Analytical model of a VCSEL considering external optical feedback

Abstract

In this work, a new tcchniquc of obtaining the transfer mutrix of a multilayer DI3R staek is presented. By extending this technique the transfer matrix of a complete VeSEL with an active layer sandwiched between a boltom DBR stack and a top DBR stack is developed. The new technique of forming the transfer matrix is termed as Sampled Transfer Matrix Method (STMM). Using the STMM it is possible to compute the transfer matrix of a DBR stack or a complete VeSEL accurately even if the laycrs arc constructcd using smoothly varying refractive index layers. It is difficult to compute the transfer matrix as well as Reflectivity and Transmitivity of a DBR stack containing smoothly varying refractive index layers by using the previously used Transfer Matrix Mcthod (TMM). In the STMM thc layers of smoothly varying refractive index layers are divided into many thin layers having a thickncss of d which is many times less than the actual thickness of the layers. Each of such a sampled laycr may be considered as a constant index layer. The transfer matrix of the complete DBR stack is computed by multiplying all of the transfer matrixes of each of the sampled layers. Reflcctivity and Transmitivity of a DBR stack and a complete VeSEL containing graded index layers as well as step index layers can be computed accurately by using this STMM. If the number of sampled layers are increased calculation for smooth variation of refractive indices of the layers provides more accurate results. Using the transfer matrix formcd by using STMM it is possible to compute the electric field distribution inside a VeSEL. The electric field intensity at any point between the center of the cavity and the end of the top or boltom DBR stack can be computed by imagining a plane at that point. Then compute the transfer matrix of the remaining portion of the VeSEL (from imagining plane to the top or boltom facet) and applying the relation presented in the section (5.3), the electric field intensity at the imagined plane can be computed. In this way the electric field distribution inside the VeSEL can be computed. The optical feedback effect on the performance parameters of a VeSEL from the external reflectors has been studied utilizing the transfer matrix formed using the above mentioned STMM. The transfer matrix of a VeSEL having external reflectors has been formed using STMM. Using this model next, the position of the external reflector is varied to determine the variations of threshold current, external differential quantum cfficiency and output power of a VeSEL. Rate equations based model of a VeSEL with optical feedback is presented in a new way. Parts of the rate equation related to optical feedback is modified and computed from the STMM based model. Then the modified Rate equations are solved numerically by using the Finite Difference (FD) method. Carrier density, Photon density, Photon fluctuation due to optical feedback and Relative Intensity Noise (RIN) has been computed. It is worthwhile mentioning here that the computation of the performance parameters of a complete VeSEL in presence of optical feedback has been done by computing the electric field inside the VeSEL. In addition to this, output optical power versus time and output optical power versus injection current have been computed using the rate equation based model. Finally, the obtained result has been analyzed and it has been found that the STMM based model of computing the performance parameters of a complete VeSEL in presence of optical feedback is capable of providing better results compared to the results that were obtained previously by using other models.