that up to 39

MW/cm2 can be generated in FIR with a 1 cm long crystal at 5 GW of incident power. However, serious

difficulties are encountered in growing large-aperture ZnGeP2 crystals that makes achieving a 100 MW

power level at 340 m very challenging. Another problem is that this material requires Type II interactionfor DFG. The later hinders its application for a high-power, two-wavelength CO2 laser system.

There are some cubic nonlinear semiconductors such as InSb, GaAs, etc., which can be used for FIR DFG

with CO2 lasers. But these crystals being cubic lack birefringence. Therefore other methods for phase-

matching in isotropic crystals must be considered. Even in isotropic crystals waves are propagating in

phase over the coherence length (Lc), the distance over which the relative phase changes by

. For FIR

difference frequency mixing the coherence length is relatively long. For example, Lc is 700 m in the caseof GaAs. This allows for the generation of FIR radiation in thin InSb [15] and GaAs [16] slabs. However,

the DFG efficiency is very low because of the short Lc. Quasi-phase matching is a technique for phase

matching nonlinear optical interactions in which the relative phase is corrected at regular intervals using a

stack of plates or periodically grown structure. This technique progressed significantly during the last

decade and it has a bright future for the FIR region where production of structures is much easier.

Unfortunately GaAs structures until now have had the status of experimental devices and are not available.

0 1.57 3.14 4.71 6.280

0.2

0.4Histogram of phase distribution

phase

%

0 1.57 3.14 4.71 6.280

0.5

1Histogram of phase distribution

phase

%


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Fig. 7: Schematic wave vector diagram for noncollinear DFG (a) and optical scheme of a GaAs nonlinear

optical device (b). Internal FIR power versus pump power density on the 10.3 m line calculated inassumption of equal power on each line (c).

Another approach to obtain phase-matched FIR DFG in isotropic nonlinear materials is noncollinear

mixing of two laser beams. This is possible in any crystal which possesses anomalous dispersion between

the incident CO2 laser radiation and FIR difference frequency radiation. Zernike [15] and Aggarwal et

al.[17] have demonstrated noncollinear mixing of two CO2 laser beams in liquid helium cooled

semiconductor samples. By using a 10 cm long GaAs crystal of folded geometry, up to 4kW in the 100

m region was generated [12]. Several reasons make GaAs the best candidate for generation of high-power

340 m radiation using a noncollinear DFG scheme. It has a relatively high value for the electro-optic

nonlinear coefficient d=43 pm/V. GaAs with high resistivity (> 108 cm) is transparent in the FIR beyond

200 m at room temperature as well as in the 10 m region of the CO2 laser [18]. High-quality, singlecrystals with a diameter of 15 cm and length up to 10 cm are commercially available. The expected surface

damage threshold could reach 10 GW/cm

2

for 100 ps CO2 laser pulses. We present results of calculationsfor a FIR nonlinear device made of GaAs below.

For noncollinear phase-matched mixing of two laser lines of frequencies 1 and 2 (1>2) to generate

the difference-frequency radiation at 3, the conditions of photon energy and momentum conservationrequire that

where

r

k1,

r

k2

andr

k3

are the respective vectors for radiation of frequencies 1(10.3 m),

2(10.6m), 3(330 m). Fig 7a. shows the direction of propagation of the incident beams and that of the

difference frequency radiation inside the crystal. According to Aggarwal et al. [17], angles and aregiven by

Sin(12 ) =

(n3

3)2

(n1

1 n

2

2)2

4n1

n2

1

2

1/ 2

; Cos =

1 + 2(2

3

)Sin 2 (0.5)

1 + 4(

1

2

3

2 )Sin2

(0.5)

12

3=

1

2and

r

k3=

r

k1

r

k2

1

10

100

1000

0.5 1 1.5 2 2.5 3

L = 5 cm

L = 3 cm

L = 1 cm

k1

k2 k3

=2.38

FIR 340 m

10.3 +10.6 m10.3 +10.6 m

=21.6

a

b

c

10.3 m Power Density (P10.3=P10.6), GW/cm2

InternalFIRPowerDensity,MW/cm2


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Refractive indices for insulating GaAs are n1n2=3.28 at 10 m region, and n3=3.61 at 340 m [18]. For

these values of refractive index we obtain =0.72 and =21.64. The corresponding external phase-matching angle is 2.38 degrees. The angle at which FIR radiation propogates inside the crystal is greaterthan the critical angle for total internal reflection. Therefore, as it shown in Fig.7b, the output face of the

GaAs crystal has to be cut at 21 degrees to release the newborn radiation.

We also calculated the 340 m power produced inside of a GaAs crystal for different interaction

lengths L using standard Boyd and Kleinman relations [19]. For an isotropic material, the interaction lengthis limited only by the pulse length because of group velocity dispersion. For 100 ps pulses, the maximum L

is approximately 6 cm. The above calculations were done assuming 0.2 cm-1 absorption at 340 m [18] and

neglecting absorption at 10 m. Results are presented in Fig. 7c. Note that hatched section in Fig. 7cindicates our provisional zone for operation where the pump intensity of 2-4 GW/cm

2is more than two

times less than the damage threshold for GaAs. As can be seen in Fig,7c the 100 MW level could beachieved even for a 1 cm2 incident area beam with L=5 cm and total pump power density 2 GW/cm2. FIR

power level could be easily scalable beyond 100 MW by increasing the beam diameter. A typical beam

diameter of the Neptune TW two-wavelength CO2 laser system is 12 cm with an intensity 10 GW/cm2

[7]. This beam, in combination with available large-aperture GaAs crystals, opens possibility to create a

unique high-power 1-10 GW source of coherent radiation in the range of 70 m 2 mm (0.2-4 THz) on thebase of noncollinear frequency mixing of CO2 laser lines.

5. ConclusionsA feasibility study of phase-locked acceleration of electrons in a plasma based accelerating structure

has shown that a THz IFEL microbuncher is a promising scheme. For Neptune PBWA experiment, it is

possible to generate high-power (>100 MW) 340 m radiation by using noncollinear DFG in GaAs.Optimization of the THz driven IFEL parameters demonstrates that requirements for the phased-injection

system could be easily achieved.

6. References1. C. Joshi and P. Corkum, Physics Today, 49, 36 (1996)

2. C.E. Clayton, L. Serafini,IEEE Trans. Plasma Science, 24, 400 (1996).

3. Y. Liu et al., Phys. Rev. Lett., 80, 4418, 1998

4. W. Kimura et al., in Proceedings of Advanced Accelerator Concepts, Santa Fe, NM, 2000

5. M.Lampel, C. Pellegrini, and R.Zhang, in Proc. Particle Accelerator Conf., Dallas, TX, 1995.6. S. Anderson et al, Proc. Particle Accelerator Conf., Chicago, IL, 20017. S.Ya. Tochitsky, C. Filip, R. Narang, C.E. Clayton, K.Marsh, and C. Joshi, Optics Letters, 24,

1717 (1999).

8. E. D. Courant, C. Pellegrini, W. Zakowicz, Phys. Rev. Lett., 32, 2813, 1985

9. L. Giannessi et al.,Nucl. Instr. Meth., 393, 434, 199710. P. Musumeci, C.Pellegrini, J.B. Rosenzweig, A. Varfolomeev, S. Tomalchev, T. Yarovoi, Proc.

Particle Accelerator Conf. ,Chicago, IL, 2001

11. P.B. Corkum, P.P. Ho, R.R. Alfano, and J.T. Manassah Optics. Lett. 10, 624 (1985).

12. G.D. Boyd, T. J. Bridges, and C.K.N. Patel, and E. Buehler,Appl.Phys. Lett. 21, 553 (1972).

13. V.V. Apollonov, R. Bocquet, A. Boscheron, A.I. Gribenyukov, V.V. Korotkova, C. Rouyer, A.G.

Suzdaltsev, Yu. A. Shakir,Int. Journal Infrared M. Waves, 17, 1465 (1996).14. F. Zernike, Phys. Rev. Lett. 22, 931 (1969).15. T.J. Bridges, A.R. Strand,Appl.Phys. Lett.20, 382 (1972).

16. R.L. Aggarwal, B. Lax, and G. Favrot,Appl.Phys. Lett.22, 329 (1973).

17. N. Lee, B. Lax, and R.L. Aggarwal, Optics Commun.18, 50 (1976).

18. C.J. Johnson, G.H. Sherman, and R. Weil,Appl. Optics, 8, 1667 (1969).19. G.D. Boyd, D.A. Kleinman,J.Appl.Phys. 39, 3597 (1968).


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