Excellence in Photonic Crystal Surface Emitting Lasers (PCSELence)
Project
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.
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
[Inoue NatComm23])
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 [Inoue PRB19]
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):
 |
(1) |
whereas the complex field functions
u± and v±
satisfy boundary conditions (BCs)
 |
(2) |
Besides, an efficient location of several leading modes
(Λ,Θ) of the related spectral problem
[Liang OE12],
 |
(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.
In the frame of the PCSELence project, we have developed analytic-expression-based
algorithms for the construction of the field coupling matrix C
entering model equations (1) and (3). Our algorithms bypass computer arithmetic-induced problems
when dealing with large and small exponentials; they are fast and exact, in contrast
to approximative approaches or procedures based on numerical integration methods
[1,2].
These algorithms were explored in our numerical solver suited for resolving spectral
problems for PCSELs with multiple photonic crystal layers and large emission areas.
We demonstrated that finite difference schemes of second and higher order created
using coarse numerical meshes provide sufficient accuracy for several major
(lowest-threshold) modes of particular device designs [2,3].
Such 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.
Moreover, our solver can also be used to predict an intrinsic linewidth if the stable
single-mode operation of PCSEL is ensured [4].
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).
- [Inoue NatComm23]
T. Inoue et al.,
“Self-evolving photonic crystals for ultrafast photonics,”
Nat Commun
14:50, 2023
- [Inoue PRB19]
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
- [Liang OE12]
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
- [1]
M. Radziunas, E. Kuhn, H. Wenzel, B. King, and P. Crump,
“Calculation of optical modes in large emission area photonic crystal surface-emitting lasers,”
in Proceedings of the 23th Int. Conf. on Numerical Simulation of Optoelectronic
Devices (NUSOD 2023), Turin, Italy, September 18-21, pp. 89-90, 2023,
DOI: 10.1109/NUSOD59562.2023.10273475.
pdf file.
- [2]
M. Radziunas, E. Kuhn, H. Wenzel,
“Solving a spectral problem for large-area photonic crystal surface-emitting lasers,”
WIAS Preprint,
(3059), 2023.
- [3]
M. Radziunas, E. Kuhn, H. Wenzel, B. King, and P. Crump
“Optical mode calculation in large-area photonic crystal surface-emitting lasers,“
to appear in IEEE Photonics Journal, DOI: 10.1109/JPHOT.2024.3380532.
WIAS Preprint,
(3075), 2023.
- [4]
H. Wenzel, E. Kuhn, B. King, P. Crump, and M. Radziunas,
“Theory of the linewidth-power product of photonic-crystal surface-emitting lasers,”
(arXiv:2402.11246 [physics.optics]), 2024.
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