Abstract

We report on the linear and nonlinear-optical properties of 4-dimethylamino-4-nitrostilbene (DANS), 4-diethylamino-1-nitrobenzyl (DANB), and 4-[N-ethyl-N-(2-hydroxyethyl)]amino-4-nitroazobenzene) (Disperse Red 1;DR1) side chain polymers whose second-harmonic generation at the telecommunication wavelength of 1.55 μm was investigated. Measured ultraviolet–visible–near-infrared spectra were analyzed with an inhomogeneously broadened line-shape model, in particular, in the long-wavelength tail of the electronic transitions, which determines the absorption loss at the second-harmonic wavelength. The nonlinear-optical coefficients were measured at different poling temperatures and poling fields by the Maker fringe technique. On the basis of the measured material parameters we calculated the normalized conversion efficiencies for guided-wave second-harmonic generation at 1.55 μm. The DR1 polymer exhibited the best nonlinearity–absorption trade-off, with a calculated normalized conversion efficiency of several hundred percent per watt, whereas the figures of merit for DANS and DANB are lower and comparable with each other.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. I. Stegeman, “Introduction to nonlinear guided wave optics,” in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1992), pp. 11–27.
  2. K. Gallo, G. Assanto, and G. I. Stegeman, “Efficient wavelength shifting over the erbium amplifier bandwidth via cascaded second order processes in lithium niobate waveguides,” Appl. Phys. Lett. 71, 1020–1022 (1997).
    [CrossRef]
  3. G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
    [CrossRef]
  4. M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
    [CrossRef]
  5. D. Hofmann, G. Schreiber, C. Haase, H. Herrmann, W. Grundkoetter, R. Ricken, and W. Sohler, “Quasi-phase-matched difference-frequency generation in periodically poled Ti:LiNbO3 channel waveguides,” Opt. Lett. 24, 896–898 (1999).
    [CrossRef]
  6. D. S. Chemla and J. Zyss, eds., Nonlinear Optical Properties of Organic Molecules and Crystals (Academic, Orlando, Fla., 1987).
  7. H. S. Nalwa and S. Miyata, eds., Nonlinear Optics of Organic Molecules and Polymers (CRC Press, Boca Raton, Fla., 1997).
  8. C. Bosshard, K. Sutter, Ph. Pre⁁tre, J. Hulliger, M. Flörsheimer, P. Kaatz, and P. Günter, Organic Nonlinear Optical Materials (Gordon & Breach, London, 1995).
  9. D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
    [CrossRef]
  10. K. Clays, J. S. Schildkraut, and D. J. Williams, “Phase-matched second-harmonic generation in a four-layered polymeric waveguide,” J. Opt. Soc. Am. B 11, 655–664 (1994).
    [CrossRef]
  11. T. C. Kowalczyk, K. D. Singer, and P. A. Cahill, “Anomalous-dispersion phase-matched second-harmonic generation in a polymer waveguide,” Opt. Lett. 20, 2273–227 (1995).
    [CrossRef] [PubMed]
  12. M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
    [CrossRef]
  13. L.-T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
    [CrossRef]
  14. D. M. Burland, R. D. Miller, O. Reiser, R. J. Twieg, and C. A. Walsh, “The design, synthesis, and evaluation of chromophores for second-harmonic generation in a polymer waveguide,” J. Appl. Phys. 71, 410–417 (1992).
    [CrossRef]
  15. M. Jäger, V. Ricci, W. R. Cho, M. Canva, and G. I. Stegeman, “Advantages of modal-dispersion phase-matching and material requirements for polymeric devicesusing efficient second harmonic generation at telecommunication wavelengths,” Mater. Res. Soc. Symp. Proc. 488, 179–191 (1998).
    [CrossRef]
  16. A. Otomo, M. Jäger, G. I. Stegeman, M. Flipse, and M. Diemeer, “Key trade-offs for second harmonic generation in poled polymers,” Appl. Phys. Lett. 69, 1991–1993 (1996).
    [CrossRef]
  17. A.-C. Le Duff, V. Ricci, T. Pliška, M. Canva, G. I. Stegeman, K. P. Chan, and R. J. Twieg, “Importance of chromophore environment on the near infrared absorption of polymeric waveguides,” Appl. Opt. 39, 947–953 (2000).
    [CrossRef]
  18. M. Jäger, G. I. Stegeman, M. C. Flipse, M. Diemeer, and G. Möhlmann, “Modal dispersion phase matching over 7 mm length in overdamped polymeric channel waveguides,” Appl. Phys. Lett. 69, 4139–4141 (1996).
    [CrossRef]
  19. Q. Zhang, M. Canva, and G. I. Stegeman, “Wavelength dependence of 4-dimethylamino-4-nitrostilbene polymer thin film photodegradation,” Appl. Phys. Lett. 73, 912–914 (1998).
    [CrossRef]
  20. K. D. Singer, M. G. Kuzyk, and J. E. Sohn, “Second-order nonlinear-optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties,” J. Opt. Soc. Am. B 4, 968–976 (1987).
    [CrossRef]
  21. C. P. J. M. van der Vorst and S. J. Picken, “Electric field poling of acceptor-donor molecules,” J. Opt. Soc. Am. B 7, 320–325 (1990).
    [CrossRef]
  22. C. J. F. Bottcher, Theory of Electric Polarization (Elsevier, Amsterdam, 1973).
  23. K. D. Singer and A. F. Garito, “Measurements of molecular second order optical susceptibilities using dc induced second harmonic generation,” J. Chem. Phys. 75, 3572–3580 (1981).
    [CrossRef]
  24. A. Skumanich, M. Jurich, and J. D. Swalen, “Absorption and scattering in nonlinear optical polymeric systems,” Appl. Phys. Lett. 62, 446–448 (1993).
    [CrossRef]
  25. P. K. Tien, “Light waves in thin films and integrated optics,” Appl. Opt. 10, 2395–2413 (1971).
    [CrossRef] [PubMed]
  26. K. D. Singer, J. E. Sohn, L. A. King, H. M. Gordon, H. E. Katz, and C. W. Dirk, “Second-order nonlinear-optical properties of donor- and acceptor-substituted aromatic compounds,” J. Opt. Soc. Am. B 6, 1339–1350 (1989).
    [CrossRef]
  27. M. Jäger, G. I. Stegeman, G. R. Möhlmann, M. C. Flipse, and M. J. B. Diemeer, “Second harmonic generation in polymeric channel waveguides using modal dispersion,” Electron. Lett. 32, 2009–2010 (1996).
    [CrossRef]
  28. W.-R. Cho, V. Ricci, T. Pliška, M. Canva, and G. I. Stegeman, “Second-harmonic generation in reactively-ion etched, Disperse Red 1 polymer waveguides at telecommunication wavelengths,” J. Appl. Phys. 86, 2941–2944 (1999).
    [CrossRef]
  29. T. Pliška, V. Ricci, L. Friedrich, A.-C. Le Duff, M. Canva, G. I. Stegeman, P. Raimond, and F. Kajzar, “Polymer waveguides for χ22-cascading at telecommunication wavelengths,” (presented at the 9th European Conference on Integrated Optics, Turin, Italy, April 14–16, 1999).
  30. P. A. M. Steeman, F. J. J. Maurer, and J. van Turnhout, “Dielectric properties of blends of polycarbonate and acrylonitrile-butadiene-styrene copolymer,” Polym. Eng. Sci. 34, 697–706 (1994).
    [CrossRef]
  31. K. Mazur, “More data about dielectric and electret properties of poly(methyl methacrylate),” J. Phys. D 30, 1383–1398 (1997).
    [CrossRef]
  32. A. Otomo, G. I. Stegeman, W. H. G. Horsthuis, and G. R. Möhlmann, “Strong field, in-plane poling for nonlinear optical devices in highly nonlinear side chain polymers,” Appl. Phys. Lett. 65, 2389–2391 (1994).
    [CrossRef]
  33. D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
    [CrossRef]
  34. Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, and M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
    [CrossRef]
  35. T. Pliška, V. Ricci, A.-C. Le Duff, M. Canva, P. Raimond, F. Kajzar, and G. I. Stegeman, “Low loss polymer waveguides fabricated by plasma etching for nonlinear-optical devices at telecommunication wavelengths,” in Conference on Lasers Electro-Optics (CLEO/US), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 313–314.
  36. W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
    [CrossRef]
  37. W. E. Torruellas, R. Zanoni, G. I. Stegeman, G. R. Möhlmann, E. W. P. Erdhuisen, and W. H. G. Horsthuis, “The cubic susceptibility dispersion of alkoxy-nitro-stilbene (MONS) and di-alkyl-amino-nitro-stilbene (DANS) side chain susbtituted polymers: comparison with the two-level model,” J. Chem. Phys. 94, 6851–6856 (1991); Erratum, J. Chem. Phys. 96, 1662 (1992).
    [CrossRef]
  38. M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
    [CrossRef]
  39. D. Beljonne, J. L. Brédas, M. Cha, W. E. Torruellas, G. I. Stegeman, J. W. Hofstraat, W. H. G. Horsthuis, and G. R. Möhlmann, “Two-photon absorption and third-harmonic generation of di-alkyl-amino-nitro-stilbene (DANS): a joint experimental and theoretical study,” J. Chem. Phys. 103, 7834–7843 (1995).
    [CrossRef]

2000 (1)

1999 (3)

D. Hofmann, G. Schreiber, C. Haase, H. Herrmann, W. Grundkoetter, R. Ricken, and W. Sohler, “Quasi-phase-matched difference-frequency generation in periodically poled Ti:LiNbO3 channel waveguides,” Opt. Lett. 24, 896–898 (1999).
[CrossRef]

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[CrossRef]

W.-R. Cho, V. Ricci, T. Pliška, M. Canva, and G. I. Stegeman, “Second-harmonic generation in reactively-ion etched, Disperse Red 1 polymer waveguides at telecommunication wavelengths,” J. Appl. Phys. 86, 2941–2944 (1999).
[CrossRef]

1998 (3)

M. Jäger, V. Ricci, W. R. Cho, M. Canva, and G. I. Stegeman, “Advantages of modal-dispersion phase-matching and material requirements for polymeric devicesusing efficient second harmonic generation at telecommunication wavelengths,” Mater. Res. Soc. Symp. Proc. 488, 179–191 (1998).
[CrossRef]

Q. Zhang, M. Canva, and G. I. Stegeman, “Wavelength dependence of 4-dimethylamino-4-nitrostilbene polymer thin film photodegradation,” Appl. Phys. Lett. 73, 912–914 (1998).
[CrossRef]

M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
[CrossRef]

1997 (5)

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

K. Gallo, G. Assanto, and G. I. Stegeman, “Efficient wavelength shifting over the erbium amplifier bandwidth via cascaded second order processes in lithium niobate waveguides,” Appl. Phys. Lett. 71, 1020–1022 (1997).
[CrossRef]

K. Mazur, “More data about dielectric and electret properties of poly(methyl methacrylate),” J. Phys. D 30, 1383–1398 (1997).
[CrossRef]

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, and M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

1996 (4)

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

M. Jäger, G. I. Stegeman, G. R. Möhlmann, M. C. Flipse, and M. J. B. Diemeer, “Second harmonic generation in polymeric channel waveguides using modal dispersion,” Electron. Lett. 32, 2009–2010 (1996).
[CrossRef]

A. Otomo, M. Jäger, G. I. Stegeman, M. Flipse, and M. Diemeer, “Key trade-offs for second harmonic generation in poled polymers,” Appl. Phys. Lett. 69, 1991–1993 (1996).
[CrossRef]

M. Jäger, G. I. Stegeman, M. C. Flipse, M. Diemeer, and G. Möhlmann, “Modal dispersion phase matching over 7 mm length in overdamped polymeric channel waveguides,” Appl. Phys. Lett. 69, 4139–4141 (1996).
[CrossRef]

1995 (2)

D. Beljonne, J. L. Brédas, M. Cha, W. E. Torruellas, G. I. Stegeman, J. W. Hofstraat, W. H. G. Horsthuis, and G. R. Möhlmann, “Two-photon absorption and third-harmonic generation of di-alkyl-amino-nitro-stilbene (DANS): a joint experimental and theoretical study,” J. Chem. Phys. 103, 7834–7843 (1995).
[CrossRef]

T. C. Kowalczyk, K. D. Singer, and P. A. Cahill, “Anomalous-dispersion phase-matched second-harmonic generation in a polymer waveguide,” Opt. Lett. 20, 2273–227 (1995).
[CrossRef] [PubMed]

1994 (4)

K. Clays, J. S. Schildkraut, and D. J. Williams, “Phase-matched second-harmonic generation in a four-layered polymeric waveguide,” J. Opt. Soc. Am. B 11, 655–664 (1994).
[CrossRef]

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

A. Otomo, G. I. Stegeman, W. H. G. Horsthuis, and G. R. Möhlmann, “Strong field, in-plane poling for nonlinear optical devices in highly nonlinear side chain polymers,” Appl. Phys. Lett. 65, 2389–2391 (1994).
[CrossRef]

P. A. M. Steeman, F. J. J. Maurer, and J. van Turnhout, “Dielectric properties of blends of polycarbonate and acrylonitrile-butadiene-styrene copolymer,” Polym. Eng. Sci. 34, 697–706 (1994).
[CrossRef]

1993 (1)

A. Skumanich, M. Jurich, and J. D. Swalen, “Absorption and scattering in nonlinear optical polymeric systems,” Appl. Phys. Lett. 62, 446–448 (1993).
[CrossRef]

1992 (2)

D. M. Burland, R. D. Miller, O. Reiser, R. J. Twieg, and C. A. Walsh, “The design, synthesis, and evaluation of chromophores for second-harmonic generation in a polymer waveguide,” J. Appl. Phys. 71, 410–417 (1992).
[CrossRef]

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

1991 (1)

L.-T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

1990 (1)

1989 (1)

1987 (1)

1981 (1)

K. D. Singer and A. F. Garito, “Measurements of molecular second order optical susceptibilities using dc induced second harmonic generation,” J. Chem. Phys. 75, 3572–3580 (1981).
[CrossRef]

1971 (1)

Ahlheim, M.

M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

Amano, M.

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, and M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

Assanto, G.

K. Gallo, G. Assanto, and G. I. Stegeman, “Efficient wavelength shifting over the erbium amplifier bandwidth via cascaded second order processes in lithium niobate waveguides,” Appl. Phys. Lett. 71, 1020–1022 (1997).
[CrossRef]

Bauer, S.

M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

Bauer-Gogonea, S.

M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

Beljonne, D.

D. Beljonne, J. L. Brédas, M. Cha, W. E. Torruellas, G. I. Stegeman, J. W. Hofstraat, W. H. G. Horsthuis, and G. R. Möhlmann, “Two-photon absorption and third-harmonic generation of di-alkyl-amino-nitro-stilbene (DANS): a joint experimental and theoretical study,” J. Chem. Phys. 103, 7834–7843 (1995).
[CrossRef]

Brédas, J. L.

D. Beljonne, J. L. Brédas, M. Cha, W. E. Torruellas, G. I. Stegeman, J. W. Hofstraat, W. H. G. Horsthuis, and G. R. Möhlmann, “Two-photon absorption and third-harmonic generation of di-alkyl-amino-nitro-stilbene (DANS): a joint experimental and theoretical study,” J. Chem. Phys. 103, 7834–7843 (1995).
[CrossRef]

Brener, I.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[CrossRef]

Brinker, W.

M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

Burland, D. M.

D. M. Burland, R. D. Miller, O. Reiser, R. J. Twieg, and C. A. Walsh, “The design, synthesis, and evaluation of chromophores for second-harmonic generation in a polymer waveguide,” J. Appl. Phys. 71, 410–417 (1992).
[CrossRef]

Cahill, P. A.

Canva, M.

A.-C. Le Duff, V. Ricci, T. Pliška, M. Canva, G. I. Stegeman, K. P. Chan, and R. J. Twieg, “Importance of chromophore environment on the near infrared absorption of polymeric waveguides,” Appl. Opt. 39, 947–953 (2000).
[CrossRef]

W.-R. Cho, V. Ricci, T. Pliška, M. Canva, and G. I. Stegeman, “Second-harmonic generation in reactively-ion etched, Disperse Red 1 polymer waveguides at telecommunication wavelengths,” J. Appl. Phys. 86, 2941–2944 (1999).
[CrossRef]

Q. Zhang, M. Canva, and G. I. Stegeman, “Wavelength dependence of 4-dimethylamino-4-nitrostilbene polymer thin film photodegradation,” Appl. Phys. Lett. 73, 912–914 (1998).
[CrossRef]

M. Jäger, V. Ricci, W. R. Cho, M. Canva, and G. I. Stegeman, “Advantages of modal-dispersion phase-matching and material requirements for polymeric devicesusing efficient second harmonic generation at telecommunication wavelengths,” Mater. Res. Soc. Symp. Proc. 488, 179–191 (1998).
[CrossRef]

Cha, M.

D. Beljonne, J. L. Brédas, M. Cha, W. E. Torruellas, G. I. Stegeman, J. W. Hofstraat, W. H. G. Horsthuis, and G. R. Möhlmann, “Two-photon absorption and third-harmonic generation of di-alkyl-amino-nitro-stilbene (DANS): a joint experimental and theoretical study,” J. Chem. Phys. 103, 7834–7843 (1995).
[CrossRef]

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

Chaban, E. E.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[CrossRef]

Chan, K. P.

Chen, A.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

Chen, D.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

Cheng, L.-T.

L.-T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

Cho, W. R.

M. Jäger, V. Ricci, W. R. Cho, M. Canva, and G. I. Stegeman, “Advantages of modal-dispersion phase-matching and material requirements for polymeric devicesusing efficient second harmonic generation at telecommunication wavelengths,” Mater. Res. Soc. Symp. Proc. 488, 179–191 (1998).
[CrossRef]

Cho, W.-R.

W.-R. Cho, V. Ricci, T. Pliška, M. Canva, and G. I. Stegeman, “Second-harmonic generation in reactively-ion etched, Disperse Red 1 polymer waveguides at telecommunication wavelengths,” J. Appl. Phys. 86, 2941–2944 (1999).
[CrossRef]

Chou, M. H.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[CrossRef]

Christman, S. B.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[CrossRef]

Clays, K.

Dalton, L. R.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

Diemeer, M.

M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

M. Jäger, G. I. Stegeman, M. C. Flipse, M. Diemeer, and G. Möhlmann, “Modal dispersion phase matching over 7 mm length in overdamped polymeric channel waveguides,” Appl. Phys. Lett. 69, 4139–4141 (1996).
[CrossRef]

A. Otomo, M. Jäger, G. I. Stegeman, M. Flipse, and M. Diemeer, “Key trade-offs for second harmonic generation in poled polymers,” Appl. Phys. Lett. 69, 1991–1993 (1996).
[CrossRef]

Diemeer, M. J. B.

M. Jäger, G. I. Stegeman, G. R. Möhlmann, M. C. Flipse, and M. J. B. Diemeer, “Second harmonic generation in polymeric channel waveguides using modal dispersion,” Electron. Lett. 32, 2009–2010 (1996).
[CrossRef]

Dirk, C. W.

Fejer, M. M.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[CrossRef]

Fetterman, H. R.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

Flipse, M.

A. Otomo, M. Jäger, G. I. Stegeman, M. Flipse, and M. Diemeer, “Key trade-offs for second harmonic generation in poled polymers,” Appl. Phys. Lett. 69, 1991–1993 (1996).
[CrossRef]

Flipse, M. C.

M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

M. Jäger, G. I. Stegeman, G. R. Möhlmann, M. C. Flipse, and M. J. B. Diemeer, “Second harmonic generation in polymeric channel waveguides using modal dispersion,” Electron. Lett. 32, 2009–2010 (1996).
[CrossRef]

M. Jäger, G. I. Stegeman, M. C. Flipse, M. Diemeer, and G. Möhlmann, “Modal dispersion phase matching over 7 mm length in overdamped polymeric channel waveguides,” Appl. Phys. Lett. 69, 4139–4141 (1996).
[CrossRef]

Gallo, K.

K. Gallo, G. Assanto, and G. I. Stegeman, “Efficient wavelength shifting over the erbium amplifier bandwidth via cascaded second order processes in lithium niobate waveguides,” Appl. Phys. Lett. 71, 1020–1022 (1997).
[CrossRef]

Garito, A. F.

K. D. Singer and A. F. Garito, “Measurements of molecular second order optical susceptibilities using dc induced second harmonic generation,” J. Chem. Phys. 75, 3572–3580 (1981).
[CrossRef]

Gordon, H. M.

Grundkoetter, W.

Haase, C.

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Herrmann, H.

Hikita, M.

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, and M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

Hofmann, D.

Hofstraat, J. W.

D. Beljonne, J. L. Brédas, M. Cha, W. E. Torruellas, G. I. Stegeman, J. W. Hofstraat, W. H. G. Horsthuis, and G. R. Möhlmann, “Two-photon absorption and third-harmonic generation of di-alkyl-amino-nitro-stilbene (DANS): a joint experimental and theoretical study,” J. Chem. Phys. 103, 7834–7843 (1995).
[CrossRef]

Horsthuis, W. H. G.

D. Beljonne, J. L. Brédas, M. Cha, W. E. Torruellas, G. I. Stegeman, J. W. Hofstraat, W. H. G. Horsthuis, and G. R. Möhlmann, “Two-photon absorption and third-harmonic generation of di-alkyl-amino-nitro-stilbene (DANS): a joint experimental and theoretical study,” J. Chem. Phys. 103, 7834–7843 (1995).
[CrossRef]

A. Otomo, G. I. Stegeman, W. H. G. Horsthuis, and G. R. Möhlmann, “Strong field, in-plane poling for nonlinear optical devices in highly nonlinear side chain polymers,” Appl. Phys. Lett. 65, 2389–2391 (1994).
[CrossRef]

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

Jäger, M.

M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
[CrossRef]

M. Jäger, V. Ricci, W. R. Cho, M. Canva, and G. I. Stegeman, “Advantages of modal-dispersion phase-matching and material requirements for polymeric devicesusing efficient second harmonic generation at telecommunication wavelengths,” Mater. Res. Soc. Symp. Proc. 488, 179–191 (1998).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

M. Jäger, G. I. Stegeman, G. R. Möhlmann, M. C. Flipse, and M. J. B. Diemeer, “Second harmonic generation in polymeric channel waveguides using modal dispersion,” Electron. Lett. 32, 2009–2010 (1996).
[CrossRef]

M. Jäger, G. I. Stegeman, M. C. Flipse, M. Diemeer, and G. Möhlmann, “Modal dispersion phase matching over 7 mm length in overdamped polymeric channel waveguides,” Appl. Phys. Lett. 69, 4139–4141 (1996).
[CrossRef]

A. Otomo, M. Jäger, G. I. Stegeman, M. Flipse, and M. Diemeer, “Key trade-offs for second harmonic generation in poled polymers,” Appl. Phys. Lett. 69, 1991–1993 (1996).
[CrossRef]

Jurich, M.

A. Skumanich, M. Jurich, and J. D. Swalen, “Absorption and scattering in nonlinear optical polymeric systems,” Appl. Phys. Lett. 62, 446–448 (1993).
[CrossRef]

Katz, H. E.

King, L. A.

Kowalczyk, T. C.

Kuzyk, M. G.

Le Duff, A.-C.

Lehr, F.

M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

Marder, S. R.

L.-T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

Maurer, F. J. J.

P. A. M. Steeman, F. J. J. Maurer, and J. van Turnhout, “Dielectric properties of blends of polycarbonate and acrylonitrile-butadiene-styrene copolymer,” Polym. Eng. Sci. 34, 697–706 (1994).
[CrossRef]

Mazur, K.

K. Mazur, “More data about dielectric and electret properties of poly(methyl methacrylate),” J. Phys. D 30, 1383–1398 (1997).
[CrossRef]

Meredith, G. R.

L.-T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

Meth, J.

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

Miller, R. D.

D. M. Burland, R. D. Miller, O. Reiser, R. J. Twieg, and C. A. Walsh, “The design, synthesis, and evaluation of chromophores for second-harmonic generation in a polymer waveguide,” J. Appl. Phys. 71, 410–417 (1992).
[CrossRef]

Möhlmann, G.

M. Jäger, G. I. Stegeman, M. C. Flipse, M. Diemeer, and G. Möhlmann, “Modal dispersion phase matching over 7 mm length in overdamped polymeric channel waveguides,” Appl. Phys. Lett. 69, 4139–4141 (1996).
[CrossRef]

Möhlmann, G. R.

M. Jäger, G. I. Stegeman, G. R. Möhlmann, M. C. Flipse, and M. J. B. Diemeer, “Second harmonic generation in polymeric channel waveguides using modal dispersion,” Electron. Lett. 32, 2009–2010 (1996).
[CrossRef]

D. Beljonne, J. L. Brédas, M. Cha, W. E. Torruellas, G. I. Stegeman, J. W. Hofstraat, W. H. G. Horsthuis, and G. R. Möhlmann, “Two-photon absorption and third-harmonic generation of di-alkyl-amino-nitro-stilbene (DANS): a joint experimental and theoretical study,” J. Chem. Phys. 103, 7834–7843 (1995).
[CrossRef]

A. Otomo, G. I. Stegeman, W. H. G. Horsthuis, and G. R. Möhlmann, “Strong field, in-plane poling for nonlinear optical devices in highly nonlinear side chain polymers,” Appl. Phys. Lett. 65, 2389–2391 (1994).
[CrossRef]

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

Otomo, A.

A. Otomo, M. Jäger, G. I. Stegeman, M. Flipse, and M. Diemeer, “Key trade-offs for second harmonic generation in poled polymers,” Appl. Phys. Lett. 69, 1991–1993 (1996).
[CrossRef]

A. Otomo, G. I. Stegeman, W. H. G. Horsthuis, and G. R. Möhlmann, “Strong field, in-plane poling for nonlinear optical devices in highly nonlinear side chain polymers,” Appl. Phys. Lett. 65, 2389–2391 (1994).
[CrossRef]

Picken, S. J.

Pliška, T.

A.-C. Le Duff, V. Ricci, T. Pliška, M. Canva, G. I. Stegeman, K. P. Chan, and R. J. Twieg, “Importance of chromophore environment on the near infrared absorption of polymeric waveguides,” Appl. Opt. 39, 947–953 (2000).
[CrossRef]

W.-R. Cho, V. Ricci, T. Pliška, M. Canva, and G. I. Stegeman, “Second-harmonic generation in reactively-ion etched, Disperse Red 1 polymer waveguides at telecommunication wavelengths,” J. Appl. Phys. 86, 2941–2944 (1999).
[CrossRef]

Reiser, O.

D. M. Burland, R. D. Miller, O. Reiser, R. J. Twieg, and C. A. Walsh, “The design, synthesis, and evaluation of chromophores for second-harmonic generation in a polymer waveguide,” J. Appl. Phys. 71, 410–417 (1992).
[CrossRef]

Ricci, V.

A.-C. Le Duff, V. Ricci, T. Pliška, M. Canva, G. I. Stegeman, K. P. Chan, and R. J. Twieg, “Importance of chromophore environment on the near infrared absorption of polymeric waveguides,” Appl. Opt. 39, 947–953 (2000).
[CrossRef]

W.-R. Cho, V. Ricci, T. Pliška, M. Canva, and G. I. Stegeman, “Second-harmonic generation in reactively-ion etched, Disperse Red 1 polymer waveguides at telecommunication wavelengths,” J. Appl. Phys. 86, 2941–2944 (1999).
[CrossRef]

M. Jäger, V. Ricci, W. R. Cho, M. Canva, and G. I. Stegeman, “Advantages of modal-dispersion phase-matching and material requirements for polymeric devicesusing efficient second harmonic generation at telecommunication wavelengths,” Mater. Res. Soc. Symp. Proc. 488, 179–191 (1998).
[CrossRef]

Ricken, R.

Rikken, G.

L.-T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

Roberts, D. A.

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

Schildkraut, J. S.

Schreiber, G.

Shi, Y.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

Shuto, Y.

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, and M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

Singer, K. D.

Skumanich, A.

A. Skumanich, M. Jurich, and J. D. Swalen, “Absorption and scattering in nonlinear optical polymeric systems,” Appl. Phys. Lett. 62, 446–448 (1993).
[CrossRef]

Sohler, W.

Sohn, J. E.

Stählin, M.

M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

Steeman, P. A. M.

P. A. M. Steeman, F. J. J. Maurer, and J. van Turnhout, “Dielectric properties of blends of polycarbonate and acrylonitrile-butadiene-styrene copolymer,” Polym. Eng. Sci. 34, 697–706 (1994).
[CrossRef]

Stegeman, G. I.

A.-C. Le Duff, V. Ricci, T. Pliška, M. Canva, G. I. Stegeman, K. P. Chan, and R. J. Twieg, “Importance of chromophore environment on the near infrared absorption of polymeric waveguides,” Appl. Opt. 39, 947–953 (2000).
[CrossRef]

W.-R. Cho, V. Ricci, T. Pliška, M. Canva, and G. I. Stegeman, “Second-harmonic generation in reactively-ion etched, Disperse Red 1 polymer waveguides at telecommunication wavelengths,” J. Appl. Phys. 86, 2941–2944 (1999).
[CrossRef]

Q. Zhang, M. Canva, and G. I. Stegeman, “Wavelength dependence of 4-dimethylamino-4-nitrostilbene polymer thin film photodegradation,” Appl. Phys. Lett. 73, 912–914 (1998).
[CrossRef]

M. Jäger, V. Ricci, W. R. Cho, M. Canva, and G. I. Stegeman, “Advantages of modal-dispersion phase-matching and material requirements for polymeric devicesusing efficient second harmonic generation at telecommunication wavelengths,” Mater. Res. Soc. Symp. Proc. 488, 179–191 (1998).
[CrossRef]

M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
[CrossRef]

K. Gallo, G. Assanto, and G. I. Stegeman, “Efficient wavelength shifting over the erbium amplifier bandwidth via cascaded second order processes in lithium niobate waveguides,” Appl. Phys. Lett. 71, 1020–1022 (1997).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

M. Jäger, G. I. Stegeman, M. C. Flipse, M. Diemeer, and G. Möhlmann, “Modal dispersion phase matching over 7 mm length in overdamped polymeric channel waveguides,” Appl. Phys. Lett. 69, 4139–4141 (1996).
[CrossRef]

M. Jäger, G. I. Stegeman, G. R. Möhlmann, M. C. Flipse, and M. J. B. Diemeer, “Second harmonic generation in polymeric channel waveguides using modal dispersion,” Electron. Lett. 32, 2009–2010 (1996).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

A. Otomo, M. Jäger, G. I. Stegeman, M. Flipse, and M. Diemeer, “Key trade-offs for second harmonic generation in poled polymers,” Appl. Phys. Lett. 69, 1991–1993 (1996).
[CrossRef]

D. Beljonne, J. L. Brédas, M. Cha, W. E. Torruellas, G. I. Stegeman, J. W. Hofstraat, W. H. G. Horsthuis, and G. R. Möhlmann, “Two-photon absorption and third-harmonic generation of di-alkyl-amino-nitro-stilbene (DANS): a joint experimental and theoretical study,” J. Chem. Phys. 103, 7834–7843 (1995).
[CrossRef]

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

A. Otomo, G. I. Stegeman, W. H. G. Horsthuis, and G. R. Möhlmann, “Strong field, in-plane poling for nonlinear optical devices in highly nonlinear side chain polymers,” Appl. Phys. Lett. 65, 2389–2391 (1994).
[CrossRef]

Steier, W. H.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

Stevenson, S. H.

L.-T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

Swalen, J. D.

A. Skumanich, M. Jurich, and J. D. Swalen, “Absorption and scattering in nonlinear optical polymeric systems,” Appl. Phys. Lett. 62, 446–448 (1993).
[CrossRef]

Tam, W.

L.-T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

Tien, P. K.

Tomaru, S.

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, and M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Torruellas, W. E.

D. Beljonne, J. L. Brédas, M. Cha, W. E. Torruellas, G. I. Stegeman, J. W. Hofstraat, W. H. G. Horsthuis, and G. R. Möhlmann, “Two-photon absorption and third-harmonic generation of di-alkyl-amino-nitro-stilbene (DANS): a joint experimental and theoretical study,” J. Chem. Phys. 103, 7834–7843 (1995).
[CrossRef]

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

Twieg, R. J.

A.-C. Le Duff, V. Ricci, T. Pliška, M. Canva, G. I. Stegeman, K. P. Chan, and R. J. Twieg, “Importance of chromophore environment on the near infrared absorption of polymeric waveguides,” Appl. Opt. 39, 947–953 (2000).
[CrossRef]

D. M. Burland, R. D. Miller, O. Reiser, R. J. Twieg, and C. A. Walsh, “The design, synthesis, and evaluation of chromophores for second-harmonic generation in a polymer waveguide,” J. Appl. Phys. 71, 410–417 (1992).
[CrossRef]

van der Vorst, C. P. J. M.

van Turnhout, J.

P. A. M. Steeman, F. J. J. Maurer, and J. van Turnhout, “Dielectric properties of blends of polycarbonate and acrylonitrile-butadiene-styrene copolymer,” Polym. Eng. Sci. 34, 697–706 (1994).
[CrossRef]

Walsh, C. A.

D. M. Burland, R. D. Miller, O. Reiser, R. J. Twieg, and C. A. Walsh, “The design, synthesis, and evaluation of chromophores for second-harmonic generation in a polymer waveguide,” J. Appl. Phys. 71, 410–417 (1992).
[CrossRef]

Wang, W.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

Watanabe, T.

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, and M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

Williams, D. J.

Wirges, W.

M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

Yilmaz, S.

M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

Yokohama, I.

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, and M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

Zhang, Q.

Q. Zhang, M. Canva, and G. I. Stegeman, “Wavelength dependence of 4-dimethylamino-4-nitrostilbene polymer thin film photodegradation,” Appl. Phys. Lett. 73, 912–914 (1998).
[CrossRef]

Zysset, B.

M. Jäger, G. I. Stegeman, S. Yilmaz, W. Wirges, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Poling and characterization of polymer waveguides for modal dispersion phase-matching,” J. Opt. Soc. Am. B 15, 781–788 (1998).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (9)

K. Gallo, G. Assanto, and G. I. Stegeman, “Efficient wavelength shifting over the erbium amplifier bandwidth via cascaded second order processes in lithium niobate waveguides,” Appl. Phys. Lett. 71, 1020–1022 (1997).
[CrossRef]

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys. Lett. 70, 3335–3337 (1997).
[CrossRef]

A. Otomo, M. Jäger, G. I. Stegeman, M. Flipse, and M. Diemeer, “Key trade-offs for second harmonic generation in poled polymers,” Appl. Phys. Lett. 69, 1991–1993 (1996).
[CrossRef]

M. Jäger, G. I. Stegeman, M. C. Flipse, M. Diemeer, and G. Möhlmann, “Modal dispersion phase matching over 7 mm length in overdamped polymeric channel waveguides,” Appl. Phys. Lett. 69, 4139–4141 (1996).
[CrossRef]

Q. Zhang, M. Canva, and G. I. Stegeman, “Wavelength dependence of 4-dimethylamino-4-nitrostilbene polymer thin film photodegradation,” Appl. Phys. Lett. 73, 912–914 (1998).
[CrossRef]

A. Otomo, G. I. Stegeman, W. H. G. Horsthuis, and G. R. Möhlmann, “Strong field, in-plane poling for nonlinear optical devices in highly nonlinear side chain polymers,” Appl. Phys. Lett. 65, 2389–2391 (1994).
[CrossRef]

W. Wirges, S. Yilmaz, W. Brinker, S. Bauer-Gogonea, S. Bauer, M. Jäger, G. I. Stegeman, M. Ahlheim, M. Stählin, B. Zysset, F. Lehr, M. Diemeer, and M. C. Flipse, “Polymer waveguides with optimized overlap integral for modal dispersion phase-matching,” Appl. Phys. Lett. 70, 3347–3349 (1997).
[CrossRef]

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994).
[CrossRef]

A. Skumanich, M. Jurich, and J. D. Swalen, “Absorption and scattering in nonlinear optical polymeric systems,” Appl. Phys. Lett. 62, 446–448 (1993).
[CrossRef]

Electron. Lett. (1)

M. Jäger, G. I. Stegeman, G. R. Möhlmann, M. C. Flipse, and M. J. B. Diemeer, “Second harmonic generation in polymeric channel waveguides using modal dispersion,” Electron. Lett. 32, 2009–2010 (1996).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, and M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[CrossRef]

J. Appl. Phys. (2)

W.-R. Cho, V. Ricci, T. Pliška, M. Canva, and G. I. Stegeman, “Second-harmonic generation in reactively-ion etched, Disperse Red 1 polymer waveguides at telecommunication wavelengths,” J. Appl. Phys. 86, 2941–2944 (1999).
[CrossRef]

D. M. Burland, R. D. Miller, O. Reiser, R. J. Twieg, and C. A. Walsh, “The design, synthesis, and evaluation of chromophores for second-harmonic generation in a polymer waveguide,” J. Appl. Phys. 71, 410–417 (1992).
[CrossRef]

J. Chem. Phys. (2)

D. Beljonne, J. L. Brédas, M. Cha, W. E. Torruellas, G. I. Stegeman, J. W. Hofstraat, W. H. G. Horsthuis, and G. R. Möhlmann, “Two-photon absorption and third-harmonic generation of di-alkyl-amino-nitro-stilbene (DANS): a joint experimental and theoretical study,” J. Chem. Phys. 103, 7834–7843 (1995).
[CrossRef]

K. D. Singer and A. F. Garito, “Measurements of molecular second order optical susceptibilities using dc induced second harmonic generation,” J. Chem. Phys. 75, 3572–3580 (1981).
[CrossRef]

J. Opt. Soc. Am. B (5)

J. Phys. Chem. (1)

L.-T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

J. Phys. D (1)

K. Mazur, “More data about dielectric and electret properties of poly(methyl methacrylate),” J. Phys. D 30, 1383–1398 (1997).
[CrossRef]

Mater. Res. Soc. Symp. Proc. (1)

M. Jäger, V. Ricci, W. R. Cho, M. Canva, and G. I. Stegeman, “Advantages of modal-dispersion phase-matching and material requirements for polymeric devicesusing efficient second harmonic generation at telecommunication wavelengths,” Mater. Res. Soc. Symp. Proc. 488, 179–191 (1998).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Polym. Eng. Sci. (1)

P. A. M. Steeman, F. J. J. Maurer, and J. van Turnhout, “Dielectric properties of blends of polycarbonate and acrylonitrile-butadiene-styrene copolymer,” Polym. Eng. Sci. 34, 697–706 (1994).
[CrossRef]

Other (8)

G. I. Stegeman, “Introduction to nonlinear guided wave optics,” in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1992), pp. 11–27.

T. Pliška, V. Ricci, L. Friedrich, A.-C. Le Duff, M. Canva, G. I. Stegeman, P. Raimond, and F. Kajzar, “Polymer waveguides for χ22-cascading at telecommunication wavelengths,” (presented at the 9th European Conference on Integrated Optics, Turin, Italy, April 14–16, 1999).

D. S. Chemla and J. Zyss, eds., Nonlinear Optical Properties of Organic Molecules and Crystals (Academic, Orlando, Fla., 1987).

H. S. Nalwa and S. Miyata, eds., Nonlinear Optics of Organic Molecules and Polymers (CRC Press, Boca Raton, Fla., 1997).

C. Bosshard, K. Sutter, Ph. Pre⁁tre, J. Hulliger, M. Flörsheimer, P. Kaatz, and P. Günter, Organic Nonlinear Optical Materials (Gordon & Breach, London, 1995).

C. J. F. Bottcher, Theory of Electric Polarization (Elsevier, Amsterdam, 1973).

W. E. Torruellas, R. Zanoni, G. I. Stegeman, G. R. Möhlmann, E. W. P. Erdhuisen, and W. H. G. Horsthuis, “The cubic susceptibility dispersion of alkoxy-nitro-stilbene (MONS) and di-alkyl-amino-nitro-stilbene (DANS) side chain susbtituted polymers: comparison with the two-level model,” J. Chem. Phys. 94, 6851–6856 (1991); Erratum, J. Chem. Phys. 96, 1662 (1992).
[CrossRef]

T. Pliška, V. Ricci, A.-C. Le Duff, M. Canva, P. Raimond, F. Kajzar, and G. I. Stegeman, “Low loss polymer waveguides fabricated by plasma etching for nonlinear-optical devices at telecommunication wavelengths,” in Conference on Lasers Electro-Optics (CLEO/US), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 313–314.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Chemical structures of DANS, DANB, and DR1 side chain polymers.

Fig. 2
Fig. 2

Ultraviolet–visible–near-infrared absorption spectrum of DANS-SCP. Open circles, data measured by transmission spectroscopy of an unpoled thin film (thickness, 0.2 μm); open diamonds, data measured in a planar waveguide (from Ref. 16). Filled diamond, loss measured in a planar DANS waveguide of 2.5-μm thickness at a wavelength of 0.78 μm. Solid curve, fitted inhomogeneously broadened absorption profile according to Eq. (9); dashed curve, Gaussian part of the inhomogeneously broadened line.

Fig. 3
Fig. 3

Ultraviolet–visible–near-infrared absorption spectrum of DANB-PMMA. Open circles, data measured by transmission spectroscopy of an unpoled thin film (thickness 0.6 μm); filled diamonds, data measured in a planar waveguide (thickness, 1.6 μm). Curves, same meaning as for Fig. 2.

Fig. 4
Fig. 4

Ultraviolet–visible–near-infrared absorption spectrum of DR1-PMMA. Open circles, data measured by transmission spectroscopy of an unpoled thin film (thickness, 1.1 μm); filled diamonds, data measured in a planar waveguide (thickness, 1.5 μm). Curves, same meaning as for Fig. 2.

Fig. 5
Fig. 5

Attenuation coefficient α of a 1.5-μm thick unpoled planar DANB-PMMA waveguide measured at 1.55–1.65-μm wavelengths. Solid line, calculated surface scattering loss.

Fig. 6
Fig. 6

Poling field dependence of the absorption coefficient for polarization parallel (α, filled diamonds) and perpendicular (α, open diamonds) to the poling field, measured on in-plane poled DANS-SCP samples at a wavelength of 0.458 μm; curves, fits to Eqs. (12) and (13), respectively.

Fig. 7
Fig. 7

Poling field dependence of the nonlinear-optical coefficient d33 for DANS-SCP, DANB-PMMA, and DR1-PMMA. The respective poling temperatures were 135, 100, and 120 °C. Dotted curves, fits according to Eq. (2); solid curves fits according to expression (7). (a) Solid and open diamonds, data from parallel-plate and in-plane poled samples, respectively. (b), (c) All data measured on parallel-plate poled samples.

Fig. 8
Fig. 8

Dependence of nonlinear-optical coefficient d33 on poling temperature for DANS-SCP and DR1-PMMA.

Fig. 9
Fig. 9

Normalized second-harmonic conversion efficiency η as a function of waveguide length L calculated on the basis of the measured absorption and nonlinear-optical coefficients as listed in Table 3 for DANS-SCP, DANB-PMMA, and DR1-PMMA. (a) Dependence assuming the actual chromophore loading as listed in Table 1; (b) assuming a chromophore number density N=1.3×1027 m-3 for all three polymers. The calculation was performed for an external poling field of 150 V μm-1, a waveguide with an effective cross section of Γ-1=10 μm2, an interface scattering loss of 0.2 cm-1 (1 dB cm-1) at both wavelengths, and a fundamental wavelength of 1.55 μm.

Fig. 10
Fig. 10

Calculated normalized second-harmonic conversion efficiency η as a function of chromophore density for DANS-SCP and DR1-PMMA for three (external) poling fields E. The relative units are defined such that unity corresponds to the actual loading of the chromophores in the polymers used for the measurements. The corresponding chromophore number densities N are indicated on the top axes. The waveguide was assumed to be 1 cm long; the other parameters are identical to those in Fig. 9.

Fig. 11
Fig. 11

Calculated normalized second-harmonic conversion efficiency η as a function of external poling field E. (a) Calculated for the actual chromophore loading; (b) chromophore number density assumed to be N=1.3×1027 m-3 for all three polymers. The guide parameters are identical to those in Fig. 9.

Tables (4)

Tables Icon

Table 1 Properties of Polymers Used in This Paper

Tables Icon

Table 2 Molecular Parameters of Chromophores Used in This Paper a

Tables Icon

Table 3 Measured Absorption Characteristics and Nonlinear-Optical Properties and Calculated Second-Harmonic Conversion Efficiencies of the Polymers Used in This Paper

Tables Icon

Table 4 Molecular Parameters of the Chromophores Derived from the Measurements of This Study and Comparison with Previously Published Data

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

d31(-2ω, ω, ω)=½Nfz2ωfxωfxωβZZZ(-2ω, ω, ω)×½ cos θ sin2 θ,
d33(-2ω, ω, ω)=½Nfz2ωfzωfzωβZZZ(-2ω, ω, ω)×cos3 θ,
fiω=ni2(ω)+23,
fi0=i(ni2+2)ni2+2i,
d33,max½Nf3βZZZ.
U(θ)=-(μ0+μind)E=-μ0,IEI-½EIαIJEJ.
d33Nfz2ωfzωfzωfz0βZZZμ0,ZE10kT.
d333d31.
χ(1)(ω)=NfωΘπ0nμ0n2Δωn-+1ω0n-ω+iΓn/2+1ω0n+ω-iΓn/2×exp-ω0n-ω0nΔωn2d(ω0n-ω0n),
Gn(ω0n-ω0n)=1πΔωnexp-ω0n-ω0nΔωn2,
1Δωn=1Δωn01-ξn+ξnω0nω2
αa,(ω)=ωcnz(ω) NfzωIm[αZZ(ω)]cos2 θ,
αa,(ω)=ωcnx(ω) NfxωIm[αZZ(ω)]½ sin2 θ.
αa,iso(ω)=13ωcn(ω) NfωIm[αZZ(ω)].
ηP2ω(L)[Pω(0)]2=2ω20c3deff2N2ω(Nω)2 Γh(Δβ, αω, α2ω, L).
h(αω, α2ω, L)=L2exp-α2ω2+αωLsinhΔαL22ΔαL22,
Lmax=1Δαlnα2ω2αω.
βZZZ(-2ω, ω, ω)
=3202Δμμ012ω012(ω012-4ω2)(ω012-ω2),

Metrics