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Diffractive Optics: Design, Fabrication, and Test
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Book Description

This book provides the reader with the broad range of materials that were discussed in a series of short courses presented at Georgia Tech on the design, fabrication, and testing of diffractive optical elements (DOEs). Although there are not long derivations or detailed methods for specific engineering calculations, the reader should be familiar and comfortable with basic computational techniques. This text is not a 'cookbook' for producing DOEs, but it should provide readers with sufficient information to assess whether this technology would benefit their work, and to understand the requirements for using the concepts and techniques presented by the authors.

Book Details

Date Published: 29 December 2003
Pages: 260
ISBN: 9780819451712
Volume: TT62
Errata

Table of Contents
SHOW Table of Contents | HIDE Table of Contents
Preface / xi
Chapter 1
Introduction / 1
1.1 Where Do Diffractive Elements Fit in Optics? / 1
1.2 A Quick Survey of Diffractive Optics / 2
1.3 A Classic Optical Element: The Fresnel Lens / 6
1.4 Light Treated as a Propagating Wave / 7
1.5 A Physical Optics Element: The Blazed Grating / 11
1.6 Fanout Gratings / 13
1.6.1 Designing a fanout grating / 14
1.7 Constructing the Profile: Optical Lithography / 14
1.8 A Theme / 15
Chapter 2
Scalar Diffraction Theory / 17
2.1 Rayleigh-Sommerfeld Propagation / 17
2.2 Fourier Analysis / 24
2.2.1 The Dirac delta function / 25
2.2.2 The convolution theorem / 26
2.3 Using Fourier Analysis / 27
2.4 Diffraction Efficiency of Binary Optics / 28
2.4.1 The square-wave grating / 29
2.4.2 Approximating the blazed grating / 31
2.5 Extended Scalar Theory / 32
2.6 Conclusion / 34
References / 35
Chapter 3
Electromagnetic Analysis of Diffractive Optical Elements / 37
3.1 Scalar Limitations / 37
3.2 Plane-wave Spectrum Method / 39
3.3 Electromagnetic Diffraction Models / 44
3.3.1 Modal method / 45
3.3.2 Finite-difference time-domain method / 50
3.4 Effective Media Theory / 54
References / 56
Chapter 4
Diffractive Lens Design / 57
4.1 Basics of Lens Design / 57
4.1.1 Describing an optical system / 57
4.1.2 The lensmaker's equation / 59
4.1.3 Chromatic aberration / 60
4.1.4 Third-order errors / 63
4.1.5 Ray intercept curves / 65
4.2 Diffractive Optics Lens Design / 66
4.2.1 The diffractive lens / 67
4.2.2 The phase profile / 68
4.2.3 Generating a single-element design / 69
4.2.4 Design of a kinoform lens / 69
4.2.5 A simplification / 70
4.3 Efficiency of Multilevel Diffractive Lenses / 71
4.3.1 At other wavelengths / 71
4.3.2 Efficiency of diffractive lenses / 73
4.3.3 A diffractive optics lens and its limitations / 74
4.4 Hybrid Lenses / 75
4.4.1 Correcting chromatic aberration with diffractive surfaces / 76
4.4.2 Entering a singlet / 77
4.4.3 Example: diffractive surface on a quartz window / 78
4.4.4 Combining refractive and diffractive surfaces / 80
References / 82
Chapter 5
Design of Diffraction Gratings / 83
5.1 Introduction / 83
5.1.1 Splitting a wavefront / 83
5.1.2 A 1x3 grating / 84
5.1.3 Complex fanouts / 87
5.2 Design Approaches / 88
5.3 Design Variables / 90
5.4 Direct Inversion / 92
5.5 Iterative Design / 95
5.5.1 Bidirectional algorithms / 96
5.5.2 Simulated annealing / 100
5.5.3 Genetic algorithms / 105
5.6 Conclusion / 112
References / 113
Chapter 6
Making a DOE / 115
6.1 The Profile / 115
6.2 Photolithography: A Method for DOE Fabrication / 116
6.3 From Equation to Component / 117
6.3.1 Converting function to form / 117
6.3.2 Example: 1x2 beam splitter / 118
6.3.3 Mask generation / 119
6.4 Interplay between Fabrication and Optical Design / 121
6.4.1 Optical functionality / 121
6.4.2 Fabrication constraints / 121
6.4.3 Effects of thin-film coatings / 122
6.4.4 Materials / 124
6.5 Facilities and Substrates / 125
6.5.1 Clean rooms and DOE fabrication / 125
6.5.2 Substrate testing and cleaning / 128
6.6 Fabrication of DOEs / 130
References / 130
Chapter 7
Photolithographic Fabrication of Diffractive Optical Elements / 133
7.1 Photolithographic Processing / 133
7.1.1 Photoresist coatings / 133
7.1.2 Spin coating photoresist / 135
7.1.3 Exposure and development / 135
7.1.4 Etching / 140
7.2 Binary Optics / 143
7.3 Conclusion / 147
References / 147
Chapter 8
Survey of Fabrication Techniques for Diffractive Optical Elements / 149
8.1 Lithographic Techniques / 149
8.1.1 Direct writing / 149
8.1.2 Interferometric exposure / 150
8.1.3 Gray-scale lithography / 151
8.1.4 Near-field holography / 153
8.1.5 Refractive micro-optics / 155
8.2 Direct Machining / 157
8.2.1 Mechanical ruling / 157
8.2.2 Diamond turning / 157
8.2.3 Other methods of direct machining / 159
8.3 Replication / 159
8.3.1 Plastic injection molding / 159
8.3.2 Thermal embossing / 160
8.3.3 Casting and UV embossing / 161
8.3.4 Soft lithography / 161
8.4 Comparison of Fabrication Methods for DOEs / 163
References / 164
Chapter 9
Testing Diffractive Optical Elements / 167
9.1 Metrology / 167
9.1.1 Optical microscopy / 167
9.1.2 Mechanical profilometry / 168
9.1.3 Atomic force microscopy / 169
9.1.4 Scanning electron microscopy / 170
9.1.5 Phase-shifting interferometry / 173
9.2 Testing Optical Performance / 174
9.2.1 Scatterometer / 175
9.2.2 Charge-coupled device / 176
9.2.3 Rotating slit scanners / 178
9.2.4 Array testing / 179
9.3 Effects of Fabrication Errors on DOE Performance / 180
References / 184
Chapter 10
Application of Diffractive Optics to Lens Design / 187
10.1 Introduction / 187
10.1.1 The aberrations of a diffractive lens / 187
10.1.2 Adapting optical design for diffractive elements: the sweatt model / 189
10.2 Diffractive Lenses / 190
10.2.1 The f lens / 191
10.2.2 Landscape lens / 193
10.2.3 Diffractive telescopes / 195
10.2.4 Superzone lenses / 197
10.2.5 Staircase lenses / 199
10.3 Hybrid Lenses / 200
10.3.1 Infrared objectives / 201
10.3.2 Infrared telescopes / 202
10.3.3 Eyepieces / 203
10.4 Thermal Compensation with Diffractive Optics / 206
10.4.1 Coefficient of thermal defocus / 206
10.4.2 Thermal effects on a mounted lens / 207
10.4.3 Hybrid lens and mount / 208
References / 210
Chapter 11
Additional Applications of Diffractive Optical Elements / 213
11.1 Introduction / 213
11.2 Multiple Lens Applications / 214
11.2.1 Lens arrays for optical coupling / 214
11.2.2 Microlenses for beam steering / 215
11.2.3 Lens arrays for sensors / 216
11.2.4 Beam homogenizers / 217
11.3 Beam-Shaping Applications / 218
11.3.1 Focusing beam shapers / 218
11.3.2 Laser resonator design / 220
11.4 Grating Applications / 220
11.4.1 Beam deflectors, splitters, and samplers / 220
11.4.2 Spot array generators / 221
11.4.3 Talbot array illuminators / 222
11.4.4 Controlled-angle diffusers / 224
11.5 Subwavelength Gratings / 225
11.5.1 Anti-reflection surfaces and wavelength filters / 226
11.5.2 Wave plates / 227
11.5.3 Subwavelength diffraction gratings and lenses / 228
11.6 Integration and Modules / 229
11.7 Example Application Area: Optical Communications / 230
11.7.1 Data communications versus telecommunications / 231
11.7.2 Example: parallel hybrid array for data communications / 231
11.8 Conclusion / 232
References / 233
Index / 237

Preface

This work is based on a series of short courses in diffractive optics that have been presented at Georgia Institute of Technology since 1994. The course was started as a hands-on workshop that provided basic theory on diffractive optics and then allowed participants to progress through a series of exercises on the design, fabrication, and testing of diffractive optical elements (DOEs). This type of course was difficult to present because of the intensive support required for the labs. When one of the authors (TJS) and two of his fellow graduate students got their doctorates, we lost all our good, cheap help and we had to radically change the course. The new offering relied on additional lectures and demonstrations to replace the exercises. When we finished with this revision, we knew that the material in the restructured course could serve as the basis for a text on diffractive optics.

This book is intended to provide the reader with the broad range of materials that were discussed in the course. We assume the reader is familiar with basic computational techniques and can stand the sight of an integral or two. It is not our intention to overwhelm the reader with long derivations or provide detailed methods for specific engineering calculations. Instead we introduce the concepts needed to understand the field. Then a number of simple examples, which someone can use as a check on their initial baseline calculations, are presented.While this text is not a "cookbook" for producing DOEs, it should provide readers with sufficient information to be able to assess whether the application of this technology would be beneficial to their work and give them an understanding of what would be needed to make a DOE.

In the work presented in the course we describe two methods of generating the binary masks needed to produce the diffractive optics elements. One is a costly technique that yields state-of- the-art results and is the basis for most commercial production. The second, exploited by the diffractive optics group at Georgia Tech, uses standard desktop publishing techniques and PostScript output to produce masks with modest feature sizes. The latter technique is useful for simple prototyping and for educational demonstrations. In this text we have separated the two approaches by discussing the high-resolution technique as the primary mask fabrication path. For those who want to get their feet wet, we have provided a few boxes set off from the main narrative that describe how the PostScript methods can replace the standard techniques at a savings of time and money, but with a loss of performance.

After a brief introductory chapter on the field, we provide a description of the theoretical basis for the operation of diffractive optical devices. In most cases a scalar theory description will suffice, particularly as an introduction. However, as the wavelength of the radiation approaches the size of the various features in the element, a more precise theory that includes a vector description of the electric fields in the vicinity of the surface is required. Next, a series of chapters describe the procedures used to design elements that can be incorporated into conventional lens designs, in addition to procedures for designing periodic structures and unconventional devices. This is followed with a description of the various steps in the fabrication and test of diffractive optical elements. Finally, we provide a short survey of a number of applications in which these devices are making an impact on today's technology.

We would like to acknowledge the contributions to the course made by some of the earlier lecturers and assistants. Tom Gaylord at Georgia Tech and Joe Mait of the Army Research Laboratory provided lectures in scalar and vector theory. Willie Rockward and Menelous Poutous (along with TJS) helped put together the exercises for the workshop and conducted the labs. The authors also wish to thank their wives, who put up with a lot. They never have figured out how we could argue so fervently over those little ripples in a piece of quartz.

Donald C. O'Shea
Thomas J. Suleski
Alan D. Kathman
Dennis W. Prather
September 2003


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