The Gouy phase shift in nonlinear interactions of waves
Optics Express, Vol. 15, Issue 12, pp. 7211-7217 (2007)
http://dx.doi.org/10.1364/OE.15.007211
Acrobat PDF (151 KB)
Abstract
We theoretically analyze the influence of the Gouy phase shift on the nonlinear interaction between waves of different frequencies. We focus on χ^{(2)} interaction of optical fields, e.g. through birefringent crystals, and show that focussing, stronger than suggested by the Boyd-Kleinman factor, can further improve nonlinear processes. An increased value of 3.32 for the optimal focussing parameter for a single pass process is found. The new value builds on the compensation of the Gouy phase shift by a spatially varying, instead constant, wave vector phase mismatch. We analyze the single-ended, singly resonant standing wave nonlinear cavity and show that in this case the Gouy phase shift leads to an additional phase during backreflection. Our numerical simulations may explain ill-understood experimental observations in such devices.
© 2007 Optical Society of America
1. Introduction
1. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118 (1961). [CrossRef]
2. J. A. Giordmaine and R. C. Miller, “Tunable Coherent Parametric Oscillation in LiNbO_{3} at Optical Frequencies,” Phys. Rev. Lett. 14, 973 (1965). [CrossRef]
3. L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of Squeezed States by Parametric Down Conversion,” Phys. Rev. Lett. 57, 2520 (1986). [CrossRef] [PubMed]
4. R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903 (1987). [CrossRef] [PubMed]
5. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693 (1981). [CrossRef]
6. H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Coherent Control of Vacuum Squeezing in the Gravitational-Wave Detection Band,” Phys. Rev. Lett. 97, 011101 (2006). [CrossRef] [PubMed]
7. Y. Yamamoto and H. A. Haus, “Preparation, measurement and information capacity of optical quantum states,” Rev. Mod. Phys. 58, 1001 (1986). [CrossRef]
8. S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett. 26, 485 (2001) [CrossRef]
9. G. D. Boyd and D. A. Kleinman, “Parametric Interaction of Focused Gaussian Light Beams,” J. Appl. Phys. 39, 3597 (1968). [CrossRef]
2. Singlepass interaction
9. G. D. Boyd and D. A. Kleinman, “Parametric Interaction of Focused Gaussian Light Beams,” J. Appl. Phys. 39, 3597 (1968). [CrossRef]
6. H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Coherent Control of Vacuum Squeezing in the Gravitational-Wave Detection Band,” Phys. Rev. Lett. 97, 011101 (2006). [CrossRef] [PubMed]
3. Nonlinear cavities
10. R. Paschotta, K. Fiedler, P. Kürz, R. Henking, S. Schiller, and J. Mlynek, “82 % efficient continuous-wave frequency doubling of 1.06 μm with a monolithic MgO:LiNbO_{3} resonator,” Opt. Lett. 19, 1325 (1994). [CrossRef] [PubMed]
6. H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Coherent Control of Vacuum Squeezing in the Gravitational-Wave Detection Band,” Phys. Rev. Lett. 97, 011101 (2006). [CrossRef] [PubMed]
11. R. Paschotta, K. Fiedler, P. Kürz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency dou-blers,” App. Phys. B 58, 117 (1994). [CrossRef]
4. Conclusion
References and links
1. | P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118 (1961). [CrossRef] |
2. | J. A. Giordmaine and R. C. Miller, “Tunable Coherent Parametric Oscillation in LiNbO_{3} at Optical Frequencies,” Phys. Rev. Lett. 14, 973 (1965). [CrossRef] |
3. | L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of Squeezed States by Parametric Down Conversion,” Phys. Rev. Lett. 57, 2520 (1986). [CrossRef] [PubMed] |
4. | R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903 (1987). [CrossRef] [PubMed] |
5. | C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693 (1981). [CrossRef] |
6. | H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, “Coherent Control of Vacuum Squeezing in the Gravitational-Wave Detection Band,” Phys. Rev. Lett. 97, 011101 (2006). [CrossRef] [PubMed] |
7. | Y. Yamamoto and H. A. Haus, “Preparation, measurement and information capacity of optical quantum states,” Rev. Mod. Phys. 58, 1001 (1986). [CrossRef] |
8. | S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett. 26, 485 (2001) [CrossRef] |
9. | G. D. Boyd and D. A. Kleinman, “Parametric Interaction of Focused Gaussian Light Beams,” J. Appl. Phys. 39, 3597 (1968). [CrossRef] |
10. | R. Paschotta, K. Fiedler, P. Kürz, R. Henking, S. Schiller, and J. Mlynek, “82 % efficient continuous-wave frequency doubling of 1.06 μm with a monolithic MgO:LiNbO_{3} resonator,” Opt. Lett. 19, 1325 (1994). [CrossRef] [PubMed] |
11. | R. Paschotta, K. Fiedler, P. Kürz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency dou-blers,” App. Phys. B 58, 117 (1994). [CrossRef] |
OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4970) Nonlinear optics : Parametric oscillators and amplifiers
ToC Category:
Nonlinear Optics
History
Original Manuscript: March 19, 2007
Revised Manuscript: May 3, 2007
Manuscript Accepted: May 21, 2007
Published: May 29, 2007
Citation
Nico Lastzka and Roman Schnabel, "The Gouy phase shift in nonlinear interactions of waves," Opt. Express 15, 7211-7217 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7211
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References
- P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7, 118 (1961). [CrossRef]
- J. A. Giordmaine and R. C. Miller, "Tunable Coherent Parametric Oscillation in LiNbO3 at optical frequencies," Phys. Rev. Lett. 14, 973 (1965). [CrossRef]
- L. Wu, H. J. Kimble, J. L. Hall, and H. Wu, "Generation of squeezed states by parametric down conversion," Phys. Rev. Lett. 57, 2520 (1986). [CrossRef] [PubMed]
- R. Ghosh and L. Mandel, "Observation of nonclassical effects in the interference of two photons," Phys. Rev. Lett. 59, 1903 (1987). [CrossRef] [PubMed]
- C. M. Caves, "Quantum-mechanical noise in an interferometer," Phys. Rev. D 23, 1693 (1981). [CrossRef]
- H. Vahlbruch, S. Chelkowski, B. Hage, A. Franzen, K. Danzmann, and R. Schnabel, "Coherent control of vacuum squeezing in the gravitational-wave detection band," Phys. Rev. Lett. 97, 011101 (2006). [CrossRef] [PubMed]
- Y. Yamamoto and H. A. Haus, "Preparation, measurement and information capacity of optical quantum states," Rev. Mod. Phys. 58, 1001 (1986). [CrossRef]
- S. Feng and H. G. Winful, "Physical origin of the Gouy phase shift," Opt. Lett. 26, 485 (2001) [CrossRef]
- G. D. Boyd and D. A. Kleinman, "Parametric interaction of focused Gaussian light beams," J. Appl. Phys. 39, 3597 (1968). [CrossRef]
- R. Paschotta, K. Fiedler, P. Kurz, R. Henking, S. Schiller and J. Mlynek, "82% efficient continuous-wave frequency doubling of 1.06 μm with a monolithic MgO:LiNbO_{3} resonator," Opt. Lett. 19, 1325 (1994). [CrossRef] [PubMed]
- R. Paschotta, K. Fiedler, P. Kurz, and J. Mlynek, "Nonlinear mode coupling in doubly resonant frequency doublers," Appl. Phys. B 58, 117 (1994). [CrossRef]
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