Progress in Optics (eBook)

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2000 | 1. Auflage
611 Seiten
Elsevier Science (Verlag)
978-0-08-092951-4 (ISBN)

Infos

Progress in Optics Volume 41

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The first volume of this text was published in 1961, only a few months after the invention of the laser. This event triggered a wealth of developments, many of which were reported in the 240 review articles which were published in this series since its inception. The present volume contains seven articles covering a wide range of subjects. The first article presents a review of various optical effects in spherical and circular micro-cavities capable of supporting high-Q resonant modes (commonly referred to as morphology-dependent resonances (MDRs) or whispering gallery modes (WGMs)). The second presents a comprehensive review of the theory and practice of optical disk data storage. Other articles include discussions on delay control systems for wideband phased array antennas, and quantum statistical properties of optical beams interacting in nonlinear couplers.

Inhalt

Front Cover 1
Progress in Optics, Volume 41 4
Copyright Page 5
CONTENTS 8
CHAPTER 1. NONLINEAR OPTICS IN MICROSPHERES 16
§ 1. Introduction 18
§ 2. Cavity Modes of Microspheres 19
§ 3. Perturbation Effects on Microsphere Resonances 35
§ 4. Cavity-modified Optical Processes in Microspheres 55
§ 5. Fluorescence and Lasing in Microspheres 68
§ 6. Nonlinear Optical Processes 84
§ 7. Conclusion 104
Acknowledgements 104
References 104
CHAPTER 2. PRINCIPLES OF OPTICAL DISK DATA STORAGE 112
§ 1. Introduction 114
§ 2. What Is in an Optical Head 116
§ 3. Focusing and Tracking 119
§ 4. Mastering 130
§ 5. Substrates 133
§ 6. Magneto-Optical (MO) Recording 142
§ 7. Phase Change Media 162
§ 8. Diffraction from Periodic Structures 174
§ 9. Future Trends in Optical Disks and Drives 185
References 189
CHAPTER 3. ELLIPSOMETRY OF THIN FILM SYSTEMS 196
§ 1. Introduction 198
§ 2. Theoretical background 198
§ 3. Principles of Ellipsometry 202
§ 4. Theory of Measurements in Ellipsometry 204
§ 5. Ellipsometric Quantities of Ideal Thin Film Systems 211
§ 6. Ellipsometric Quantities of Imperfect Thin Film Systems 226
§ 7. Experimental methods 250
§ 8. Conclusion 291
Acknowledgments 293
References 293
CHAPTER 4. OPTICAL TRUE-TIME DELAY CONTROL SYSTEMS FOR WIDEBAND PHASED ARRAY ANTENNAS 298
§ 1. Introduction to Phased Array Antennas 300
§ 2. Photonic Technology in Phased Array Antennas 305
§ 3. Bulk Optics and Acousto-Optics True-Time Delay 312
§ 4. Optical Fiber True-Time Delay Lines 319
§ 5. Optical Waveguide-Based True-Time Delay Lines 339
§ 6. Substrate-Guided Wave True-Time Delay Modules 352
§ 7. Wavelength-Division Multiplexed Optical True-Time Delay Lines 358
§ 8. Summary 369
Acknowledgements 370
References 370
CHAPTER 5. QUANTUM STATISTICS OF NONLINEAR OPTICAL COUPLERS 376
§ 1. Introduction 378
§ 2. Quantum Evolution of Interacting Optical Fields 381
§ 3. Quantum Statistical Properties of Interacting Optical Fields 385
§ 4. Couplers Based on Second-Harmonic and Subharmonic Generation 390
§ 5. Couplers Based on Nondegenerate Optical Parametric Processes 407
§ 6. Couplers Based on the Kerr Effect 410
§ 7. Couplers Based on Raman and Brillouin Scattering 416
§ 8. Miscellaneous Couplers 427
§ 9. Conclusions 430
§ 10. Acknowledgments 431
References 431
CHAPTER 6. QUANTUM PHASE DIFFERENCE, PHASE MEASUREMENTS AND STOKES OPERATORS 436
§ 1. Introduction 438
§ 2. Stokes Operators and Phase Difference 440
§ 3. Quantum Relative Phase Formalisms 449
§ 4. Phase-Shift Detection in SU(2) Interferometers 469
§ 5. From Two-Mode Phase to One-Mode Phase and Back 480
§ 6. Conclusions 488
§ 7. Acknowledgement 488
References 488
CHAPTER 7. OPTICAL SOLITONS IN MEDIA WITH A QUADRATIC NONLINEARITY 498
§ 1. Introduction 500
§ 2. Derivation of the Basic Equations 506
§ 3. Modulational Instability of Continuous Plane Wave Solutions 521
§ 4. Solitons in Planar Waveguides 525
§ 5. Solitons in Periodic Waveguide Structures - Bragg Solitons 548
§ 6. Solitons and Their Bifurcations in Nonlinear Couplers 557
§ 7. Discrete Solitons in Waveguide Arrays 562
§ 8. Multidimensional Solitons 569
§ 9. Conclusions 578
Acknowledgments 579
References 580
Author Index 584
Subject Index 604
Contents of Previous Volumes 608
Cumulative Index 618

Textauszug

1

Nonlinear Optics in Microspheres

Mitchell H. Fields; Jürgen Popp; Richard K. Chang    Department of Applied Physics and Center for Laser Diagnostics, Yale University, P.O. Box 208284, New Haven, CT 06520-8284, USA

§1 Introduction

Dielectric microparticles, particularly in the form of spheres and cylinders with the radius larger than the wavelength, have attracted a diverse group of scientists and engineers. They are theorists and computationalists and also experimentalists in fields that include quantum optics, nonlinear optics, linear optics, electromagnetics, combustion diagnostics, fuel dynamics, colloid chemistry, atmospheric science, telecommunications, industrial hygiene, and pulmonary medicine. Most of the earlier research on dielectric microparticles concentrated on elastic scattering and internal absorption by spheres and infinite cylinders by using the well-developed Lorenz–Mie formalism. With the advent of modem computers and development of computationally intensive approaches (such as the T-matrix and the generalized Lorenz–Mie techniques), the determination of the scattered and internal field distributions was extended to spheroids, spheres with inclusions and finite length cylinders when these microcavities with high symmetry are illuminated by plane waves or tightly focused beams at or outside the rim.

In the late 1970s, Ashkin and Dziedzic [1977] reported on the observation of optical resonances in the radiation levitation forces exerted on evaporating liquid droplets. Soon afterwards, resonance peaks were observed in the fluorescence spectra of fluorescent polystyrene latex spheres (pls) and fluorescence and Raman scattering from silica fibers. These optical resonances are referred to now as morphology-dependent resonances (MDRs) and whispering-gallery modes (WGMs). After realization that the dielectric sphere (cylinder) was acting as a 3-d (2-d) microcavity with Q values around 108–109, lasing and a series of nonlinear optical experiments rapidly ensued on pls as well as liquid droplets, columns, and within capillary tubes. Some precaution is required in the adaptation of standard laser and nonlinear optics formalisms to such interactions in microcavities. For example, in these microcavities the concept of the phase-matching condition for plane waves needed to be recast into spatial overlap of various MDRs or WGMs, which consist of countercirculating waves within the spherical (circular) dielectric surface. Nevertheless, the standard Lorenz–Mie theory can readily calculate the wavelengths and Q of the resonances, even for the large size parameters (ratios of the circumference to the wavelength) of the microparticles used in the experiments.

Some current research is directed toward nonspherical (noncircular) dielectric microparticles. When the shape distortion amplitude is small, the powerful 1st and 2nd order time-independent perturbation theory can be used to predict the frequency splitting of the degenerate azimuthal modes and their precession frequency. When the shape distortion amplitude is large, however, the perturbation theory fails and the T-matrix method is too computer intensive even for the modem supercomputers. The recently introduced ray-dynamics approach to these resonances, where the rays become chaotic in a manner determined by the Kolmogorov–Arnold–Moser (KAM) theory of classical Hamiltonian dynamics, provides clear physical insights and can predict the Q of the deformed cavity, the directionality of the refractively leaked radiation, and the location on the deformed interface where the leakage predominantly occurs. Recent experiments with deformed quantum-cascade and liquid-droplet lasers have motivated and benefited from this ray-dynamics approach.

This chapter will briefly review the essential characteristics of all the aforementioned topics. Our work on lasing and nonlinear optical effects in microdroplets is emphasized. Because of space limitations, we have not emphasized the elegant developments of a new type of optical resonator (with Q > 1010) for cavity quantum electrodynamics (CQED) experiments and thresholdless lasers. We also have not emphasized the many current applications of microcavities in combustion diagnostics of burning fuel droplets, in telecommunication of add/drop filters for WDM systems, in chemistry of reactions without containers, and in biological airborne particle detection. We apologize to many authors and groups for leaving out some of articles because of page restrictions.

§2 Cavity Modes of Microspheres

In this section we review several treatments that explore the physical and mathematical properties of the resonance modes and interaction of light with dielectric microspheres. These modes of microspheres are commonly referred to as morphology-dependent resonances (MDRs) (Hill and Benner [1988]), whispering-gallery modes (WGMs) (Garret, Kaiser and Long [1961]) and quasi-normal modes (QNMs) (Ching, Leung and Young [1996]). Many of the novel optical properties of microspheres are associated with the electromagnetic modes of the cavity. Significant confinement of the electric field occurs at specific resonance frequencies that satisfy the appropriate boundary conditions. The modes of microspheres are confined in three dimensions, whereas the modes of Fabry–Perot cavities are confined in one dimension.

2.1 RAY AND WAVE OPTICS

The most intuitive picture describing the optical resonances of microspheres is based upon ray and wave optics. A ray of light propagating within a sphere of radius a and index of refraction m(ω) will undergo total internal reflection if the angle of incidence with the dielectric interface, θinc, is θinc ≥ θc = arcsin(1/m(ω)). The rays of a mode have the property that all subsequent bounces have the same angle of incidence. Hence, the light is confined to a band within the great circle of the sphere. A ‘caustic region’ can be defined as an inner-sphere region within the dielectric sphere to which the propagating bouncing rays are tangent. The radius of the caustic sphere is approximately the radial distance to a cord defined by a ray with θinc ≈ θc. A small fraction of the light on an MDR is contained in the caustic sphere. (Note that for the case of a perfect sphere, geometric optics does not provide a method for the light to escape as long as θinc ≥ θc. This problem is resolved by wave theory; diffraction due to the curvature of the sphere surface causes light to leak tangentially from the sphere rim.)

For the case of a sphere with circumference 2πa λ and light propagating with θinc ≈ 90 °, the resonance condition is that the optical path length is approximately equal to the circumference of the sphere. The permitted limits of n wavelengths in the dielectric is the path length for one roundtrip with wavelengths for waves that are either confined mostly within the dielectric (λ/m(ω)) or extended mostly into the surrounding air (λ):

πaλ≤n≤2πaλ/m(ω).

  (2.1)

Using the dimensionless size parameter

=2πa/λ,

  (2.2)

the resonance condition occurs for integer n in the range

≤n≤m(ω)x.

  (2.3)

The phase-matching condition for the n = m(ω)x mode and the external wave corresponds to the case where an internal ray completes one roundtrip as the nλ of the plane wave reaches the sphere surface.

The integer n can be identified as the angular momentum of the mode by equating

n≈ap≈aℏk

  (2.4)

for the case of near-glancing incidence of the ray (θinc ≥ θc). In many papers the symbol ℓ is used instead of n.

The great-circle orbit of the rays need not be confined to the x–y plane (e.g., the equatorial plane). If the normal to the orbit is inclined at an angle θ with respect to the z-axis, the z-component of the angular momentum of the mode is

=ncosθ.

  (2.5)

For a perfect sphere, all of the m modes are degenerate (with 2n + 1 degeneracy). The degeneracy is partially lifted when the cavity is axisymmetrically (along the z-axis) deformed from sphericity. For such distortions the integer values for m are ±n, ±(n – 1),…0, where the ± degeneracy remains because the resonance modes are independent of the circulation direction, i.e., clockwise or counterclockwise. Highly accurate measurements of the clockwise and counterclockwise circulating m-mode frequencies reveal a splitting due to...

Produkt-Details

• Erscheint lt. Verlag: 13.12.2000
• Mitarbeit: Herausgeber (Serie): Emil Wolf
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Optik
• Themenwelt: Technik
• ISBN-10: 0-08-092951-6 / 0080929516
• ISBN-13: 978-0-08-092951-4 / 9780080929514