Power Spectral Density of Injection-Locked Optoelectronic Oscillators: Effects of Phase Noise

Abstract

Injecting a spectrally pure oscillator signal into a noisy optoelectronic oscillator (OEO) can result in a drastic reduction of the phase noise; however, a unified explanation of this effect may be obscured by implementation-specific models. We show based on an analytically tractable theory that the power spectral density <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S_f(\omega)$</tex-math></inline-formula> of an ideal injection-locked (IL) oscillator signal is composed of a narrow Lorentzian peak at the center frequency lying on top of a broader roughly Lorentzian pedestal using an Ornstein-Uhlenbeck model obtained from the Adler equation in the weak-noise limit. The injected signal imposes its phase on the IL oscillator providing a restoring force for the phase, leading to this fundamentally different behavior of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S_f(\omega)$</tex-math></inline-formula> compared with a self-sustaining oscillator. Our treatment is shown to be grounded in the physics-based approach for IL OEOs of A. F. Talla, R. Martinenghi, G. R. Goune Chengui, J. H. Talla Mbé, K. Saleh, A. Coillet, G. Lin, P. Woufo, and Y. K. Chembo, “Analysis of phase-locking in narrow-band optoelectronic oscillators with intermediate frequency,” <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><b>I</b></i> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EEE J. Quantum Electron.</i> , vol. 51, 5000108, 2015.