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.

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}*,

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

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
*η _{edge}* 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