(2003 OC) Frequency characteristics and dynamical behaviors of self-modulation in vertical-cavity su.pdf

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(2003 OC) Frequency characteristics and dynamical behaviors of self-modulation in vertical-cavity su.pdf

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(2003 OC) Frequency characteristics and dynamical behaviors of self-modulation in vertical-cavity su

Frequency characteristics and dynamical behaviors of self-modulation in vertical-cavity surface-emitting lasers Qiansuo Yanga,b,*, Akihiro Sasoha a Shock Wave Research Center, Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba, Sendai 980-8577, Japan b Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China Received 11 September 2002; received in revised form 21 February 2003; accepted 25 February 2003 Abstract The frequency characteristics of a VCSEL with a quarter-wave plate (QWP) and an external reflector are investi- gated with the translation matrix of the vectorial field. Two series of eigenmode with a shift of half the free spectrum range are linearly polarized, respectively, along the neutral axes of QWP. We also numerically explore the polarization self-modulation phenomenon by using a vectorial laser equation and considering the inhomogeneous broadening of the gain medium. If the external cavity is so short that the shift is bigger than the homogeneous broadening, two stable longitudinal modes oscillate, respectively, on the neutral axes of QWP because they consume different carriers. With a long external cavity, the competition of the modes for the common carriers causes the intensity fluctuation of the modes with a period of one round-trip time of the external cavity. 2003 Published by Elsevier Science B.V. Keywords: Translation matrix; Optical feedback; Modulation; Quarter-wave plate; Polarization; VCSEL; Modal analysis 1. Introduction The light from a vertical-cavity surface-emitting laser (VCSEL) is linearly polarized along one of the two orthogonal crystal directions, and the linearly polarized modes arise from an intracavity birefringence aligned on the crystal axes (defined as x- and y-directions) [1]. When an external reflector and a quarter- wave plate (QWP), whose optical axes are oriented at 45 with respect to x-direction, are used to provide an optical feedbac