CA1202695A - Traveling wave electrooptic devices - Google Patents

Abstract

TRAVELING WAVE ELECTROOPTIC DEVICES

Abstract Prior art techniques for velocity matching the optical wave and the modulating electrical wave in traveling wave, electrooptic devices includes the use of phase reversals and intermittent interaction. This results in a device whose frequency response includes a single peak. It has been discovered that by reducing the length of the interaction intervals between the electrical and optical systems, a multiplicity of harmonically related frequency peaks can be obtained. Furthermore, by combining the phase reversal and intermittent interaction techniques in a common device, the available bandwidth can be doubled.

Description

~2~)2~

TRAVELING WAVE ELECTROOPTIC l)EVICES

Technical Field This application relates to traveling wave electrooptic devices such as switches, modulators, phase shifters and mode converters.
Background of the Invention Traveling wave electrooptic devicesr in which the optical wave and the modulating (i.e., microwave) electrical wave propagate with the same velocities, have very broad operating bandwidths. However, Eor important materials used in the fabrication of these devices, such as lithium niobate, there is an inherent mismatch between the two velocities. As a consequence if modulation above the "walk-off" frequency is to be obtained, the electrical signal wavepath must be specially designed in order to compensate for the velocity mismatch which exists9 In one approach the problem of velocity mismatch is dealt with by means of a meandering electrode. The electrode is shaped so as to interact with the optical wavepath over a first interval where the direction of ~he electrical signal has one sense (i.e., polarity), and not to interact over a second interval where the sense is reversed In another approach, there is interaction over the entire length of the electrode. However, the electrodes are periodically displaced so as to introduce a structural polarity reversal which compensates for the electrical polarity reversal caused by the velocity mis~atch.
In both of the above-described types of devices the resulting frequency characteristic includes a single peak at a designated frequency Furthermore/ the ability to control where this bandwidth falls (i.e., what frequencies are included within the response characteristic of the device) is limitedO What is needed is a technîque for distributing the available bandwidth over the frequency spectrum of interest. For example, to generate or switch a ~Y~
~, ...

~2a~ 5 pulse train of very narrow pulses r~quires a device whose response includes a plurality of harrnonically related passbands~ Prior art traveling wave devices do not possess s~ch a frequency characteristic.
Summary of the Invention The present invention is based upon the discovery that by reducing the length of the interaction intervals between the electrical and optical wavepaths, a multiplicity of har~onically related frequency peaks can be obtained. More specifically, for any pair of carrier and modulating signal wavelengths there is a coherence length over which the polarity of the modulating signal is in a given direction. By making the interaction intervals small relative to this coherence length the desired result is obtained.
According to the invention there is provided a device comprising: a substrate comprising electrooptic material; first waveguiding means adapted for guiding electromagnetic radiation of optical wavelengths, such radiation to be referred to as the "optical signal", the first waveguiding means comprising at least one waveguide formed in the substrate, the waveguide to be referred to as the "optical waveguide"; and second waveguidinq means, disposed on the substrate, adapted for supporting a pro-pagating electrical signal comprising a wavelength ~m''the second waveguiding means comprising a multiplicity of spaced sections; to be referred to as the "on" sec~ions, that are disposed such that the propagating electrical signal does operatively interact with the optical wave~
guide by means of the electrooptic effect, such relation-ship to be referred to as an "electrooptically interacting"
relationship, and further comprising at least one further section, to be referred to as the "off" section, that is disposed such that the propagating electrical signal does not operatively interact with the optical waveguide by means of the electrooptic effect, such relationship to .

~2~2~.g3S

be referred to as an "electrooptically noninteracting relationship, the "off" section being located between two "on" sections; characterized in that each "on"
section is substantially of length Lon, the at least one "off" section is substantially of length Loff, with Lo~f > ( l-No/Nm)Lon where: No is the effective refractive index of the optical. waveguide at the wavelength of the optical signal; and: N is the effective refractive index of the second waveguiding means at the wavelength ~m of the electrical signal.
Brief Description of the Drawing FIG. 1 shows a prior art traveling wave, electrooptic phase shifter em21Oying phase reversal electrodes to affect velocity matching;
FIG. 2 shows the variations in A~ as seen by photons entering the phase shifter of FIG. 1 at two different phases of the modulating signal;
FIG. ~ shows the modulatin~ si~nal as a function of time;
FIG. 4 shows the effect of the phase re~ersal electrode configuration on the variation of ~ alon~ the optical waveguide;
FIG. 5 shows the amplitude-frequency response of the phase shifter of FIG. 1 for different numbers of electrode sections;
FIGS . ~ and 7 show the time and frequency characteristics of a train of pulses;
FIG. 8 shows the phase-shifter of FIG. 1 modified in accordance with the present invention;
FIGS. 9 and 10 show the effect upon the distribution along the phase shifter of FIG. 8 when modified in accordance with the invention;

s FIGS. 11, 12 and 13 show the effect upon the frequency characteristic of the phase shifter of FIG. 8 for diffeeent "on-off" aspect ratios;
FIGS~ 14, 15, 161 17 and 18 show various other embodiments of the present invention;
FIG. 19 shows, in block diagram, a device using both phase-reversal and intermittent interaction electrode configurations in accordance with the present invention;
FIG. 20 shows the response characteristic of the de~ice of FIG. 19; and FIG. 21 shows an illustrative embodiment of a modulator using both phase reversal and intermittent interaction electrode configurations.
Detailed Description While the principles of the invention are equally applicable to a variety of traveling wave devices such as phase shifters, directional couplers, and mode converters, the frequency response analysis is more straightforward in the case of the phase shifter. Accordingly, an electrooptic phase shifter is used as the illustrative embodiment to be described in detail hereinbelow. The application of the principles of the invention to other devices is also described.
Prior Art Electrooptic Devices with Phase Reversal Referring to the drawings, FIG. 1 shows a prior art phase shifter with effective velocity matching~ The device 10 comprises a dielectric waveguiding strip 11 embedded in a substrate 12 of lower refractive index birefringent material, and means for modulating the propagation constants of the orthogonally polarized TE and TM modes of wave propagation by means of the electrooptic effect. In the illustrative embodiment of FIG. 1 this modulation is effected by means of a pair of conductive finger electrodes 13 and 14 superimposed upon the substrate and waveguiding strip. The electrodes, which form a planar strip transmission line, extend coextensively over an interval ~ of the optical wavepath and are arranged 2fi~5i relative to ~ach other such that the fingers 13-1, 13-2 ...
of electrode 13, and the fingers 14-1~ 14~2 ... of electrode 14 are interleaved. The length of each of the fingers along the direction of wave propagation is equal to S the coherence length do for the desired operating frequency. The coherence length is defined in greater detail hereinbelow.
The transmission line for~ed by the electrodes is energized at one end by a modulation signal source 15, and is match-terminated by an appropriate impedance 16 at its other end.
As known by workers in these arts, because of the velocity mismatch between the optical and electrical signals, the two signals do not propagate in synchronism.
This produces what is referred to as a i'walk-off" effcc~.
In the instant case! where the optical wave propagates at a faster velocity than the electrical wave, photons entering at any instant tend to "ca~ch up" with the electrical waveO
As a result, in the absence of any compensating arrangements, the electrical field, and hence the difference ~ in the phase constants seen by the two modes, varies as a function of distance along the phase shifter.
For the case of a uniform electrode configuration (not shown), the Q~ variations seen by a photon entering at the instant the modulating signal (represented by curve 30 in FIG. 3) is zero as illustrated by curve 20 in FIG. 2, where the electrode segments dl, d2 d6 are all equal. Because the optical signal propagates more rapidly than the electrical signal, these photons "catch up" with portions of the previously applied modulating signal deplcted by the -t portion of curve 30O In particular, in an interval dl + d2, the photons see a complete modulating voltage (Vm) cycle and the corresponding spatial ~ variation. The spatial intervals dl, d2, ..O d6 over which the polarity of ~ is either positive or negative is called the coherence length and is given, as a function of the design wavelength ~m~ by q 1~' ~.`

- 5a -~m N
d= 2-- 1 N
m ,m, where ~m is the wavelength of the modulating signal in free space;
Nm is the effective refractive index at the modulating signal wavelength;
and No is the effective refractive index at the opti~al signal wavelength.
A similar ~ variation occurs for photons entering at other times during the modulating signal cycle, as indicated by curve 21 in FIG. 2. The latter corresponds to a 90 degree phase shift in the modulating signal, as represented by curve 31 in FIG. 3O
Both of the curves 20 and 21 in FIG~ 2 illustrate the effect of walk-off on ~. Specifically, there is a regular recurring phase (iOe., polarity) reversal in such that the integrated effect over the length of the device is very small. To avoid the effect of ~alk-off, one prior known approach utilizes a 180 degree phase (i.e., polarity) reversal in B~ by introducing a physical displacement of the two electrodes so that the direction of the modulating field is reversed. Thus, over the first interval, finger 13-1 of electrode 13 extends over the waveguiding strip 11 whereas over the second interval finger 14-1 of electrod~ 14 extends over strip 11. In particular, by making each of the intervals equal to do the effect of this physically produced phase reversal is to produce a rectification of the spatial variations ofQ~ as illustrated by curve 40 in FIG. 4. Thus, with respect to photons entering when the modulatin~ signal a~plitude i5 zero, the induced phase shift in each section has the same sense and, as a result, all the sectiwns add in phase. The electrode sections are essentially phase locked with ~ ~n~
~VA~

respect to their effect upon the optical wave.
Conse~uently, the total interaction length Ndo, where ~ ;s -the number of fingers, can be arbitrarily long (in the absence of losses) without degradation due to velocity mismatch, and ~he drive vol~age can be correspondingly reduced.
Because the coherence length depends upon the modulating frequency, the velocity match condition is also a function of the modulating signal frequency, fd~ as given by

2~Nm . f ~d = ~, t2) ~ d where ~ No/Mm~ Thus, for any arbitrary frequency fm ~ fd, the electrode induced reversal of the electric field is not matched to the walk-off induced polarity reversal, and incomplete or no effective velocity matching results.
FIG~ 5 shows the effect of phase reversal upon frequency characteristic of traveling wave devices. In the case of a uniform electrode of length L = 2do, the response curve 40 is a maximum at zero frequency and decreases to zero response at a frequency fdJ as given by equation (2).
The response for fm>fd is a series of decreasing lobes.
For the case of L = 2do with polarity reversal, a broad response is obtained which is zero at zero Erequency and peaks at a frequency slightly below fd, as illustrated by curve 41. As additional sections of electrode are added there is an increase in the amplitude of the response~
which tends to peak at fm = fd~ and a reduction in the bandwidth. In addition, there is a series of smaller lobes above and below fd which decrease in amplitude. The side lobes in all cases are too small to be useul, but large enough to be detrimental in that they consume bandwidth.
Further reference will be made to these curves hereinbelow.

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While the ability to change the frequency response of traveling wave devices from lowpass to bandpass at some arbitrary high frequency i9 useful, there are applications for which such a response is inadequate. ~or example, to modulate a cw optical wave so as to produce a train of optical pulses requires a modulating signal of the type illustrated in FIG. 6. This modulating signal comprises a train of pulses of width r and spacing T. The frequency equivalent of such a signal, illustrated in FIG. 7, includes a plurality of harmonically related components that are spaced apart an amount l/T, and whose amplitudes decrease with increasing frequency reaching a -3dB level at frequency 1/l. Clearly the essentially single response characteristics of the prior art devices illustrated in FIG. 5 are inadequate to satisfy these requirements.
Electrooptical Devices with Multifrequency Response Characteristics Employing Phase Reversal A traveling wave electrooptic device having a multifrequency response characteristic is obtained in accordance with the present invention by limiting the interval over which interaction between the optical wave and the modulating wave occurs to a distance that is less than the coherence length do.
1. Phase Shifter with Phase Reversal In a first embodiment of the invention, using the basic phase shiEter of FIG. 1 for purposes of illustration, the electrode configuration is modified so that in addition to providing the above~described polarity reversals, intervals are introduced along which there is no interaction between the propagating waves. One realization of such an electrode configuration is illustrated in FIG~ 8 which shows a portion of the phase shifter comprising a dielectric waveguiding strip 55 embedded in a substrate 56.
Modulating electrodes 50 and 51, superimposed upon the waveguiding strip and substrate, are shaped to include regions of interaction and regions of noninteraction~

~%~2~

Along a first interaction region formed by electrode portions 50~1 and 51-1, the former extends over waveguiding strip 55. In a second interaction region formed by electrode portions 50~3 and 51-3, the latter extends over waveguiding strip 55. This displacement of the electrode portions relative to the optical wavepath provides the desired polarity reversal described hereinabove with regard to FIG. 1. ~nlike the prior art embodiment, however, the two interaction portions are separated by a noninteraction region made of electrode portions 50-2 and 51-2 neither one of which is in the region of waveguiding strlp 55. T~e lengths Lonl~ Lon2 ~- of the interactiOn regions along the y direction (i.e. along the direction of optical wave propagation) are all equal and designed to be less than the coherence length do~ but very much larger than the distance Ls occupied by the noninteraction regions in the direction along the optical waveguide. As an example, in a phase shifter designed to operate at lOGhz, Lon = 7.5mm and Ls = lO0 ~m.
The effect of this modified electrode configuration upon the optical wave can be understood by referring to FIGS. 9 and lO which show, respectively, the modulating voltage as a function of distance along the electrodes, and the resulting induced ~ as a function of distance along the optical wavepath. ~ith regard to FIG. 9, the particular modulation signal illustrated is a sinusoid. Interaction with the optical wave, however, occurs only along the interaction intervals Lonlr L
Lon3, .... No interaction is produced along the "off"
regions Loffl- Loff2~ - Thus, a photon enterin~ at a time corresponding to phase ~ of the modulating signal sees the modulaking wave portion 80-l as it traverses the first "on" interval Lonl~ Neglecting Ls which, as indicated above, is very much smaller than Lon, the optical wave upon entering the second interaction interval sees modulating wave portion 30-2. The latter, of course, is the wave portion that has been rectified by the polarity reversal ~L2~2~95 _ 9 produced by the tran5verse electrode displacement~
Similarly, along each interaction reyion the photon sees only the peak portions 80 lr 80-2, 80-3 ... of the modulating signal, producin-~ the rectiEied ~ curve ~2 shown in FI~. 10.
If we define an aspect ratio R as L

R = ~ , (3) ~ Lon we have for the prior art device, wherein Loff = ~ an aspect ratio of zero~ For the present invention, by contrast, R > 0. It will be noted that the larger the aspect ratio the smaller the portion of the ~ curve that is used, but the larger the average value of a~.
The velocity match condition for any arbitrary aspect ratio is given by 2~Nmfd~Lon (l+R) = ~, (4) c which is the more generalized version of equation (2)o To analyze the response characteristic of a phase shifter incorporating the teachings of the present invention, an expression for the integrated, electrooptically-induced Q~ was derived as a function o~
the modulating frequency, fm. The result of th;s derivation is given by sin(~ /2) sLn ~(~2 * ~)1 30 ~a = (~oL) ~ 2 coS(~2/2) sin(a - 2~fmto) (5) 35 where ~O is the maximum electrooptically induced difference in the phase constants;
N is the number of sections;

~LZ~69~S

L is the total interaction length;
2~rN
~l c fm~Lon ; . (6) ~2 = ---- f ~L ~1 + R) (7) c m on 10= ~c~~fm~(L + -~-- (8) and ~ is a phase constant equal to ( 2 ) (~2 + ~r) + ~1/2O (9) It will be noted that the amplitude portion oE
equation (5) is the product of two frequency sensitive terms. The first term, sin (~l/2)/(~l/2), has the same sin x/x response characteristic as the nonvelocity matched device illustrated by curve 40 in FIG. S. This function decreases from its maximum value at zero frequency, reaching zero for ~1 = 2~ at a cutoff frequency fm = fc that is inversely proportional to Lon (see equakion [6]~.

~ ll The second term, [sin (N/2)(~2 ~ ~)]/cos (~2/2), is essentially a phase~loclclng term that describes the additive efEect of the N sections. This term peaks whenever ~2r given by equation (8), is equal to an odd multiple of ~. The frequencies, ~d~ 3fd -- nfd, a~ which the peaks occur is an inverse function of the coherence length tLon + Lo~f/~)O The number of peaks that appear in the overall device response depends upon the relative values of fc and fd. The former, fc~ which is a function of Lon, can be made large by making Lon small. fd~ on the other hand, is a function of both Lon and Loff. Thus, the envelope term and the phase locking term can be independently designed to provide the desired overall response characteristic. This is illustrated in FIGS. ll, 12 and 13 which show the response curves for four (N = 4) electrode sections (i.e., pairs of "on"-"off"
intervals), when R = 0, 2 and lO. In the pL-ior art case, shown in FIG~ ll, where R - 0, there is one principal lobe (i.e., R + l = l), and the cutoff frequency, fc~ is equal to 2fd. FIG. 12 shows the response for ~ = 2. For this case fc is equal to 6fd~ and there are three principal lobes. FIG. 13 shows four of the eleven principal lobes for the case of R = lO. In all cases, the envelope term is shown in broken line. The resultiny amplitude characteristic is shown in solid line.
As indicated hereinabove, the principles of the invention are equally applicable to other devices usiny the phase reversal method of simulating velocity match, and to other velocity matching techniques such as the intermittent interaction produced by the prior meandering electrode arrangement. Examples of these applications are illustrated in FIGS. 14 through 18.
2. Mode Converter with Phase Reversal FlG. 14 shows a portion of a TE~TM mode converter in accordance with the invention comprising a waveguidiny strip 90 embedded in a substrate 91 o lower refractive index electrooptic material. A pair of electrodes 92 and 93, forming a planar strip transmission line, are suitably disposed along an interval L of strip 70. In operation, a modulation signal source and a matching terminating impedance (neither shown) are connected at opposite ends of the electrodes.
Because of the difference in the refractive indices seen by the two modes, finger electrodes are employed to produce a phase match between the optical TE
and TM modes where the spatial period, ~\, of the fingers is N - N
l\ ~o L TE TM~ (10) 15 where ~O is ~he free-space wavelength of the optical signal of interest;
and ~TE and NTM are the effective refractive indices seen by the TE and TM modes, respectively.
Depending upon the cut of the substrate material, the electrode fingers are either interleaved or arranged opposite each other, as shown in FIG. 14.
As known by workers in these arts, to compensate for the effect of walk-off, a polarity reversal is introduced in the modulating signal at intervals equal to the coherence length. This is done by means of a discontinuity in the finger spacing along the electrodes equal to l\~2. The electroda configuration is further modified in accordance with the present invention by the addition of an ~loff'l interval, Loff~ along the electrodes in the manner explained in connection with the phase shifter shown in FIG~ 8~ Specifically, after an interval, Lon, which is less than the coherence length, the electrodes are transversely displaced away from the optical wavepath formed by waveguiding strip 90, thereby decoupling the two circuits. To provide the desired polarity reversal in the electric field direction along the next 'lon"

- 13 ~

interval, the longitudinal distance L5 alony the optical waveguiding s-~rip occupied by the displaced electrodes is made equal to l~(n+l/2), where n is any integer, and Ls is measured between corresponding points on the electrodes.
It should be again noted that the "on" interval, Lon, is typically very much larger than the spatial period, ¦\, and also very much larger than Ls~ The relative magnitudes of Lon and Loff (i.e., the value of R) are determined in accordance with those considerations discussed hereinabove.

3. Directional Coupler with Phase Reversal FIG. 15 shows the principles of the invention applied to a directional coupler 100. As in ~he prior art, the coupled waveguides 101 and 102 are a pair of substantially identical parallel waveguiding strips embedded in a substrate 106 of lower index electrooptic material. S~perimposed upon the substrate and the optical waveguides are three conductive electrodes 103, 104 and 105 which extend coextensively along an interval L oE the coupled optical waveguides. In this embodiment, the electrodes comprise an inner electrode 103 and two outer ground electrodes 104 and 105 which, together form a coplanar strip transmission line.
To provide the desired polarity reversal, the inner electrode meanders so as to extend alternately over each of the optical wavepaths 101 and 102. The outer electrodes 104 and 105 sirnilarly meander such that one or the other of said electrodes extends over those portions of the optical waveguides not covered by the inner electrode.
Along the first interacting interval~ L
electrode 103 is located above waveguide 101, and electrode 105 is located above waveyuide 102. This i5 followed by an "off" interval, along which the center electrodes is displaced relative to both optical wavepaths so that no interaction occurs~ The two outer elec~rodes are similarly displaced so as to maintain continuity along the strip transmission line. Following this "off"

~Z~;)2~5g~Si interval r the center electrode extends over the other waveguide 102 and electrode 104 extencls over waveguide 101, thus providing a polarity reversal over the secon~ "on"
interval. This is then followed by a second "off" interval and a subsequent polarity reversal as the electro~es extend along the entire coupling interval L, of which only a portion is shownO
In each of the devices shown in FIGS r 8, 14 and 15 the technique of periodic phase reversal is employed to resolve the problem of velocity mismatch.
Electrooptic Devices with Multifrequency Response Characteristics Employing Intermittent Interaction In a second class of traveling wave devices, as priorly knvwn9 effective velocity match is achieved by means of intermittent interaction. In accordance with this technique, the electrodes are simply decoupled from the optical waveguide by removing them from the region of the optical waveguide whenever the velocity misma-tch results in a polarity reversal of the modulating signal. Thus, in such prior art devices,Loff = ~ Lon and ~ = 1. In accordance with the present invention, the relative values of Loff and Lon are changed such that R > 1. In particular, the length Lon of the "on' interval is reduced as required to obtain the desired frequency response.
The frequency fd at which the velocity match condition is satisfied for a given aspect ratio R and interaction interval Lon is given by 2 Nmfd~Lon (1 ~ R) - 2rf (11) If equation (11) is compared with the corresponding equation (4~ for the phase reversed electrode devices, it will be noted that the velocity matched frequency, fd, of the intermittent interaction device for the same value of Lon and R is twice ~hat of the phase reversed electrode devices, and that in the case of the intermittent interaction device, peaks occur at all harmonics, not only the odd harmonics. Use will he made of this fact as will be explained hereinbelow.
FIGS. 16, 17 and 18 show various embodiments of intermittent interaction traveling wave devices, in accordance with the present invention, including, respectively, a directional coupler, a phase shifter and a mode converter. They are in many respects similar to the devices described hereinabove wherein the electro~les are configured to include a series of "on" intervals of the length Lon separated by "off~ intervals of length Loff~
These devices differ, however, in that there is no phase reversal provided by the positlon of the electrode structures and, as a consequence, the relative lengths of the "on" and ~off" intervals are different than on the previously described devices.

4. Directional Coupler with Intermittent Interaction In the embodiment of FIG. 16 the electrodes 154 and 155 extend over the optical waveguiding strips 151,152 of optical directional coupler 150 to form a first ~on"
interval. This is followed by a first "offl interval wherein the electrodes loop away from the optical waveguides. At the end of the "off" interval~ the electrodes are returned and occupy the same positions relative to the optical paths. Thus, electrode 154 extends over wavepath 151, and electrode 155 extends over wavepath 152. This ~on-off" electrode configuration is repeated along the entire length of the device.

5. Phase Shifter with Intermittent Interaction In the phase shifter illustrated in FIG. 17~ one of the electrodes, 161, extends over the optical waveguiding strip 160 along each of the "on" intervals. In the intervening "off" intervals the two electrodes 161 and 162 loop away from the optical wavepath.

.~

6. Mode Conv~rter with Intermittent Interaction The mode converter shown in FIG~ 18 is substantially identical with that shown in FIG~ 14 comprising a pair of finger electrodes disposed along opposite side of optical waveguide 170. In the phase reversal embodiment of FIG. 1~, the length Ls along the optical wavepath occupied by the "off~ region is equal to l~(n+l/2)O In the embodiment of FIG. 17, where there is no phase reversal, Ls=n¦~. In all of the embodinents 10 LSLon<do-Uniform Broadband Response For many modulator applications, a nominally flat frequency response from zero to some high frequency is required~ While the artificial velocity matching techniques described herein provide a means for moving the available bandwidth to higher frequencies or, as explained hereinabove, to divide it among many harmonically related frequencies, there is no net increase in the to~al available bandwidth. It is merely redistributed across the band of interest. HoweverO as indicated hereinabove, the response peaks for the two types of velocity matching electrode configurations do not occur at the same frequencies. For the phase reversal electrode configuration, the peaks occur at odd harmonics of fd. For the intermittent interaction electrode configuration, peaks occur at zero frequency and all harmonics of 2fd. If, therefore, the two electrode configurations are combined in a single device, the response peaks can be interleaved to form either a uniform response wherein the peaks of one response fills the void~s of the other, or to form a comb response. In either case, an approximate doubling of the available bandwidth can be realized.
FIG. 19 shows, in block diagram, a traveling wave optical device 180 including, in cascade, a set of phase reversal electrodes 181, and a set of intermittent interaction electrodes 182. For a given material system, ~;~ the envelope term, illustrated by curve 200 in FIG~ 20, has ~, the same cutoff frequency fc for the two electrode sections. The response peaks for the phase reversal electrodes, given by the dashed curve 191, occur at quencies fd, 3fd~ 5fd and 7fd. The response peaks for the intermittent interaction electrodes, given by solid curve 192, occur at zero frequency and harmonics of 2fd.
The net device response is given by curve 1930 In some devices, it is possible to make more efficient use of the modulating signal circuit. Instead of simply cascading the two electrode configurations, as indicated in FIG. 19, it may he feasible to utilize a single electrode circuit wherein the "off" interval for one optical signal serves as the "on" interval for the other and vice-versa. An example of such dual use is illustratecl in FIG. 21 which shows two phase shifters connected in parallel to form an interferometer.
Each phase shifter comprises an optical waveguide 122, 123. The two are coupled at one end to a common input waveguide 120 and at their other end to a common output waveguide 128. A pair of electrodes 124~ 125 are disposed along the two optical waveguides to form, along one of the waveguides 123, an intermittent interaction electrode configuration, and along the other waveguide 122 a phase reversal electrode configuration.
More specifically, the electrodes are disposed along waveguide 123 to form a first "on" interval 126-1. They are then directed away from waveguide 123 to form a first "oEf" interval. However, a portion of that lloffll interval is positioned alongside waveguide 122 to form a first "on"
30 interval 127-1 therealong. At the end of interval 127-1, the electrodes are displaced back alongside waveguide 123 to form a second "on~ interval 126-2. Following this, they are again displaced alongside waveguide 122 to form a second "on" interval 127-2 for this waveguide.
It will be noted that along waveguide 123~ the relative positions of the electrodes and the waveguide are the same. That is, in ~oth "on" sections 126-1 and 126-2 `~ ~2~6~S

electrode 124 is positioned above waveguide 123. Thus, the electrodes form an intermittent interaction configuration with respect to waveguide 123. By contrast, along waveguide 122, the relative positions of the electrodes changes such that whereas electrode 124 is positioned over waveguide 122 along "on" interval 127-1, electrode 125 is positioned over the waveguide along the second "on"
interval 127-2. Thus, insofar as waveguide 122 is concerned, the electrodes are in the phase reversal configuration, For modulator applications, such as broadband signal encoding for lightwave systems, it is necessary that the phase as well as the amplitude response be relatively flat over the frequency range of interest. Therefore, when broadbanding by using the combination of the phase reversal and intermittent interaction electrodes, it is important that the phase response be equal at the harmonics o~ f~.
Investigation of equation 15) indicates that that is the case provided an even number of sections is used for the intermittent interaction electrode and an odd number for the phase reversal electrode.
It will be appreciated that over the "on"
interval the location of the electrodes relative to the optical waveguide depends upon the cut of the substrate crystal. In the various illustrative embodiments it was assumed that the crystaL cut was such that the operative electric field direction was normal to the plane of the device. As such, the electrodes were shown located above the optical waveguides. If, however, the crystal cut is such that the operative electric field direction is parallel to the plane of the device, the optical waveguide would be placed differently, i.e~, between the elec-trodes.
Thus, other electrode configurations will result, depending upon the nature and properties of the materials employed.
The specific embodiments described are merely intenc~ed to be illustrative.

Claims (18)

Claims:

1. A device comprising:
a substrate comprising electrooptic material;
first waveguiding means adapted for guiding electromagnetic radiation of optical wavelengths, such radiation to be referred to as the "optical signal", the first waveguiding means comprising at least one waveguide formed in the substrate, the waveguide to be referred to as the "optical waveguide"; and second waveguiding means, disposed on the substrate, adapted for supporting a propagating elec-trical signal comprising a wavelength .lambda.m', the second waveguiding means comprising a multiplicity of spaced sections, to be referred to as the "on" sections, that are disposed such that the propagating electrical signal does operatively interact with the optical waveguide by means of the electrooptic effect, such relationship to be referred to as an "electrooptically interacting"
relationship, and further comprising at least one further section, to be referred to as the "off" section, that is disposed such that the propagating electrical signal does not operatively interact with the optical waveguide by means of the electrooptic effect, such relationship to be referred to as an "electrooptically noninteracting"
relationship, the "off" section being located between two "on" sections;

CHARACTERIZED IN THAT
each "on" section is substantially of length Lon, the at least one "off" section is substantially of length Loff, with Loff > ( 1-No/Nm)Lon where: No is the effective refractive index of the optical waveguide at the wavelength of the optical signal;
and: Nm is the effective refractive index of the second waveguiding means at the wavelength .lambda.m of the electrical signal.

2. The device of claim 1, wherein the device is an optical phase shifter, the optical waveguide being adapted for guiding at least one TE mode and at least one TM mode of the optical signal, associated with each of the modes being a phase constant, and wherein the second waveguiding means are disposed such that the electrooptic interaction can change the value of at least one of the phase constants.

3. The device of claim 1, wherein the device is a directional coupler, with the first waveguiding means comprising a pair of coupled optical waveguides, associated with each of the optical waveguides being a phase constant, and wherein the second waveguiding means are disposed such that the electrooptic interaction can change the value of at least one of the phase constants.

4. The device of claim 1, wherein the device is a mode converter, the optical waveguide being adapted for guiding at least one TE mode and at least one TM mode of the optical signal, associated with the device being an electrooptically induced TE/TM coupling coefficient, and wherein the second waveguiding means are disposed such that the electrooptic interaction can change the TE/TM
coupling coefficient.

5. The device of claim 1, wherein the second waveguiding means are disposed such that, at the optical waveguide, the operative electric field due to a given "on" section has a polarity that is opposite to the polarity of the operative electric field due to the "on" section adjacent to the given "on" section.

6. The device according to claim 1 wherein said device is characterized by a coherence length, do, given by and wherein Lon<do.

7. The device of claim 6, wherein the first waveguiding means comprise coupled first and second optical waveguides, the second waveguiding means comprise a plurality of electrodes including a center electrode and a first and a second outer electrode;
wherein the electrodes are disposed such that in a first "on" section the center electrode and the first outer electrode are in electrooptically inter-acting relationship with the first and the second optical waveguides, respectively, and the second outer electrode is in electrooptically noninteracting relationship with the optical waveguides;
wherein the electrodes further are disposed such that in a second "on" section, adjacent to the first "on" section, the center electrode and the second outer electrode are in electrooptically interacting relationship with the second and first optical waveguides, respectively, and the first outer electrode is in electrooptically non-interacting relationship with the optical waveguides; and wherein the first and second "on" sections are separated by an "off" section in which the electrodes are disposed such that none of the three electrodes are in electrooptically interacting relationship with one of the two optical waveguides.

8. The device of claim 1, wherein the first wave-guiding means comprise a single optical waveguide, and the second waveguiding means comprise a pair of electrodes, with a gap therebetween, and wherein the electrodes are disposed such that in at least a part of each "on" section the gap between the electrodes is closer to the optical waveguide than the gap is in at least a part of each "off"
section.

9. The device of claim 8, wherein the optical waveguide is adapted for guiding at least one TE mode and at least one TM mode of the optical signal, and wherein the electrodes in at least some of the "on" sections comprise finger electrodes whose nominal finger-to-finger spacing is equal to A, where A = .lambda.o (NTE-NTM)-1 wherein .lambda.o is the free-space wavelength of the optical signal; and NTE and NTM are the effective refractive indices of the optical waveguide for the TE and TM modes, respectively.

10 . The device of claim 9, wherein the distance Ls along the optical waveguide of the "off" section is substantially equal to nA?, where n is a positive integer, and Ls Lcn.

11. The device of claim 9, wherein the distance Ls along the optical waveguide of the "off" section is substantially equal to (n+1/2)A? where n is a positive integer, and Ls << Lcn.

12. The device of claim 1, wherein the second wave-guiding means comprise a first portion comprising a first plurality of "on" sections and, in series with the first portion, a second portion having a second plurality of "on" sections, and wherein in the first portion the second waveguiding means are disposed such that, at the optical waveguide, the operative electric field due to a given "on" section has a polarity that is opposite to the polarity of the operative electric field due to the "on" section adjacent to the given "on" section.

13. The device of claim 1, wherein the first wave-guiding means comprise a pair of optical waveguides, and wherein the second waveguiding means are disposed such that at least a part of the second wavequiding means is in electrooptically interacting relation with both members of the pair of optical waveguides.

14. The device according to claim 5 wherein Lon + Loff (1-No/Nm) = do.

15. The device according to claim 1 wherein:
said device includes N pairs of "on-off"
intervals;
and wherein Lon + Loff /(1-No/Nm) = 2do.

16. The device according to claim 8 wherein:
said electrodes, along successive "on" inter-vals, are transversely displaced relative to said optical waveguide to produce a polarity reversal in the direction of the electric field operative along said optical waveguide.

17. The device according to claim 13 wherein:
said waveguiding means is a pair of electrodes forming a planar strip transmission line;
and wherein the "on" interval along one of said optical waveguides is the "off" interval for the other of said optical waveguides, and said "off" interval along said one optical waveguide is the "on" interval for said other optical waveguide.

18. The device according to claim 17 wherein:
the input ends of said optical waveguides are coupled to a first common port;
and wherein the output ends of said optical waveguides are coupled to a second common port.