OSA's Digital Library

Advances in Optics and Photonics

Advances in Optics and Photonics


  • Editor: Bahaa E. A. Saleh
  • Vol. 2, Iss. 3 — Sep. 30, 2010

Angular dispersion: an enabling tool in nonlinear and quantum optics

Juan P. Torres, Martin Hendrych, and Alejandra Valencia  »View Author Affiliations

Advances in Optics and Photonics, Vol. 2, Issue 3, pp. 319-369 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (1465 KB) Open Access

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The dispersive properties of materials, i.e., their frequency-dependent response to the interaction with light, in most situations determines whether an optical process can be observed. Although one can always search for a specific material with the sought-after properties, this material might be far from optimum or might not even exist. Therefore, it is of great interest to develop methods that could tune the dispersive properties of a medium independently of the working frequency band. Pulses with angular dispersion, or pulse-front tilt, precisely allow us to achieve this goal. In this tutorial, we show the basics of how angular dispersion can manage to tune the dispersion parameters that characterize the propagation of light in a medium, thus permitting the observation and application of various optical processes in nonlinear and quantum optics that could not be realized otherwise. To keep the focus on first principles, the list of topics addressed is not exhaustive. More specifically, we consider the role of angular dispersion for pulse stretching and compression, broadband second-harmonic generation, the generation of temporal solitons in nonlinear χ ( 2 ) media, the tunable generation of terahertz waves by means of optical rectification of femtosecond pulses, and the tuning of the frequency correlations and of the bandwidth of entangled paired photons.

© 2010 Optical Society of America

ToC Category:
Nonlinear Optics

Original Manuscript: December 18, 2009
Revised Manuscript: April 12, 2010
Manuscript Accepted: April 16, 2010
Published: May 19, 2010

Virtual Issues
(2010) Advances in Optics and Photonics

Juan P. Torres, Martin Hendrych, and Alejandra Valencia, "Angular dispersion: an enabling tool in nonlinear and quantum optics," Adv. Opt. Photon. 2, 319-369 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. I. Newton, Opticks: or a Treatise of the Reflections, Refractions, Inflections and Colours of Light, 4th ed. (William Innys, 1730), http://books.google.com/books?id=XXu4AkRVBBoC.
  2. Y. R. Shen, Principles of Nonlinear Optics (Wiley-Interscience, 2002).
  3. P. N. Butcher, D. Cotter, Elements of Nonlinear Optics (Cambridge Univ. Press, 1991).
  4. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  5. Richardson Gratings, Diffraction Grating Handbook (Newport, 2000), http://gratings.newport.com/information/handbook/handbook.asp.
  6. H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1983).
  7. O. E. Martínez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59, 229–232 (1986). [CrossRef]
  8. O. E. Martínez, “Grating and prism compressors in the case of finite beam size,” J. Opt. Soc. Am. B 3, 929–934 (1986). [CrossRef]
  9. J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28, 1759–1763 (1996). [CrossRef]
  10. J. Hebling, K. L. Yeh, M. C. Hoffmann, B. Bartal, K. A. Nelson, “Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities,” J. Opt. Soc. Am. B 25, B6–B19 (2008). [CrossRef]
  11. V. G. Dimitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Crystals (Springer, 1997). [CrossRef]
  12. J. P. Torres, S. Carrasco, L. Torner, E. W. Van Stryland, “Frequency doubling of femtosecond pulses in walk-off-compensated N-(4-nitrophenyl)-L-prolinol,” Opt. Lett. 25, 1735–1737 (2000). [CrossRef]
  13. R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, P. Foggi, “Matching of group velocities by spatial walk-off in collinear three-wave interaction with tilted pulses,” Opt. Lett. 21, 973–975 (1996). [CrossRef] [PubMed]
  14. R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, P. Foggi, “A collinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–464 (1998). [CrossRef]
  15. E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969). [CrossRef]
  16. S. Szatmari, P. Simon, M. Feuerhake, “Group-velocity-dispersion-compensated propagation of short pulses in dispersive media,” Opt. Lett. 21, 1156–1158 (1996). [CrossRef] [PubMed]
  17. O. E. Martínez, J. P. Gordon, R. L. Fork, “Negative group-velocity dispersion using refraction,” J. Opt. Soc. Am. A 1, 1003–1006 (1984). [CrossRef]
  18. R. L. Fork, O. E. Martínez, J. P. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett. 9, 150–152 (1984). [CrossRef] [PubMed]
  19. J. C. Diels, W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1995).
  20. J. Hebling, Z. Márton, “Theory of spectroscopic devices,” J. Opt. Soc. Am. B 23, 966–972 (2006). [CrossRef]
  21. J. P. Gordon, R. L. Fork, “Optical resonator with negative dispersion,” Opt. Lett. 9, 153–155 (1984). [CrossRef] [PubMed]
  22. O. E. Martínez, “Hybrid prism-grating ultrashort pulse compressor,” Opt. Commun. 83, 117–122 (1986). [CrossRef]
  23. S. Akturk, X. Gu, E. Zeek, R. Trebino, “Pulse-front tilt caused by spatial and temporal chirp,” Opt. Express 12, 4399–4410 (2004). [CrossRef] [PubMed]
  24. X. Gu, S. Akturk, R. Trebino, “Spatial chirp in ultrafast optics,” Opt. Commun. 242, 599–604 (2004). [CrossRef]
  25. J. A. Fullop, J. Hebling, “Applications of tilted-pulse-front excitation,” in Recent Optical and Photonic Technologies, K. Y. Kim, ed. (Inteh, 2010), chap. 11, http://sciyo.com/books/show/title/recent-optical-and-photonic-technologies?PHPSESSID=0imuiv8409jhevei6sb4toh0d5
  26. C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761 (1982). [CrossRef]
  27. R. L. Fork, C. H. Brito Cruz, P. C. Becker, C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation of femtosecond optical pulses,” Opt. Lett. 12, 483–485 (1987). [CrossRef] [PubMed]
  28. D. Strickland, G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985). [CrossRef]
  29. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, 1991). [CrossRef]
  30. Y. Zaouter, J. Boullet, E. Mottay, E. Cormier, “Transform-limited 100 μJ340 MW pulses from a nonlinear-fiber chirped-pulse amplifier using a mismatched grating stretcher-compressor,” Opt. Lett. 33, 1527–1529 (2008). [CrossRef] [PubMed]
  31. A. Yariv, Optical Electronics in Modern Communications (Oxford Univ. Press, 1997).
  32. R. W. Boyd, Nonlinear Optics (Academic, 2008).
  33. A. Yariv, Quantum Electronics (Wiley, 1975).
  34. P. W. Milonni, J. H. Eberly, Lasers (Academic, 1988).
  35. G. Szabó, Zs. Bor, “Frequency conversion of ultrashort pulses,” Appl. Phys. B 58, 237–241 (1994). [CrossRef]
  36. O. E. Martínez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25, 2464–2468 (1989). [CrossRef]
  37. V. D. Volosov, S. G. Karpenko, N. E. Kornienko, V. L. Strizhevskii, “Method for compensating the phase-matching dispersion in nonlinear optics,” Sov. J. Quantum Electron. 4, 1090–1098 (1975). [CrossRef]
  38. T. R. Zhang, H. R. Choo, M. C. Downer, “Phase and group velocity matching for second harmonic generation of femtosecond pulses,” Appl. Opt. 29, 3927–3933 (1990). [CrossRef] [PubMed]
  39. A. Dubietis, G. Valiulis, G. Tamosauskas, R. Danielius, A. Piskarskas, “Nonlinear second-harmonic pulse compression with tilted pulses,” Opt. Lett. 22, 1071–1073 (1997). [CrossRef] [PubMed]
  40. G. Szabó, Zs. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990). [CrossRef]
  41. B. Richman, S. Bisson, R. Trebino, E. Sidick, A. Jacobson, “Efficient broadband second-harmonic generation by dispersive achromatic nonlinear conversion using only prisms,” Opt. Lett. 23, 497–499 (1998). [CrossRef]
  42. A. Schober, M. Charbonneau-Lefort, M. Fejer, “Broadband quasi-phase-matched second-harmonic generation of ultrashort optical pulses with spectral angular dispersion,” J. Opt. Soc. Am. B 22, 1699–1713 (2005). [CrossRef]
  43. M. J. Ablowitz, Solitons and the Inverse Scattering Transform (Society for Applied and Industrial Mathematics (SIAM), 1981). [CrossRef]
  44. P. G. Drazin, R. S. Johnson, Solitons: an Introduction (Cambridge Univ. Press, 1989). [CrossRef]
  45. N. N. Akhmediev, A. Ankiewicz, Solitons: Nonlinear Pulses and Beams (Chapman & Hall, 1997).
  46. A. Hasewaga, Y. Kodama, Solitons in Optical Communications (Clarendon, 1995).
  47. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980). [CrossRef]
  48. M. Segev, B. Crosignani, A. Yariv, B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992). [CrossRef] [PubMed]
  49. C. R. Menyuk, R. Schieck, L. Torner, “Solitary waves due to χ(2):χ(2) cascading,” J. Opt. Soc. Am. B 11, 2434–2443 (1992). [CrossRef]
  50. L. Torner, D. Mazilu, D. Mihalache, “Walking solitons in quadratic nonlinear media,” Phys. Rev. Lett. 77, 2455–2458 (1996). [CrossRef] [PubMed]
  51. S. Carrasco, J. P. Torres, L. Torner, F. Wise, “Walk-off acceptance for quadratic soliton generation,” Opt. Commun. 191, 363–370 (2001). [CrossRef]
  52. R. Schieck, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996). [CrossRef]
  53. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995). [CrossRef] [PubMed]
  54. X. Liu, L. J. Qian, F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999). [CrossRef]
  55. P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, A. Piskarskas, “Observation of temporal solitons in second harmonic generation with tilted pulses,” Phys. Rev. Lett. 81, 570–573 (1998). [CrossRef]
  56. X. Liu, K. Beckwitt, F. W. Wise, “Two-dimensional optical spatiotemporal solitons in quadratic media,” Phys. Rev. E 62, 1328–1340 (2000). [CrossRef]
  57. F. Wise, P. Di Trapani, “The hunt for light bullets–spatiotemporal solitons,” Opt. Photon. News 13(2), 29–32 (February 2002).
  58. J. Hebling, K.-L. Yeh, K. A. Nelson, M. C. Hoffmann, “High-power THz generation, THz nonlinear optics, and THz nonlinear spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 14, 345–353 (2008). [CrossRef]
  59. K. L. Vodopyanov, “Optical generation of narrow-band terahertz packets in periodically-inverted electro-optics crystals: conversion efficiency and optimal laser pulse format,” Opt. Express 14, 2263–2276 (2006). [CrossRef] [PubMed]
  60. J. Hebling, G. Almasi, I. Z. Kozma, J. Kuhl, “Velocity matching by pulse front tilt for large area THz-pulse generation,” Opt. Express 10, 1161–1166 (2002). [CrossRef] [PubMed]
  61. A. G. Stepanov, J. Kuhl, I. Z. Kozma, E. Riedle, G. Almasi, J. Hebling, “Scaling up the energy of THz pulses created by optical rectification,” Opt. Express 13, 5762–5768 (2005). [CrossRef] [PubMed]
  62. J. Hebling, A. G. Stepanov, G. Almasi, B. Bartal, J. Kuhn, “Tunable THz pulse generation by optical rectification of ultrashort pulses with tilted pulses,” Appl. Phys. B 78, 593–599 (2004). [CrossRef]
  63. M. C. Hoffmann, K. L. Yeh, J. Hebling, K. A. Nelson, “Efficient terahertz generation by optical rectification at 1035 nm,” Opt. Express 15, 11706–11713 (2007). [CrossRef] [PubMed]
  64. V. Giovannetti, S. Lloyd, L. Maccone, Science 306, 1330–1336 (2004). [CrossRef] [PubMed]
  65. V. Giovannetti, L. Maccone, S. Lloyd, “Quantum-enhanced positioning and clock synchronization,” Nature 412, 417–419 (2001). [CrossRef] [PubMed]
  66. A. Valencia, G. Scarcelli, Y. H. Shih, “Distant clock synchronization using entangled photon pairs,” Appl. Phys. Lett. 85, 2655–2657 (2004). [CrossRef]
  67. T. Aichele, A. I. Lvovsky, S. Schiller, “Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state,” Eur. Phys. J. D 18, 237–245 (2002). [CrossRef]
  68. J. P. Torres, F. Macià, S. Carrasco, L. Torner, “Engineering the frequency correlations of entangled two-photon states by achromatic phase matching,” Opt. Lett. 30, 314–316 (2005). [CrossRef] [PubMed]
  69. O. Kuzucu, M. Fiorentino, M. A. Albota, F. N. C. Wong, F. X. Kärtner, “Two-photon coincident-frequency entanglement via extended phase matching,” Phys. Rev. Lett. 94, 083601 (2005). [CrossRef] [PubMed]
  70. M. Hendrych, M. Mičuda, J. P. Torres, “Tunable control of the frequency correlations of entangled photons,” Opt. Lett. 32, 2339–2341 (2007). [CrossRef] [PubMed]
  71. P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008). [CrossRef] [PubMed]
  72. T. E. Keller, M. H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997). [CrossRef]
  73. W. P. Grice, A. B. U’Ren, I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A 64, 063815 (2001). [CrossRef]
  74. X. Shi, A. Valencia, M. Hendrych, J. Torres, “Generation of indistinguishable and pure heralded single photons with tunable bandwidth,” Opt. Lett. 33, 875–877 (2008). [CrossRef] [PubMed]
  75. J. P. Torres, M. W. Mitchell, M. Hendrych, “Indistinguishability of entangled photons generated with achromatic phase matching,” Phys. Rev. A 71, 022320 (2005). [CrossRef]
  76. K. W. Chan, J. P. Torres, J. H. Eberly, “Transverse entanglement migration in Hilbert space,” Phys. Rev. A 75, 050101(R) (2007). [CrossRef]
  77. M. Hendrych, X. Shi, A. Valencia, J. P. Torres, “Broadening the bandwidth of entangled photons: a step towards the generation of extremely short biphotons,” Phys. Rev. A 79, 023817 (2009). [CrossRef]
  78. S. Carrasco, J. P. Torres, L. Torner, A. V. Sergienko, B. E. Saleh, M. C. Teich, “Spatial-to-spectral mapping in spontaneous parametric down-conversion,” Phys. Rev. A 70, 043817 (2004). [CrossRef]
  79. A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99, 243601 (2007). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited