Phase-matching Arrangements In Parametric Traveling-wave Devices

Abstract

The phase deficiency in a parametric traveling-wave device, due to dispersion in the wavepath, is compensated by means of a grating distributed along a surface of an otherwise uniform nonlinear material. In one embodiment of the invention the grating is fixed. In a second, tunable embodiment of the invention, an acoustic surface wave serves as a moving grating.

Description

This invention relates to parametric optical devices.

BACKGROUND OF THE INVENTION

It is known that in traveling-wave parametric devices, such as parametric amplifiers and harmonic generators, efficient interaction requires that the so-called "Tien conditions" be satisfied. As set forth in a paper by P. K. Tien, entitled "Parametric Amplification and Frequency Mixing in Propagating Circuits," published in the Sept. 1968 issue of the Journal of Applied Physics, pp. 1,347-1,357, optimum parametric interaction occurs when

f.sub.1 +f.sub.2 =f.sub.3 (1)

And

.beta..sub.1 +.beta..sub.2 =.beta..sub.3 (2)

Where

f.sub.1, f.sub.2 and f.sub.3 are the frequencies of the propagating waves; and

.beta..sub.1, .beta..sub.2, and .beta..sub.3 are their phase constants.

Because nonlinear materials are also dispersive, the preferred phase conditions are not readily realized in the absence of special arrangements such as, for example, the use of birefringent materials, as described in U.S. Pat. No. 3,234,475, or the use of a fourth, variable frequency, electromagnetic signal, such as is described in the copending application by S. E. Miller, Ser. No. 813,425, filed Apr. 4, 1969, and assigned to applicant's assignee. Such devices and arrangements, however, limit the type of nonlinear materials that can be used, or require unduly complicated circuitry.

SUMMARY OF THE INVENTION

The present invention is based upon the recognition that the phase deficiency .DELTA..beta. of a parametric system can be directly and efficiently met by means of a spatial mixing process produced by introducing a periodicity in the waveguiding structure. This can be done by means of a fixed grating or, if the parametric device is to be tunable, by means of an acoustic surface wave. This, in the first embodiment of the invention to be described hereinbelow, a fixed grating having a periodicity .DELTA..beta., such that the Tien phase condition is satisfied, is placed along one surface of the wave path.

In a second embodiment of the invention, an acoustic wave, launched so as to propagate along the optical wave path, serves as a moving surface grating having the required periodicity. In this arrangement, the parametric device is tunable by varying the acoustic wave frequency.

It is an advantage of the present invention that the spatial mixing is produced by means of a relatively strong interaction with either a fixed or moving grating. As such, optimum phase conditions are readily established and the resulting energy transfer is efficiently accomplished over relatively short interaction distances.

These and other objects and advantages, the nature of the present invention, and its various features, will appear more fully upon consideration of the various illustrative embodiments now to be described in detail in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a first embodiment of the invention using a fixed grating;

FIG. 2, included for purposes of explanation, shows the manner in which the phase constant varies as a function of frequency; and

FIG. 3 shows a second embodiment of the invention using a moving grating.

DETAILED DESCRIPTION

Referring to the drawings, FIG. 1 shows a first embodiment of an optical, traveling-wave parametric device, in accordance with the present invention, comprising a source 14 of electromagnetic wave energy; a waveguide 10 for guiding and operating up said wave energy; and output utilization apparatus 15 for receiving and utilizing the transmitted wave energy.

Waveguide 10 is basically the same structure as is described in an article by E. A. J. Maracatili entitled "Dielectric Rectangular Waveguide and Directional Coupler for Integrated Optics," published in the Sept., 1969 issue of the Bell System Technical Journal. As described therein, the waveguide comprises a transparent (low-loss) uniform dielectric guiding strip 12 of refractive index n.sub.1, embedded in a second, transparent dielectric substrate 11 of slightly lower refractive index n.sub.2 < n.sub.1. In the illustrative embodiment shown in FIG. 1, strip 12 is embedded in substrate 11 with its upper surface exposed. Alternatively, the guiding strip can be totally surrounded by the substrate or can be placed on top of the substrate. For a full discussion of the design and operation of this type of waveguiding structure, see the above-identified article by Marcatili.

In addition to being transparent at the frequencies of interest, strip 12 is also nonlinear. That is, strip 12 is made of a material, such as potassium dihydrogen phosphate (KDP), lithium niobate, or gallium arsenide, whose index of refraction varies as a function of the intensity of the signal. As is known, when a signal of angular frequency .omega. is applied to such a material, a modulation process occurs, resulting in the generation of sum and difference frequencies. Thus, for example, harmonics of the applied signal frequency are produced. The efficiency with which this occurs depends, among other factors, upon how closely the Tien phase condition is satisfied. In a second harmonic generator, optimum interaction occurs where

.beta..sub.2 = 2.beta. (3)

where .beta. and .beta..sub.2 are the phase constants of the fundamental and second harmonic waves, respectively.

Typically, however, most media are dispersive. Thus, the second harmonic phase constant .beta..sub.2 is not equal to 2.beta. as required by equation (3). This is illustrated in FIG. 2 which shows a typical .beta.-.omega. curve 20 and an idealized, linear .beta.-.omega. curve 21. The phase constant .beta. at frequency .omega. is defined by point 1, which is common to curves 20 and 21. At frequency 2.omega., the phase constant .beta.'.sub.2 defined by point 2 on curve 20 is not equal to 2.beta. because of the curvature of the actual .beta.-.omega. curve. The deficiency in the phase constant of the harmonic wave is equal to the difference .DELTA..beta. between the actual phase constant .beta.'.sub.2 , defined by point 2 on curve 20, and the idealized phase constant .beta..sub.2 , defined by point 3 on curve 21.

In accordance with the present invention, the deficiency in the magnitude of the phase constant of the harmonic wave is made up by means of a spatial mixing process. Just as .omega. defines the temporal variations of a signal, .beta. defines its spatial variations. And just as a mixing process creates new temporal variations, a spatial mixing process creates new spatial variations. Referring to FIG. 2, it is apparent that in order to satisfy the preferred phase condition for efficient harmonic generation, a new space-time relationship, which differs from curve 20 by an amount .DELTA..beta. is needed. In accordance with one embodiment of the invention, spatial sidebands are produced by means of a fixed grating 13 placed upon a surface of guiding strip 12. The grating, most generally, can be any arrangement which introduces a series of uniformly spaced discontinuities along the direction of wave propagation, where the spacing d between discontinuities is related to the phase constant difference .DELTA..beta. by

d=2.pi.m/.DELTA..beta. (4)

where m is an integer.

The interaction of the optical waves with the grating gives rise to a family of new space-time relationships, defined by curves 22, 23, and 24, for difference values of m. As can be seen, by choosing d for the grating in accordance with equation (4), there now exists a realizable solution of the Tien phase condition since, for m = 1, there is a .beta.-.omega. relationship defined by curve 23 for which the second harmonic phase constant, .beta..sub.2 = .beta.'.sub.2 + .DELTA..beta., is equal to 2.beta. .

It should be noted that the phase constants of the several waves will be slightly perturbed by the presence of a grating. Hence, the phase relationship using the unperturbed phase constants, is correct to only a first order approximation.

Grating 13 can be formed along the upper surface of strip 12 by means of any one of the many well-known techniques. For example, the grating can be ruled onto the guiding strip, or formed by means of a deposition process. The optimum length of the grating, to produce maximum or any other degree of interaction, can be determined experimentally. In the visible region of the spectrum, this is easily done by visually noting the intensity of the signal of interest, i.e., the harmonic wave in a harmonic generator, along the direction of wave propagation. This intensity will vary along this direction, reaching a maximum at regularly spaced intervals. The optimum length for maximum interaction is defined by one of the maxima.

It will also be noted that the guiding strip 12 need be made of a nonlinear material only over a region coextensive with grating 13.

FIG. 3 shows an alternative embodiment of the invention including, as in FIG. 1, a waveguide 30 comprising a nonlinear, transparent guiding strip 31 embedded in a transparent substrate 32. For purposes of illustration, the embodiment of FIG. 3 is a parametric amplifier and, as such an input signal E.sub.s, derived from signal source 33, is directed into one end of guide 30 along with a pump signal E.sub.p derived from a pump source 34. Advantageously, both sources are highly coherent signal sources such as lasers.

Output utilization apparatus 35 is located at the other end of guide 30 to receive the amplified signal E.sub.s, along with pump signal E.sub.p, and an induced idler signal E.sub.i. The latter two signal components can be selectively attenuated by means of filters.

The conditions for parameter amplifications are given by

f.sub.p =f.sub.s +f.sub.i (5)

and

.beta..sub.p =.beta..sub.s +.beta..sub.i (6)

where

f.sub.p, f.sub.s, and f.sub.i are the frequencies of the pump, the signal and the idler waves, respectively; and

.beta..sub.p, .beta..sub.s, and .beta..sub.i are the phase constants of the pump, the signal and the idler waves, respectively.

The frequency condition is automatically satisfied by virtue of the modulation process produced by the nonlinear guiding strip 31 wherein the pump and signal waves interact to generate the difference frequency idler wave. For this interaction to grow, however, and the signal to be amplified, the phase condition given by equation (6) must also be satisfied. However, because of the dispersion discussed in connection with FIG. 2, .beta..sub.p is, in general, different than .beta..sub.2 + .beta..sub.i by an amount .DELTA..beta.. This difference is made up in the embodiment of FIG. 3 by means of a moving acoustic grating induced along the strip by longitudinally spaced electroacoustic surface wave transducers 40 and 41. The latter can be any one of the many known electroacoustic transducers. Those illustrated in FIG. 3 are the type described by J. H. Rowen in U.S. Pat. No. 3,289,114, and comprise wedge-shaped members 42 and 43 to which are bonded bulk transducers 44 and 45, respectively. An electrical signal source 46 is coupled to one of the transducers 40, and an output absorptive load 47 is coupled to the other transducer 45.

In operation, transducer 40 launches an acoustic surface wave along guiding strip 31 in response to the signal derived from source 46. The frequency of this signal is such that the acoustic wavelength .lambda..sub.a of the induced acoustic wave is related to .DELTA..beta. by

.lambda..sub.a =2.pi.m/.DELTA..beta. (7)

where m is an integer.

The acoustic wave thus induced along the optical wave path, produces spatial sidebands in the same manner as the fixed grating in the embodiment of FIG. 1. By selecting the frequency of the acoustic wave in accordance with equation (7), the optimum phase condition for parametric interaction is realized.

The second transducer couples the acoustic wave energy to terminating load 47, thus defining the overall length of the amplifier.

It will be noted that there will be a slight Doppler frequency shift produced by the moving grating. However, the acoustic wave frequency is typically much less than the frequencies of the optical waves and, hence, the resulting frequency shift can generally be neglected. It will also be noted that this second embodiment of the invention is tunable. That is, if the optical signal frequency is changed, a new optimum phase condition can be readily established by merely adjusting the frequency of the acoustic wave.

While the invention has been described with reference to optical waves and with reference to a particular waveguiding structure, it will be readily recognized that the same techniques can just as readily be utilized at the lower millimeter and microwave frequencies. In addition, the invention is not limited to the specific parametric interaction described hereinabove but, more generally, is applicable to any parametric system of the form

p.omega..sub.1 +m.omega..sub.2...+n.omega..sub.n =0 (8)

and

p.beta..sub.1 +m.beta..sub.2...+n.beta..sub.n =q.DELTA..beta. (9)

where

p, m, n and q are integers, and

.DELTA..beta. is the phase deficiency of the system.

Thus, in all cases it is understood that the above-described arrangements are illustrative of but a small number of the many possible specific embodiments which can represent applications of the principles of the invention. Numerous and varied other arrangements can readily be devised in accordance with these principles by those skilled in the art without departing from the spirit and scope of the invention.

Claims

I claim:

1. A traveling electromagnetic wave parametric device comprising:

a dispersive waveguide supportive of electromagnetic wave energy having angular frequencies .omega..sub.1, .omega..sub.2 and .omega..sub.3, where .omega..sub.1 +.omega..sub.2 =.omega..sub.3 ;

a uniform, nonlinear material extending longitudinally along a portion of said guide in the direction of wave propagation;

said material having distributed along a surface thereof a plurality of discontinuities longitudinally spaced apart a distance d=2.pi.m/.DELTA..beta., where m is an integer, .DELTA..beta. is the phase differential required to satisfy the phase relationship .beta..sub.1 +.beta..sub.2 =.beta..sub.3 +.DELTA..beta., and .beta..sub.1, .beta..sub.2, and .beta..sub.3 are, to a first-order approximation, the phase constants, respectively, of said wave energy.

2. The device according to claim 1 wherein .omega..sub.1 =.omega..sub.2 and .beta..sub.1 =.beta..sub.2.

3. The device according to claim 1 wherein said discontinuities form a fixed grating.

4. The device according to claim 1 wherein said discontinuities form a moving grating.

5. The device according to claim 1 including a first electroacoustic transducer for launching an acoustic surface wave along said material, and a second longitudinally spaced transducer for receiving said acoustic wave;

and wherein the distance d is equal to the wavelength .lambda..sub.a of said acoustic wave.

6. A frequency doubler comprising:

a parametric device according to claim 2;

a source of wave energy having an angular frequency .omega..sub.1 coupled to one end of said device;

and output apparatus for receiving wave energy having an angular frequency .omega..sub.3 =2.omega..sub.1 coupled to the other end of said device.

7. An amplifier comprising:

a parametric device according to claim 1;

a signal source having an angular frequency .omega..sub.1, and a pump source having an angular frequency 107 .sub.3 coupled to one end of said device;

and output apparatus for receiving amplified wave energy at angular frequency .omega..sub.1 coupled to the other end of said device.

8. A traveling electromagnetic wave parametric device comprising:

a dispersive waveguide including a uniform, nonlinear material extending longitudinally therealong in the direction of wave propagation;

said guide being supportive of electromagnetic wave energy having angular frequencies .omega..sub.1, .omega..sub.2....omega..sub.n with phase constants .beta..sub.1, .beta..sub.2....beta..sub.n, respectively, where

p.omega..sub.1 +m.omega..sub.2...+n.omega..sub.n =0

and

p.beta..sub.1 +m+.sub.2...+n.beta..sub.n =q.DELTA..beta.,

where p, m, n and q are integers;

characterized in that said material has distributed along a surface thereof a plurality of discontinuities longitudinally spaced apart a distance d=2.pi./.DELTA..beta..