Improved simulation of VCSEL distributed Bragg reflectors

Abstract

In this paper, the Floquet-Bloch theory (FBT) has been applied to the accurate simulation of distributed Bragg reflectors in vertical cavity surface emitting lasers (VCSELs). A number of comparisons with other methods largely used in commercial CAD tools is presented. Performance predictions for long-wavelength GaInAsP VCSELs are derived.

Absorption loss influence on optical characteristics of multilayer distributed Bragg reflector: wavelength-scale analysis by the method of single expression

“…Widely used calcula− tion method is the coupled mode theory (CMT) [18][19][20][21]. The CMT provides simple analytical expressions also for mirrors having graded interfaces, however, the applicability of the method is limited by DBR structures with low index contrast [22]. The calculation method close to the CMT is the Tanh substitution technique, which is used to find the reflectance of abrupt and graded multilayer mirrors [23].…”

An improved model for computing the reflectivity of a AlAs/GaAs based distributed bragg reflector and vertical cavity surface emitting laser

“…Several techniques such as, Transfer Matrix Method (TMM) (Carroll et al 1998), the coupled mode theory (CMT) (Bhattacharya 1992), Floquet-Bloch Theory (FBT) (Leonardis et al 2007), Tanh substitution technique (Corzine et al 1991) and Thin-Film Optics based technique (Matin et al 1998) have been applied for analyzing the characteristics of the DBR having step index as well as graded index variation. None of the above mentioned techniques have taken into consideration of variation of refractive index of the DBR layers with the change of wavelength.…”

Mathematical analysis of the lasing eigenvalue problem for the optical modes in a layered dielectric cavity with a quantum well and distributed Bragg reflectors

“…Thin active regions shaped as quantum wells (QWs) or layers of random quantum dots and embedded in epitaxially grown semiconductor microresonators are widely used in photonics. The area of applications of such active cavities covers fundamental aspects such as alteration of spontaneous emission characteristics in various systems and visualization of quantum optical phenomena, and also device applications such as fabrication of vertical cavity surface emitting lasers (VCSELs) (Yu 2003;Piprek 2005;Streiff et al 2003;Yang et al 1995;Huffaker and Deppe 1997;Klein et al 1998;Noble et al 1998;Chung et al 2004;Zhang et al 2006;De Leonardis et al 2007), microdisk lasers, and photonic-crystal membrane band-edge lasers (Campenhout et al 2005). …”

“…Mathematically this means solving the time-harmonic Maxwell eigenvalue problem with the outgoing-wave radiation condition at infinity for the complex-valued natural frequencies or wavenumbers, k. Such eigenvalues form a discrete set and can be numbered, say, by using the index n. In these analyses, the modes with the largest Q-factors have been identified as the lasing modes (Yang et al 1995;Huffaker and Deppe 1997;Klein et al 1998;Noble et al 1998;Chung et al 2004;Zhang et al 2006;De Leonardis et al 2007). The eigenfunctions corresponding to these eigenvalues are the natural electromagnetic fields of the cavity; they decay in time as e −|Im k n |ct however grow in space as e |Im k n |R far from the cavity (c is the light velocity).…”