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Diffractive Optics for Polarization Control of
Vertical-Cavity Surface-Emitting Lasers
DISSERTATION
to obtain the academic degree of
DOKTOR-INGENIEUR
(DR.-ING.)
from the Faculty of Engineering Science and Computer Sciences
Ulm University
by
Johannes Michael Ostermann
from Reutlingen, Germany
Referees: Prof. Dr. rer. nat. Karl Joachim Ebeling
Prof. Dr. rer. nat. Wolfgang Elsaßer¨
Dean of Faculty: Prof. Dr. rer. nat. Helmuth Partsch
Ulm, July 10th, 2007To Pierluigi Debernardi
who had the idea for this thesisAcknowledgement
This thesis would not have been possible without Pierluigi Debernardi. It was his idea
to use surface gratings for polarization control of VCSELs. By allowing me to use and
teachingmehowtousehisexcellentVELM-model,hegavemethetheoreticalbackground
necessary for this thesis. I am very grateful to him for the very deep collaboration and the
friendship we have since we met the first time at the beginning of my PhD thesis.
On the other hand, this thesis would not have been possible as well without the expertise
in VCSELs and the excellent research conditions, which were built up in the last 15 years
in the Institute of Optoelectronics at Ulm University by Prof. Dr. Karl Joachim Ebeling,
Dr.-Ing. Rainer Michalzik, and Dr.-Ing. Jurgen Mahnß. I am very grateful to them for¨ ¨
their help and support.
All students working with me during the years of this PhD thesis contributed strongly
with their semester and diploma theses to the success of surface grating VCSELs. They
all did a great job. Christof Jalics developed processing techniques for surface grating
VCSELs, Andrea Kroner did the first measurements on surface grating VCSELs, Martin
Feneberg investigated surface grating VCSELs more systematically and in more detail,
MichaelSchumanntransferredtheideaofsurfacegratingsto760-nmVCSEL,andPhilipp
Gentner helped me in building an improved measurements setup.
When I run out of epitaxial material, U-L-M photonics GmbH helped me out with one
of their excellent wafers. After we had obtained the first breaking results with surface
gratings, U-L-M photonics became interested in this technique. This opened up the pos-
sibility for some common projects. The wafer mapping station of U-L-M photonics was of
special help for me, since it allowed me to analyze thousands of surface grating VCSELs
to prove the polarization control provided by surface grating and to find the best grating
parameters. I would like to thank particularly Lin Borowski and Christian Wimmer for
their collaboration.
My special thanks go to all people I have worked with during this thesis. I would like
to mention some explicitly: The first one is Heiko Unold who taught me how to process
VCSELs.PhilippGerlachhelpedmewitheverythingthathadtobefasterthan50Hz.Felix
Mederer answered from the first day of my work on VCSELs till the day before my PhD
defenseallmyquestionsrelatedtoVCSELs,especiallytodatacomwithVCSELs.Iamalso
very thankful to Fernando Rinaldi, who managed with his ingenuity to grow in just a few
trials very good epitaxial material for 760-nm VCSELs. Markus Sondermann did not only
perform the dichroism measurements at the University of Munster together with me, but¨
he answered also with his never-ending patience all my never-ending questions about the
spin-flip-modelandpolarizationswitchesinVCSELs.GiuseppeVirone,GiuseppeAddamo,
and Oscar Peverini helped me that I felt very fast at home at the Politecnico di Torino
and they made my time there a very pleasant one. Besides that, they taught me also a
lot about electromagnetic modeling. My thanks go as well to Prof. Dr. Anders Larsson
˚and Asa Haglund, who invited me to stay and work with them for four very nice and
interesting weeks at Chalmers University.IwouldliketothankallcurrentandformermembersoftheInstituteofOptoelectronicsfor
their support. I would like to thank especially Josef Theisz, who did not only manufacture
all components I needed for my measurement setups, but also encouraged me every time
I came to his workshop. I do not want to imagine the Institute of Optoelectronics without
Susanne Menzel. She is taking care for the coffee supply and makes very, very special
doctoral caps. Both are essential ingredients for every PhD thesis. Many thanks go also
to Ihab Kardosh and Michael Riedl who took care of the computers and software at the
institute besides all their other duties. I would also like to thank Andrea Kroner and
Wolfgang Schwarz for the good time in our common office and Philipp Gerlach for our
coffee breaks on Sunday afternoons.
I am very grateful to Birgit Abler, Martin Feneberg, Jens Gotz, Christof Jalics, Andrea¨
Kroner, Rainer Michalzik, and Heiko Unold for proofreading this thesis in parts or com-
pletely before I handed it in.
Although it may seem at the end, as if everything in the years, I worked for this thesis,
was fun and went well, there have also been some hard times. I would like to thank my
girl friend Birgit Abler and my parents for their support especially during these hard and
frustrating periods.
Finally,IwouldliketothankthemembersofthePhDcommission,Prof.Dr.KarlJoachim
Ebeling, Prof. Dr. Wolfgang Els¨aßer, Prof. Dr.-Ing. Wolfgang Menzel, and Prof. Dr. Hans
Peter Großmann, for their work and that they accepted this thesis and thereby set an
endpoint to this work.Contents
1 Introduction and Motivation 1
2 Polarization Properties and Polarization Control 3
2.1 Fundamentals of VCSELs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Polarization of VCSELs: Experimental Findings . . . . . . . . . . . . . . . . 11
2.3 Polarization of VCSELs: Theoretical Explanations . . . . . . . . . . . . . . 17
2.4 Demand for and Previous Attempts on Polarization Control . . . . . . . . . 25
3 Concept and Design of Surface Gratings 31
3.1 Concept of Surface Gratings for Polarization Control . . . . . . . . . . . . . 32
3.2 Fully Vectorial, Three-Dimensional VCSEL Model . . . . . . . . . . . . . . 34
3.3 Simulation of VCSELs With a Surface Grating . . . . . . . . . . . . . . . . 41
3.4 Design of Surface Gratings. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4 Processing of Surface Grating VCSELs 55
4.1 Integration Into Fabrication Process . . . . . . . . . . . . . . . . . . . . . . 55
4.2 Definition of the Grating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3 Etching Process of the Grating . . . . . . . . . . . . . . . . . . . . . . . . . 60
5 Investigation of Grating Parameters 65
5.1 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2 Polarization-Stable Single-Mode VCSELs . . . . . . . . . . . . . . . . . . . 68
5.3 Polarization-Stable Multimode VCSELs . . . . . . . . . . . . . . . . . . . . 73
5.4 Grating Depth and Grating Period . . . . . . . . . . . . . . . . . . . . . . . 77
5.5 Yield of Polarization-Stable VCSELs . . . . . . . . . . . . . . . . . . . . . . 84
5.6 Performance of First Generation Grating VCSELs . . . . . . . . . . . . . . 88
5.7 Diffraction Induced by a Surface Grating . . . . . . . . . . . . . . . . . . . 89
5.8 VCSELs With Small Grating Depth and Large Duty-Cycle . . . . . . . . . 101
6 Polarization Control Under Demanding Conditions 105
6.1 Polarization Control Under Variation of the Substrate Temperature . . . . 105
6.2 Polarization Control Under Optical Feedback . . . . . . . . . . . . . . . . . 107
6.3 Polarization Control Under External Stress . . . . . . . . . . . . . . . . . . 113
iCONTENTS
6.4 Polarization Control Under High-Frequency Modulation . . . . . . . . . . . 116
6.5 Polarization Division Multiplexing . . . . . . . . . . . . . . . . . . . . . . . 123
7 Direct Measurement of the Dichroism 129
7.1 Underlying Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.2 Spectral Measurements at Laser Threshold . . . . . . . . . . . . . . . . . . 132
7.3 Determination of the Modal Dichroism . . . . . . . . . . . . . . . . . . . . . 133
7.4 Comparison of Measurements and Simulations . . . . . . . . . . . . . . . . 138
7.5 Modal Dichroism and OPSR . . . . . . . . . . . . . . . . . . . . . . . . . . 140
8 Inverted Grating VCSELs 143
8.1 Concept of Inverted Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . 143
8.2 Polarization Control Induced by an Inverted Grating . . . . . . . . . . . . . 146
8.3 Performance of Inverted Grating VCSELs . . . . . . . . . . . . . . . . . . . 149
8.4 Diffraction Induced by an Inverted Grating . . . . . . . . . . . . . . . . . . 151
8.5 Layer Structures Other Than Normal and Inverted . . . . . . . . . . . . . . 156
9 Grating Relief VCSELs 159
9.1 Single-Mode VCSELs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
9.2 Concept of Surface Reliefs and Surface Grating Reliefs . . . . . . . . . . . . 160
9.3 Processing of Grating Relief VCSELs . . . . . . . . . . . . . . . . . . . . . . 164
9.4 Polarization Control Induced by a Grating Relief . . . . . . . . . . . . . . . 165
9.5 Performance of Grating Relief VCSELs. . . . . . . . . . . . . . . . . . . . . 167
9.6 Diffraction Induced by a Grating Relief . . . . . . . . . . . . . . . . . . . . 169
9.7 Grating Relief VCSELs for Oxygen Sensing . . . . . . . . . . . . . . . . . . 170
10 Summary and Conclusion 177
A Layer Structure and Expansion Modes 183
B Optical Contact Lithography of Gratings 185
C Details of Technological Processes 189
D Investigated Wafers 191
E Index of Mathematical Symbols 197
F Index of Abbreviations 201
Publications 203
Bibliography 208
iiChapter 1
Introduction and Motivation
1The high number of different physical effects influencing the polarization of the emitted
light is a particularity of vertical-cavity surface-emitting laser diodes (VCSELs) [1,2].
In gas and solid state lasers the polarization of the emitted electromagnetic radiation
is not always well-defined either, but can easily be selected, for example, by inserting a
Brewster window into the laser cavity. In semiconductor edge-emitting laser diodes (EEL)
the dominant polarization is determined by the cavity and the gain anisotropies [3,4].
However, the situation is different in VCSELs. Their monolithic cavity with its cylindrical
symmetry lacks any anisotropy which could pin the polarization reliably. The same holds
for the isotropic gain provided by the quantum wells in standard VCSELs [5]. While the
polarization of the individual transverse modes in VCSELs is approximately linear, the
orientation of the polarization is a priori unknown, varies from laser to laser [6], and –
even worse – changes frequently during operation [7].
These polarization fluctuations lead to very rich and interesting phenomena from the
laser physics point of view [8–11]. Concurrently, one of the toughest challenges for laser
engineersworkingonandimprovingVCSELsistoavoidthesepolarizationfluctuationsand
torealizeVCSELswitha well-definedandstablepolarization[12–14].Greatachievements
havebeenmadeinthedesignandprocessingofVCSELsinthelastyears.Transversesingle-
mode VCSELs with optical output powers exceeding 6mW [15,16] were realized as well
as transverse multimode VCSELs with optical output powers of more than 300mW [17].
Smallthresholdcurrentsofwellbelow100μA[18],largemodulationbandwidthsexceeding
20GHz [19], and wallplug efficiencies of above 50% [20] were achieved as well. However,
the issue of polarization control of VCSELs is not yet solved in a satisfactory way.
The first VCSELs were mainly designed for data communication.Meanwhile it turned out
that VCSELs are also ideal laser sources for sensing applications like spectroscopy [21] or
1Strictly speaking, the term ’polarization’ describes the oscillation of the electric field in the plane
perpendicular to the propagation direction of the electric field. This oscillation can occur on a linear, a
circular, or an elliptical path with different orientations of its principal axes. Since VCSELs are linearly
polarized in a first approximation, the term ’polarization’ is frequently used in this thesis as a synonym
for ’orientation of the linear polarization’.
1CHAPTER 1. INTRODUCTION AND MOTIVATION
forpositionsensingasneededinopticalcomputermice.Foralltheseapplications,VCSELs
with a stable polarization are either highly desirable or even required.
Despite the efforts which have been put into the research and development of methods for
polarization control of VCSELs in the last 15 years, an overall satisfactory solution has
not been obtained yet. Up to now, the best results were achieved by epitaxial growth on
substrates with higher indices in combination with strained quantum wells for VCSELs
emitting around 960nm [22,23]. However, even with this technique, the suppression of the
weaker polarization still decreases during relaxation oscillations. Attempts to apply the
same technique to VCSELs with different emission wavelengths have only been partially
successful. Furthermore, the performance of VCSELs grown on substrates with higher
indices has not yet reached the one of standard VCSELs.
InthisPhDthesis,anewapproachforpolarizationcontrolofVCSELsisinvestigated.The
main idea is to monolithically integrate a semiconductor surface grating into the topmost
layer of the upper Bragg mirror of VCSELs, resulting in a polarization-dependent reflec-
tivity of the respective mirror. With this approach, two new methods enter the research
onandthemanufacturingprocessofVCSELs.Uptonow,VCSELhavebeenmainlysimu-
lated in a scalar way and their processing has been based on microtechnology. In contrast,
the footing of the research performed for this thesis is rigorous electromagnetic modeling
and nanotechnology.
The thesis is organized as follows: First, the fundamentals of VCSELs and their main
polarization phenomena are introduced. Subsequently, previous attempts for polarization
control are discussed. The concept of surface gratings for polarization control and a ful-
ly vectorial, three-dimensional model for electromagnetic simulations of VCSELs [24] are
presented in Chap.3. Using this model, the design of surface grating VCSELs is theoreti-
callyinvestigatedinthesamechapter,beforethefabricationprocessofgratingVCSELsis
outlinedinChap.4.Basicphenomenaofpolarization-stablesingle-andmultimodegrating
VCSELsarediscussedinChap.5andadetailedanalysisofthedependenceofthepolariza-
tion control and the overall performance of grating VCSELs on their grating parameters
is performed. The stability of the achieved polarization control is tested in Chap.6 under
demanding conditions. However, studying whether a VCSEL remains polarization-stable
under varying temperature, external optical feedback, externally applied stress, and high-
frequency modulation still does not provide sufficient quantitative information about the
effective strength of the polarization control. A method to measure this strength directly
is therefore highly desirable and is presented in Chap.7. While integrated surface gratings
provide an unrivaled polarization control, they can potentially introduce severe optical
losses due to diffraction. Therefore, the topic of Chap.8 is how these diffraction losses can
be reduced or be avoided almost completely by an improved grating design. In Chap.9, a
technique for combined mode and polarization control for polarization-stable,single-mode
VCSELs is presented, before a summary and a conclusion are given in Chap.10.
2Chapter 2
Polarization Properties and
Polarization Control of VCSELs
This chapter starts with a short introduction to VCSELs focussing on those of their prop-
ertiesthathaveaninfluenceonthepolarizationoftheiremittedelectromagneticradiation.
Subsequently, the rich polarization phenomena observed in VCSELs are discussed on the
basis of some measurements and a literature survey. The survey includes a short presen-
tation of the spin-flip model, the standard theoretical model to describe the polarization
dynamics of VCSELs. Although the effects associated with the unstable polarization of
VCSELs are not the main topic of this thesis, they are presented to demonstrate why a
special polarization control is needed in VCSELs and why such a polarization control is so
demanding as the high number of only partially or not at all successful previous attempts
for polarization control of VCSELs prove. These attempts are discussed in the last section
of this chapter.
2.1 Fundamentals of VCSELs
The basic difference between EELs and VCSELs is the propagation direction of their
generatedlight.Whilethe emissiondirectionof EELs is withinthe planeof the wafer,itis
normal to the wafer surface for VCSELs. This can be seen in Fig.2.1, which schematically
shows the layer structure of a VCSEL. Typical semiconductors on which VCSELs are
based are Gallium Arsenide (GaAs) and Indium Phosphide (InP). All VCSELs presented
inthisthesisarefabricatedfromthematerialsystemAluminumIndiumGalliumArsenide
(AlInGaAs), since such VCSEL structures have been available. However, all techniques
described in this thesis are expected to work as well for VCSELs based on InP. On top of
ausuallyn-typesubstrateandaGaAs-bufferlayer,thebottomBraggmirrorisepitaxially
grown. Above the bottom mirror, typically three closely spaced quantum wells in one
antinode of the optical standing wave inside the VCSEL resonator serve as active gain
medium. Another Bragg mirror on top of the quantum wells terminates the laser cavity.
3CHAPTER 2. POLARIZATION PROPERTIES AND POLARIZATION CONTROL
In the simplest case, top-emitting VCSELs have a large-area n-contact on the back side
of the substrate and a p-type ring contact on top of the upper Bragg mirror. Thus, in
VCSELs, the current flow and the propagation direction of the optical field are parallel to
eachother,butorthogonaltotheplaneofthequantumwells.Onthecontrary,inEELsthe
propagation directionof the optical field is orthogonal to the currentflow and in the plane
of the quantum well(s). Accordingly, the ratio of the distance which the light propagates
through the gain medium to the effective cavity length is much smaller in VCSELs than
in EELs. Consequently, the modal gain is lower in VCSELs than in EELs. Therefore,
the outcoupling losses of the mirrors and the internal losses in the non-active layers of a
VCSEL have to be very small to achieve lasing operation.
^z´=[001]
light
^y´=[110]
^p - contact x´=[110]
top Bragg mirroroxide }
quantum wells bottom Bragg mirror}
current substrate
n - contact
Figure 2.1: Schematic diagram of a typical VCSEL together with the coordinate system
and its orientation with respect to the crystal axes as it is used in this thesis.
To realize an emission orthogonal to the wafer on the one hand and to achieve the high
required mirror reflectivity on the other hand, distributed Bragg reflectors (DBRs) turned
outtobethekeyelementofVCSELs[25–27].SuchBraggmirrorsconsistofanalternating
1sequence of layers with high and low refractive indices and quarter-wavelength (λ/4)
thickness. In a Bragg mirror, the electromagnetic fields reflected at the single interfaces
are in-phase which each other due to the optical path difference of a multiple of half the
wavelength and the additional phase change of π, which occurs when light is reflected at
an optical denser medium. Thus, the reflectivity of Bragg mirrors is virtually only limited
by the losses due to absorption and scattering inside the mirrors [28,29]. For top-emitting
VCSELs, the upper mirror usually consists of 20 to 25 layer pairs and the bottom mirror
of more than 30. In this way, the reflectivity of both mirrors typically exceeds 99.5% [28].
Though the reflectivity of Bragg mirrors is slightly higher for incident waves polarized
1In this thesis, the vacuum wavelength is denoted by λ . In contrast to that, the term wavelength refers0
to the material wavelength presented by the symbol λ.
4

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