The program written for this study allows calculations for periodically-rephased modulators since the modulator is already broken up into a series of incremental matrices. Thus if the modulator is allowed to be mismatched for a few matrices and then rephased for the next few and so on, we have the results shown for a four segment modulator (3 rephasings). modulators are considered

Bridges, William B.

Cummings, Uri V.

Caltech Authors - Main

2: 15pm-2:30pm 
w w 3  
Effects of Velocity Mismatch and Transit Time on 
Linearized Electro-Optic Modulators 
Uri V. Cummings and William B. Bridges 
California Institute of Technology 
Pasadena California 
Gain, noise figure, and dynamic range limited by intermodulation and harmonic distortion were 
calculated for simple analog optical links employing different linearized electro-optic modulators with a 
representative set of link parameters in Ref.[l]. However, that analysis ignored the effects of transit time 
and velocity mismatch. Since linearized modulators typically involve critical cancellations to reduce 
distortion, it is important to determine how transit-time and velocity mismatch affect the linearization. 
We have used a numerical algorithm introduced by Farwell and Chang [2] to analyze the same links as 
in [I] with additional representative values of velocity mismatch (microwave velocity = d4.0, optical 
velocity = d2.2, typical of a transmission line on lithium niobate) and a modulator length of 10 mm. As 
in [2], the modulator structure is divided into many short segments, with a matrix written for each 
segment. The modulating voltage is assumed uniform in magnitude and phase over the segment, but 
the phase of successive segments is shifted by an amount appropriate to the velocity mismatch. The 
program then multiplies all the matrices (typically 128) to relate the output to input. Voltages at two 
closely-space microwave frequencies fl and f2 are applied and the output FFT-analyzed to find the 
amplitudes of the signal (f,), second harmonic (2fl),and intermodulation (2fl - f2). The dynamic range 
(broad band) is determined by finding the input power that makes the intermodulation distortion (IMD) or 
the second harmonic component equal to the noise level. If only a sub-octive bandwidth link is required, 
then the dynamic range (narrow band) is limited by the IMD alone. 
The results for worst-case velocity mismatch are shown in Fig. I, which compares the dynamic ranges 
for four different modulators (see ref. 1 for modulator and link details): the simple directional coupler 
modulator biased at its minimum second harmonic point (43% of the transfer voltage) [DCM.43], the 
same DCM, but biased at its maximum dynamic range point (79% of the transfer voltage) [DCM.79], the 
directional coupler with two added d-c sections for linearization, from ref. [2], referred to here as the 
UCSD modulator, considered as limited by intermodulation distortion alone [UCSDw/o2] or limited by 
intermodulation or second harmonic, whichever is worse [UCSDw2]. In the case of the DCM.43, the 
limitation switches from IMD below 1GHz to second harmonic above. For DCM.79, the second harmonic 
is so bad even at very low frequencies, that only the IMD limited (narrow band) dynamic range is shown. 
Figure 2 shows the gain degradation with frequency for these same three modulators, plus the simple 
Mach-Zehnder for reference. As suggested by Farwell and Chang, the calculation scales as fi*L*An, 
with L=10 mm and An= 1.8 for our calculations, so these curves apply as well to partially velocity- 
matched modulators [e.g., ref. 31 by re-scaling the abscissa to the appropriate length and residual 
velocity mismatch. 
The curves in Figs 1 and 2 show that the second harmonic severely decreases the dynamic range of the 
UCSD modulator at just a few hundred MHz. The simple DCM dynamic ranges are only slightly less 
rapidly decreased. We conclude that velocity matching is required to preserve linearization at much 
lower frequencies than would be required to simply preserve gain. 
The program written for this study also easily allows calculations for periodically-rephased modulators 
[e.g., 4,5] since the modulator is already broken up into a series of incremental matrices. Thus if the 
modulator is allowed to be mismatched for a few matrices and then rephased for the next few and so on, 
we have the results shown in Fig. 3 for a four segment modulator (3 rephasings). The same three 
modulators are considered. With rephasing, the DCM.43 dynamic range is flat to beyond 30 GHz at its 
d-c value, limited only by IMD, not second harmonic. The DCM.79 (IMD-limited, but with terrible second 
harmonic) is also greatly improved. The UCSD modulator dynamic range drops off less rapidly, but still 
seriously. Rephasing more often improves all modulators, as shown in Table I .  
1 74 
We have also added electrode loss to the calculation (requiring only an exponential decrease in 
amplitude from matrix to matrix), and have compared the effect of loss on perfectly velocity matched 
modulators. It appears that loss alone reduces the dynamic range of linearized modulators by upsetting 
the critical distortion-canceling conditions. The effects of loss are less destructive in the rephased 
modulators, since each segment is "re-amplituded" as well as rephased. 
Modulator 
DCM.43 
This work was supported by USAF Rome Laboratory under contract F30602-92-C-0005, N.P. Bernstein, 
program manager. The authors wish to thank J. H. Schaffner for many technical discussions. 
D. R. 1 3 dB freq. (GHz) 
109.6 1 1.4 I 11.6 I 36 I 98 
DC I 1 seg 1 2  seg 1 4  seg 1 8  seg 
[ l ]  W. B. Bridges and J. H. Schaffner, "Distortion in Linearized Electro-optic Modulators," IEEE Trans. 
On Microwave Theory and Tech., Vol. 43, pp2184-2197 
UCSDw2 
UCSDw/o2 
Mach-Zehnder 
[2] M. L. Fawell and W. S. C. Chang, 'Simulating the Response of Coupled Channel and Interferometric 
Modulator Designs," J. Lightwave Tech., Vol. 13, pp 2059-2068, October 1995. 
120.8 0.01 0.026 0.12 0.8 
129.1 0.02 0.075 0.60 3.0 
109.8 16.8 31.6 47.4 63.2 
[3] G. K. Gopalakrishna, C. H. Bulmer, W. K. Bums, and R. W. McElhanon, " 40GHz Low Half-Wave 
Voltage Ti:LiNb03 Intensity Modulator," Elect. Lett., Vol. 28, pp 826-827, April 23, 1992. 
[4] J. H. Schaffner and W. B. Bridges, "Broad Band, Low Power Electro-Optic Modulators Apparatus and 
Method with Segmented Electrodes," U. S. Patent 5,291,565, September 1994. 
[5] W. B. Bridges, F. T. Sheehy and J. H. Schaffner, "Wave-Coupled Electrooptic Modulator for 
Microwave and Millimeter-Wave Modulation," Photon. Tech. Lett. Vol. 3, pp 133-135, February 1991. 
Fig. 1 
130 I I I I 
Dynamic Range + 
120 
110 
100 
B 
90 
80 
0 5 10 15 20 25 
GHz 
Fig. 3 
1 30 I I I 
D.R. 4 electrode segments + 
125 
1 20 
115 
Fig. 2 
-20 I I I I 
Gain +-- 
-65 60 0  5 10 15 20 25 
GHz 
I DCM.79 1128.8 I 0.42 1 1.1 I 6 . 1  I 21 I 
an I J 
"Y 
0 5 10 15 20 25 
GHz 
Table 1. 
1 75 


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Effects of Velocity Mismatch and Transit Time on Linearized Electro-Optic Modulators

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Effects of Velocity Mismatch and Transit Time on Linearized Electro-Optic Modulators

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