General model and modulation strategies for Sagnac-based encoders

In recent decades, there has been an increasing demand for faster modulation schemes. Electro-optic modulators are essential components in modern photonic systems, enabling high-speed control of light for applications ranging from telecommunications to quantum communication. Conventional inline and Mach-Zehnder modulators, while widely adopted, are limited by bias drift, high operating voltages, and polarization-mode dispersion. Sagnac loop-based modulators have recently emerged as a promising alternative, offering inherent stability against environmental fluctuations and eliminating the need for active bias control. In this work, we present a comprehensive model of the Sagnac modulator that captures both intensity and polarization modulation. We analyze the role of asymmetry in the loop, highlighting its impact on the achievable repetition rate, and propose modulation strategies to overcome these constraints. Finally, we investigate the symmetric Sagnac configuration and demonstrate practical techniques for achieving robust modulation while mitigating experimental challenges, including optical pulse carving and polarization modulation at repetition rates up to 1.5 GHz, the maximum achievable for our hardware implementation without increasing the modulation voltage. Our results establish the Sagnac modulator as a versatile and stable platform for next-generation photonic and quantum communication systems.