General model and modulation strategies for Sagnac-based encoders

TL;DR

This paper tackles bias drift and polarization challenges in conventional electro-optic modulators by introducing a comprehensive Sagnac-loop model that captures both intensity and polarization modulation. It develops a complete traveling-wave framework with co- and counter-propagating transfer functions, and extends it to symmetric configurations, proposing modulation schemes—time-shifted, differential, and balanced—to maximize repetition rate while mitigating practical constraints. The authors demonstrate polarization and intensity modulation in a symmetric Sagnac setup, validating the model experimentally at high speed and achieving robust state preparation with large polarization-extinction ratios, enabling effective BB84-like encoding. The results establish Sagnac modulators as versatile, low-drift platforms for next-generation photonic and quantum communication systems, including direct optical pulse generation within the interferometer and high-rate polarization encoding.

Abstract

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. Our results establish the Sagnac modulator as a versatile and stable platform for next-generation photonic and quantum communication systems.

Figures (8)

• Figure 1: Polarization and intensity modulator based on the Sagnac scheme. $\phi$-mod indicates the electro-optic phase modulator, while the white arrow indicates the direction of the RF microwave signal. $\Delta L$ quantifies the asymmetry of the phase modulator within the Sagnac loop. For symmetric configuration $\Delta L=0$.
• Figure 2: Phase $\phi_s(t)$ for rectangular driving signal $s(t)$. We considered the case $\tau_{\rm d}\geq \tau_{\rm s}+\tau_{\rm mod}$ and $\tau_{\rm s}\geq2\tau_{\rm mod}$. The signal $s(t)$ is reported in units of $V_0$, while $\phi_s(t)$ in given in unit of $\frac{V_0}{V_\pi}$. For simplicity we set $t_0=0$.
• Figure 3: Modulations proposed in this work, characterized by signal $s(t)$ (top) and phase response $\phi(t)$ of the configuration (bottom). From left to right: a) time-shifted modulations for the asymmetric configuration (for $\tau_{\rm s}=2\tau_{\rm mod}+\tau_{\rm op}$); b) differential asymmetric modulations (for $\tau_{\rm s}=\tau_{\rm op}$); c) differential symmetric modulation (for $\tau_{\rm s}=\tau_{\rm op}$); d) balanced symmetric modulations (for $\tau_{\rm s}=\tau_{\rm op}$). For the asymmetric configuration we choose $\tau_{\rm d}=\tau_{\rm op}+\tau_{\rm mod}$, while for the symmetric configuration we have $\tau_{\rm d}=0$. It should be noted that the voltage required to apply a $\pi/2$ phase on the optical pulse for the symmetric differential configuration is higher than all others by a gain factor of $g_V$ defined in Eq. \ref{['eq:gain-factor']}. The locations of the pulses have been chosen to maximize the repetition rate.
• Figure 4: Generated states at $1.5$ GHz of repetition rate using the symmetric balanced configuration and projected on the $Y$ basis, with a polarization extinction ratio of $\rm{PER}_Y=23.147\pm0.003$ dB observed between the $\ket{L}$ and $\ket{R}$ states.
• Figure 5: Measured intensity at the output of an asymmetric ($\tau_{\rm d}=5$ ns) iPOGNAC when injecting continuous wave light in a fixed $\ket{D}$ polarization state and projecting in the $\ket{A}$ state, driven by a rectangular electrical signal when varying $\tau_s$ (bottom) and $V$ (top).