Ï is the photon lifetime, which is defined at threshold and can be written as ... case of a homogeneous and isotropic external resonator, ÏÏÏ. == e o. [. cdL cdn. /).
Polarization dependence of the effect of external optical feedback on semiconductor lasers ∗, 1
Q. Zou
, S. Azouigui
2, 1
2
, A. Ramdane , and B.-E. Benkelfat
1
1
Département Electronique et Physique, Institut National des Télécommunications, Groupe des Ecoles des Télécommunications, Laboratoire SAMOVAR, UMR 5157, CNRS 9 rue Charles Fourier, 91011 Evry cedex, France 2
Laboratoire de Photonique et de Nanostructures, UPR 20, CNRS Route de Nozay, 91460 Marcoussis, France Abstract
We present an extension of an early work on external optical feedback in semiconductor lasers. A more general formalism has been developed, which takes into consideration the anisotropy properties of an external cavity. The expressions are derived for description of the feedback phenomena in a system composed of a laser diode and a FabryPerot cavity which is optically birefringent. We show that the emission behavior of such a system can be strongly affected by the polarization states of the feedback waves, and that therefore multiple solutions become possible for stabilization of a composite mode. Particular attention is paid to the angle-dependent phase condition. Examples are given for a laser emitting at the wavelength of 1.54 µm and for an external cavity made of a quartz crystal. Keywords: semiconductor lasers, external optical feedback, hysteresis cycle, mode hopping, phase noise, anisotropic Fabry-Perot cavity, optical birefringence, polarization of light
1. Introduction High-spectral-quality semiconductor lasers are important components for many applications, such as optical-fiber sensing and optical-fiber transmission. It has been widely recognized that the behaviors of a semiconductor laser can be significantly affected by external optical feedback 1, and that this effect can be used for improvement of the performance of a laser such as linewidth narrowing and single-mode selection. External optical feedback, on the other hand, is also responsible for some undesirable phenomena such as mode instability and mode hopping. In parallel with experimental investigations, theoretical approaches have been developed 2, 3 to predict the transient as well as the steady-state behaviors of a composite laser system. Good agreement between experiment and theory has been found by use of these methods which are essentially based on the model proposed by R. Lang and K. Kobayashi 4. However, it seems that the problem of optical feedback from an external anisotropic cavity has not been addressed yet. The purpose of this paper is to present an extension of this model in order that it also covers situations where the operating conditions of a laser system could be affected by external feedback coming from an anisotropic cavity. We will first establish the rate equations for a system composed of a laser diode and a birefringent Fabry-Perot cavity and derive the corresponding stationary solutions. Then we will show that it is possible to have multiple solutions for the stabilization of a lasing mode by rotation of the birefringent element inside the external cavity, since this allows a continuous tuning of the feedback coefficient. Examples will be given for a solitary laser emitting at the wavelength of 1.54 µm and for an external cavity made of a quartz crystal. Consider the configuration of Figure 1. A single-longitudinal-mode laser diode is in resonance with a Fabry-Perot resonator, inside which are inserted a polarizer and a birefringent plate. We neglect the thickness and the absorption of the polarizer. We assume that the mirror is dispersionless and passive, and that it does not modify the polarization state of an incident light beam. We also consider small feedback effect (i.e. γ
