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Fundamentals of Micro-Optics

From optical fundamentals to advanced applications, this comprehensive guide tomicro-optics covers all the key areas for those who need an in-depth introductionto micro-optic devices, technologies, and applications. Topics covered range frombasic optics, optical materials, refraction, and diffraction, to micromirrors, microlenses,diffractive optics, optoelectronics, and fabrication. Advanced topics, such as tunableand nano-optics, are also discussed. Real-world case studies and numerous workedexamples are provided throughout, making complex concepts easier to follow, whilstan extensive bibliography provides a valuable resource for further study. With exer-cises provided at the end of each chapter to aid and test understanding, this is an idealtextbook for graduate and advanced undergraduate students taking courses in optics,photonics, micro-optics, microsystems, and MEMS. It is also a useful self-study guidefor research engineers working on optics development.

Hans Zappe is Professor of Micro-Optics in the Department of Microsystems Engi-neering at the University of Freiburg, Germany. He has 20 years’ experience working onoptical micro- and nanosystems, integrated optics, and semiconductor lasers, and he isinternationally renowned for his teaching and research. He has previously authored twotextbooks, and his current research interests include the use of micro-optics for medicalapplications and the development of tunable micro-optical components and systems.

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“. . . presents this exciting field of research comprehensively and gives in-depth insightinto its key aspects of passive and active micro-optics . . . an exciting and inspiringread for anyone in this field of research, written by one of the leading scientists ontunable micro-fluidics. . . Most felicitous are the very good compromise between com-pactness, completeness, readability, and clearness, the huge number of exercises withthe instructor-only manual, the extensive bibliography, the perspectives for applicationtoday and tomorrow, and finally the fascinating application oriented case studies. . .Graduates, young and senior scientists and engineers will apply this book with enthusi-asm and success. Congratulations on this extended volume.”

Hartmut Hillmer, Universität Kassel

“. . .an excellent and comprehensive overview of the science and practice of minia-turized optical systems. . . The comprehensive coverage, thoughtful explanations, andmany well-chosen examples and problems make this an excellent text for a course onthe fundamentals of micro-optics, and its clear and concise style makes it ideal for self-studies.”

Olav Solgaard, Stanford University

“. . .an excellent textbook that offers, within one cover, a broad sampling of micro-optical devices and technologies along with a treatment of the relevant physical funda-mentals with sufficient depth to support real engineering. The textbook will be embracedboth by students who are seeing these concepts for the first time and by practicing engi-neers who will find it a useful reference for day-to-day design work. Professor Zappe’sstyle is light and entertaining, but he shows attention to detail and careful notation thatstudents will appreciate. Throughout the work, he shares his passion for the historyand context of optical device engineering, and the extensive bibliography is a valuablegateway for further in-depth study.”

David Dickensheets, Montana State University

“. . .a comprehensive summary of an exciting new field by a well-known researcher whohas himself made many important contributions. The text is well written and accessi-ble, with many references to real-world examples. . . The text is up to date, with goodcoverage of modern themes such as micro-electro-mechanical systems, electrowet-ting, polymer optoelectronics, quantum dots, plasmonics, and optical metamaterials. . .The figures and photographs are well chosen, and contain examples from the leadingresearchers in the field. The illustrative examples and tutorial problems are well thought-out and instructive.”

Richard Syms, Imperial College London






Fundamentals ofMicro-Optics

HANS ZAPPEUniversity of Freiburg, Germany






C A M B R I D G E U N I V E R S I T Y P R E S S

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Library of Congress Cataloging in Publication dataZappe, Hans P.Fundamentals of micro-optics / Hans Zappe.

p. cm.Includes bibliographical references.ISBN 978-0-521-89542-2 (hardback)1. Integrated optics. 2. Optical MEMS. 3. Optics.4. Optical instruments. I. Title.TA1660.Z366 2010621.36′93–dc22

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On ne peut me connaîtremieux que tu me connais. . .






Contents

Preface page xiAcknowledgments xiiiNotation xv

Part I Essential optics 1

1 Introduction 3

1.1 Optics: history in a nutshell 41.2 Micro-optics: a smaller nutshell 101.3 Micro-optics for the home: the DMD 14

2 The physics of light 17

2.1 Basic electromagnetics 172.2 Wave propagation 252.3 Electromagnetic waves 302.4 Polarization 362.5 Wavefronts 402.6 Gaussian beams 46

3 Optical materials 55

3.1 Refractive index 563.2 Dispersion 683.3 Attenuation 773.4 Glass 823.5 Semiconductors 863.6 Other materials 93

4 Optical interfaces 101

4.1 Reflection and refraction 1014.2 Reflected and transmitted fields 1064.3 Power transmission and reflection 1124.4 Internal reflection 1144.5 Evanescent field 119






viii Contents

5 Interferometry 125

5.1 Coherence and interference 1255.2 Interferometers 1355.3 Optical multilayers 150

Part II Micro-optics 167

6 Reflective micro-optics 169

6.1 Reflection 1696.2 Planar mirrors 1726.3 Nonplanar mirrors 1756.4 Micromirrors 1816.5 Adaptive micro-optics 1896.6 Micromirrors: case studies 193

7 Refractive micro-optics 203

7.1 Lens fundamentals 2047.2 Imaging 2127.3 Advanced lenses 2257.4 Primary aberrations 2357.5 Chromatic aberrations 2447.6 Microlenses: case studies 248

8 Diffractive micro-optics 265

8.1 Diffraction 2668.2 Practical apertures 2708.3 Gratings 2838.4 Diffractive microlenses 2998.5 Diffractive micro-optics: case studies 310

9 Guided-wave micro-optics 321

9.1 Waveguides: ray-optic model 3229.2 Waveguides: electromagnetic model 3379.3 Channel waveguides 3499.4 Waveguide characterization 3549.5 Waveguide components 3639.6 Optical fibers 3699.7 Waveguide micro-optics: case studies 379

10 Active micro-optics 393

10.1 Physics of light emission 39310.2 Light-emitting diodes 40310.3 Laser diodes 411






Contents ix

10.4 Photodetectors 42810.5 Phase and intensity modulators 43710.6 Other active components 44610.7 Active micro-optics: case studies 452

11 Micro-optical fabrication 463

11.1 Basic semiconductor processing 46411.2 Self-assembly lenses 46611.3 Lithography for microlenses 47211.4 Replication 48011.5 Specialized processes 48511.6 Assembly 489

Part III Neoteric optics 499

12 Tunable micro-optics 501

12.1 Liquid microlenses 50212.2 Membrane microlenses 50812.3 LCD-based tunable micro-optics 51412.4 Tunable diffractive micro-optics 51612.5 A tunable micromenagerie 520

13 Fluidic micro-optics 523

13.1 Optofluidics 52413.2 Fluidic waveguides 52413.3 Optofluidic lasers 52513.4 Fluidic microlenses 53013.5 Filters and displays 53113.6 Other optofluidic concepts 533

14 Nano-optics 535

14.1 Nanophotonics 53514.2 Photonic crystals 53714.3 Plasmonics 55214.4 Metamaterials 556

References 558Index 605






Preface

Certains hommes parlent durant leur sommeil. Il n’y a guère que les conférenciers pour parler pendant lesommeil des autres.1

Alfred Capus

Microsystems have evolved from laboratory curiosities to pervasive constituents of acolorful spectrum of technical products. We can shake our MP3 players to change thesong order; print on square meters of paper at 600 dot per inch resolution; have our doc-tors perform on-the-spot diagnostics; interact with computer games through our bodymotions; or have our lives saved by an inflated airbag: all these are possible because amicrosystem is embedded somewhere, usually as invisible as it is indispensable.

The micro-electro-mechanical systems that first emerged from university laborato-ries in the 1980s combined mechanics with the technologies of electronics, leadingto the term MEMS. But the technology has expanded enormously since then, so thatthe microelectronics and micromechanics of the germinal MEMS field now includemicrofluidics, microacoustics, micromagnetics, microchemistry, microbiology, and, notleast, micro-optics. The integration of these disparate disciplines into highly functionalmicrosystems with myriad applications is a key reason for the explosive development ofthese technologies, and as a result, the essence of much microsystems research is nowoften highly interdisciplinary.

Of these diverse disciplines, optical microsystems have seen particularly strongdevelopment, due primarily to the insatiable demand for communications bandwidth.Long- and medium-range telecommunications networks are almost completely opti-cal, and it is the availability of micro-optical components, such as laser diodes,microlenses, fiber couplers, photodetectors, modulators and optical switches, and theirintegration into complex communications subsystems, that allows us to convey hun-dreds of petabytes about the planet. . . daily.

Micro-optics developed as a branch of classical optics in the latter half of the twen-tieth century, and focused initially on miniaturized refractive lenses and novel forms ofdiffractive optics. In recent years it has begun to meld with the capabilities of microsys-tems such that the fields of micro-optics, optical microsystems, integrated optics, andoptical MEMS share many technologies, components, and envisaged applications. Thus

1 “Some people talk in their sleep. Lecturers talk while other people sleep.” Alfred Capus (1857–1922),French journalist and playright.






xii Preface

if we consider “micro-optics” in this text, we do so in the context of numerous otheroverlapping disciplines, and realize that the field is now much more than microscopiclenses and clever holograms.

As a result, whereas optical telecommunications continues to provide considerableimpetus for further development of optical microsystems, the range of micro-opticalapplications has expanded significantly. Beyond the laser-based reader heads used inconventional optical data storage, and the micromirror arrays on which many beamersrely, micro-optics is found in systems ranging from clinical instrumentation, includingintra-corporal imaging and advanced optical medical diagnostics, to advanced scientificimaging concepts, with which astronomers use MEMS-based adaptive optical mirrorsfor wavefront correction to compensate for atmospheric distortion. As an increasingspectrum of industrial manufacturers becomes aware of the capabilities of micro-optics,the applications spectrum will likewise grow.

We therefore address the varied aspects of the micro-optics field in the text that fol-lows, and run the gamut from the basics of classical optics to advances in nanophoton-ics. The scope is wide, but the focus is on the engineering of micro-optics: the readershould feel confident in the analysis or design of a micro-optical component or systemafter ploughing through the text. If, in addition, a fascination with photons ensues, I willhave the same feeling of success as I do after holding an optics lecture in which no oneaudibly snored.

Freiburg and Zurich, January 2010






Acknowledgments

That this text saw completion is due in no small part to contributions from a great manypeople, all with better things to do than provide me with materials, pictures, data, orinformation. It is with sincere gratitude that I acknowledge the selfless support of themany students, senior scientists, colleagues, and random victims who happened to be inthe lab at the wrong time who all cheerfully lent me a hand.

I am particularly grateful to many present and past members of the Laboratoryfor Micro-optics in the Department of Microsystems Engineering at the University ofFreiburg for their unwavering support, and also to many of my past students for theircontributions. Thanks are due to Bernd Aatz for the fringes of Chapters 5, 7, and 8, andall the ZEMAX simulations in Chapter 7; to Stefan Reichelt, now at SeeReal Technolo-gies, Dresden (D), for the lens profiles in Chapter 5; to Khaled Aljasem and AndreasFischer, the latter now at Chalmers University of Technology, Göteborg (S), for themicromirror photos of Chapter 6; to David Kallweit, now at the Fraunhofer Institute forPhotonic Microsystems, Dresden (D), for his mirror pictures in Chapter 6 and gratingstructures of Chapter 8; to Armin Werber, now at Carl Zeiss SMT, Oberkochen (D),for all the pneumatics and balloon pictures in Chapter 6, the pneumatic microlens pro-cess of Chapter 11, and the membrane microlens diagrams and photos of Chapter 12;to Christoph Friese, now at Robert Bosch in Reutlingen (D), for his SU-8 adaptive opti-cal mirrors, presented in Chapter 6; to Fabian Zimmer, now at the Fraunhofer Institutefor Photonic Microsystems, Dresden (D), for the polymer lens profile in Chapter 7; toAndreas Mohr, now at the Fraunhofer Institute for Solar Energy Systems, Freiburg (D),for the embossed Fresnel lens in Chapter 7; to Daniel Hofstetter, now at the Univer-sité de Neuchâtel (CH), for the DBR grating photograph of Chapter 8, the Michelsoninterferometer displacement sensor presented in Chapter 9, and the photograph of thequantum cascade laser of Chapter 10; to Eva Geerlings, now at Sick AG, Waldkirch (D),and her colleagues at the Fraunhofer Institute for Applied Solid State Physics, Freiburg(D), for the photos of the external cavity structure of Chapter 8; to Dennis Hohlfeld,now at the Holst Center of IMEC, Eindhoven (NL), for the thermo-optic filter photo-graph of Chapter 8, and the silicon optical bench with fibers in Chapter 11; to BerndMaisenhölder, now at Oerlikon Balzers (CH), for the Mach–Zehnder-based refractiveindex sensor of Chapter 9; to Robert Gehrke for the LED photograph and spectra ofChapter 10; to Jens Fiala and Niklas Weber for the photograph of the implantable pulseoxymeter in Chapter 10; to Daniel Mader for the photos of the molded PDMS micro-optical/microfluidic structures in Chapter 11 and the multi-chamber microlens picture






xiv Acknowledgments

of Chapter 12; to Holger Krause, now working on oil platforms off the coast of Nigeria,for the sol-gel lens photos of Chapter 11; to Wolfgang Mönch for the photoresist reflowlens pictures of Chapter 11; to Michael Engler, who now has his own optical designcompany, for the mold and injection-molded Fresnel lens of Chapter 11; to FlorianKrogmann, now at IST AG, Wattwil (CH), for the silicon optical bench of Chapter 11and the liquid microlens pictures of Chapter 12; to Thorsten Faber, now at the Fraun-hofer Institute for the Mechanics of Materials, Freiburg (D), for the actuated liquidlenses of Chapter 12; to Ryaz Pasha Shaik for the two-dimensional repositionable liq-uid lens of Chapter 12; to Khaled Aljasem and Wei Zhang for the membrane lens dataof Chapter 12; and to Christoph Schlägl and Yaxiu Sun for the bandgap calculations and2D photonic crystal photos of Chapter 14.

In addition, I am most indebted to Wolfgang Mönch, Andreas Seifert, Daniel Mader,Philipp Waibel, Philipp Müller, and Yaxiu Sun for reading through portions of themanuscript and providing corrections and useful comments. Additional and repeatedthanks go to Daniel Mader for putting up with inane LATEX questions; to Simon Dreherfor writing the LATEX routine that allows the citations at the start of each chapter;to Philipp Waibel for compensating for my inadequacies in Mathematica; to ClaudiaDuppé for taming my propensity for excessive hyphenation; and to Nadja Katthagenfor keeping the wolves at bay when I needed a few hours without someone desperatelyclamoring for the Dean’s opinion or signature on something.

I also extend warm thanks to friends and colleagues distributed about the globe fortheir generous contributions of photos and figures representing some cutting-edge workin micro-optics. Thank you to Markus Rossi of Heptagon Oy (SF and CH) for theFresnel-like diffractive lens and the DOE of Chapter 8; to Oliver Ambacher and Wolf-gang Bronner of the Fraunhofer Institute for Applied Solid State Physics (D) for thephotograph of the OEIC chip in Chapter 9; to Kerry Vahala of Caltech (USA) for thedisk laser photograph in Chapter 10; to James Harris of Stanford University (USA) forthe SEM of the tunable VCSEL in Chapter 10; to George Whitesides of Harvard Uni-versity (USA) for the diagrams of his optofluidic dye laser of Chapter 13; to DemetriPsaltis and Wuzhou Song of the EPFL (CH) for the schematics and optical characteris-tics of their opto-fluidic DFB lasers of Chapter 13; to Jason Heikenfeld and KaichangZhou of the University of Cincinnati (USA) for the photos of their electrowetting dis-play of Chapter 13; to Susumu Noda of Kyoto University (JP) for the characteristics andphotos of his photonic crystal resonant cavities in Chapter 14; to Martin Wegener of theKarlsruhe Institute of Technology (D) for the photo of his split ring metamaterials inChapter 14; to Mark Reed of Yale University (USA) for his nanowires in Chapter 14; toShawn-Yu Lin of the Rensselaer Polytechnic Institute (USA) for his bent photonic crys-tal waveguides of Chapter 14; to Kent Choquette of the University of Illinois (USA) forthe photonic crystal on a VCSEL in Chapter 14; and to Philip Russell of the Max PlanckInstitute for the Science of Light (D) for his sampler of photonic crystal cross-sectionsof Chapter 14.

Finally, I extend my appreciation to all the Microsystems Engineering students whoprovided suggestions and corrections based on preliminary versions of the text used inthe Mikrooptik and Optical Microsystems courses.






Notation

List of symbols

Notes:

• Vector quantities are given in boldface type.• SI units are given except for those cases where non-SI units are traditional.

a aperture dimension ma spacing between cells (period) of a photonic crystal mA area m2

A aperture function –b aperture dimension mB magnetic flux density Wb/m2

BW bandwidth Hzc speed of light in vacuum m/sC contrast –d spacing or displacement md penetration depth of evanescent field mD aperture diameter mD dispersion parameter ps/km · nmDM fiber dispersion due to the material ps/km · nmDT total fiber dispersion ps/km · nmDWG fiber dispersion due to the waveguide ps/km · nmD electric flux density C/m2

E electric field (scalar) V/mE electric field (vector) V/mE energy JEa electric field at a given point in an aperture V/mEB electric field of backward propagating wave V/mEc conduction band energy eVEC electric field due to diffraction from a circular aperture V/mED electric field due to diffraction from dual slits V/mEF electric field of forward propagating wave V/mEg energy gap eV






xvi Notation

Ei electric field at a given point in an image V/mEi electric field incident on an interface V/mEN electric field due to diffraction from N slits V/mEr electric field reflected from an interface V/mER electric field due to diffraction from a rectangular aperture V/mES electric field due to diffraction from a 1D slit V/mEt electric field transmitted through an interface V/mEv valence band energy eVEx(y) x-directed electric field in a waveguide V/mE0 magnitude of electric field V/mE ′

0 electric field pre-factor for diffraction integrals V/m2

f focal length mfC focal length for red wavelengths mfd focal length of the diffractive part of a hybrid lens mfF focal length for blue wavelengths mfi focal length inside a medium, or on image side of lens mfo focal length on object side of lens mfr focal length of the refractive part of a hybrid lens mf0 focal length outside a medium mF force NF finesse –FFK Franz–Keldysh coefficient m2/V2

Fi transmission matrix for thin film i –f/# f-number (of a lens) –g circular aperture radius mg(ν) lineshape function Hz−1

h Planck’s constant Jsh height of the source of a ray above the optical axis mh half of the waveguide core thickness mH magnetic field (vector) A/mHi magnetic field incident on an interface A/mHr magnetic field reflected from an interface A/mHt magnetic field transmitted through an interface A/mI current AI optical intensity W/m2

Id photodetector dark current AImax maximum optical intensity W/m2

Imin minimum optical intensity W/m2

Is photodetector signal current AI(z) optical intensity as function of position W/m2

I(ν) optical intensity as function of frequency W/m2

I ′ optical power WJ current density A/m2






Notation xvii

k propagation constant m−1

k wavevector m−1

kB Boltzmann constant J/KkI imaginary part of the wavevector m−1

kr radial propagation constant (for diffraction) m−1

kR real part of the wavevector m−1

kx x-directed propagation constant m−1

kxg x-directed propagation constant inside waveguide core m−1

kxL x-directed propagation constant in lateral evanescent field m−1

ky y-directed propagation constant m−1

kyc y-directed propagation constant in waveguide cap m−1

kyg y-directed propagation constant in waveguide core m−1

kys y-directed propagation constant in waveguide substrate m−1

kz z-directed propagation constant m−1

k0 wavevector in free space m−1

k0 propagation constant in free space m−1

K spring constant N/mL length mLc coherence length mLC overlap length in a waveguide coupler mLopt optical path length mLx lateral waveguide curve transition distance mLz axial waveguide curve transition distance mLπ coupling length for waveguide proximity coupler mm mass kgm azimuthal index of Zernike polynomial –m diffraction order –m zone number in a diffractive Fresnel-like lens –m waveguide mode number –me electron mass kgm′ waveguide mode number for a mirror waveguide –m∗ electron effective mass kgM magnification (for a Gaussian beam) –MT transverse magnification –MT (C) transverse magnification for red wavelengths –MT (F ) transverse magnification for blue wavelengths –M magnetization Wb/m2

n refractive index –n maximum order of Zernike polynomial –n carrier concentration cm−3

nA refractive index of ambient in liquid lens systems –nc refractive index of waveguide cap material –nc refractive index of fiber cladding material –






xviii Notation

nc electron density in the conduction band cm−3

nC refractive index at Fraunhofer C-line –ncladding refractive index of the waveguide cladding material –ncore refractive index of the waveguide core material –nd refractive index at Fraunhofer d-line –ne extraordinary refractive index –ne refractive index at Fraunhofer e-line –ne electron density cm−3

nF refractive index at Fraunhofer F-line –ng refractive index of waveguide or fiber core material –ni refractive index, incident side of interface –nL refractive index inside a lens –no ordinary refractive index –ns refractive index of waveguide substrate material –nt refractive index, transmitted side of interface –nv electron density in the valence band cm−3

n0 refractive index outside a lens –N waveguide effective index –N number (of atoms, spots, . . .) –NA numerical aperture –NAwg numerical aperture of a waveguide facet –NEP noise-equivalent power WNi number of illuminated grating periods –Nm

n normalization factor for Zernike polynomial –P polarization C/m2

P number of phase levels in binary optics –Pd dark power (in a photodetector) WPopt input optical power (in a photodetector) WQ charge CQ quality factor –r distance mr reflectivity –r linear electro-optic (Pockels) coefficient m/Vr 3D spatial vector mr contour vector (for a contour integral) mra aperture radial dimension mrAiry radius of Airy disk mri image radial dimension mrg fiber core radius mrTE TE reflection coefficient –rTM TM reflection coefficient –r0 radius mR reflectance –






Notation xix

R radius of curvature mR aperture / image spacing, for diffraction mR spectrometer resolution –R responsivity A/WRL Gaussian beam radius of curvature, left (input) mRm

n radial function of Zernike polynomial –RR Gaussian beam radius of curvature, right (output) mR(z) Gaussian beam radius of curvature mR1 radius of curvature of left lens surface mR2 radius of curvature of right lens surface ms sag height (of a lens) ms quadratic electro-optical (Kerr) coefficient m2/V2

S surface vector (for a surface integral) m2

S Poynting vector (for energy transfer) W/m2

S scalar power density W/m2

S scale factor for microlens size –SGH Goos–Hänchen shift mSi spacing between lens and image mS/N signal-to-noise ratio –So spacing between lens and object mt time st transmittivity –t waveguide core thickness mtc coherence time stmax maximum thickness of a Fresnel-like diffractive lens mtPR initial photoresist thickness for reflow microlens mtstep height of a phase step for a Fresnel-like diffractive lens mtTE TE transmission coefficient –tTM TM transmission coefficient –T period sT temperature KT transmittance –v velocity m/svg group velocity m/svp phase velocity m/sV Abbe number –V volume m−3

V visibility –V Verdet constant (magneto-optics) rad/TmVπ modulator voltage required for phase shift of π VVcyl volume of a photoresist cylinder before microlens reflow m3

Vhemi volume of a hemispherical microlens after reflow m3

w width m






xx Notation

wx width in the x direction mwy width in the y direction mWE electric energy density J/m3

WH magnetic energy density J/m3

W (z) Gaussian beam (half-) width mW0 Gaussian beam waist (half-) width mW0L Gaussian beam waist (half-) width at left (input) mW0R Gaussian beam waist (half-) width at right (output) mxa aperture x dimension (for diffraction) mxi image x dimension (for diffraction) my height of the intersection of a ray with the lens surface mya aperture y dimension (for diffraction) myi image y dimension (for diffraction) myi image size myo object size mzi distance between image and focal point mzL spacing between Gaussian beam waist and lens, left (input) mzo distance between object and focal point mz0 Rayleigh range (half of depth of focus) mz0L Rayleigh range (half of depth of focus) at left (input) mz0R Rayleigh range (half of depth of focus) at right (output) mzR spacing between Gaussian beam waist and lens, right

(output)m

Z impedance ΩZ0 impedance of free space ΩZm

n Zernike polynomial –

α absorption coefficient m−1

α evanescent decay constant m−1

α blaze angle (for blazed gratings) radα thermal coefficient of expansion K−1

αdB logarithmic absorption coefficient dB/mαwg waveguide loss m−1

α0 residual absorption losses in a laser material m−1

β z-directed propagation constant in a waveguide m−1

β0 Bragg (resonance) condition in a 1D periodic structure m−1

β1D propagation constant for coupled waves in a periodicstructure

m−1

γ damping coefficient s−1

γ optical gain m−1

γth threshold gain m−1

Γ phase retardation radΓ confinement factor, for waveguides –δ phase shift between two electric fields rad






Notation xxi

∆rmin optical resolution m∆x spacing between peak and first minimum in an Airy disk m∆β detuning from resonance in a periodic structure m−1

∆λ linewidth m∆λFP free spectral range m∆ν linewidth Hz∆νFP free spectral range Hzε dielectric constant –εd permittivity of a dielectric layer F/mεm permittivity of a material F/mε0 permittivity of free space F/mζ dummy variable –η efficiency –η electrowetting parameter –ηabs absolute efficiency (of a grating) –ηabs relative efficiency (of a grating) –θc critical angle radθdiv divergence angle due to diffraction radθi angle of incidence radθo angle of diffraction radθpe external polarization (Brewster) angle radθpi internal polarization (Brewster) angle radθr angle of reflection radθt angle of transmission radθtilt maximum tilt angle of a micromirror radθV contact angle with applied bias radθ0 contact angle with no applied bias radΘ polarization rotation angle radκ coupling coefficient for waveguide proximity coupler m−1

κm coupling coefficient in coupled wave analysis m−1

λ wavelength mλB blaze wavelength mλC wavelength of Fraunhofer C-line mλd wavelength of Fraunhofer d-line mλe wavelength of Fraunhofer e-line mλF wavelength of Fraunhofer F-line mλ0 wavelength in free space mΛ spatial period (e.g., of a grating) mµ magnetic constant –µm permeability of a material H/mµ0 permeability of free space H/mν frequency Hzνd Abbe number based on Fraunhofer d-line –






xxii Notation

νD Abbe number for diffractive lens –νe Abbe number based on Fraunhofer e-line –ξ opto-thermal expansion coefficient K−1

ξd opto-thermal expansion coefficient of a diffractive lens K−1

ξr opto-thermal expansion coefficient of a refractive lens K−1

ρ charge density C/m3

σ conductivity Ω−1m−1

σlv interfacial energy between liquid and vapor J/m2

σsl interfacial energy between substrate and liquid J/m2

σsv interfacial energy between substrate and vapor J/m2

τ lifetime sυ(x) step function –φ phase radφ tilt of polarization ellipse radφ(z) Gouy phase shift radΦ(x, y) phase function of a diffractive lens radΦ(ν) optical energy density per volume per frequency J/m3HzΦν optical energy density per volume J/m3

χ susceptibility –ψ(x) envelope function of Gaussian beam V/mΨ(x, y) phase function of a DOE wrapped to 2π radω angular frequency rad/sωp plasma frequency rad/sω0 resonance frequency rad/s

List of acronyms and abbreviations

1D one-dimensional2D two-dimensional3D three-dimensionalAFM atomic force microscopeAPS active pixel sensorAR anti-reflectionAWG arrayed waveguide gratingBBO barium borateBD Blu-ray discCA chromatic aberrationCCD charge-coupled detectorCD compact discCMOS complementary metal oxide semiconductorCOC cyclo-olefin copolymerCRT cathode ray tubeCVD chemical vapor deposition






Notation xxiii

DBR distributed Bragg reflector (laser)DFB distributed feedback (laser)DI de-ionized (water)DOE diffractive optical elementDOF depth of focusDVD digital versatile discEAP electroactive polymerEDFA erbium-doped fiber amplifierEWOD electrowetting-on-dielectricsFBG fiber Bragg gratingfcc face-centered cubicFOG fiber-optic gyroFSR free spectral rangeFT Fourier transformFTTH fiber-to-the-homeFWHM full width at half-maximumGaAs gallium arsenideGGG gadolinium gallium garnetHEBS high-energy beam sensitive (glass)HeCd helium–cadmiumHEMT high electron mobility transistorHeNe helium–neonHR high-reflectionIBM ion beam millingITU-T International Telecommunication UnionInP indium phosphideIR infraredITO indium tin oxideKDP KH2PO4

KTP KTiOPO4

LBO lithium triborateLCD liquid crystal displayLED light-emitting diodeLiNbO3 lithium niobateLPCVD low-pressure chemical vapor depositionLSF line spread functionLTCC low-temperature co-fired ceramicMEH-PPV poly(2-methoxy-5-(2’ethyl-hexoxy)-1,4-phenylene-vinylene)MEMS microelectromechanical systemsµTAS micro-total-analysis systemsMMI multimode interference couplerMOEMS micro-opto-electromechanical systemsMOS metal-oxide-semiconductor






xxiv Notation

MOSFET metal-oxide-semiconductor field-effect transistorMOMS micro-opto-mechanical systemsMSM metal-semiconductor-metal (photodetector)MUMPS multi user MEMS processesNA numerical apertureNEP noise-equivalent powerNIR near infraredOCT optical coherence tomographyOEIC optoelectronic integrated circuitOMEMS opto-micro-electromechanical systemsOPD optical path differenceOPL optical path lengthOXC optical cross-connectPC polycarbonatePCF photonic crystal fiberPDMS polydimethylsiloxanePDOT poly(3, 4-ethylene-dioxythiophene)PECVD plasma-enhanced chemical vapor depositionPEDOT alternative for poly(3, 4-ethylene-dioxythiophene)PFPE perfluoropolyetherPIC photonic integrated circuitPLC planar lightwave circuitPLZT lead-lanthanum zirconate-titanatePMMA poly methyl methacrylatePOF plastic optical fiberPPV poly-(para-phenelyne vinylene)PS polystyrenePSD position-sensitive detectorPSF point spread functionPTFE polytetrafluoroethylene (Teflon©)QCL quantum cascade laserQCSE quantum-confined Stark effectRGB red, green, blueRIBE reactive ion beam etchingRIE reactive ion etchingrms root mean squareSA spherical aberrationSEM scanning electron microscopeSERS surface-enhanced Raman spectroscopySHG second harmonic generationSI Système InternationalSiOB silicon optical benchSLED superluminescent light-emitting diode






Notation xxv

SMD surface mount deviceSMSR side-mode suppression ratioSOA semiconductor optical amplifierSOI silicon-on-insulatorSPR surface plasmon resonanceSRAM static random access memorySUMMiT Sandia ultra-planar multilevel MEMS technologySXGA super extended graphics arrayTDLAS tunable diode laser absorption spectroscopyTE transverse electricTEM transverse electromagneticTIR total internal reflectionTM transverse magneticUV ultravioletVCSEL vertical-cavity surface-emitting laserVOA variable optical attenuatorWDM wavelength division multiplexingYAG yttrium aluminum garnetYIG yttrium iron garnetYVO yttrium aluminum vanadate






fundamentals of micro-opticsassets.cambridge.org/.../9780521895422_frontmatter.pdffundamentals of...

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