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Determination of phase noise spectra in optoelectronic microwave oscillators a Langevin app
Determination of Phase Noise Spectra in
Optoelectronic Microwave Oscillators:
a Langevin Approach
Y. Kouomou Chembo??, K. Volyanskiy?,
L. Larger§, E. Rubiola? and P. Colet‖
FEMTO-ST Institute
CNRS and Universite? de Franche Comte?, Besanc?on, France
May 21, 2008
Abstract
We introduce a stochastic model for the determination of phase noise
in optoelectronic oscillators. After a short overview of the main results
for the phase diffusion approach in autonomous oscillators, an extension
is proposed for the case of optoelectronic oscillators where the microwave
is a limit-cycle originated from a bifurcation induced by nonlinearity and
time-delay. This Langevin approach based on stochastic calculus is also
successfully confronted with experimental measurements.
Keywords: Optoelectronic oscillators, phase noise, microwaves, semiconduc-
tor lasers, stochastic analysis.
?FEMTO-ST, Dept. of Optics. Corresponding author, e-mail: yanne.chembo@femto-st.fr
and ckyanne@yahoo.fr.
?Y.K.C. acknowledges a research fellowship from the Re?gion de Franche-Comte? in France,
and a financial support from MEC (Spain) and FEDER under projects TEC2006-10009
(PhoDeCC) and FIS2007-60327 (FISICOS).
?FEMTO-ST, Dept. of Optics, and St. Petersburg State University of Aerospace Instru-
mentation.
§FEMTO-ST, Dept. of Optics.
?FEMTO-ST, Dept. of Time and Frequency. Home page .
‖Instituto de F??sica Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Palma de
Mallorca, Spain.
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Y. K. Chembo al. May 21, 2008 2
Contents
1 Introduction 3
2 The phase diffusion approach in autonomous oscillators 3
3 Application of the phase diffusion approach to OEOs: stochastic
delay-differential equations 5
4 Noise power density spectrum below threshold (γ 1) 8
5 Phase noise spectrum above threshold (γ 1) 10
6 Conclusion 13
A Determination of the output noise power for γ = 0 14
B Derivation of the stochastic phase equation 15
C
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