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Spie Press Book

Design and Fabrication of Diffractive Optical Elements with MATLAB
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Book Description

This book supplements the available literature on diffractive optical elements (DOEs) by equipping readers with the skills to begin designing, simulating, and fabricating diffractive optics. The design of DOEs using MATLAB is presented with simple equations and step-by-step procedures for simulation—from the simplest 1D grating to the more complex multifunctional DOEs—along with analysis of their diffraction patterns. The fundamentals of fabrication techniques such as photolithography and focused ion beam lithography are presented with basic instructions for the beginner. Examples of error analysis and error-correction techniques are also discussed. The material is supported by practical exercises and clearly commented MATLAB codes (the codes are also on an accompanying CD), making this book useful even to a novice programmer.

The coverage of topics is comprehensive and ranges from theoretical analysis of light diffraction and propagation to basic design of diffractive optical elements. This book can be recommended for undergraduate and graduate students, scientists, and engineers in industry as well as high school teachers and lecturers at universities."
-Jürgen Jahns, Chair of Micro- and Nanophotonics, FernUniversität in Hagen, Germany

Without a doubt, the authors have vast experience in the subject matter and have conveyed their expertise in a lucid manner in this excellent textbook. The MATLAB codes scattered throughout the book provide effective tools for practicing the various techniques and algorithms involved in designing DOEs.”
-Joseph Rosen, Benjamin H. Swig Chair in Optoelectronics, Ben-Gurion University of the Negev, Israel

Book Details

Date Published: 2 January 2017
Pages: 276
ISBN: 9781510607057
Volume: TT109

Table of Contents
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Table of Contents

Foreword by R. S. Sirohi
Symbols and Notation
Acronyms and Abbreviations

1 Introduction
1.1 Fundamentals of Diffractive Optics
      1.1.1 Introduction
      1.1.2 Refractive and diffractive optics
      1.1.3 Scalar diffraction formulation
1.2 Software for Designing Diffractive Optics
1.3 Concluding Remarks

2 Design of Diffractive Optical Elements
2.1 Design of Simple Diffractive Optical Elements
      2.1.1 Design and analysis of 1D gratings
      2.1.2 Design of 1D gratings with MATLAB®
      2.1.3 Design of 2D gratings
      2.1.4 Binary circular gratings
      2.1.5 Fresnel zone plates
2.2 Conclusions
2.3 Exercises

3 Design and Analysis of Advanced Diffractive Optical Elements
3.1 Design of Multilevel and Grayscale DOEs
      3.1.1 Design procedure for multilevel and grayscale gratings
      3.1.2 Design procedure for multilevel and grayscale FZPs
      3.1.3 Design procedure for multilevel and grayscale spiral phase plates
      3.1.4 Design procedure for a gradient axilens
3.2 Design of DOEs using Algorithms
      3.2.1 Design procedure of DOEs using IFTA
3.3 Design Procedure of Beam-Shaping DOEs using a Simplified Mesh Technique
      3.3.1 Mesh generation method
      3.3.2 Determination of the phase element
3.4 Conclusions
3.5 Exercises

4 Analysis of DOEs in the Fresnel Diffraction Regimes
4.1 Analysis of DOEs with the Fresnel Diffraction Formula
      4.1.1 Fresnel diffraction pattern of a circular aperture
      4.1.2 MATLAB simulations of the Fresnel diffraction pattern of a binary phase axicon
      4.1.3 MATLAB simulations of the Fresnel diffraction pattern of an axilens
      4.1.4 MATLAB simulations of the Fresnel diffraction pattern of nonperiodic DOEs
4.2 Talbot Imaging
4.3 Conclusions
4.4 Exercises

5 Substrate Aberration Correction Techniques and Error Analysis
5.1 FZP in Finite Conjugate Mode
      5.1.1 Design of FZPs in finite conjugate mode
5.2 Characterization of Substrate Aberrations
5.3 Aberration Correction Schemes
      5.3.1 Aberration correction by inclusion of a glass substrate
      5.3.2 Aberration correction during fabrication
      5.3.3 Discussion
5.4 Aberration Analysis in Fabrication and Experiments for FZPs
      5.4.1 Error in object location along the z direction
      5.4.2 Error due to a shift in the location of zones
      5.4.3 Error due to a lateral shift in the object location
      5.4.4 Error in resist thickness and duty ratio
5.5 Conclusions
5.6 Exercises
Notes and References

6 Multifunctional Diffractive Optical Elements
6.1 Modulo-2π Phase Addition Technique
      6.1.1 Comparison of a multifunctional binary DOE with two binary DOEs in tandem
      6.1.2 Design of multifunctional DOEs
      6.1.3 The composite effect of multifunctional DOEs
      6.1.4 Conclusion
6.2 Analog Method
6.3 Conclusions
6.4 Exercises

7 Computer-Generated Holographic Optical Elements
7.1 Fundamentals of CGHs
7.2 Design of Simple CGHs with MATLAB
      7.2.1 Design of 1D gratings
      7.2.2 Design of FZPs
      7.2.3 Design of diffractive axicons
7.3 Design of Multifunctional CGHs with MATLAB
      7.3.1 Design of 1D gratings
      7.3.2 Design of off-axis axicons
      7.3.3 Design of forked gratings
      7.3.4 Design of binary helical axicons
      7.3.5 Design of off-axis axilenses
      7.3.6 Accelerating beams
7.4 Multiple-Beam Interference CGH
7.5 Computer-Generated Amplitude Fourier Holograms
7.6 Computer-Generated Amplitude Fresnel Holograms
7.7 Conclusions
7.8 Exercises

8 Fabrication of Diffractive Optical Elements
8.1 Design of Lithography Files
      8.1.1 Lithography file generation with LinkCADTM
      8.1.2 Special lithography files
8.2 Photolithography
8.3 Electron Beam Lithography
      8.3.1 Substrate selection
      8.3.2 Resist selection and thickness optimization
      8.3.3 Electron beam lithography optimization
      8.3.4 Fabrication of multilevel structures
      8.3.5 Fabrication and testing results
8.4 Focused Ion Beam Lithography
      8.4.1 FIB milling on substrates
      8.4.2 FIB milling on a fiber tip
8.5 Conclusions

Appendix: MATLAB Functions
Solutions to the Exercises


Diffractive optics, if not yet a household word, is certainly a household phenomenon. Many systems encountered in our everyday world contain or use diffractive optics. A good example is DVD players or barcode scanners. Elements that work on the principles of diffraction, or diffractive optical elements (DOEs), can successfully replace refractive elements used in different systems. This is because DOEs are capable of manipulating light in ways not possible by conventional refractive optical elements. In addition, DOEs are light in weight and compact compared to their refractive counterparts. The development of this technology will encourage the conversion of bulky refractive optical systems into highly compact, lightweight diffractive optical systems. It is our belief that fabrication of diffractive optics needs to be further developed and simplified so that more diffractive elements replace refractive elements in the future. We hope that this book will ease this transition.

Several excellent books (See Chapter 1, Refs. 6, 33, and 57–59) already exist that explain the basics and important concepts in the field of DOEs. This book does not intend to replace them. Rather, the idea is to supplement the available information with a text that will equip one with the skills required to start designing, simulating, and even fabricating diffractive optics. Given the many different applications and uses of diffractive optics, the importance of this field cannot be underestimated. Surprisingly, there are only a few books that provide a hands-on approach to the field. The lacuna of such information from a single source motivated us to create a resource based on our practical experience. In this book, learning occurs with assistive MATLAB® codes that enable visualization of the ideas presented and a better understanding of the parameters controlling different aspects of light. We believe that this manner of treatment will enable a new graduate student to quickly grasp the fundamentals of diffractive optics, beginning with the design of simple DOEs and moving to more complex ones.

We hope the reader will benefit from this practical approach to designing and fabricating diffractive optical elements. Experimentalists will be able to design appropriate structures that can be used in many different applications such as spectroscopy, optical trapping, or beam shaping. The design of DOEs is presented with simple equations and step-by-step procedures for simulation—from the simplest 1D grating to the more-complex multifunctional DOEs—along with analysis of their diffraction patterns using MATLAB. The fundamentals of fabrication techniques such as photolithography, electron beam lithography, and focused ion beam lithography with basic instructions for the beginner are presented. Basic error analysis and error-correction techniques for a few cases are also discussed. It must be noted that this book will focus only on passive DOEs; SLMs are not required for demonstration. However, the MATLAB codes provided can be used for displaying DOE designs on SLMs as well. Thus, we hope that this book will help not only new students but also scientists in the industry to quickly learn techniques to help with the design, simulation, and testing of DOEs.

The book consists of eight chapters. A brief summary of the content of each chapter is as follows:

Chapter 1 introduces the fundamentals of diffractive optics and compares diffractive and refractive optics. A quick review of the theoretical formulation of diffraction are presented, along with different theoretical approximations and their validity regimes.

Chapter 2 presents the fundamentals of design and far-field analysis of simple binary DOEs such as 1D and 2D gratings, axicons, and Fresnel zone plates (FZPs). It shows the beginner how to make simple calculations to extract the intensity values and spacing between the different diffraction maxima.

Chapter 3 discusses the design, simulation aspects, and far-field analysis of multilevel and blazed DOEs such as multilevel gratings, diffractive axicons, blazed FZPs, axilenses, spiral phase plates, etc. It also discusses the basic algorithms for designing DOEs to obtain any desired intensity profile.

Chapter 4 describes the design and analysis of DOEs in the Fresnel diffraction regime to simulate diffraction patterns at different planes in the propagation direction. It also discusses some interesting phenomena such as the Talbot effect.

Chapter 5 presents the basic aberration correction techniques used to reduce and avoid errors while designing DOEs.

Chapter 6 introduces the art of creating different advanced multifunctional DOEs, along with their design, simulation, and analysis. The important properties of multifunctional DOEs are also discussed.

Chapter 7 describes the design and analysis of holographic optical elements for different applications. Computer-generated Fourier and Fresnel holography techniques are also discussed.

Chapter 8 presents the fundamentals of designing lithography files and the fabrication of DOEs using photolithography, electron beam lithography, and focused ion beam lithography, with basic fabrication recipes provided.

The content of the chapters is supported throughout by clearly commented MATLAB codes, making this book useful even to a novice programmer.

Happy Diffracting!

A. Vijayakumar and Shanti Bhattacharya
November 2016

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