PROCEEDINGS LETTERS

r S I G N A L L I N E S

.os URE

797

TABLE I

Mwuc AMPLIFIER F’ERFOR~WNCE DATA

Net gain Instantaneous bandwidth

see Fig. 2 see Fig. 2

Tunable range Noiw temperature

1.9 to 3.1 GHz IO K (maximum)

Input VSWR Gain stability 0.05 dB per 5 minutes (maximum change)

2 : 1 (maximum)

Phase stability jitter: i3‘ (maximum)

Running time 24 hours per charge (minimum) Attitude tiltable 0’ to 90’ elevation

drift : 1 per 5 minutes (maximum)

width combination within the performance limits of the amplifier. The magnet is equipped with persistent current switches for the most efficient and stable operation. Once the magnet has been energized, these switches allow the driving current to circulate within the coils indefinitely without external current sources. Power supplies are used only to tune the amplifier.

Table I and Fig. 2 summarize the measured characteristics of the ampli- fier system. The noise temperature was measured by the hot-cold Y-factor method at 25-MHz increments from 1.9 to 3.1 GHz. A liquid nitrogen cooled cold load and a heated load were used. Gain and phase stability measurements were made with a bridge-type system.

D. J. MILLER G. G. WEIDNF.R

Appl. Phys., Advanced Technology RCA Defense Electronic Products

Camden, N. J. 08102

Some Possible Parametric Interwths in m-v semicondnctors

A A 1” Abstract-Some three-frequency, phase-matched, forward-wave,

parametric interactions possible in llCV “ionic“ semiconductors are discussed. A tunable infrared parametric oscillator. with frequency

/ A \ 2 0 feasible. variable over a widerange with applied magnetic field, is shown to be

Polar semiconductors comprising mainly 111-V compounds are known to have large electrooptic nonlinearity coefficients--in fact, some of the highest of nonlinear materials. Also associated with these crystals are non- linearities due to free carriers.’ Furthermore, most of these semiconductors are 43 m cubic crystals, hence optically isotropic. It is the purpose of this

20 - - 10 I letter to discuss some three-frequency parametric interactions possible in 2: 4 these materials in the collinear phase-matched condition allowing large I” coherence lengths. The free camer effects are taken into account in the

0 2

- frequencies. presence of a magnetic field that allows an easy variation of interaction

vibrations results in the expression of permittivity OF the material, neglect- For diatomic ionic crystals (with optical isotropy) the effect of lauice

0

FREQUENCY (GHzl

0 1.9 2.1 2.3 2.5 2.7 2.9 3.1 ing carrier effects, as

Fig. 2. Maser frequency response. w: - w2 E = E ,

o: - o2 + j y o (1)

garnet isolator which is distributed along the opposite side of the meander line from the rutile. The development of this amplifier represents an exten- sion and refinement of the tzchniques employed in an earlier laboratory model.’

A superconducting magnet provides the magnetic field required.for operation of the rutile and ferrite. The magnet is cylindrical, 8.9 cm (3.5 inches) in diameter, and 27.9 cm (1 1 inches) in length, with a 2.5- by 2.5-cm (1- by 1-inch) gap. It is divided into two sections, each producing an inde- pendently controllable field. The two fields are readily adjustable at the control panel, allowing selection of any center frequency, gain, and band-

IEEE Tram. Microwave Theory and Techniques, vol. MlT-12, pp. 421428, July 1964. L. C. Moms and D. J. Miller, “A broad tunabk bandwidth traveling-wave maser,”

where o, is the resonance frequency associated with transverse lattice vibrations (TO phonuns), o, is the frequency of longtudinal (LO) phonons, E , is the high-frequency (w2 >> o: or 0:) permittivity of the material, and y the damping frequency of lattice vibrations (y/o,=O.Ol<< 1, for 111-V semiconductors) Except in the immediate vicinity of the “reststrahlen” frequency o,, damping effects are therefoye negligible.

The presence of carriers in a magnetic field (Bo =Bo9) changes the scalar permittivity into a tensor. For wave propagation at right angles to Bo (assuming Z to be lined up with k),

Manuscript received January 22, 1969.

of nonparabok amduction bands,” 1968 Inremar’l. Quontm Elecrronics Conf., Digest ‘ C. K. N. Patel and N. Van Tran, “Interband contribution to mobile carrier nonlinearity

of Technical Papers (Miami Fla.), pp. 7 W .

I98

k2 = w 2 p 0 ~ , ( ~ : , + ExiE, = E 3 3 / & 1 3 E = (E$ + E,2)Bo (2)

PROCEEDINGS OF THE IEEE, MAY 1969

k 2 = w ~ ~ , & , E , , for ordinary waves

E = Ey911B0 (3)

where c i j (i, j = 1, 2, 3) are the respective terms of the permittivity tensor. The nonzero terms are

and

E22 = ~ - w: - w2 wii w: - w2 w(w - j v c i ) c

where vCi is the collision frequency of ith carriers of number density ni and effective mass ~.

It is the extraordinary waves, whose propagation is directly affected by the applied magnetic field, that are of interest here. Since parametric inter- actions in IR/far-IR are of interesf the collision effects are negligible.

The w-k diagram based on solutions of (2) are shown in Fig l(a) and (b) For a,, considerably removed from wl.

wo; N f w , ; [ { l + 4w;,/w:e}1’2 T 11

and

0’; = w1 + wf(w: - w:)i2w:(ol k q e ) .

As apparent from the frequencies involved, modes a and c are strongly affected by plasmons, while modes e and g are affected primarily by lattice vibrations modified somewhat by the presence of carriers The frequencies’ wlf correspond to purely longitudinal waves Ell.& given by zeros of c1 :

the latter corresponding to the plasma-cyclotron-resonance (PCR) longi- tudinal mode of plasmas with little participation of the ionic nature of the material.

Referring to Fig. l(a) and l(bX phase-matched forward-wave parametric interaction is possible for points L, I, and any one of the points 1,Z 3,4, or 5 with energy and momentum relations satisfied; i.e., wL = q + w j and k,= k,+ kj, where wj , k j correspond to points 1, 2, 3, 4, or 5, respectively. For pump power density (at w,) in excess of a threshold value Pp, coherent oscillations at idler I and the third frequency are achieved The threshold pump power density for a single pass condition is derived as

where c is the velocity of light, t/ the intrinsic impedance of free space, L the length of the crystal along k j , ,y the nonlinearity coefficient evaluated from the electrooptic tensor and polarizations of the three waves, and R,, R, the reflectivities of the boundary at the two ends Depending upon whether the third frequency is 1, 2, 3, 4, or 5 [in Fig l(a)], the following possibilities exist.

1) The interaction corresponding to L, I , and 1 results in stimulated emission at Stokes f rquency~u~d-LO ,frequency corresponding to d m . Whib the LO power is difficult to couple out on account of the longitudinal E field, a variable magnetic field may be used to obtain a tunable source of radiation at IR wavelengths. For a

aml plasma cyclotrm resonance in thin fihn polar semiconductors,” J. Phys. Soe. J a m 2 S. Iwasa, Y. Sawada, and E. Burstein, “Transmission studies of plasna resonance

(Suppl.), VOL 21, pp. 742-745.1966.

Wce > Wf %e < W l

101 ( b l

Fig. I . The 0-k of an n-type semiconductor including lattice vibratious for waves with Eli?,, kli?, , . (Typical values of EJE, are marked at various points.)

a and c are “extraordinary” plasma waves with Eli?, b is the plasma cyclotron resonance (F’CR) mode €llLIB, d is transverse optical (TO) phonons f is longitudinal optical (LO) phonons €116 e and g are optical waves with dispersion caused by lattice vibrations (LO phonons).

10.6 p (CO, laser) pump, wl+ = 5 x 1013 rad/s, L= 1 cm InSb Raman cell, n,=3.96, and ~ “ 0 . 5 x m/v, a threshold power density of less than 1 MWlcm’ is calculated assuming R , = R, = 0.7. The threshold is even lower for larger wl. The interaction corresponding to L, I , and 2 can lead to coherent oscillations at I and at w 2 = w 1 . Unlike mode b, mode g can be coupled out to waves having a component in the k x Bo or xdirec- tion, therefore making it possible to obtain tunable power at far-IR frequencies close to d m . The pump power threshold is only slightly larger than that calculated above, since w , < w l . Interaction corresponding to L, I , and 3 or 4 can result in Raman shifting of incident frequency by frequencies close to LO frequency of the material without much carrier effects. While the threshold for oscillation in this case is too high, interaction between I, I, and 5 may be used to modulate the laser at frequencies in the microwave/millimeter-wave band.

ACKNOWLEDGMENT The author has benefited from several discussions with Prof. R. W.

OM P. GANDHI Microwave Device and Phys. Electronics Lab.

University of Utah Salt Lake City, Utah

Grow during the course of the work.

On the Output Spectrum of Unlocked Driven Oscillators Abstract-A method is given to determine the components of the

signal of an unlocked driven oscillator. The phase modulation signal, which perturbs the free oscillation, is expanded in a Fourier series.

Some years ago Stover’ gave a calculation to explain the output spec- trum of an unlocked driven oscillator. He used an expansion in powers of a small parameter, which is equal to one when the oscillator becomes locked. However, there is a more straightforward method for h d i n g the components of the unlocked driven signal. It consists in expanding the

Manuscript received January 27, 1969. H. L. Stover, “Theoxtical explanation for the output spectra of unlocked driven

oscillators,” Proc. IEEE (Lerrers), vol. 54, pp. 310-311, February 1966.