How to properly create a reciprocal phase shifter/modulator

In INTERCONNECT we always use a piece of Waveguide plus an Optical Modulator to build a phase shifter and then comes to a phase modulator later for signal modulations. The piece of Waveguide serves as the optical delay line and the Optical Modulator provides the phase perturbation; the two of them together gives the phase shifting effect and the lengths of the two should be matched. This design generally works as expected but the resulted phase shifter is not reciprocal. This nonreciprocal effect will not cause serious problems for the phase shifter itself, but when it comes to the phase modulator, this aspect becomes crucial.

The nonreciprocal effect comes from the path mismatch that the signals go through in time domain. Figure 1 shows two designs of a phase shifter (phase_shifters_nonreciprocal_effect.icp (1.2 MB)). In Design 1, the optical signal goes through the Optical Modulator first to do the phase modulation and then goes through the waveguide for the actual delay. In Design 2, the optical signal goes through the waveguide first for the delay and then do the phase modulation. Ideally the two designs will end up with the same result given that the source is a continuous wave Laser.

However, since INTERCONNECT’s multi-thread dynamic data flow engine allows the concurrent running of elements that are immediately available for calculation, in both of the designs, the Optical Modulator starts to work at time 0. In Design 1, the optical signal feeds into the Optical Modulator right away and get modulated; while in Design 2, the waveguide will delay the optical signal before it goes to the Optical Modulator, so that the first several samples of the driving signal feeding into the Optical modulator are wasted and that results in a shorter first bit of the driving signal. Figure 2 shows the two outputs measured by Oscilloscope 1 & 2 in the same plot, the nonreciprocal effect is obvious in the inside enlarged plot of the beginning of the signals. This effect causes a broad delay phenomenon in structures like Design 1.

For the phase shifter design, we may not care about the delay very much; but for the Mach-Zehnder modulator design, a delay in one of the branches will cause a significant problem at the end. The example file modulator_nonreciprocal_effect.icp (1.1 MB) contains two Mach-Zehnder modulator compact models. The first model ‘MZM_1’ has the two branches both with waveguide in front of the Optical Modulator Measured and the second model ‘MZM_2’ has the modulated branch with the Optical Modulator Measured in front of the waveguide. The two compact models are shown in Figure 3.

The circuit schematics are shown in Figure 4 and the received signals measured by Oscilloscope 1 & 2 are plotted in Figure 5. There is a clear difference between the two modulated signals so users have to be especially careful when design and use the modulator compact models.

A simple way to solve this problem is to split the waveguide into two identical pieces and place the Optical Modulator in between. The total length of the two pieces of waveguides should match the length of the Optical Modulator. Then this model becomes reciprocal. Compact models in Lumerical compact model libraries (LCML) also adopts this design.

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