Vibrational and Angular Stability of Optical Systems for Space Applications

87 Pages·2015·3.35 MB·English

by  Jillene Bydder

UNIVERSITY OF CRETE
INTER-INSTITUTIONALPOSTGRADUATE STUDY PROGRAMME
«OPTICS & VISION»

Vibrational and Angular Stability
of Optical Systems for Space Applications

Thesis submitted in partial fulfillment of the requirements for the
Master of Science in
Inter-Institutional Postgraduate Study Programme
“Optics and Vision“

IOANNIS DROUGKAKIS

Supervising Committee
Dimitris G. Papazoglou
Assistant Professor, Materials Science and Technology Department, UoC.
Wolf Von Klitzing
Cretan Matter Waves research group leader, IESL-FORTH
Michael I. Taroudakis
Professor, Mathematics and Applied Mathematics Department, UoC
ABSTRACT
Stability of optical systems is a critical issue for optical space applications since long
and short term fluctuations in temperature and flight induced vibrations can
dramatically affect their performance. The technical requirements in respect to the
angular positioning, optical path length, positional and beam alignment are at the
limits of current mounting and optical component fabrication technology. A number
of ongoing and proposed space missions, such as STE-QUEST, use fiber-free space-
fiber schemes in order to manipulate laser beams.
In this thesis we have focused on the analysis and the optimization of the
performance of a typical a fiber-free space-fiber optical communication link. The
receiver and transmitter subsystems were composed by a fiber connected to a fiber
coupler. Using a rigorous approach on a simplified optical system we have deduced
analytical formulas for the power coupling as a function of all system parameters and
possible misalignments of the optical components. This allowed us to optimize the
transmitter/receiver optics so that the optical system is less sensitive to
misalignments. The optimized system, composed by commercial optical components,
was numerically tested using a commercial ray tracing analysis software. The
sensitivity to misalignments was thus numerically estimated. The results were in
excellent agreement with our analytical formulation.
This thesis is a part of the “Optical Breadboard Technologies for Complex Space
Missions” project financed by the European Space Agency (ESA) and took place in
IESL-FORTH facilities.

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ΠΕΡΙΛΗΨΗ
Η σταθερότητα των οπτικών συστημάτων είναι υψίστης σημασίας για τις σχετικές
διαστημικές αποστολές , μιας και οι διακυμάνσεις στην θερμοκρασία και οι δονήσεις
που προκαλούνται κατά τη διάρκεια της πτήσης, μπορούν να επηρεάσουν σημαντικά
την απόδοση τους. Οι τεχνικές προδιαγραφές σχετικά με την ακρίβεια της
τοποθέτησης των υποσυστημάτων, τον οπτικό δρόμο και την ευθυγράμμιση την
δέσμης είναι στα όρια των σύγχρονων τεχνολογιών τοποθέτησης και κατασκευής
οπτικών. Ένας μεγάλος αριθμός διαστημικών αποστολών που είναι ήδη σε εξέλιξη ή
έχουν προταθεί, όπως το STE-QUEST , χρησιμοποιούν διατάξεις στις οποίες δέσμες
λέιζερ μεταδίδονται από οπτική ίνα σε οπτική ίνα με ελεύθερη διάδοση.
Στα πλαίσια αυτής της διπλωματικής εστιάσαμε στην ανάλυση και βελτιστοποίηση
ενός τυπικού συστήματος οπτικής σύνδεσης ίνας – ελεύθερης διάδοσης - ίνας. Τα
υποσυστήματα του πομπού και του δέκτη αποτελούνταν από μια οπτική ίνα
συνδεδεμένη με ένα οπτικό ζεύκτη ινών. Ακολουθώντας μια αναλυτική προσέγγιση
σε ένα απλοποιημένο οπτικό σύστημα αναπτύξαμε αναλυτικές σχέσεις για την
διαπερατότητα ισχύος ως συνάρτηση όλων των οπτο-μηχανικών παραμέτρων και
των πιθανών απευθυγραμμίσεων των οπτικών στοιχείων. Αυτό μας επέτρεψε να
βελτιστοποιήσουμε τα οπτικά του πομπού και του δέκτη έτσι ώστε το συνολικό
οπτικό σύστημα να είναι λιγότερο ευαίσθητο σε απευθυγραμμίσεις. Στην συνέχεια
η οπτική συμπεριφορά του βελτιστοποιημένου οπτικού συστήματος, αποτελούμενο
από εμπορικά διαθέσιμα οπτικά, εξετάστηκε αριθμητικά χρησιμοποιώντας
κατάλληλο λογισμικό ανάλυσης διάδοσης ακτινών. Με αυτό τον τρόπο μετρήθηκε
αριθμητικά η ευαισθησία στις απευθυγραμμίσεις. Τα αποτελέσματα βρέθηκαν σε
απόλυτη συμφωνία με τις αναλυτικές σχέσεις.
Η παραπάνω εργασία αποτελεί μέρος του ερευνητικού προγράμματος “Optical
Breadboard Technologies for Complex Space Missions” που χρηματοδοτήθηκε από
τον Ευρωπαϊκό Οργανισμό Διαστήματος (ESA) πραγματοποιήθηκε στις
εγκαταστάσεις του Ινστιτούτου Ηλεκτρονικής Δομής και Λέιζερ (ΙΗΔΛ) του Ιδρύματος
Τεχνολογίας και Έρευνας (Ι.Τ.Ε)
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Acknowledgements

I would like to thank my supervisor Prof. Dimitris Papazoglou for all the time he has
dedicated to my work over the past one year and for his thorough and constructive
review of this thesis. I am grateful for allowing me to work on a very interesting thesis
topic and for the patience he showed to me. I would also like to thank Dr. Wolf von
Klitzing for giving me the opportunity to be involved in a research group and for the
fruitful exchange of knowledge we had. It is a great learning experience for me to be
part of all the steps needed for constructing an optical setup, from the design phase,
which is part of my diploma thesis, to the implementation of the theoretical findings
in an optical breadboard. Finally, thanks to my family for their enduring
encouragement and understanding throughout this process.

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TABLE OF CONTENTS
Chapter 1 ....................................................................................................... 7
Introduction................................................................................................... 7
Chapter 2 ....................................................................................................... 9
Optical communication links .......................................................................... 9
2.1 Optical beam propagation ............................................................................................... 9
2.1.1 Gaussian beam modes ............................................................................................... 9
2.1.2 ABCD Matrices ......................................................................................................... 17
2.2 Optical Fibers .................................................................................................................. 22
2.2.1 Operation Principle .................................................................................................. 22
2.2.2 Fiber modes ............................................................................................................. 25
2.2.3 Single-Mode Optical Fibers...................................................................................... 28
2.2.4 APC fibers ................................................................................................................. 29
2.2.5 Coupling of Gaussian beams ................................................................................... 30
2.3Technology Review ......................................................................................................... 33
2.3.1 Fiber Couplers .......................................................................................................... 33
2.3.2 Anti-Reflection Coatings .......................................................................................... 34
Chapter 3 ..................................................................................................... 37
Theoretical analysis of power transmission in communication links ............ 37
3.1 Fiber to fiber link ............................................................................................................ 37
3.1.1 Generic fiber coupling analysis ................................................................................ 37
3.1.2 Fiber to fiber coupling ............................................................................................. 43
3.1.2 Common Misalignments .......................................................................................... 45
3.1.2.1 Longitudinal Displacement ............................................................................... 45
3.1.2.2 Lateral Displacement ........................................................................................ 46
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3.1.2.3 Tilt of the fibers ................................................................................................. 47
3.2 Fiber free-space to fiber ................................................................................................. 48
3.2.1 Generic fiber coupling analysis ................................................................................ 48
3.2.2 Commonly used configurations, perfectly aligned link ........................................... 51
3.2.2.1 Symmetric 4f system (Distance L equal to two focal lengths) .......................... 54
3.2.2.2 Distance L equal to the Rayleigh range of the collimated beam ...................... 55
3.2.2.3 Distance L equal to two times the Rayleigh range of the collimated beam ..... 56
Chapter 4 ..................................................................................................... 59
Stability Analysis .......................................................................................... 59
4.1 Rigorous Analysis ............................................................................................................ 59
4.1.1Misaligned optical system ........................................................................................ 59
4.1.2 Sensitivity analysis ................................................................................................... 59
4.1.3 Optimization ............................................................................................................ 61
4.1.4 Lens Selection .......................................................................................................... 64
4.1.5 Conclusions .............................................................................................................. 65
4.2 Optical System Analysis using optical raytracing sofware ............................................. 67
4.2.1 Optical simulation software .................................................................................... 67
4.2.2 ZEMAX introduction ................................................................................................ 68
4.2.3 Confirmation, using ZEMAX, of the validity of analytical equations ....................... 72
4.2.4 Key system performances ....................................................................................... 75
4.2.4.1 System sub-components ................................................................................... 75
4.2.4.2 Stability analysis ................................................................................................ 75
Conclusions .................................................................................................. 84
Bibliography ................................................................................................ 85

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Chapter 1
Introduction
Many optical devices used in space applications such as interferometers, telescopes and
microscopes, are based on stable optical benches, which use optical materials such as fused
quartz [1], silicon carbide, and glass ceramics like Zerodur [2, 3, 4]. One of the most important
element of these benches, is fiber-to fiber coupling. A typical fiber to fiber coupling scheme
consists of a transmitter and a receiver coupler and the optical design can be seen in Fig.1.2.
The transmitter part consists of an optical fiber coupled to a collimating lens. The collimated
beam is transmitted to the receiver coupler, which is a symmetric optical system, consisting
of a collecting lens and a fiber. A typical opto-mechanical design for a system like, commonly
used in laboratory environments, can be seen in Fig.1.3. This setup allows the manipulation
of light, such as frequency or intensity modulation, overlapping and splitting using free-space
components with low losses. A number of space missions, such as STE-QUEST, based on laser-
cooled atomic clock PHARAO use this setup for controlling many different laser beams in
frequency and amplitude, in order to cool and manipulate atomic clouds [5, 6, 7, 8]. The need
for accurate and stable breadboards comes from the fact that the beam must be coupled into
single mode optical fiber after having traversed a number of passive optical elements. The
technical requirements in respect to the angular positioning, optical path length, positional
and beam alignment, in order to achieve the high power transmission required, are at the
limits of current mounting and optical component fabrication technology. The demanding
application environment that includes long and short term fluctuations in temperature and
flight induced vibrations occur, imposes additional constrains. Bounding techniques are
crucial in order to achieve stability and reliability of the optical bench and needs to provide a
stable bond, allow precise alignment and cure reasonably fast. Examples of bonding
techniques are hydroxide-catalysis bonding [9,10,11] ,which has been successfully used in the
Gravity Probe-B telescope [12], and adhesive bonding using two component epoxy [13]. The
optical stability of such systems will be studied, using both analytical descriptions and
simulated ray-tracing.
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Chapter 2 introduces the reader to the technologies used in fiber-to-fiber coupling schemes.
A basic introduction to the component properties and techniques used in application where
high coupling efficiencies are crucial is made.
Chapter 3 provides in-depth theoretical treatment and analysis of our scheme and calculation
of values of interest and merit functions that are used to derive conditions for the stability of
a specific breadboard. A generic fiber coupling analysis, using thin lenses, has been made
describing power transmission of a perturbed Gaussian beam reaching a receiver fiber. This
analysis was applied in a simple transmitter-receiver link by correlating the input beam waist
and possible misalignments with the receiver and transmitter characteristics, obtaining
analytical equations.
Chapter 4 includes ray-tracing simulations for potential misalignments of a breadboard with
the specifications obtained by Chapter 3, using optical design software ZEMAX. We also
evaluate the generic analysis results using the Physical Optics Propagation (POP) function. The
numerical analysis made at this chapter, takes into account optical aberrations induced by
the optical elements and optical materials/surface losses which were not included in the
analysis at the previous chapter.

Fig. 1.2 Simple transmitter-receiver link optical interface

Fig. 1.3 Simple transmitter-receiver link opto-mechanical interface
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Chapter 2
Optical communication links
2.1 Optical beam propagation
2.1.1 Gaussian beam modes
A Gaussian beam is a monochromatic electromagnetic radiation with the characteristic that
the transverse magnetic and electric field amplitudes and intensity profiles are given by the
Gaussian function. This is called the fundamental mode and is the intended output of most
lasers because of its property to be focused into the most concentrated spot. The electric field
amplitude of such a beam is given by equation 2.1.
x2  y2
 exp( ) (2.1)
 w2
The spot size w used at the above equation is position dependent and in particular its
variations with distance is hyperbolic. The minimum value of w is called the beam waist radius
w0. For such a beam the Gaussian profile is maintained during propagation and is determined
by a single parameter, which is w0. The Gaussian beam is only one solution of the paraxial
Helmholtz equation.
Paraxial approximation
The propagation of harmonic optical waves is described by the Helmholtz equation:
(2 k2)(x,y,z)0, (2.2)
Where k = 2π/λ is the wavenumber,  is the wavelength, and Ψ(x, y, z) is the complex field
amplitude. Let’s assume that the wave is propagating along z axis and describe it as a carrier
wave with a slow changing amplitude u(x,y,z) :
(x,y,z)u(x,y,z)exp(ikz), (2.3)
Substituting this into the wave equation yields the reduced wave equation
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2u 2u 2u 2u
  2ik 0 (2.4)
x2 y2 z2 z
In the paraxial approximation
2u u 2u 2u 2u 2u
 2ik ,  ,  (2.5)
z2 z z2 x2 z2 y2
And we obtain the paraxial equation which is:
2 2 
(  2ik )u0 (2.6)
x2 y2 z
The general solution to the exact wave equation - which corresponds to a uniform spherical
wave diverging from a source point r0(x0, y0, z0) is given by:
exp[ik(r,r )]
u(r;r ) o (2.7)
o (r,r )
o
Where u(r;r ) is the field at point r and (r,r ) (xx )2 (yy )2 (zz )2 , and when
o o o o o
we are in the Fresnel approximation, all terms of the power series of ρ higher that the
quadratic are dropped, yielding a “paraxial-spherical wave” solution [14]
1 ik[(xx )2 (y y )2]
u(x,y,z) exp{ o o }
zz 2(zz )
o o (2.8)
1 ik[(xx )2 (y y )2]
 exp{ o o },
R(z) 2R(z)
Where R(z) is the radius of curvature and (x ,y ,z ) are coordinates of the origin. The problem
o o o
with this approximation is that the beam extents to infinity in the transverse direction.
In order to avoid this we can use complex source coordinates and a paraxial beam propagating
in the z direction can be written as:
1 x2  y2
u(x,y,z) exp(ik( ), (2.9)
q(z) 2q(z)
Where q(z)q zz is the complex radius
o o
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