Electro-optical modulation is divided into external and direct action. The latter type of modulation includes direct modulation of laser radiation to laser pump currents.The modulation bandwidth can reach up to 10..20 GHz for various lasers. As a rule, this uses amplitude modulation or modulation of the laser radiation intensity. The effects of the refractive index in lasers were studied. This work is devoted to the modulation of quantum-dimensional laser diodes. The effect of the pump current on the refractive index of the laser active medium was studied. Both a constant component and a variable component.

Different types of electro-optical modulators are used for external modulation of laser radiation. Mach-Zehnder modulators with a modulation bandwidth of up to 10 are widely used...40ghz. But in such modulators, the refractive index of the material depends on the modulating voltage. The temperature of the modulation region does not exceed significant values.

Another class of external modulators includes absorption modulators, for example, on semiconductor quantum-dimensional structures. Due to the high power density in such modulators, the refractive index also depends on the DC value and the average value of the variable component. The dispersion of the refractive index due to temperature changes has a significant effect here. If necessary, I can name some works.

As the carrier concentration changes, both the real and imaginary part of the complex refractive index change. The change in the real part is desired whereas the presence of imaginary part deteriorates the performance of the modulator or switch. In a configuration based on Mach-Zehnder Interferometer, one either use the y-splitter or a directional coupler at both the ends of phase shifter section. Usually, the directional couplers are used in case of a switch and y-splitters are used in case of a modulator. In a switch design, an increase in imaginary part of refractive index results in an increase in the insertion loss as well as cross-talk whereas in case of modulator, an increase in the imaginary part results in the increase of insertion loss only.

Hence, for a modulator design with y-splitter at the input and output end, one needs to worry about the insertion loss only. In case of a switch design, in addition to the insertion loss, the cross talk is also one of the major issue. However, the cross-talk can be eliminated using various techniques such as using the phase shifter in both the arms or by using the directional coupler with appropriate splitting ratios at the input and output.

Thanks Nikhil. This is of course expected but for a practical design of a high speed modulator, is there a way to have low loss along with a high RF modulation depth?

As far as refractive index modulation depth is concerned, nothing much can be done to reduce loss. If one need a large change in real part of refractive index, the imaginary part is also gonna change proportionally due to Kramers-Kronig relation. However, a little bit optimization in terms of controlling the charge profile and device geometry can be done. But still the response in terms of insertion loss is limited due to Kramers-Kronig relations.

I am not much aware about the transient response of these modulators. Maybe the following papers might help a little:

• Xi Xiao, Hao Xu, Xianyao Li, Zhiyong Li, Tao Chu, Yude Yu, and Jinzhong Yu, "High-speed, low-loss silicon Mach–Zehnder modulators with doping optimization," Opt. Express 21, 4116-4125 (2013)
• Xu, H., Xiao, X., Li, X., Hu, Y., Li, Z., Chu, T., Yu, Y. and Yu, J., 2012. High speed silicon Mach-Zehnder modulator based on interleaved PN junctions. Optics express, 20(14), pp.15093-15099.

Amin, Rubab, Can Suer, Zhizhen Ma, Ibrahim Sarpkaya, Jacob B. Khurgin, Ritesh Agarwal, and Volker J. Sorger. "Active material, optical mode and cavity impact on nanoscale electro-optic modulation performance." Nanophotonics 7, no. 2 (2017): 455-472.