LightPipes for Mathcad Beam Propagation Toolbox Manual version 1.3 Toolbox Routines: Gleb Vdovin, Flexible Optical B.V. Rontgenweg 1, 2624 BD Delft The Netherlands Phone: +31-15-2851547 Fax: +31-51-2851548 e-mail: [email protected] web site: www.okotech.com ©1993--1996, Gleb Vdovin Mathcad dynamic link library: Fred van Goor, University of Twente Department of Applied Physics Laser Physics group P.O. Box 217 7500 AE Enschede The Netherlands web site: edu.tnw.utwente.nl/inlopt/lpmcad ©2006, Fred van goor. 1-3 1. INTRODUCTION.............................................................................................. 1-5 2. WARRANTY .................................................................................................... 2-7 3. AVAILABILITY................................................................................................. 3-9 4. INSTALLATION OF LIGHTPIPES FOR MATHCAD ......................................4-11 4.1 System requirements........................................................................................................................ 4-11 4.2 Installation........................................................................................................................................ 4-13 5. LIGHTPIPES FOR MATHCAD DESCRIPTION ..............................................5-15 5.1 First steps.......................................................................................................................................... 5-15 5.1.1 Help ................................................................................................................5-15 5.1.2 Starting the calculations...................................................................................5-15 5.1.3 The dimensions of structures ...........................................................................5-16 5.1.4 Apertures and screens......................................................................................5-16 5.1.5 Graphing and visualisation. .............................................................................5-18 5.2 Free space propagation.................................................................................................................... 5-19 5.2.1 FFT propagation (spectral method)..................................................................5-19 5.2.2 Direct integration as a convolution: FFT approach...........................................5-22 5.2.3 Direct integration.............................................................................................5-23 5.2.4 Finite difference method..................................................................................5-23 5.2.5 Splitting and mixing beams .............................................................................5-26 5.2.6 Interpolation....................................................................................................5-29 5.2.7 Phase and intensity filters................................................................................5-30 5.2.8 Zernike polynomials........................................................................................5-31 5.2.9 Spherical co-ordinates .....................................................................................5-32 5.2.10 User defined phase and intensity filters............................................................5-34 5.2.11 Random filters.................................................................................................5-35 5.2.12 FFT and spatial filters......................................................................................5-35 5.2.13 Laser amplifier ................................................................................................5-36 5.2.14 Diagnostics: Strehl ratio, beam power..............................................................5-37 5.2.15 Polarization. ....................................................................................................5-38 5.2.16 Reflection from and transmission through multilayer coatings.........................5-40 6. EXAMPLE MODELS.......................................................................................6-45 6.1 Shearing interferometer .................................................................................................................. 6-45 6.2 Rotational shearing interferometer ................................................................................................ 6-47 6.3 Radial shear interferometer............................................................................................................ 6-49 6.4 Michelson Interferometer................................................................................................................ 6-51 6.5 Twyman-Green interferometer....................................................................................................... 6-55 1-4 6.6 Unstable laser resonator.................................................................................................................. 6-57 6.6.1 Calculation of the far field...............................................................................6-60 6.7 Propagation in a lens-like/ absorptive medium. ............................................................................ 6-63 6.8 Inverse problem: reconstructing the phase from measured intensities....................................... 6-71 6.9 Optical information processing....................................................................................................... 6-75 6.10 Generation and reconstruction of interferograms. ....................................................................... 6-77 7. COMMAND REFERENCE ..............................................................................7-81 8. REFERENCES................................................................................................8-87 1-5 1. Introduction LightPipes for Mathcad is a set of functions written in C available to Mathcad. It is designed to model coherent optical devices when the diffraction is essential. The toolbox consists of a number of functions. Each function represents an optical element or a step in the light propagation. There are apertures, intensity filters, beam-splitters, lenses and models of free space diffraction in LightPipes. There are also more advanced tools for manipulating the phase and amplitude of the light. The program operates on a large data structure, containing square two-dimensional arrays of complex amplitudes of the optical field of the propagating light beam. The LightPipes for Mathcad routines are modifications of the LightPipes C routines written by Gleb Vdovin for Unix, Linux, DOS and OS2 workstations or PC. The Mathcad version of LightPipes has a number of advantages: 1. Enhanced readability of the document with text added to the commands. 2. The graphics-, animation- and other features of Mathcad can be combined with the LightPipes commands. 3. You can use variable arguments in the function calls and handle complex data structures in a very simple way. 4. Enhanced flexibility and fast execution. Most of the commands of LightPipes for Mathcad are the same as the Unix/DOS version. Only the commands handling the in- and output of the results to disk and the plot commands have been skipped as one can use the build-in commands of Mathcad for disk communications and graphics with more advantage. The names of the commands are proceeded with the letters “LP” in order to keep the commands together in the Mathcad’s function list and to prevent the confusion with existing Mathcad functions. The arguments are tested during execution of the command and error messages appear in the case of bad arguments. (Mathcad’s “red” error boxes). 2-7 2. Warranty There is no warranty for the program, to the extent permitted by applicable law. Except when otherwise stated in writing the copyright holders and/or other parties provide the program “as is” without warranty of any kind, either expressed or implied, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose. The entire risk as the quality and performance of the program is with you. Should the program prove defective, you assume the cost of all necessary servicing, repair or correction. 3-9 3. Availability The LightPipes for Mathcad package for beam propagation is copyright ©(1993--1996) of Gleb Vdovin and ©(1998) of Fred van Goor. This document (also © of Gleb Vdovin and Fred van Goor) may be freely distributed together with the demo executables. No part of this document can be reproduced without written permission of the authors. A demo version of LightPipes for Mathcad with a limited functionality of 64x64 grid dimension and this manual are freely available from WWW: http://www.okotech.com LightPipes for Mathcad with unlimited grid dimension (limited by your computer memory) is available from: Flexible Optical B.V. Rontgenweg 1, 2624 BD Delft The Netherlands Phone: +31-15-2851547 Fax: +31-51-2851548 e-mail: [email protected] web site: www.okotech.com Additional information and more examples can be found on: http://edu.tnw.utwente.nl/inlopt/lpmcad 4-11 4. Installation of LightPipes for Mathcad 4.1 System requirements. LightPipes for Mathcad must be installed on a system with the following hardware and software: Hardware: 1. An 80386- , 80486 or Pentium based IBM or compatible computer. 2. At least 4 megabytes of memory. 3. A hard disk with at least 2 megabytes of free space. Because the calculations