Photonic crystals (PhCs) are periodically structured optical media offering the opportunity for spontaneous emission (SpE) to be strongly controlled in spatial terms (directions) or in absolute terms (rates). We discuss the application of this concept for practical light-emitting sources, summarizing the principles and actual merits of various approaches based on two- and three-dimensional PhCs. We take into consideration the numerous constraints on real-world light-emitting structures and materials. The various mechanisms through which modified photonic bands and band gaps can be used are first revisited in view of their use in light sources. We then present an in-depth discussion of planar emitters and enhanced extraction of light thanks to grating diffraction. Applications to conventional III-V semiconductors and to III-nitrides are reviewed. Comparison with random surface roughening reveals some common physical limitations. Some advanced approaches with complex structures or etched active structures are also discussed. Finally, the most promising mechanism to enhance the SpE rate, the Purcell effect, is considered. Its implementation, including through plasmonic effects, is shown to be effective only for very specific sources. We conclude by outlining the mix of physics and material parameters needed to grasp the relevant issues.

http://iopscience.iop.org/article/10.1088/0034-4885/75/12/126501/pdf

Photonic crystal light-emitting sources

1.55- mu m gain-coupled InGaAsP-InP distributed feedback (DFB) lasers which use a strained-layer multi-quantum-well (MQW) active grating for a mixed index and gain coupling have been fabricated and studied. The lasers exhibit distinct longitudinal-mode behaviour due to gain-coupling effects, including a high single-mode yield. Cavity length dependence of the mode behavior has been experimentally studied and simulated using a transfer-matrix method. Both experimental and theoretical results indicate that the shorter cavity lasers with the present structure have higher kappa /sub gain/L/ kappa /sub inde/ ratios and wider Fabry-Perot mode spacing than the longer cavity ones; these features enable the shorter cavity lasers to have a high single-mode yield (90%) and a high side-mode-suppression ratio (55 dB). >

Partly gain-coupled 1.55 mu m strained-layer multiquantum-well DFB lasers

A new approach for the calculation of the optical spectrum of semiconductor lasers is presented. It is based on a solution of the inhomogeneous coupled wave equations using the Green's function method. The spontaneous emission is modeled by Langevin noise functions. In contrast to previous theories, lasers with gain-coupled distributed feedback sections are properly described. The theoretical model is used in a fitting procedure for parameter extraction.

Green's function based simulation of the optical spectrum of multisection lasers

A general small-signal model for the intensity and phase noise spectra of multisection distributed feedback (DFB) semiconductor lasers is developed by using the transfer-matrix approach based on the Green's function method The spontaneous emission enhancements due to nonuniform longitudinal field distribution and the effective amplitude-phase coupling effect (the effective linewidth enhancement factor) are taken into account in the formulation Analytical expressions for the spectra of the relative intensity noise and the FM noise of the main mode in the multimode operation are presented by using the transfer functions in a flow-graph representation Facet reflectivities and external optical feedback are included in the model The effects of the grating coupling coefficient, the random grating-phase at the facets, the phase-shift position, the external optical feedback, and the side mode on the noise spectra are analyzed systematically for a lambda /4-shifted DFB laser >

Transfer-matrix analysis of the intensity and phase noise of multisection DFB semiconductor lasers

An analytical expression for the threshold condition of DFB semiconductor lasers is derived based on the local-normal-mode transfer-matrix method (TMM). The threshold condition is expressed in terms of an equivalent reflection coefficient of a DFB laser structure and a Bloch-wave propagation constant. It is shown that the TMM threshold condition can reproduce the one which is derived by the coupled-wave method (CWM) under certain conditions. It is also shown that the CWM can predict very accurately the spatially averaged values of the threshold modal gain and the detuning frequency which are obtained by the TMM if the coupling coefficient in the CWM is replaced by the TMM coupling coefficient. >

Threshold condition of DFB semiconductor lasers by the local-normal-mode transfer-matrix method: correspondence to the coupled-wave method

Absfract-A unified formulation of the spontaneous emission noise in semiconductor DFB lasers is presented by using a transfer-matrix approach. Analytical expressions for the noise power per unit frequency bandwidth below threshold and the spontaneous emission rate into the lasing mode are obtained based on the Green’s function method. Three DFB laser structures are analyzed: 1) a standard DFB structure with facet reflectivities, 2) a multisection DFB structure composed of n sections, which models a phase-shifted DFB laser and a multielectrode (tunable) DFB laser, and 3) a periodic layered DFB structure which models a surface-emitting DFB laser. It is shown that the spontaneous emission noise of a complicated DFB laser structure can be calculated easily by the transfer matrix of each section of the structure and its derivative to frequency.

Toshihiko Makino

Papers

Transfer-Matrix Formulation of Spontaneous Emission Noise of DFB