Coded sequence travelling-wave optical modulator

A travelling wave modulator in which the phase velocity of a first wave is modulated by a second travelling wave. Means are provided to alter the polarity of the second wave in accordance with a pseudorandom code. Barker codes and Golay codes are particularly suitable for improving the bandwidth-to-voltage ratio of the modulator over a comparable conventional modulator.

BACKGROUND OF THE INVENTION 
This invention relates in general to travelling-wave optical modulators and 
more particularly to travelling-wave modulators having an electrode 
structure that increases the bandwidth-to-drive-voltage ratio over 
conventional travelling-wave optical modulators. The structure of 
conventional optical modulators is discussed in chapter 14 of the text by 
Amnon Yariv entitled Quantum Electronics, 2nd Edition, John Wiley & Sons, 
Inc., 1975. In such modulators, optically transparent materials are used 
that, for a given direction of transmission of light in the material, 
exhibit an ordinary index of refraction n.sub.o for a first polarization 
of the light and exhibit an extraordinary index of refraction n.sub.e for 
a second polarization that is perpendicular to the first one. At least one 
of these indices of refraction is changeable in response to an applied 
voltage. The index of refraction can be changed by the applied voltage, 
for example, via the electrooptic effect or the photoelastic effect. 
Each of these polarizations functions as a separate channel for 
transmission of light. Because the phase velocity of each of these 
channels is equal to the speed of light c divided by the index of 
refraction for that channel, the phase velocities for these two channels 
will generally be unequal. Since the phase of light at the output of the 
modulator is equal to the input phase plus 2*pi*f*L/v (where f is the is 
the frequency of the light, L is the length of the light path in the 
modulator and v is the phase velocity of the light), these modulators can 
be used to modulate the output phase of light in at least one of these 
channels. For sufficiently small applied voltages, the variation of phase 
velocity as a function of applied field is substantially linear so that 
the phase modulation is proportional to the applied voltage. 
Phase modulation can be converted to amplitude modulation by interference 
of the light in one of these channels with another beam of light, such as 
the beam of light in the other channel. In such an amplitude modulator, 
the light in these two channels can be combined by a polarizer placed at 
the output of the modulator and orientated in a direction midway between 
the directions of polarization of the two channels. Alternatively, an 
interferometer, such as a Mach-Zehnder interferometer can be used to 
combine two beams of the same polarization to produce amplitude modulation 
(see, for example, Rod. C. Alferness, "Waveguide electro-optic 
modulators", IEEE transactions on microwave theory and techniques, Vol. 
MTT-30, pp. 1121-1137, 1982). In such a device, the two channels of 
propagation are physically distinct waveguides. 
In the linear electrooptic modulators, for each of the channels, the 
relation of phase velocity to applied voltage depends on the direction of 
the associated electric field produced in the modulator. The phase shift 
is proportional to the magnitude of the electric field and to the length L 
of the light path through the modulator. When the applied electric field 
is parallel to the direction of transmission, the amount of phase shift is 
independent of the length for a given applied voltage. An applied field 
perpendicular to the direction of transmission is advantageous because the 
electrodes do not then interfere with the propagation of the optical beam 
and because the amount of modulation, for a given applied voltage, can be 
increased by increasing the length of the crystal. 
For modulation frequencies high enough that the transit time of the optical 
beam through the crystal is on the order of or greater than the period of 
the modulator frequency, the amount of modulation is proportional to the 
time integral of the applied signal over the transit time of the beam. 
Over such transit time, negative values of the applied voltage will offset 
the effects of positive values. In order to avoid such cancellation, the 
voltage is applied as a travelling wave that travels in the same direction 
as the optical beam. If the velocity of the travelling wave applied 
voltage equals the velocity of the optical beam in the modulator, then a 
given segment of the optical beam is subjected to a constant applied 
electric field as it travels through the modulator. 
Unfortunately, the group velocity of the applied voltage signal is 
generally not equal to the group velocity of the light in the modulator. 
This results because the group velocity (in the absence of dispersion) is 
equal to the speed of light c divided by the index of refraction of the 
medium and because the index of refraction for the frequencies of the 
applied voltage is different from the index of refraction for the 
frequencies of the optical signal. For example, in LiNbO.sub.3 the index 
of refraction for an rf applied voltage is on the order of 4 whereas the 
index of refraction for optical frequencies is on the order of 2. As a 
result of this, a given segment of the optical beam does not experience a 
constant applied electric field. The effect of this can be easily seen for 
an optical signal 
EQU V.sub.o =A.sub.o *e.sup.i(w.sbsp.o.sup.t-k.sbsp.o.sup.z) ( 1) 
having its phase modulated by an applied voltage 
EQU V.sub.a =A.sub.a *e.sup.i(w.sbsp.a.sup.t-k.sbsp.a.sup.z) ( 2) 
The z axis has been chosen to lie along the direction of propagation of 
these two travelling waves and the point z=0 has been chosen to be at the 
input end of the modulator. The phase velocities of the optical beam and 
the applied voltage signal are v.sub.o =w.sub.o /k.sub.o and v.sub.a 
=w.sub.a /k.sub.a, respectively. The portion of the optical beam that 
enters the modulator at time t is located at 
EQU z=z.sub.o (t')=v.sub.o *(t'-t) (3) 
at time t'. This portion of the optical field experiences at the point 
(t',z(t')) a retardation proportional to the applied field at the 
point--namely 
EQU V.sub.a (t',z.sub.o (t'))=A.sub.a 
*e.sup.i[w.sbsp.a.sup.t'-k.sbsp.a.sup.*v.sbsp.o.sup.*(t'-t)]( 4) 
The total phase shift on this portion of the wave is equal to the time 
integral over t'-t from t'-t=0 to t.sub.o where t.sub.o is the transit 
time for the optical beam to cross the modulator and is equal to L*k.sub.o 
/w.sub.o. The effect of this is that the retardation is reduced by the 
factor 
EQU [e.sup.i(w.sbsp.r.sup.t.sbsp.o.sup.) -1]/iw.sub.r t.sub.o 
=e.sup.i(w.sbsp.r.sup.t.sbsp.o.sup./2) *sinc(w.sub.r t.sub.o /2)(5a) 
EQU where 
w.sub.r =w.sub.a -v.sub.o *k.sub.a =w.sub.a *(1-v.sub.o /v.sub.a)(5b) 
compared to the retardation that would result if the velocities v.sub.o and 
v.sub.a were equal. This walkoff of the phase of the applied voltage 
signal relative to the phase of the optical signal thus produces a 
reduction factor that is dependent on the frequencies of both signals. 
The sinc function first goes to zero when its argument w.sub.r */t.sub.o /2 
equals .+-.pi. Using equation (5a), the first null occurs when w.sub.a 
=2pi/(t.sub.a -t.sub.o)=2pi/(L/v.sub.a -L/v.sub.o), where t.sub.a is the 
transit time for the microwave to cross the modulator. This shows that the 
bandwidth varies inversely with L. This means that the bandwidth can be 
increased by decreasing the length of the modulator. Unfortunately, 
reducing the length of the modulator equivalently reduces the time during 
which the applied voltage affects the optical signal so that the magnitude 
of the modulation varies inversely with the length L of the region of 
modulation. Therefore, in the variation of the length L, there is a 
tradeoff between the bandwidth and the magnitude of the applied voltage 
required to produce a given amount of phase change. A measure of the 
applied voltage needed in the modulator is the voltage V.sub.pi which is 
defined to be the value of the dc voltage needed to produce a phase change 
of pi in the output optical signal. The ratio of bandwidth (BW) and 
V.sub.pi is a figure of merit that is independent of the length of the 
modulation region. This bandwidth-voltage-ratio (BVR) is thus a useful 
figure of merit of the modulators. 
In one technique of increasing the upper limit of the useful band of 
applied frequencies (see Rod. C. Alferness, et al, "Velocity-matching 
techniques for integrated optic travelling wave switch/modulators", IEEE 
J. Quant. Electron, vol. QE-20, pp. 301-309, 1984), the electrodes have a 
shape that periodically reverses the applied electric field in the 
modulator as a function of z. Such periodic field reversals are used to 
offset the negative portions of the relative phase between the applied 
signal and the optical signal. Unfortunately, this cancellation is 
complete only at one value of w.sub.r, and, in addition, these periodic 
filed reversals degrade the low frequency performance. In effect, these 
periodic field reversals serve to shift the effective band upward in 
frequency without broadening the width of the band. 
In another modulator (see A. Djupsjobacka, "Novel type of broadband 
travelling-wave integrated-optic modulator", Electronics Letters, pp. 
908-909, 1985) there is only a single phase reversal produced by laterally 
offsetting the electrodes three-fourths of the distance along the 
modulator. It is asserted incorrectly that this design acts like a low 
pass filter and a high pass filter in series, whereas in fact it functions 
as a low pass filter and a high pass filter in parallel. Unfortunately, 
the increase in bandwidth with this structure is offset by a voltage 
reduction factor of 2. Thus, this device exhibits a reduced 
bandwidth-voltage-ratio (BVR) relative to a conventional Mach-Zehnder 
modulator having no polarity reversals. It would be useful to have a 
design that increases the bandwidth-voltage-ratio (BVR) and also retains a 
low value of V.sub.pi down to dc applied voltages. 
SUMMARY OF THE INVENTION 
In accordance with the disclosed preferred embodiment, a modulator is 
presented that includes an electrode structure that increases the 
effective bandwidth of applied voltages and retains a low value of 
v.sub.pi down to dc applied voltage. This invention is illustrated in the 
case of electrooptic modulation of an optical frequency, but the field 
reversal pattern produced by the electrodes has applicability to the 
modulation of any first type travelling wave signal by application of a 
second type travelling wave signal. 
In the disclosed electrooptic modulators, the structure of the electrodes 
used to apply a voltage signal to the modulator introduces field reversals 
into the applied electric field in a pattern defined by a spread spectrum 
pseudorandom code. Barker Codes of length 4, 5 and 13 have been 
particularly effective in extending the bandwidth while retaining 
effective modulation down to dc applied voltages. In another embodiment, a 
Golay pair is used to define the pattern of field reversals in a pair of 
optical modulators. The light from both modulators is then detected and 
combined to produce modulation over an increased bandwidth. 
Two particular embodiments utilize an x-cut LiNbO.sub.3 and a z-cut 
LiNbO.sub.3 crystal, respectively. In the first embodiment, the electrodes 
are positioned relative to the optical waveguide so that the electric 
field produced in the optical waveguide is substantially parallel to the 
surface of the modulator. In the second embodiment, the electrodes are 
positioned relative to the optical waveguide so that the electric field 
produced in the optical waveguide is substantially perpendicular to the 
surface of the modulator.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
In FIGS. 1-3 are shown a top view and two cross-sectional views of a 
mach-Zehnder type travelling wave electrooptic amplitude modulator 
utilizing electrodes that are configured to produce a pattern of electric 
field reversals in the optical paths of the modulator in accordance with a 
spread spectrum pseudorandom code. This electrode structure results in a 
large increase in bandwidth while preserving operation down to dc applied 
voltages. The substrate 10 of the modulator is a material that transmits 
optical waves without significant loss and that exhibits at least one 
index of refraction that is variable in response to an applied electric 
field. A particularly suitable choice for the substrate in LiNbO.sub.3 
because it exhibits a particularly strong electrooptic response. The 
length L of the electrodes is on the order of 11 centimeters. 
An optical waveguide 11 is formed in the substrate, for example, by doping 
the substrate with titanium within the waveguide region of the substrate. 
Titanium is used as the dopant because it fits easily into the crystal 
lattice, it diffuses well into the crystal and it increases the indices of 
refraction so that the doped region functions as an optical waveguide. In 
the embodiment shown in FIG. 1, waveguide 11 divides into two branches 12 
and 13 which recombine into an output path 14. These waveguide segments 
have cross-sectional dimensions on the order of 5 microns. This structure 
is known as a Mach-Zehnder modulator and is used to convert the phase 
modulation produced in branches 12 and 13 into amplitude modulation in 
output path 14. Typically, branches 12 and 13 will each exhibit two 
indices of refraction along two principal axis directions perpendicular to 
the direction of propagation of light in those paths. The light input into 
waveguide 11 is polarized so that the light in each of branches 12 and 13 
is along one of these principal axes. Since each polarization direction 
functions like a separate channel, if the polarization were not along one 
of these principal axes, the light beam would travel in both channels at 
different speeds, thereby producing additional, unwanted phase variations. 
A set of electrodes 15-17, overlays portions of branches 12 and 13 in a 
region in which these two branches are parallel. An applied voltage 
V.sub.a is applied to these electrodes in such a way that electrode 16 is 
at the voltage V.sub.a above the voltage of electrodes 15 and 17. These 
polarities and the locations of the electrodes produce electric fields 
between the electrodes that are in opposite directions in branches 12 and 
13. Thus, when the phase is being retarded in one branch, it is being 
advanced in the other branch. This push-pull modulation relationship 
between the two branches produces in output path 14 an amplitude 
modulation proportional to twice the phase modulation produced in each of 
branches 12 and 13. 
FIG. 4 is an enlarged view of a portion of FIG. 2, illustrating the 
electric fields produced in substrate 10 and waveguide 13 by the applied 
voltage when electrode 16 is more electropositive than electrode 17. It 
should be noticed that waveguide 13 is located under the end of one of the 
electrodes so that the electric field within waveguide 13 is substantially 
perpendicular to the top surface of substrate 10. In this embodiment, a 
z-cut LiNbO.sub.3 crystal is used because in such a crystal the index of 
refraction of the crystal is more strongly affected by electric fields 
perpendicular to the top surface 19 of the substrate than to electric 
fields in other directions. One advantage of this embodiment is that the 
gap between the electrodes can be quite small (on the order of a few 
microns) so that a strong electric field is produced by a modest applied 
voltage on the order of 10 volts. Another advantage is that the electric 
field in branch 13 can be reversed in polarity by translating electrodes 
16 and 17 laterally relative to waveguide 13 so that waveguide 13 is 
located under the edge of electrode 16. Thus, the electrode shapes in FIG. 
1 result in waveguide 13 being located under the edge of electrode 17 in 
the cross-section shown in FIG. 2 and results in waveguide 13 being 
located under the edge of electrode 16 in the cross-section shown in FIG 
3. 
In an alternative embodiment illustrated in FIG. 5, the substrate is an 
x-cut LiNbO.sub.3 crystal. In such a cut, the indices of refraction are 
most strongly affected by electric fields parallel to the top surface 19 
of the substrate. Therefore, in this embodiment, the electrodes are more 
widely spaced and the waveguides are located substantially midway in the 
gaps between the electrodes so that the electric fields within the optical 
waveguides are substantially parallel to top surface 19. Although the gaps 
in such embodiments will typically be larger than in the embodiment of 
FIGS. 1-4, these gaps will still be on the order of several microns so 
that strong electric fields are produced for a modest applied voltage on 
the order of several volts. A disadvantage of this cut is that the 
polarity of the electric field in the waveguide branches cannot be 
straightwardly reversed by a lateral offset of all electrodes as in FIG. 
1. As can be seen from FIG. 5, a lateral translation of electrodes 16 and 
17 will not produce a polarity reversal. Instead, the positions of 
electrodes 16 and 17 must be interchanged in order to reverse the polarity 
of the electric field in waveguide branch 13. Such a waveguide structure 
is shown in FIG. 6. This embodiment has four electrodes 63-66 instead of 
three as in FIG. 1. As in FIG. 1, in this device an optical waveguide 
splits into a branch 61 and a branch 62 in each of which the optical wave 
is phase modulated. Electrodes 63-66 are configured to produce the 
opposite polarity of phase modulation in branch 61 as in branch 62 so that 
there is the same type of push-pull phase modulation as in FIG. 1. In the 
region between input end 67 and dashed line 68 and in the region dashed 
line 611 and output end 612, the electric field in branch 61 is produced 
by the voltage difference between electrodes 64 and 65 and the electric 
field in branch 62 is produced by the voltage difference between 
electrodes 65 and 66. In the region between dashed line 69 and dashed line 
610, the electric filed in branch 61 is produced by the voltage difference 
between electrodes 63 and 64 and the electric field in branch 62 is 
produced by the voltage difference between electrodes 64 and 65. 
In the embodiment of FIGS. 1-3, V.sub.a is applied to an input end 18 of 
electrodes 15-17 and produces travelling waves that travel along the 
electrodes parallel to branches 12 and 13. The other end of each electrode 
is terminated in a matched impedance to avoid reflections from that end. 
As discussed in the Background of the Invention, the group velocities of 
these applied voltage travelling waves are typically unequal to the group 
velocity of the optical beams in the optical waveguides. As indicated in 
the Background of the Invention, the optical group velocity is on the 
order of half the speed of light and the group velocity of the applied 
voltage is on the order of one fourth the speed of light. Therefore, the 
shapes of the electrodes are selected to produce a set of polarity 
inversions that compensate for the walkoff between the phase of the 
electrical and optical signals in a way that increases the bandwidth and 
retains functional operation down to dc applied signals. 
In order to achieve this increased bandwidth, the electrodes are divided 
into a set of N equal segments along their length and the polarity between 
the electrodes in these segments is selected in accordance with a spread 
spectrum pseudorandom code. This electrode structure is applicable not 
only to the Mach-Zehnder modulator, but is also applicable generally to 
phase modulators as well as to other types of amplitude modulators. In 
general, the amplitude modulators produce phase modulation in one beam and 
then interfere it with another beam, that may or may not be phase 
modulated, to produce amplitude modulation. The enhanced operation due to 
this electrode structure can be seen to result as follows. 
The general concept is illustrated under the assumptions that dispersion 
effects, losses in the optical signal, losses in the applied voltage, and 
reflections in the electrodes at the output end of the modulator can be 
neglected. Models taking these factors into account indicate that these 
neglected effects will not in general qualitatively change these results. 
In the end of waveguide 11 an optical signal V.sub.o of angular frequency 
w.sub.o is injected having, at that point, a time dependence 
EQU V.sub.o (t)=A.sub.o (t)e.sup.iw.sbsp.o.sup.t (6) 
where A.sub.o (t) is the amplitude. This produces a travelling wave in 
waveguide 11 of phase velocity V.sub.o =w.sub.o /k.sub.o where k.sub.o is 
the wavenumber of this travelling wave. Half of this optical signal 
travels into branch 12 and the other half enters branch 13. The distance 
along each branch from the input end of waveguide 11 is indicated by the 
parameter z. Thus, in each of branches 12 and 13 the optical signal has 
the form 
EQU V.sub.o (t,z)=V.sub.o (t-z/v.sub.o)=A.sub.o 
(t-z/v.sub.o)*e.sup.i[w.sbsp.o.sup.(t-z/v.sbsp.o.sup.)] (7) 
At end 18 of electrodes 15-17 an applied voltage V.sub.a (t) is applied. 
This produces a travelling wave voltage signal having a group velocity 
v.sub.a. In the electrodes, the distance from end 18 will be represented 
by the parameter z. Thus, in the electrodes the applied voltage has the 
form V.sub.a (t-z/v.sub.a). 
Branch 12 consists of a section 112 located between ends 18 and 110 of the 
electrodes, section 111 between waveguide 11 and section 112, and section 
113 between section 112 and waveguide 14. Likewise, branch 13 consists of 
sections 114-116 that are analogous to sections 111-113 of branch 12. The 
total length of branch 12, extending from the input end of waveguide 11 to 
the output end of waveguide 14 is denoted as L.sub.12. Likewise, the total 
length of branch 13 is denoted as L.sub.13. The lengths of sections 
111-116 are denoted by L.sub.111 -L.sub.116, respectively. As can be seen 
from FIG. 1, the lengths L.sub.112 and L.sub.115 are both equal to the 
length L of the electrodes. The transit time for the unmodulated optical 
signal to traverse the lengths L.sub.12, L.sub.13, and L.sub.111 
-L.sub.116 are denoted by t.sub.12, t.sub.13, and t.sub.111 -t.sub.116, 
respectively. Because of these finite transit times, the optical signal at 
the output of waveguide 14 via branch 12 is 
EQU (1/2)*V.sub.o (t-L.sub.12 /v.sub.o)=V(t-t.sub.12) (8) 
Similarly, the optical signal at the output of waveguide 14 via branch 13 
is 
EQU (1/2)*V.sub.o (t-L.sub.13 /v.sub.o)=V(t-t.sub.13) (9) 
Therefore, the output signal O.sub.o (t) is 
EQU O.sub.o (t)=[V.sub.o (t-t.sub.12)+V.sub.o (t-t.sub.13)]/2=[A.sub.o 
(t-t.sub.12)e.sup.iw.sbsp.o.sup.*(t-t.sbsp.12.sup.) +A.sub.o 
(t-t.sub.13)e.sup.iw.sbsp.o.sup.*(t-t.sbsp.13.sup.) [/2 (10) 
The time differential 
EQU t.sub.d =t.sub.12 -t.sub.13 (11) 
is typically selected to be on the order of 1/w.sub.o which is on the order 
of 10.sup.-15 s whereas t.sub.12 =L.sub.12 /v.sub.o is on the order of 
(10.sup.-2)m/(10.sup.8 m/s)=10.sup.-10 /s. Since A.sub.o (t) typically 
varies at 20 GHz or less, we have that A.sub.o (t-t.sub.12) is 
substantially equal to A.sub.o (t-t.sub.13). Thus, 
EQU O.sub.o (t)=A.sub.o 
(t-t.sub.12)*e.sup.iw.sbsp.o.sup.*(t-t.sbsp.d.sup./2)*cos(w.sub.o 
*t.sub.d)(12) 
Therefore, the power O.sub.o (t)*O.sub.o.sup.* (t) produced by an optical 
detector that is responsive to O.sub.o (t) will be [A.sub.o 
(t-t.sub.12)].sup.2 *cos.sup.2 (w.sub.o *t.sub.d). This has the form shown 
in FIG. 7. 
In response to the applied signal, t.sub.12 and t.sub.13 will be varied by 
amounts that are on the order of 1/w.sub.o. This will produce variations 
in the output power from the optical detector. In order to make these 
variations in power substantially linear in the applied voltage signal, 
t.sub.d is chosen to bias the output power signal at a linear point of the 
power curve. Thus, t.sub.d is chosen to be an odd multiple of 1/2w.sub.o. 
This time difference can be produced by a pathlength difference between 
L.sub.12 and L.sub.13 sufficient to produce this value of t.sub.d. This 
will be referred to as a geometric bias. Likewise, this value of t.sub.d 
can be produced by a constant bias potential difference between electrodes 
15-17. This will be referred to as a voltage bias. 
The effect of the applied voltage travelling wave V.sub.a (t-z/v.sub.a) can 
be understood by its effect on the light in branch 12. In the region of 
the modulator between ends 108 and 110 of the electrodes, the applied 
voltage produces an electric field that increases the transit time of a 
given point of the optical travelling wave by an amount T.sub.12 
(t-L.sub.12 /v.sub.o) proportional to the time integral of the electric 
field experienced by that point of the optical travelling wave. Thus, at 
the modulator output at time t (i.e., at spacetime point (t,L.sub.12)), 
the optical signal in branch 12 has the form 
EQU A.sub.o (t-L.sub.12 
/v.sub.o)*e.sup.iw.sbsp.o.sup.*[t-L.sbsp.12.sup./v.sbsp.o.sup.+T.sbsp.12.s 
up.(t-L.sbsp.12.sup./v.sbsp.o.sup.)] (13) 
where T.sub.12 (t-L.sub.12 /v.sub.o) is proportional to the integral over 
time of the electric field experienced by the portion of the optical 
signal that reaches z=L.sub.12 at time t. The portion of the optical wave 
arriving at the output point z=L.sub.12 at time t travels in branch 12 
along the spacetime path 
EQU z=z.sub.o (t')=L.sub.12 +v.sub.o *(t'-t) (14) 
This portion of the optical wave experiences at time t' the electric field 
at the spacetime point (t', z.sub.o (t'))--namely, an electrical field 
proportional to 
EQU g(z)*V.sub.a (t-z/v.sub.a) (15) 
where g(z) is the field polarity reversal pattern produced by the electrode 
structure. The function g(z) is zero outside of the interval 
(L.sub.18,L.sub.18 +L) and within this interval has values +1 or -1 in 
accordance with a spread spectrum pseudorandom code. Since the optical 
wave travels at substantially constant velocity v.sub.o, this time 
integral can also be written, using equation (7), as an integral over 
z.sub.o : 
##EQU1## 
where t.sub.12 =L.sub.12 /v.sub.o, where S is a response strength factor 
that takes into account the distance between the electrodes, the geometric 
arrangement of the electric fields produced by the electrodes through 
waveguides 12, and the electrooptic responsivity of the modulator 
waveguides, where s=z.sub.o *(1/v.sub.a -1/v.sub.o)+t.sub.12 and where 
h(s)=Sg(z.sub.o). This can be reexpressed as the convolution 
EQU T.sub.12 (t-t.sub.12)=(h V.sub.a)(t-t.sub.12) (17 ) 
Aside from a scale factor, h(s) has the same functional shape as the 
electric field reversals produced by the electrode shape. In addition, 
h(s) is also the impulse response of this modulator. This can be seen by 
letting the applied voltage be a delta function voltage pulse, then 
equation (10) implies that T.sub.12 (t)=h(t-t.sub.12). Thus, w.sub.o 
*h(t-t.sub.12) is indeed the phase modulation response of the modulator to 
a delta function voltage pulse. 
The frequency response of this modulator is obtained by Fourier 
transforming equation 11. Since the Fourier transform of a convolution of 
two functions is the product of the Fourier transform of each of these 
functions, the frequency response of the modulator for the light in branch 
12 is 
EQU T.sub.12 (w)=h(w)*V.sub.a (w) (18) 
where the tilde denotes the Fourier transform function of the corresponding 
time domain function. 
For a sinusoidal applied voltage of frequency w (i.e., for V.sub.a 
(w)=.delta.(w-w.sub.o)), T.sub.12 (w)=h(w). Therefore, in order to 
increase the bandwidth of the system while retaining operation down to dc 
values (i.e., w=0), we need to keep h(w) reasonably flat over an increased 
range that extends down to w=0. As discussed above h(s)=Sg(z.sub.o), 
s=z.sub.o *(1/v.sub.a -1/v.sub.o)+t.sub.12, and g(z.sub.o) is a step 
function that is zero outside of the interval (L.sub.18,L.sub.18 +L) and 
within that interval is equal to +1 or -1 as determined by a spread 
spectrum pseudorandom code. 
In accordance with the present invention, it is expected that electrodes 
that produce parity reversals in accordance with a spread spectrum 
pseudorandom code will produce an increased bandwidth because such codes 
exhibit a broad spectrum, which is why they are referred to as spread 
spectrum codes. Such codes are widely used in radar and communications. 
Unfortunately, in many of such applications, the codes are intentionally 
selected to discriminate against dc signals. Such codes would thus be 
unsuitable in modulators for which dc operation is required. However, such 
codes can be used to expand the bandwidth in modulators that do not need 
to operate down to dc. 
In the following, such a code having N elements will be denoted by 
{g.sub.o, . . . , g.sub.N- 1} where each g.sub.k is equal to -1 or -1. The 
function g(z) can be expressed in terms of the g.sub.k and the function 
##EQU2## 
The function g.sub.chip (z) is thus a step function of unit height and of 
length equal to the length of a section of electrode whose polarity is 
determined by one element in the code. Thus, g(z) has the form 
##EQU3## 
where L.sub.18 is the distance from the input of waveguides 11 to the 
point in branch 12 located at end 18 of the electrodes. This can be 
rewritten as the convolution 
EQU g(z)=(a g.sub.chip) (21) 
where 
##EQU4## 
is referred to herein as the array factor. Because equation (21) is a 
convolution, its Fourier transform is 
EQU g(w)=a(w)*g.sub.chip (w) (23) 
The function g.sub.chip (w) is easily evaluated and is equal to 
(1/N)sinc(w/N). This has the same functional shape as h(w) for electrodes 
having no polarity reversals, but is N times wider. Thus, if the term a(w) 
in equation (23) can be made reasonably constant over the bandwidth of the 
term g.sub.chip (w), then the bandwidth of this modulator will be N times 
wider than the bandwidth of a Mach-Zehnder modulator having no polarity 
reversals along the electrodes. 
Because the detector is responsive to the modulation of the incident 
intensity of the optical signal, it follows that the electrically detected 
power at frequency w is proportional to the absolute square of a(w). Thus, 
we need a code that makes the absolute square of a(w) substantially 
constant over the bandwidth of g.sub.chip (w). Since the Fourier transform 
of a delta function is constant and since the absolute square of a(w) is 
equal to the Fourier transform of the autocorrelation of a(t), the 
pseudorandom code that is used should have a large central peak with very 
small sidelobes. Barker codes are known to have such characteristics. In 
particular, Barker codes have sidelobes that are -1, 0, or +1 (see, for 
example, R. H. Barker, "Group synchronization of binary digital systems" 
in W. Jackson, Ed., Communication Theory, Academic Press, New York, 1953). 
Thus, the bandwidth can be increased by a factor on the order of N by use 
of a Barker code of length N. 
Unfortunately, some choices of the particular Barker code to be used 
significantly degrade modulator performance for a dc applied voltage 
signal. Thus, for those modulators that should operate down to dc, such 
codes should not be used. The amplitude of modulation with a dc applied 
voltage is proportional to a(0) which is proportional to the sum of the 
g.sub.k. Thus, those codes that have a substantially equal number of +1 
and -1 terms have poor dc performance. On the other hand, if substantially 
all of the terms are either just +1 or just -1, then the characteristics 
will be similar to a modulator with no polarity reversals. This suggests 
that approximately 1/4 of the terms have one sign and 3/4 should have the 
opposite sign. Those Barker codes that satisfy these criteria are the 
codes of length 4, 5 and 13. These codes are presented in FIG. 8. 
In order to select among the possible codes, a criterion is needed to 
define performance. Since it is desired to have improved bandwidth and 
have good modulation down to dc applied voltages, the figure of merit that 
is used is the product of the dc gain (which is equal to h(0)) times the 5 
dB bandwidth. This figure of merit is proportional to the 
bandwidth-to-voltage ratio discussed previously. 
The first of the four Barker codes presented in FIG. 8 produces at best a 
modest improvement in the figure of merit compared to the figure of merit 
for a conventional Mach-Zehnder modulator. In the reference by 
Djupsjobacka discussed in the Background of the Invention, a modulator 
that is the same as one designed according to the present invention 
utilizing the first Barker code in FIGS. 8A-8D. This reference indicates a 
30% increase in the figure of merit compared to a conventional modulator, 
but our calculations indicate that it is more like a slight decrease in 
the figure of merit by a factor of 0.95 when the right microwave and 
optical indices are used in the calculations. 
Computer simulations and experimental data have been used to compare the 
responses of devices having electrodes configured according to the Barker 
Codes of FIGS. 8A-8D against a conventional device of the same dimensions. 
These devices shared the following common characteristics: (1) active 
length L is 1 cm; (2) center conductor width W is 30 microns; (3) 
characteristic impedance Z.sub.o is 22 Ohms; (4) the optical wavelength is 
1.3 microns; (5) the optical index is 2.148; (6) the index for the applied 
voltage is 4.225. The bandwidths for the conventional device and for the 
devices using the codes of FIGS. 8A-8D are 10.6 GHz, 18.3 GHz, 41.5 GHz, 
43.1 GHz and 111.03 GHz, respectively. 
Since V.sub.pi is the dc voltage needed to produce a phase change of pi in 
the optical signal and since for dc applied voltage, the electric fields 
experienced by the optical wave have the same form as the Barker Code for 
that device, the average electric field experienced by the optical signal 
in such a device is proportional to (n.sub.+ -n.sub.-)/(n.sub.30 
+n.sub.-), where n.sub.+ is the number of pluses in the code and n.sub.- 
is the number of minuses in the code. Therefore, the value of V.sub.pi in 
these devices is increased by the amount (n.sub.+ +n.sub.-)/(n.sub.+ 
-n.sub.-) compared to the conventional device. For the first through 
fourth devices in FIGS. 8A-8D, these values are 2, 2, 5/3, and 13.9, 
respectively. The bandwidth-to-voltage ratio (using a 5 dB criterion for 
bandwidth) for the first through fourth devices relative to the 
conventional device are thus 0.86, 1.95, 2.03 and 4.02, respectively. 
Thus, any of the three codes in FIGS. 8B-8D produces an increase of at 
least 1.5 times the figure of merit of a conventional Mach-Zehnder 
modulator. The Barker code of length 13 exhibits the largest improvement. 
In FIG. 10 is illustrated the electrode pattern implementing that code. It 
should be noticed that phase reversals in accordance with a code that is 
the same as one of these codes, but reversed in order, will have a 
comparable bandwidth-to-voltage ratio. However, when modulator losses are 
not negligible, it has been found that a somewhat improved 
bandwidth-to-voltage ratio is achieved for the choice of order that 
locates a greater number of phase reversals near the input end of the 
modulator than near the output end. One exception to this is the code of 
length four shown in FIG. 8B. However, in the following, when we refer to 
the Barker code of length N, we will be referring generically to both 
choices of code ordering. 
There are also generalized Barker codes of length M*N that are generated as 
the outer product of a Barker code of length M and a Barker code of length 
N. This outer product is illustrated in FIG. 11 for the case of the outer 
product of the Barker code {+,-,+,+,+} with the Barker code {+,+,-,+}. 
Each element in the first Barker code (shown in line (a)) is multiplied by 
a copy of the second Barker code (a copy of this code is shown in line (b) 
for each element in line (a)) and these multiplied copies are ordered as 
shown to produce the 20 element generalized code of line (c). Although 
these generalized Barker codes do not satisfy the requirement of Barker 
codes (that the sidelobes in their autocorrelation function have only 
values of -1, 0, or +1), they still have sidelobes that are much smaller 
than the main lobe. Such generalized Barker codes are also suitable for 
defining the pattern of polarity reversals in the modulator. 
Other pseudorandom codes can also be used to improve this figure of merit. 
In FIG. 9 is presented an amplitude modulator that utilizes a pair of 
Mach-Zender modulators 91 and 92 having their electrodes configured in 
accordance with a Golay pair {G.sub.1,G.sub.2 } of pseudorandom codes. 
Modulator 91 has electrodes on its top branch 93 configured to produce 
polarity inversions in accordance with code G.sub.1 and has its bottom 
branch 94 configured to produce polarity inversions in accordance with the 
negative of code G.sub.1. This produces the push-pull phase behavior 
exhibited in the device in FIG. 1. Modulator 92 has electrodes on its top 
branch 95 configured to produce polarity inversions in accordance with 
code G.sub.2 and has its bottom branch 94 configured to produce polarity 
inversions in accordance with the negative of code G.sub.2. 
The output optical signals from modulators 91 and 92 are each sequentially 
passed though an optical network 97 under test. The output optical signals 
from modulators 91 and 92 are detected by an optical detector 98. The 
output signal from detector 98 for each of modulator 91 and 92 is detected 
in a spectrum analyzer 910 to produce the Fourier transform of each 
signal. If the optical network has a transfer function H(w), then the 
Fourier transform of the signal from modulator 91 is 
EQU H(w)*a.sub.91 (w)*g.sub.chip (w)*V.sub.a (w) (24) 
and the Fourier transform of the signal for modulator 92 is 
EQU H(w)*a.sub.92 (w)*g.sub.chip (w)*V.sub.a (w) (25) 
where a.sub.91 (w) is the array factor for modulator 91 and a.sub.92 (w) is 
the array factor for modulator 92. Each of these Fourier transforms is 
supplied to a calculator 911 which adds the absolute square of these two 
signals to produce an output signal o(w) equal to 
EQU O(w)=.vertline.H(w).vertline..sup.2 *.vertline.g.sub.chip 
(w).vertline..sup.2 *.vertline.V.sub.a (w).vertline..sup.2 * 
*[.vertline.a.sub.91 (w).vertline..sup.2 +.vertline.a.sub.92 
(w).vertline..sup.2 ] (26) 
In general, the absolute square of the Fourier transform of a function is 
equal to the Fourier transform of the autocorrelation of that function. 
Thus, the term in brackets is the Fourier transform of the sum of the 
autocorrelations of each of the array factors for modulators 91 and 92. 
Because these array factors are defined by Golay codes, by definition the 
sum of their autocorrelation functions is proportional to a delta function 
(see, for example, R. H. Pettit, "Pulse Sequence with Good Correlation 
Properties", Microwave Journal 63-67 (1967) and M. J. E. Golay, 
"Complementary Series", Proc. IRE 20 82-87 (1961). Therefore, the term in 
brackets is constant. As a result of this, the modulator bandwidth is just 
that of g.sub.chip (w).sup.2. For a Golay code of N elements, this results 
in an increase by N of the bandwidth of the modulator compared to a 
conventional Mach-Zehnder modulator. However, for Golay codes, it can be 
shown that the balance between positive and negative bits is such that the 
ratio (n.sub.+ +n.sub.-)/(n.sub.+ -n.sub.-) is proportional to the square 
root of N. Thus, V.sub.pi increases by a factor proportional to the square 
root of N so that the overall improvement in the bandwidth-to-voltage 
ratio increases as the square root of N. 
Suitable Golay codes are presented in the references R. H. Pettit, "Pulse 
Sequences with Good Correlation Properties", Microwave Journal 63-67 
(1967) and M. J. E. Golay, "Complementary Series", Proc. IRE 20 82-87 
(1961). One particular set of Golay codes that are easy to generate for a 
length L=2.sup.n-1 for some integer n are as follows. A Golay pair of 
length 1 is the pair of sequences .sup.1 G.sup.1.sub.k ={1} and .sup.1 
G.sup.2.sub.k ={1}. The superscript to the left of G indicates that this 
is a Golay code for n=1. Higher order values of n are generated by the 
following iteration: 
##EQU5## 
where n.sup.G2* is the conjugate of n.sup.G2.sub.k. By conjugate is meant 
that each element in .sup.n G.sup.2* is equal to minus the corresponding 
element in .sup.n G.sup.2. For example, for n=3, the sequences are: 
EQU .sup.3 G.sup.1.sub.k ={1,1,1,-1} and 
EQU .sup.3 G.sup.2.sub.k ={1,1,-1,1} 
Three other Golay pairs of length 2.sup.n can be produced from this pair by 
reversing the polarity of all of the elements in: just .sup.n 
G.sup.1.sub.k ; just .sup.n G.sup.1.sub.k ; or in both .sup.n 
G.sup.1.sub.k and .sup.n G.sup.2.sub.k.