Optical eigenmodes of a cylindrical microcavity

Abstract

Abstrac t.T he optical mode structure of a cylindrical microcavity has been investigated using a transfer matrix approach. We derive exact algebraic equations from which the frequencies of the optical eigenmodes of the two polarizations can be obtained, as well as approximate explicit algebraic expressions for those frequencies. In trod u c tionSemiconductor microcavities have attracted increasing interest in the last decade as a result of their application in the investigation of light± matter interactions [1] in low-dimensional systems, and because of their practical use for vertical cavity surf ace emitting lasers [2]. T he typical microcavity consists of two Bragg re¯ectors (which are essentially one-dimensional photonic band gap structures [3]) enclosing a central layer of one or more wavelengths in thickness. T he Bragg re¯ectors provide localization of light only in the dimension which is perpendicular to the layers of the structure, and theref ore the eigenmodes of the microcavity are two-dimensional photonic states.Structures which provide two-dimensional [4] and full three-dimensional localization of light [5] promise to be useful in the development of optoelectronic devices possessing enhanced properties. T wo-dimensional localization by cylindrical multilayered structures has been demonstrated experimentally [6] and the theory of the propagation of electromagnetic waves through cylindrical structures has received some attention [7± 9]. In particular, the present authors, with S okolow ski, have considered the properties of cylindrical Bragg re¯ectors using the transf er matrix technique [9].T he aim of this work is to investigate theoretically the optical eigenmode structure of a multilayered cylindrical microcavity of the type shown in ® gure 1, where light propagates in the plane perpendicular to the axis of symmetry z , but not along the axis as occurs in an optical ® ber [10,11]. However, the formalism can be applied to a wide range of other problems, including the study of non-

Trends in microdisk laser research and linear optical modelling

“…More complicated separable 2-D configurations are concentric circular ones, which have important prototype-ABR-assisted disk-on-substrate lasers. Modelling of such passive cavities has been attempted many times in the 2000s (Kaliteevski et al 2000;Scheuer and Yariv 2003;Jebali et al 2004Jebali et al , 2007, although results published contain only the information on the frequencies and not Q-factors; the analysis of Jebali et al (2007) appears inadequate as it neglected the mode discreteness and used different field functions for estimating the stored and the radiated power values.…”

Lasing spectra and thresholds of supermodes in an active microdisk assisted with a passive microring in view of the mode overlap coefficients

“…It is quite obvious that similar phenomena should take place in the other circularly layered microlasers that have been studied as passive cavities in [5][6][7][8][9][10][11][12].…”

Tamm plasmon polaritons in multilayered cylindrical structures

“…2, is presented in Ref. 28 for the case of TE-and TM-polarized waves (β = 0). The same approach can be used to obtain the reflection coefficients marked r 2 in Fig.…”

“…27 but here for simplicity we use constant, quarter wavelength thicknesses which are generally accepted to provide effective reflection of cylindrical waves in most circumstances. 28 Also, for a TPP to exist there should be a phase change equal to an integer multiple of 2π or zero in a "round trip" of the radiation in the cavity formed by the metal and the Bragg reflector, as illustrated in Fig. 2 for a metal core and in Fig.…”