Laser beam analysis, propagation, and spatial shaping techniques

Laser beam analysis, propagation, and spatial shaping techniques

James R. Leger, Univ. of Minnesota, USA

Course Description

The propagation and focusing properties of real laser beams are greatly influenced by beam shape, phase distortions, degree of coherence, and aperture truncation effects.  The ability to understand, predict, and correct these real-world effects is essential in optical engineering.   This short course develops the analytical tools for measuring and quantifying the important characteristics of a real laser beam, allowing the optical engineer to calculate the performance of the beam in a given optical system.  In addition, the intensity, phase, and polarization of laser beams can often be engineered to enhance system performance.  The course explores a wide variety of engineering approaches to beam optimization using intuitive design methods coupled with a rigorous mathematical treatment of fundamental limits.
The course starts with a basic and highly descriptive discussion of the propagation characteristics of coherent light from an ideal laser.  Simple analytical formulae are developed to calculate the properties of this ideal Gaussian beam in a complex optical system.  These concepts are extended to higher-order coherent fields, including Hermite Gaussian beams, beams with top-hat intensity shapes and “non-diffracting” beams.  Finally, the propagation characteristics of coherent light arrays are described mathematically.  A set of simple analytical equations is derived to predict the focusing ability of complex coherent light distributions, where the effects of beam intensity and phase distribution can immediately be discerned. 
Laser beam characterization methods such as M2, Strehl ratio, and TDL are reviewed.  Incoherent and partially coherent light distributions are investigated, and the focusing limits dictated by the radiance theorem are developed. Simple expressions for estimating the effects of laser aberrations and coherence on beam focusing and propagation are reviewed.  Coupling of light into single and multi-mode fibers, as well as far-field light concentration limits are explored as real-world examples.  The concept of ├ętendue is introduced as an engineering tool to optimize optical design, and simple analytical approaches are presented to estimate the effects of spatial beam shape and phase aberrations on beam concentration of incoherent light.
The course ends with a description of various beam shaping techniques.  Intensity beam shaping methods are described for applications where the phase at the target is unimportant.  Next, methods for shaping the complex light amplitude in the near- and far-field are developed.  Polarization methods including cylindrical vector beams are reviewed.  Finally, several intra-cavity beam shaping methods are shown that engineer the intensity and phase of the light inside a laser resonator and improve laser performance.

Intended Audience

Advanced beginner: This course is designed to provide laser engineers, optical system designers, and technical management professionals with a working knowledge of laser beam characterization, analysis, and modification.  Physical and intuitive explanations of most topics are designed to make the concepts accessible to a wide range of participants.

Benefits and Learning Objectives

This course will enable participants to:
  • measure the quality of a laser beam using several methods
  • interpret the meaning of various laser specifications
  • understand Gaussian laser beam properties from an intuitive standpoint
  • predict the propagation and focusing properties of non-ideal and aberrated laser beams
  • determine the concentration limits of a light field
  • design optimal beam concentration optics
  • compare different beam profiles for specific applications and calculate ideal performance
  • design beam shaping optics using polarization and phase manipulation

Instructor Biography

James LegerProf. James Leger received his BS degree in Applied Physics from the California Institute of Technology (1974) and Ph.D. degree in Electrical Engineering from the University of California, San Diego (1980). He has held previous positions at the 3M Company, and MIT Lincoln Laboratory.  He is currently professor of Electrical Engineering at the University of Minnesota, where he holds both the Cymer Professorship of Electrical Engineering and the Mr. and Mrs. George W. Taylor distinguished professorship.  His research group is studying a wide variety of optical techniques, including laser mode control and beam shaping techniques, spectral and coherent laser beam combining, optical metrology, solar energy optics, design of nonclassical imaging systems, and microoptical engineering.  Prof. Leger is currently serving as deputy editor of Optics Express, and has recently served as a member of the CLEO (US) steering committee and the Board of Directors of the Optical Society of America.
Prof. Leger has been awarded the 1998 Joseph Fraunhofer Award/Robert M. Burley Prize by the Optical Society of America, the 1998 Eta Kappa Nu outstanding teaching professor award, the 2000 George Taylor Award for Outstanding Research at the University of Minnesota, the 2006 Eta Kappa Nu Outstanding teaching Professor award, the ITSB professor of the year award (2006), the Morse Award for Outstanding Undergraduate Teaching (2006), the George Taylor Distinguished Teaching Award (2007), and the George Taylor Service Award (2008).  He has recently been inducted into the academy of distinguished teachers at the University of Minnesota.  He is a Fellow of the Optical Society of America, Fellow of the Institute of Electrical and Electronic Engineers (IEEE), and Fellow of the International Society of Optical Engineers (SPIE).