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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 14 — May. 10, 2008
  • pp: 2630–2636

Robust chirped mirrors

Omid Nohadani, Jonathan R. Birge, Franz X. Kärtner, and Dimitris J. Bertsimas  »View Author Affiliations

Applied Optics, Vol. 47, Issue 14, pp. 2630-2636 (2008)

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Optimized chirped mirrors may perform suboptimally, or completely fail to satisfy specifications, when manufacturing errors are encountered. We present a robust optimization method for designing these dispersion-compensating mirror systems that are used in ultrashort pulse lasers. Possible implementation errors in layer thickness are taken into account within an uncertainty set. The algorithm identifies worst-case scenarios with respect to reflectivity as well as group delay. An iterative update improves the robustness and warrants a high manufacturing yield, even when the encountered errors are larger than anticipated.

© 2008 Optical Society of America

OCIS Codes
(310.6860) Thin films : Thin films, optical properties
(320.0320) Ultrafast optics : Ultrafast optics
(310.4165) Thin films : Multilayer design

ToC Category:
Thin Films

Original Manuscript: December 19, 2007
Revised Manuscript: March 4, 2008
Manuscript Accepted: March 7, 2008
Published: May 6, 2008

Omid Nohadani, Jonathan R. Birge, Franz X. Kärtner, and Dimitris J. Bertsimas, "Robust chirped mirrors," Appl. Opt. 47, 2630-2636 (2008)

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  1. R. Szipöcs, K. Ferencz, C. Spielmann, and F. Krausz, “Chirped multilayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett. 19, 201-203 (1994). [CrossRef] [PubMed]
  2. F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Scheuer, M. Tilsch, and T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22, 831-833 (1997). [CrossRef] [PubMed]
  3. N. Matuschek, F. X. Kärtner, and U. Keller, “Theory of double-chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197-208 (1998). [CrossRef]
  4. F. X. Kaertner, U. Morgner, T. R. Schibli, E. P. Ippen, J. G. Fujimoto, V. Scheuer, G. Angelow, and T. Tschudi, “Ultrabroadband double-chirped mirror pairs for generation of octave spectra,” J. Opt. Soc. Am. B 18, 882-885 (2001). [CrossRef]
  5. B. Sullivan and J. Dobrowolski, “Deposition error compensation for optical multilayer coating: I. Theoretical description,” Appl. Opt. 31, 3821-3835 (1992). [CrossRef] [PubMed]
  6. V. Pervak, A. Tikhonravov, M. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Opt. 87, 5-12 (2007).
  7. V. Yakovlev and G. Tempea, “Optimization of chirped mirrors,” Appl. Opt. 41, 6514-6520 (2002). [CrossRef] [PubMed]
  8. A. Ben-Tal and A. Nemirovski, “Robust convex optimization,” Math. Oper. Res. 23, 769-806 (1998). [CrossRef]
  9. A. Ben-Tal and A. Nemirovski, “Robust optimization--methodology and applications,” Math. Program. 92, 453-480(2002). [CrossRef]
  10. D. Bertsimas and M. Sim, “Robust discrete optimization and network flows,” Math. Program. 98, 49-71 (2003). [CrossRef]
  11. D. Bertsimas and M. Sim, “Tractable approximations to robust conic optimization problems,” Math. Program. 107, 5-36(2006). [CrossRef]
  12. D. Bertsimas, O. Nohadani, and K. M. Teo, “Robust optimization in electromagnetic scattering problems,” J. Appl. Phys. 101, 074507 (2007). [CrossRef]
  13. J. A. Kong, Electromagnetic Wave Theory (EMW, 2000).
  14. J. R. Birge and F. X. Kärtner, “Efficient analytic computation of dispersion from multilayer structures,” Appl. Opt. 45, 1478-1483 (2006). [CrossRef] [PubMed]
  15. J. R. Birge and F. X. Kärtner, “Efficient optimization of multilayer coatings for ultrafast optics using analytic gradients of dispersion,” Appl. Opt. 46, 2656-2662 (2007). [CrossRef] [PubMed]
  16. O. D. Mücke, R. Ell, A. Winter, J. Kim, J. R. Birge, L. Matos, and F. X. Kärtner, “Self-referenced 200 mHz octave-spanning ti:sapphire laser with 50 attosecond carrier-envelope phase jitter,” Opt. Express 13, 5163-5169 (2005). [CrossRef] [PubMed]
  17. D. Bertsimas, O. Nohadani, and K. M. Teo, “Robust optimization for unconstrained simulation-based problems,” Oper. Res. (to be published).
  18. P. Verly, “Fourier transform technique with refinement in the frequency domain for the synthesis of optical thin films,” Appl. Opt. 35, 5148-5154 (1996). [CrossRef] [PubMed]
  19. ILOG CPLEX, “High-performance software dor mathematical programming and optimization,” http://www.ilog.com/products/cplex (2007).
  20. A. Tikhonravov, M. Trubetskov, and G. DeBell, “Applictions of the needle optimization technique to the design of optical coatings,” Appl. Opt. 35, 5493-5508 (1996). [CrossRef] [PubMed]

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