Photonic Transistor Design Principles for Switching Gain $>=2$

A novel two-staged photonic transistor with high operating speed, low switching power and high switching gain was recently proposed. Based on the manipulation of optical interference in an active directional coupler by optically controlled absorption and gain, two complementary device types were conceptually evaluated through the use of time domain technique showing $\sim 10^{5}$ times higher figure of merit compared to conventional approaches. With the joint usage of both device types, the photonic transistor could function as wavelength converter, pulse regenerator and logical operator. In this work, we identify the operational regimes of the photonic transistor that helps in reducing the footprint and operating intensities to achieve a switching gain of at least $\sim$2 (or 3 dB). A recently proposed theoretical framework that calculates the spatial profiles of optical fields and complex permittivities seen by them in photonic structures with multiple active and passive sections is utilized for the purposes. We show that the operational intensity and wavelengths of interacting fields in the photonic transistor must be such that $\alpha_{0}{\rm L}_{1}>=26$ and ${\rm g}_{0}{\rm L}_{2}>=3.2$ to achieve a ${\rm switching}\ {\rm gain}>=2$, where $\alpha_{0}={\rm absorption}\ {\rm coefficient}$ of the short wavelength, ${\rm g}_{0}={\rm pumped}\ {\rm medium}\ {\rm gain}\ {\rm coefficient}$ seen by long wavelength beams, ${\rm L}_{1}={\rm length}\ {\rm of}\ {\rm first}\ {\rm stage}$ and ${\rm L}_{2}={\rm length}\ {\rm of}\ {\rm second}\ {\rm stage}$.