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Journal of the Optical Society of America B

Characterizing semiconductor laser phase noise using delayed self-homodyne measurements with optical coherent reception for quantum random number generation

Angel Valle A

Published Aug 18, 2026• 0 citations
Publisher

Abstract

We report on the experimental and theoretical analysis of the phase noise of the light emitted by a single-mode laser diode. We analyze the time dependence of the variance of the optical phase obtained in a delayed self-homodyne with optical coherent reception setup. This analysis is of interest since that phase is used for quantum random number generation. We show that the variance linearly grows from the initial time until the time delay corresponding to the extra fiber length of the setup. We show experimentally and theoretically that this initial growth can be used for measuring the phase diffusion coefficient with a delayed self-homodyne setup. This is confirmed by comparing with the results obtained with a heterodyne setup. After that time delay, the variance continues to grow more slowly than in the initial growth. We explain that behavior by the progressively important effect of low-frequency noises on the phase noise as the measurement time window increases.

DOI
10.1364/josab.608209

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We report on the experimental and theoretical analysis of the phase noise of the light emitted by a single-mode laser diode. We analyze the time dependence of the variance of the optical phase obtained in a delayed self-homodyne with optical coherent reception setup. This analysis is of interest since that phase is used for quantum random number generation. We show that the variance linearly grows from the initial time until the time delay corresponding to the extra fiber length of the setup. We show experimentally and theoretically that this initial growth can be used for measuring the phase diffusion coefficient with a delayed self-homodyne setup. This is confirmed by comparing with the results obtained with a heterodyne setup. After that time delay, the variance continues to grow more slowly than in the initial growth. We explain that behavior by the progressively important effect of low-frequency noises on the phase noise as the measurement time window increases.
The quantum phase noise in a pulsed semiconductor laser is studied thoroughly in the context of its utilization as a quantum entropy source in a quantum random number generator (QRNG) device. We performed a numerical analysis of the phase diffusion process for a semiconductor laser in the continuous-wave operation mode and gain-switched (GS) mode. The result demonstrates the amplification of randomness in the GS mode, which is gauged physically by the variance VarΔϕ. The variance value, which is mathematically related to the temporal distance between the laser pulses used in the experimental setup, also determines the stability of the setup. Furthermore, we show how the QRNG probability distribution is influenced by several experimental factors such as the quality of the interference process and the noise in the detection system.
Random Number Generators (RNGs) are crucial for applications ranging from cryptography to simulations. Depending on the source of randomness, RNGs are classified into Pseudo-Random Number Generators (PRNGs), True Random Number Generators (TRNGs), and Quantum Random Number Generators (QRNGs). This work presents the end-to-end development of a high-speed, high-efficiency, phase-noise-based QRNG system that taps into the quantum phase noise of a single-frequency laser, with randomness originating from spontaneous emission. Using a self-heterodyne measurement with a semiconductor laser (linewidth ≈\approx≈ 5.23 GHzGHzGHz) operated near threshold and a $\sim$48 cmcmcm fiber delay line, a raw data generation rate of 2.0 GbpsGbpsGbps is achieved. To ensure uniform randomness in the QRNG output, robust extraction techniques developed in-house, such as the Toeplitz Strong Extractor (TSE), are used. Randomness validation using the NIST and Diehard test suites confirms that all statistical tests pass at standard confidence levels. The developed system achieves a post-processed generation rate of 1.0 GbpsGbpsGbps in operation and attains a Technology Readiness Level (TRL) of 7, approaching TRL 8, making it suitable for real-time secure applications such as cryptographic key generation and stochastic modeling.
Second generation quantum technologies aim to outperform classical alternatives by utilizing engineered quantum systems. Maintaining the coherence required to enable any quantum advantage requires detailed knowledge and control over the noise that the hosting system is subjected to. Characterizing noise processes via their power spectral density is routinely done throughout science and technology and can be a demanding task. Determining the phase noise power spectrum in leading quantum technology platforms, for example, can be either outside the reach of many phase noise analyzers or prohibitively expensive. In this work, we present and characterize a low-complexity, low-cost optical phase noise analyzer based on the short-delay optical self-heterodyne measurements for quantum technology applications. Using this setup, we compare two ≈1 Hz linewidth ultra-stable oscillators near 729 nm. Their measurements are used as a baseline to determine and discuss the noise floor achieved in this measurement apparatus with a focus on limitations and their tradeoffs. The achieved noise floor in this all-stock-component implementation of an optical phase noise analyzer compares favorably with commercial offerings. This setup can be used particularly without a more stable reference or operational quantum system as a sensor as would be the case for many component manufacturers.
The statistics of the optical phase of the light emitted by a semiconductor laser diode when subject to periodic modulation of the applied bias current are theoretically analyzed. Numerical simulations of the stochastic rate equations describing the previous system are performed to describe the temporal dependence of the phase statistics. These simulations are performed by considering two cases corresponding to random and deterministic initial conditions. In contrast to the Gaussian character of the phase that has been assumed in previous works, we show that the phase is not distributed as a Gaussian during the initial stages of evolution. We characterize the time it takes the phase to become Gaussian by calculating the dynamical evolution of the kurtosis coefficient of the phase. We show that, under the typical gain-switching with square-wave modulation used for quantum random number generation, quantity is in the ns time scale; that corresponds to the time it takes the system to lose the memory of the distribution of the initial conditions. We compare the standard deviation of the phase obtained with random and deterministic initial conditions to show that their differences become more important as the modulation speed is increased.