Abstract

We develop an effective numerical algorithm to design engineered quasi-phase-matching gratings in nonlinear crystals for the parametric generation of harmonics of arbitrary order from a fundamental frequency input. We use the method to design and numerically demonstrate a lithium niobate parametric generator excited by a continuous-wave source in the regime of pump depletion.

©2008 Optical Society of America

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References

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  1. R. S. Craxton, “Theory of high efficiency third harmonic generation of high power Nd-glass laser radiation,” Opt. Commun. 34, 474–478 (1980).
    [Crossref]
  2. E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
    [Crossref] [PubMed]
  3. R. A. Ganeev, H. Singhal, P. A. Naik, U. Chakravarty, V. Arora, J. A. Chakera, R. A. Khan, M. Raghuramaiah, S. R. Kumbhare, R. P. Kushwaha, and P. D. Gupta, “Optimization of the high-order harmonics generated from silver plasma,” Appl. Phys. B 87, 243–247 (2007).
    [Crossref]
  4. J. Zhou, J. Peatross, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
    [Crossref] [PubMed]
  5. Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-X-ray harmonic emission,” Phys. Rev. A 58, R30–R33 (1998).
    [Crossref]
  6. S. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
    [Crossref]
  7. Y. Y. Zhu and N. B. Ming, “Dielectric super-lattices for nonlinear optical effects,” Opt. Quantum Electron. 31, 1093–1128 (1999).
    [Crossref]
  8. A. H. Norton and C. M. de Sterke, “Aperiodic 1-dimensional structures for quasi-phase matching,” Opt. Express 12, 841–846 (2004).
    [Crossref] [PubMed]
  9. S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C .Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
    [Crossref]
  10. O. Pfister, J. S. Wells, L. Hollberg, L. Zink, D. A. Van Baak, M. D. Levenson, and W. R. Bosenberg, “Continuous-wave frequency tripling and quadrupling by simultaneous three-wave mixings in periodically poled crystals: application to a two-step 1.19–10.71-µm frequency bridge,” Opt. Lett. 22, 1211–1213 (1997).
    [Crossref] [PubMed]
  11. J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal,” Appl. Phys. B 78, 265–267 (2004).
    [Crossref]
  12. K. L. Vodopyanov, O. Levi, P. S. Kuo, T. J. Pinguet, J. S. Harris, and M. M. Fejer, “Optical parametric oscillation in quasi-phase-matched GaAs,” Opt. Lett. 29, 1912–1914 (2004).
    [Crossref] [PubMed]
  13. J. C. G. de Sande, G. Leo, and G. Assanto, “Phase-matching engineering in birefringent AlGaAs waveguides for difference frequency generation,” IEEE J. Lightwave Technol. 20, 651–660 (2002)
    [Crossref]
  14. A. De Rossi, V. Berger, G. Leo, and G. Assanto, “Form birefringence phase matching in multilayer semiconductor structures: tuning and tolerances,” IEEE J. Quantum Electron. 41, 1293–1302 (2005)
    [Crossref]
  15. G. Assanto, I. Torelli, and S. Trillo, “All-optical processing by means of vectorial interactions in secondorder cascading: novel approaches,” Opt. Lett. 19, 1720–1722 (1994)
    [Crossref] [PubMed]
  16. G. Assanto, “Transistor action through nonlinear cascading in Type II interactions,” Opt. Lett. 20, 1595–1597 (1995).
    [Crossref] [PubMed]
  17. U. K. Sapaev and G. Assanto, “Femtosecond pulse synthesis by efficient second-harmonic generation in engineered quasi phase matching gratings,” Opt. Express 15, 7448–7457 (2007).
    [Crossref] [PubMed]
  18. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, (Springer, Berlin, 1999).
  19. L. H. Deng, X. M. Gao, Z. S. Cao, W. D. Chen, Y. Q. Yuan, W. J. Zhang, and Z. B. Gong, “Improvement to Sellmeier equation for periodically poled LiNbO3 crystal using mid-infrared difference-frequency generation,” Opt. Commun. 268, 110–114 (2006).
    [Crossref]
  20. G. I. Stegeman, M. Sheik-Bahae, E. VanStryland, and G. Assanto, “Large nonlinear phase shifts in second-order nonlinear optical processes,” Opt. Lett. 18, 13–15 (1993).
    [Crossref] [PubMed]
  21. G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. VanStryland, “Coherent interactions for all-optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673–681 (1995).
    [Crossref]

2007 (2)

R. A. Ganeev, H. Singhal, P. A. Naik, U. Chakravarty, V. Arora, J. A. Chakera, R. A. Khan, M. Raghuramaiah, S. R. Kumbhare, R. P. Kushwaha, and P. D. Gupta, “Optimization of the high-order harmonics generated from silver plasma,” Appl. Phys. B 87, 243–247 (2007).
[Crossref]

U. K. Sapaev and G. Assanto, “Femtosecond pulse synthesis by efficient second-harmonic generation in engineered quasi phase matching gratings,” Opt. Express 15, 7448–7457 (2007).
[Crossref] [PubMed]

2006 (1)

L. H. Deng, X. M. Gao, Z. S. Cao, W. D. Chen, Y. Q. Yuan, W. J. Zhang, and Z. B. Gong, “Improvement to Sellmeier equation for periodically poled LiNbO3 crystal using mid-infrared difference-frequency generation,” Opt. Commun. 268, 110–114 (2006).
[Crossref]

2005 (1)

A. De Rossi, V. Berger, G. Leo, and G. Assanto, “Form birefringence phase matching in multilayer semiconductor structures: tuning and tolerances,” IEEE J. Quantum Electron. 41, 1293–1302 (2005)
[Crossref]

2004 (3)

2003 (1)

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

2002 (1)

J. C. G. de Sande, G. Leo, and G. Assanto, “Phase-matching engineering in birefringent AlGaAs waveguides for difference frequency generation,” IEEE J. Lightwave Technol. 20, 651–660 (2002)
[Crossref]

1999 (1)

Y. Y. Zhu and N. B. Ming, “Dielectric super-lattices for nonlinear optical effects,” Opt. Quantum Electron. 31, 1093–1128 (1999).
[Crossref]

1998 (1)

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-X-ray harmonic emission,” Phys. Rev. A 58, R30–R33 (1998).
[Crossref]

1997 (3)

S. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[Crossref]

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C .Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[Crossref]

O. Pfister, J. S. Wells, L. Hollberg, L. Zink, D. A. Van Baak, M. D. Levenson, and W. R. Bosenberg, “Continuous-wave frequency tripling and quadrupling by simultaneous three-wave mixings in periodically poled crystals: application to a two-step 1.19–10.71-µm frequency bridge,” Opt. Lett. 22, 1211–1213 (1997).
[Crossref] [PubMed]

1996 (1)

J. Zhou, J. Peatross, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[Crossref] [PubMed]

1995 (2)

G. Assanto, “Transistor action through nonlinear cascading in Type II interactions,” Opt. Lett. 20, 1595–1597 (1995).
[Crossref] [PubMed]

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. VanStryland, “Coherent interactions for all-optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673–681 (1995).
[Crossref]

1994 (1)

1993 (1)

1980 (1)

R. S. Craxton, “Theory of high efficiency third harmonic generation of high power Nd-glass laser radiation,” Opt. Commun. 34, 474–478 (1980).
[Crossref]

Aquila, A.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

Arora, V.

R. A. Ganeev, H. Singhal, P. A. Naik, U. Chakravarty, V. Arora, J. A. Chakera, R. A. Khan, M. Raghuramaiah, S. R. Kumbhare, R. P. Kushwaha, and P. D. Gupta, “Optimization of the high-order harmonics generated from silver plasma,” Appl. Phys. B 87, 243–247 (2007).
[Crossref]

Assanto, G.

U. K. Sapaev and G. Assanto, “Femtosecond pulse synthesis by efficient second-harmonic generation in engineered quasi phase matching gratings,” Opt. Express 15, 7448–7457 (2007).
[Crossref] [PubMed]

A. De Rossi, V. Berger, G. Leo, and G. Assanto, “Form birefringence phase matching in multilayer semiconductor structures: tuning and tolerances,” IEEE J. Quantum Electron. 41, 1293–1302 (2005)
[Crossref]

J. C. G. de Sande, G. Leo, and G. Assanto, “Phase-matching engineering in birefringent AlGaAs waveguides for difference frequency generation,” IEEE J. Lightwave Technol. 20, 651–660 (2002)
[Crossref]

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. VanStryland, “Coherent interactions for all-optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673–681 (1995).
[Crossref]

G. Assanto, “Transistor action through nonlinear cascading in Type II interactions,” Opt. Lett. 20, 1595–1597 (1995).
[Crossref] [PubMed]

G. Assanto, I. Torelli, and S. Trillo, “All-optical processing by means of vectorial interactions in secondorder cascading: novel approaches,” Opt. Lett. 19, 1720–1722 (1994)
[Crossref] [PubMed]

G. I. Stegeman, M. Sheik-Bahae, E. VanStryland, and G. Assanto, “Large nonlinear phase shifts in second-order nonlinear optical processes,” Opt. Lett. 18, 13–15 (1993).
[Crossref] [PubMed]

Attwood, D. T.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

Backus, S.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

Berger, V.

A. De Rossi, V. Berger, G. Leo, and G. Assanto, “Form birefringence phase matching in multilayer semiconductor structures: tuning and tolerances,” IEEE J. Quantum Electron. 41, 1293–1302 (2005)
[Crossref]

Bosenberg, W. R.

Cao, Z. S.

L. H. Deng, X. M. Gao, Z. S. Cao, W. D. Chen, Y. Q. Yuan, W. J. Zhang, and Z. B. Gong, “Improvement to Sellmeier equation for periodically poled LiNbO3 crystal using mid-infrared difference-frequency generation,” Opt. Commun. 268, 110–114 (2006).
[Crossref]

Chakera, J. A.

R. A. Ganeev, H. Singhal, P. A. Naik, U. Chakravarty, V. Arora, J. A. Chakera, R. A. Khan, M. Raghuramaiah, S. R. Kumbhare, R. P. Kushwaha, and P. D. Gupta, “Optimization of the high-order harmonics generated from silver plasma,” Appl. Phys. B 87, 243–247 (2007).
[Crossref]

Chakravarty, U.

R. A. Ganeev, H. Singhal, P. A. Naik, U. Chakravarty, V. Arora, J. A. Chakera, R. A. Khan, M. Raghuramaiah, S. R. Kumbhare, R. P. Kushwaha, and P. D. Gupta, “Optimization of the high-order harmonics generated from silver plasma,” Appl. Phys. B 87, 243–247 (2007).
[Crossref]

Chang, Z.

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-X-ray harmonic emission,” Phys. Rev. A 58, R30–R33 (1998).
[Crossref]

Chen, W. D.

L. H. Deng, X. M. Gao, Z. S. Cao, W. D. Chen, Y. Q. Yuan, W. J. Zhang, and Z. B. Gong, “Improvement to Sellmeier equation for periodically poled LiNbO3 crystal using mid-infrared difference-frequency generation,” Opt. Commun. 268, 110–114 (2006).
[Crossref]

Christov, I.

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-X-ray harmonic emission,” Phys. Rev. A 58, R30–R33 (1998).
[Crossref]

Christov, I. P.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

J. Zhou, J. Peatross, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[Crossref] [PubMed]

Craxton, R. S.

R. S. Craxton, “Theory of high efficiency third harmonic generation of high power Nd-glass laser radiation,” Opt. Commun. 34, 474–478 (1980).
[Crossref]

De Rossi, A.

A. De Rossi, V. Berger, G. Leo, and G. Assanto, “Form birefringence phase matching in multilayer semiconductor structures: tuning and tolerances,” IEEE J. Quantum Electron. 41, 1293–1302 (2005)
[Crossref]

de Sande, J. C. G.

J. C. G. de Sande, G. Leo, and G. Assanto, “Phase-matching engineering in birefringent AlGaAs waveguides for difference frequency generation,” IEEE J. Lightwave Technol. 20, 651–660 (2002)
[Crossref]

de Sterke, C. M.

Deng, L. H.

L. H. Deng, X. M. Gao, Z. S. Cao, W. D. Chen, Y. Q. Yuan, W. J. Zhang, and Z. B. Gong, “Improvement to Sellmeier equation for periodically poled LiNbO3 crystal using mid-infrared difference-frequency generation,” Opt. Commun. 268, 110–114 (2006).
[Crossref]

Dmitriev, V. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, (Springer, Berlin, 1999).

Du, J.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal,” Appl. Phys. B 78, 265–267 (2004).
[Crossref]

Fejer, M. M.

Ganeev, R. A.

R. A. Ganeev, H. Singhal, P. A. Naik, U. Chakravarty, V. Arora, J. A. Chakera, R. A. Khan, M. Raghuramaiah, S. R. Kumbhare, R. P. Kushwaha, and P. D. Gupta, “Optimization of the high-order harmonics generated from silver plasma,” Appl. Phys. B 87, 243–247 (2007).
[Crossref]

Gao, X. M.

L. H. Deng, X. M. Gao, Z. S. Cao, W. D. Chen, Y. Q. Yuan, W. J. Zhang, and Z. B. Gong, “Improvement to Sellmeier equation for periodically poled LiNbO3 crystal using mid-infrared difference-frequency generation,” Opt. Commun. 268, 110–114 (2006).
[Crossref]

Gaudiosi, D.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

Ge, C .Z.

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C .Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[Crossref]

Gibson, E. A.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

Gong, Z. B.

L. H. Deng, X. M. Gao, Z. S. Cao, W. D. Chen, Y. Q. Yuan, W. J. Zhang, and Z. B. Gong, “Improvement to Sellmeier equation for periodically poled LiNbO3 crystal using mid-infrared difference-frequency generation,” Opt. Commun. 268, 110–114 (2006).
[Crossref]

Gullikson, E. M.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

Gupta, P. D.

R. A. Ganeev, H. Singhal, P. A. Naik, U. Chakravarty, V. Arora, J. A. Chakera, R. A. Khan, M. Raghuramaiah, S. R. Kumbhare, R. P. Kushwaha, and P. D. Gupta, “Optimization of the high-order harmonics generated from silver plasma,” Appl. Phys. B 87, 243–247 (2007).
[Crossref]

Gurzadyan, G. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, (Springer, Berlin, 1999).

Harris, J. S.

He, J. L.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal,” Appl. Phys. B 78, 265–267 (2004).
[Crossref]

Hollberg, L.

Kapteyn, H. C.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-X-ray harmonic emission,” Phys. Rev. A 58, R30–R33 (1998).
[Crossref]

J. Zhou, J. Peatross, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[Crossref] [PubMed]

Khan, R. A.

R. A. Ganeev, H. Singhal, P. A. Naik, U. Chakravarty, V. Arora, J. A. Chakera, R. A. Khan, M. Raghuramaiah, S. R. Kumbhare, R. P. Kushwaha, and P. D. Gupta, “Optimization of the high-order harmonics generated from silver plasma,” Appl. Phys. B 87, 243–247 (2007).
[Crossref]

Kumbhare, S. R.

R. A. Ganeev, H. Singhal, P. A. Naik, U. Chakravarty, V. Arora, J. A. Chakera, R. A. Khan, M. Raghuramaiah, S. R. Kumbhare, R. P. Kushwaha, and P. D. Gupta, “Optimization of the high-order harmonics generated from silver plasma,” Appl. Phys. B 87, 243–247 (2007).
[Crossref]

Kuo, P. S.

Kushwaha, R. P.

R. A. Ganeev, H. Singhal, P. A. Naik, U. Chakravarty, V. Arora, J. A. Chakera, R. A. Khan, M. Raghuramaiah, S. R. Kumbhare, R. P. Kushwaha, and P. D. Gupta, “Optimization of the high-order harmonics generated from silver plasma,” Appl. Phys. B 87, 243–247 (2007).
[Crossref]

Leo, G.

A. De Rossi, V. Berger, G. Leo, and G. Assanto, “Form birefringence phase matching in multilayer semiconductor structures: tuning and tolerances,” IEEE J. Quantum Electron. 41, 1293–1302 (2005)
[Crossref]

J. C. G. de Sande, G. Leo, and G. Assanto, “Phase-matching engineering in birefringent AlGaAs waveguides for difference frequency generation,” IEEE J. Lightwave Technol. 20, 651–660 (2002)
[Crossref]

Levenson, M. D.

Levi, O.

Liao, J.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal,” Appl. Phys. B 78, 265–267 (2004).
[Crossref]

Liu, H.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal,” Appl. Phys. B 78, 265–267 (2004).
[Crossref]

Ming, N. B.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal,” Appl. Phys. B 78, 265–267 (2004).
[Crossref]

Y. Y. Zhu and N. B. Ming, “Dielectric super-lattices for nonlinear optical effects,” Opt. Quantum Electron. 31, 1093–1128 (1999).
[Crossref]

S. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[Crossref]

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C .Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[Crossref]

Murnane, M. M.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-X-ray harmonic emission,” Phys. Rev. A 58, R30–R33 (1998).
[Crossref]

J. Zhou, J. Peatross, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[Crossref] [PubMed]

Naik, P. A.

R. A. Ganeev, H. Singhal, P. A. Naik, U. Chakravarty, V. Arora, J. A. Chakera, R. A. Khan, M. Raghuramaiah, S. R. Kumbhare, R. P. Kushwaha, and P. D. Gupta, “Optimization of the high-order harmonics generated from silver plasma,” Appl. Phys. B 87, 243–247 (2007).
[Crossref]

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, (Springer, Berlin, 1999).

Norton, A. H.

Paul, A.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

Peatross, J.

J. Zhou, J. Peatross, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[Crossref] [PubMed]

Pfister, O.

Pinguet, T. J.

Qin, Y. Q.

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C .Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[Crossref]

Raghuramaiah, M.

R. A. Ganeev, H. Singhal, P. A. Naik, U. Chakravarty, V. Arora, J. A. Chakera, R. A. Khan, M. Raghuramaiah, S. R. Kumbhare, R. P. Kushwaha, and P. D. Gupta, “Optimization of the high-order harmonics generated from silver plasma,” Appl. Phys. B 87, 243–247 (2007).
[Crossref]

Rundquist, A.

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-X-ray harmonic emission,” Phys. Rev. A 58, R30–R33 (1998).
[Crossref]

Sapaev, U. K.

Sheik-Bahae, M.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. VanStryland, “Coherent interactions for all-optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673–681 (1995).
[Crossref]

G. I. Stegeman, M. Sheik-Bahae, E. VanStryland, and G. Assanto, “Large nonlinear phase shifts in second-order nonlinear optical processes,” Opt. Lett. 18, 13–15 (1993).
[Crossref] [PubMed]

Singhal, H.

R. A. Ganeev, H. Singhal, P. A. Naik, U. Chakravarty, V. Arora, J. A. Chakera, R. A. Khan, M. Raghuramaiah, S. R. Kumbhare, R. P. Kushwaha, and P. D. Gupta, “Optimization of the high-order harmonics generated from silver plasma,” Appl. Phys. B 87, 243–247 (2007).
[Crossref]

Stegeman, G. I.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. VanStryland, “Coherent interactions for all-optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673–681 (1995).
[Crossref]

G. I. Stegeman, M. Sheik-Bahae, E. VanStryland, and G. Assanto, “Large nonlinear phase shifts in second-order nonlinear optical processes,” Opt. Lett. 18, 13–15 (1993).
[Crossref] [PubMed]

Tobey, R.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

Torelli, I.

Trillo, S.

Van Baak, D. A.

VanStryland, E.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. VanStryland, “Coherent interactions for all-optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673–681 (1995).
[Crossref]

G. I. Stegeman, M. Sheik-Bahae, E. VanStryland, and G. Assanto, “Large nonlinear phase shifts in second-order nonlinear optical processes,” Opt. Lett. 18, 13–15 (1993).
[Crossref] [PubMed]

Vodopyanov, K. L.

Wagner, N.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

Wang, H.

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-X-ray harmonic emission,” Phys. Rev. A 58, R30–R33 (1998).
[Crossref]

Wang, H. F.

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C .Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[Crossref]

Wang, H. T.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal,” Appl. Phys. B 78, 265–267 (2004).
[Crossref]

Wells, J. S.

Xu, F.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal,” Appl. Phys. B 78, 265–267 (2004).
[Crossref]

Yuan, Y. Q.

L. H. Deng, X. M. Gao, Z. S. Cao, W. D. Chen, Y. Q. Yuan, W. J. Zhang, and Z. B. Gong, “Improvement to Sellmeier equation for periodically poled LiNbO3 crystal using mid-infrared difference-frequency generation,” Opt. Commun. 268, 110–114 (2006).
[Crossref]

Zhang, W. J.

L. H. Deng, X. M. Gao, Z. S. Cao, W. D. Chen, Y. Q. Yuan, W. J. Zhang, and Z. B. Gong, “Improvement to Sellmeier equation for periodically poled LiNbO3 crystal using mid-infrared difference-frequency generation,” Opt. Commun. 268, 110–114 (2006).
[Crossref]

Zhou, J.

J. Zhou, J. Peatross, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[Crossref] [PubMed]

Zhu, S.

S. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[Crossref]

Zhu, S. N.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal,” Appl. Phys. B 78, 265–267 (2004).
[Crossref]

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C .Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[Crossref]

Zhu, Y. Y.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal,” Appl. Phys. B 78, 265–267 (2004).
[Crossref]

Y. Y. Zhu and N. B. Ming, “Dielectric super-lattices for nonlinear optical effects,” Opt. Quantum Electron. 31, 1093–1128 (1999).
[Crossref]

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C .Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[Crossref]

S. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[Crossref]

Zink, L.

Appl. Phys. B (2)

R. A. Ganeev, H. Singhal, P. A. Naik, U. Chakravarty, V. Arora, J. A. Chakera, R. A. Khan, M. Raghuramaiah, S. R. Kumbhare, R. P. Kushwaha, and P. D. Gupta, “Optimization of the high-order harmonics generated from silver plasma,” Appl. Phys. B 87, 243–247 (2007).
[Crossref]

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal,” Appl. Phys. B 78, 265–267 (2004).
[Crossref]

IEEE J. Lightwave Technol. (1)

J. C. G. de Sande, G. Leo, and G. Assanto, “Phase-matching engineering in birefringent AlGaAs waveguides for difference frequency generation,” IEEE J. Lightwave Technol. 20, 651–660 (2002)
[Crossref]

IEEE J. Quantum Electron. (2)

A. De Rossi, V. Berger, G. Leo, and G. Assanto, “Form birefringence phase matching in multilayer semiconductor structures: tuning and tolerances,” IEEE J. Quantum Electron. 41, 1293–1302 (2005)
[Crossref]

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. VanStryland, “Coherent interactions for all-optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673–681 (1995).
[Crossref]

Opt. Commun. (2)

R. S. Craxton, “Theory of high efficiency third harmonic generation of high power Nd-glass laser radiation,” Opt. Commun. 34, 474–478 (1980).
[Crossref]

L. H. Deng, X. M. Gao, Z. S. Cao, W. D. Chen, Y. Q. Yuan, W. J. Zhang, and Z. B. Gong, “Improvement to Sellmeier equation for periodically poled LiNbO3 crystal using mid-infrared difference-frequency generation,” Opt. Commun. 268, 110–114 (2006).
[Crossref]

Opt. Express (2)

Opt. Lett. (5)

Opt. Quantum Electron. (1)

Y. Y. Zhu and N. B. Ming, “Dielectric super-lattices for nonlinear optical effects,” Opt. Quantum Electron. 31, 1093–1128 (1999).
[Crossref]

Phys. Rev. A (1)

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, “Temporal phase control of soft-X-ray harmonic emission,” Phys. Rev. A 58, R30–R33 (1998).
[Crossref]

Phys. Rev. Lett. (2)

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C .Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).
[Crossref]

J. Zhou, J. Peatross, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[Crossref] [PubMed]

Science (2)

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft X-ray generation in the water window with Quasi-Phase Matching,” Science 302, 95–98 (2003).
[Crossref] [PubMed]

S. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[Crossref]

Other (1)

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, (Springer, Berlin, 1999).

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Figures (3)

Fig. 1.
Fig. 1. Conversion efficiencies versus propagation for an FF input at λ=5.0µm, by adopting the model Eq. (1) and (1) maintaining a uniform QPM grating optimized for SHG; (2) modulating the QPM grating in order to maximize the third harmonic; (3) modulating the QPM grating in order to maximize the fourth harmonic. Black, red, blue, green, magenta, cyan and yellow lines graph the calculated intensity evolutions of FF, 2nd, 3rd, 4th, 5th, 6th and 7th harmonics, respectively.
Fig. 2.
Fig. 2. Conversion efficiencies versus propagation for an FF input at λ=5.0µm, by adopting the model Eq. (1) and modultating the QM domain sizes in order to maximize the throughput at (1) 5th, (2) 6th and (3) 7th harmonic frequencies. Black, red, blue, green, magenta, cyan and yellow lines correspond to FF, 2nd, 3rd, 4th, 5th, 6th and 7th harmonics, respectively.
Fig. 3.
Fig. 3. Conversion efficiencies versus z for (1) 3rd and (2) 7th harmonics and various domain resolutions: red-0.1 µm, green-0.5 µm and magenta-1.0 µm. (3) Conversion efficiencies versus z for the 6th harmonic and domain resolution 0.1µm, calculated for various FF input intensities: magenta (0.1 GW/cm2), cyan (0.5 GW/cm2), black (1.0 GW/cm2), red (1.5 GW/cm2) and blue (2.0 GW/cm2).

Equations (7)

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

d A 1 dz = i 2 π δ ( z ) n 1 λ d eff [ A 1 * A 2 Δ 1 + A 2 * A 3 Δ 2 + A 3 * A 4 Δ 3 + A 4 * A 5 Δ 4 + A 5 * A 6 Δ 5 + A 6 * A 7 Δ 6 ]
d A 2 dz = i 4 π δ ( z ) n 2 λ d eff [ A 1 2 2 Δ 1 * + A 1 * A 3 Δ 2 + A 2 * A 4 Δ 7 + A 3 * A 5 Δ 8 + A 4 * A 6 Δ 9 + A 5 * A 7 Δ 10 ]
d A 3 dz = i 6 π δ ( z ) n 3 λ d eff [ A 1 A 2 Δ 2 * + A 1 * A 4 Δ 3 + A 2 * A 5 Δ 8 + A 3 * A 6 Δ 11 + A 4 * A 7 Δ 12 ]
d A 4 dz = i 8 π δ ( z ) n 4 λ d eff [ A 2 2 2 Δ 7 * + A 1 * A 5 Δ 4 + A 2 * A 6 Δ 9 + A 3 * A 7 Δ 12 + A 3 A 1 Δ 3 * ]
d A 5 dz = i 10 π δ ( z ) n 5 λ d eff [ A 1 A 4 Δ 4 * + A 2 A 3 Δ 8 * + A 1 * A 6 Δ 5 + A 2 * A 7 Δ 10 ]
d A 6 dz = i 12 π δ ( z ) n 6 λ d eff [ A 1 A 5 Δ 5 * + A 2 A 4 Δ 9 * + A 3 2 2 Δ 11 * + A 1 * A 7 Δ 6 ]
d A 7 dz = i 14 π δ ( z ) n 7 λ d eff [ A 1 A 6 Δ 6 * + A 2 A 5 Δ 10 * + A 3 A 4 Δ 12 * ]

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