Excellence in Photonic Crystal Surface Emitting Lasers (PCSELence)


This Leibniz Association’s Cooperative Excellence project is led by Ferdinand-Braun Institute (FBH) in Berlin (project coordinator: Dr. Paul Crump). Weierstrass Institute (WIAS) acts as a partner institution in this project (PIs: Dr. Mindaugas Radziunas, Dr. Jürgen Fuhrmann, Dr. Patricio Farrell; project researcher: Dr. Eduard Kuhn). A further (associated) project partner is the Center of Excellence for Photonic-Crystal Surface-Emitting Lasers at Kyoto University (led by Prof. Susumu Noda).

The project's timespan is 01.01.2023- 31.03.2026, whereas WIAS starts on 01.04.2023. The main aims of the project are modeling and design (FBH+WIAS), as well as fabrication and characterization (FBH) of novel high-power Photonic Crystal Surface Emitting Laser (PCSEL) devices. This will be achieved by combining the expertise of the cooperation partners in semiconductor laser modeling, design, fabrication, and characterization.

Short description

Semiconductor diode lasers are small, efficient, and relatively cheap devices used in many modern applications. Multiple applications require emission powers exceeding several ten Watts from a single diode and up to a few kiloWatts from a combined laser system. In this project, we consider novel Photonic Crystal Surface-Emitting Lasers (PCSELs), which, in contrast to conventional high-power edge-emitting broad-area lasers (BALs), are capable of emitting high power (up to 80 W at the moment [1]) beams of nearly perfect quality in the (z) direction, perpendicular to the (x/y) plain of active material. The critical part of PCSELs, enabling an efficient coupling of within the active layer generated optical fields and their redirection along the z axis, is a properly constructed 2-dimensional photonic crystal layer. In simple cases, this PC layer can be vertically homogeneous or consist of several vertically homogeneous layers (e.g., three layers as shown in Figure 1). In many more general cases, when the borders of the PC features are not vertical, the whole PC layer still can be reasonably well approximated by multiple very thin vertically homogeneous layers.

Figure 1: Schematics of the PCSEL with PC layer consisting of three vertically homogeneous sublayers.

The initial model to be considered and integrated numerically [2]) is derived from Maxwell equations and is a 1 (time)+2 (space) dimensional system of PDEs for complex optical fields u(t,x,y)=(u+,u-)T, v(t,x,y)=(v+,v-)T, and real carrier density N(t,x,y):

whereas the complex field functions u± and v± satisfy boundary conditions (BCs)
Besides, an efficient location of several leading modes (Λ,Θ) of the related spectral problem [3],
defined by a system of four 2-D PDEs, is of great importance when designing PCSEL devices.

Several significant challenges arising when treating the above-stated problems are a nontrivial construction of the implicitly defined 4×4 field coupling matrix C, requiring a solution of the Helmholtz problem and multiple integrations of the calculated mode profile with different separately constructed exponentially growing and decaying Green's functions, as well as simulations and (spectral) analysis of large discrete problems relating up to several million variables in large-emission-area (large L) PCSELs.

First results

Recently, we have obtained the first results in calculating the main optical modes of below-threshold operating PCSEL devices (“cold cavity case”). These calculations are beneficial when looking for PCSEL designs with low thresholds and good main mode gain separation, which is crucial when seeking a single-mode high-quality emission.

Figure 2: Spectra of the benchmark problem. Left, top panels: main eigenvalues in the system with L=2000 μm. Violet: eigenfunctions of C. Green and orange: exact eigenvalues of the decoupled 1D systems for horizontally/vertically propagating fields. Blue: eigenvalues of the full 2D problem. Bottom panels: total field intensity of five leading modes (indicated by symbols in upper panels). Right: evolution of two main eigenvalues in the discretized systems with increasing finesse of numerical mesh for two different domain sizes.

Figure 2 represents typical results of our simulations. Here we calculate a bunch of the most important modes of the discretized spectral problem (3) (see small light-blue dots in the upper-left panel); compare their eigenvalues to those of two limit-case problems (large bullets in the same panel); inspect spatial distributions of five main modes (lower-left panels); and consider the dependence of two main modes on the discretization of the domain (right-side panels). It is crucial to maximizing the real part of the eigenvalue Λ of the main mode (shift by the square box indicated eigenvalue in the upper-left panel as close to the horizontal abscissa axis as possible), increase the gain separation between two principal modes (shown, e.g., in the right-side panels), and reduce the field loss fraction of the main mode at the domain bounds (factor ηedge indicated within lower-left panels).


[1] T. Inoue et al., “Self-evolving photonic crystals for ultrafast photonics,” Nat Commun 14:50, 2023

[2] T. Inoue et al., “Comprehensive analysis of photonic-crystal surface-emitting lasers via time-dependent three-dimensional coupled-wave theory,” Phys. Rev. B 99:035308, 2019

[3] Y. Liang et al., “Three-dimensional coupled-wave analysis for square-lattice photonic crystal surface emitting lasers with transverse-electric polarization: finite-size effects,” Optics Express 20(14):15945, 2012


For further information please contact
Dr. Mindaugas Radziunas
Weierstrass-Institute for Applied
Analysis and Stochastics
Mohrenstrasse 39
10117 Berlin
Tel.: (030) 20372-441
Fax : (030) 2044975
E-mail: radziunas@wias-berlin.de
WWW: http://www.wias-berlin.de