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1
T. Malica1, D.M. Kane1, J.P. Toomey1, and K. A. Shore2
MQ~Photonics Research Centre and Dept of Physics and Astronomy, Macquarie University, Sydney, Australia
2
School of Electronic Engineering, Bangor University, Wales, UK
Précis-Insights into analysis of an experimental semiconductor laser with external optical feedback system
gained from simulation with theoretical models.
Over the years, theoretical semiconductor laser equation models have enabled the research community to map out
semiconductor laser behavior and study dynamics. These dynamics arise on introducing a perturbation to the otherwise stable
semiconductor laser. An external cavity mirror providing optical feedback to a laser is one of the easier ways of achieving this,
as shown in Fig1. These theoretical models predict regions of stability and provide insights on chaotic behavior and other
complex phenomena, thus, informing where certain dynamics might be achieved in experiments, with lasers, within a
predefined parameter space. Some of the more well-known and widely used models are Lang-Kobayashi (L-K, limited to weak
optical feedback) [1] and the travelling wave model (TWM) [2,3]. The TWM has since evolved to the iterative TWM (ITWM)
[4,5] which incorporates multiple reflections for a multi-modal system and can predict the laser dynamics for higher levels of
optical feedback compared to the L-K model.
Previously, experiments have been performed using a GaAlAs high power laser diode lasing at 830nm semiconductor laser
and the system complexity was mapped successfully over a wide range of parameters [6]. In order to verify the accuracy of the
theoretical models we performed simulations using both L-K and ITWM with the parameters stated in Table1. We expected
similar trends as seen in high resolution maps produced experimentally. Our simulation results suggest otherwise and indicate
that varying the external feedback results in, to date, unexpected dynamics where the system transitions more than once
between complex and stable dynamics as the level of optical feedback is increased. Hence, there is a need to further critically
appraise the ITWM with respect to its validity to describe experimental results.
Since the L-K model has been extensively studied and has proven to produce accurate results for low optical feedback levels,
we use it as a benchmark to test the accuracy of the ITWM at lower-feedback levels. The results of this comparison and the
critical appraisal of the ITWM at higher levels of optical feedback will be presented.
Fig1. Schematic diagram of the laser setup with external optical feedback
using a mirror where ‘r1’, ‘r2’ and ‘r3’ are the amplitude reflectances of the
laser facets and external cavity mirror respectively while ‘τin’ and ‘τRT’ are
internal and external round trip times.
Parameters
Value
Symbol
Unit
Refractive index
Carrier lifetime
Volume of active
region
Transparency
carrier density
External cavity
roundtrip time
Wavelength
Internal cavity
length
3.4
2x109
1.5x10-16
n
τn
V
s
m-3
1.5x1023
No
m-3
0.33x10-9
τext
s
850x10-9
300x10-6
λ
Lin
m
m
Table1. Parameters used for simulations
Acknowledgement
TM is supported by an international Macquarie University Research Excellence Scholarship. The development of the iterative
travelling wave model code has been contributed to by several researchers including Lloyd Langley at University of Bath and
Paul Spencer and Zubaida Sattar at Bangor University.
[1]
[2]
[3]
[4]
[5]
[6]
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pp. 347–355, 1980.
F. Sporleder, ‘Travelling wave line model for laser diodes with external optical feedback’. Proceedings-International U.R.S.I. Symposium, 1983.
J. Mork, PhD Thesis: Nonlinear dynamics and stochastic behaviour of semiconductor lasers with optical feedback. Denmark Technical University,
1988.
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