Velocity-matching techniques are often used to improve the frequency response of the traveling wave modulator. In Ref. [2.3] many velocity matching techniques are described and referenced. In waveguide-based modulators the fields propagate down coplanar electrodes on the surface; some field lines penetrate into the crystal (these are useful for modulation) and other field lines are in the air. While Eqn. (2.4) assumes an equal split, it is possible to create thick enough electrodes so that more than half of the electric field is in air, resulting in nm = f(nair, nmb) = no. This is done by up-plating the coplanar waveguide. Unfortunately, this matching technique also decreases the modulator sensitivity to the electric field (increases Vπ) since the field drawn up into the air between the electrodes no longer passes through the optical waveguides. In addition to up-plating the electrodes, a thick SiO2 buffering layer can be deposited between the crystal and the electrodes. The microwave index of refraction of SiO2 is less than that of lithium niobate so the electric field that passes through the SiO2 layer also reduces the effective refractive index of the transmission line electrode structure. A number of successful high frequency modulator experiments have been made exploiting the velocity matching technique beyond 40 GHz, for example, velocity matching techniques were used to go above 30 GHz in Ref. [2.4] and truly exceptional work was done to get 100 GHz velocity matched modulators in ref. [2.5].
This kind of velocity matching is a limited solution because it leads to loss in sensitivity, which must be made up by increasing the length of the modulator and, at such high frequencies,
electrode loss becomes a serious compounding problem. In essence, the electrode loss will limit the “length” of the modulator no matter how long it is made physically. An alternative technique that addresses the velocity mismatch problem is called “velocity matching on the average” and has been demonstrated in several forms. See, for example Ref. [2.6]. A velocity- mismatched electrode may be divided into sections, where each section is typically made shorter than the maximum length of a useful modulating electrode at the target frequency, as determined by electrode loss and velocity mismatch. The modulating electric field is then arranged to be “re-phased” at the beginning of each modulator section, so that it never gets too far out of step with the modulated optical wave; it is “velocity matched on the average.”
One method of accomplishing this was the “phase reversal” modulator demonstrated by Alferness, et al [2.7] in which the electrode sections were made 180o long in phase (at some desired modulation frequency), then connected to the next electrode section with an electrical transposition, and so forth down the entire structure. This assured “phase matching on the average,” but only at one frequency, where the sections are 180º in phase delay. This is not true velocity matching or true-time-delay matching. The bandwidth of the modulator decreased as more sections were added.
Another technique was proposed and patented by Schaffner and Bridges, Ref. [2.8], in which the modulating signal is divided by a multi-branched transmission-line feed that has varying lengths that just compensate for the optical delay down the waveguide under the electrode structure. Each section of the modulator is then fed at its entrance end with the proper delay to equal the optical delay to that section. This is a true velocity matching scheme and has the advantage of not narrowing the bandwidth, but it does have the disadvantage of dividing the modulating signal by the number of paths, all of which have transmission loss.
A third technique is the “antenna-coupled” technique proposed and patented by Bridges in Ref. [2.9], in which small antennas are put on the surface of the modulator and connected to the inputs of each section. The modulator is then illuminated by a plane wave at the correct angle so that the modulating wave received at each antenna is in synchronism with the optical wave entering that section, as shown schematically in Figure 2 - 9. This has the advantage of low-loss free-space transmission to the segment inputs, but now is limited to band-pass
operation by the bandwidth of the on-surface antennas and the wave radiating structure (but
Figure 2 - 9: Schematic of antenna-coupled phase modulator. The microwave signal is received by the antenna elements in synchronism with the arriving optical wave that travels through the waveguide.
Selection of the appropriate angle of incidence of the microwave yields a velocity matched modulator “on the average,” discussed in Ref. [2.6].
not further narrowed by cascading, as in the phase reversal modulator). The electrical signal power is also reduced by the number of sections used, but this is partially offset by the lower exponential attenuation in the modulating electrodes, as shown by Sheehy in Ref. [1.2]. The antenna-coupled structure has been demonstrated with MZMs again in Ref. [1.3] and with DCMs in Ref. [2.10], which is detailed in the last chapter of this thesis. The issue of velocity mismatch limiting the gain of a simple modulator is well-known. However, how velocity mismatch affects the various linearization schemes used with modulators was unknown before
the research treated in this thesis was undertaken. This behavior is a major topic of this thesis, and the results turn out to be quite interesting.
C h a p t e r 3
DISTORTION IN MODULATION