Abstract

Recently attention has been focused on quasi-phase-matched self-frequency-conversion (SFC) laser generation in rare-earth-doped optical superlattice crystals, mainly because of their ability to generate multicolor lasers simultaneously across the visible portion of the spectrum through a single crystal. We present a general model for quasi-phase-matched SFC lasers in rare-earth-doped optical superlattice crystals that we fabricated by combining quasi-phase-matching theory and self-sum-frequency mixing (or self-frequency doubling) laser patterns. This model takes into account the TEM00 distribution of Gaussian beams with loose focusing, absorption, and coupling of pump beams and the effects of imperfect periodic structures. We analyze two types of errors, random period errors and linearly tapered period errors, in the periodicity of these structures to determine their effects on SFC laser properties (e.g., on effective nonlinear coefficients and phase-matching curves). Finally the model is applied to simulate SFC laser generation in a Nd3+ doped aperiodically poled lithium niobate crystal. By choice of one set of parameters, the calculated results, especially for threshold, total visible laser output power, and spectrum of relative laser intensity in the visible, explain the experimental phenomena in detail and indicate the validity of this model. Most significantly, the model presented makes understandable the simultaneous laser generation of multiple visible wavelengths (686, 605, 542, 482, 441, and 372 nm) from a single crystal.

© 2002 Optical Society of America

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  1. S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phased-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
    [CrossRef]
  2. I. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [CrossRef]
  3. D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, “Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains,” Appl. Phys. Lett. 37, 607–609 (1980).
    [CrossRef]
  4. N. B. Ming, J. F. Hong, and D. Feng, “The growth striations and ferroelectric domain structures in Czochralski-grown LiNbO3 single crystals,” J. Mater. Sci. 17, 1663–1670 (1982).
    [CrossRef]
  5. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
    [CrossRef]
  6. J. Capmany, “Simultaneous generation of red, green, and blue continuous-wave laser radiation in Nd3+-doped aperiodically poled lithium niobate,” Appl. Phys. Lett. 78, 144–146 (2001).
    [CrossRef]
  7. J. Capmany, V. Bermudez, D. Callejo, J. Garcia Sole, and E. Dieguez, “Continuous wave simultaneous multi-self-frequency conversion in Nd3+-doped aperiodically poled bulk lithium niobate,” Appl. Phys. Lett. 76, 1225–1227 (2000).
    [CrossRef]
  8. J. Capmany, E. Montoya, V. Bermudez, D. Callejo, E. Dieguez, and L. E. Bausa, “Self-frequency doubling in Yb3+ doped periodically poled LiNbO3:MgO bulk crystal,” Appl. Phys. Lett. 76, 1374–1376 (2000).
    [CrossRef]
  9. T. Y. Fan, A. Cordova-Plaza, M. J. F. Digonnet, R. L. Byer, and H. J. Shaw, “Nd:MgO:LiNbO3 spectrscopy and laser devices,” J. Opt. Soc. Am. B 3, 140–147 (1986).
    [CrossRef]
  10. D. Jaque, S. A. Sanz-Garcia, J. Capmany, and J. Garcia Sole, “Continuous wave laser radiation at 693 nm from LiNbO3:ZnO:Nd3+ nonlinear laser crystal,” Appl. Phys. B 70, 483–486 (2000).
    [CrossRef]
  11. X.-Y. Chen, Z.-D. Luo, and Y.-D. Huang, “Modeling of the self-sum-frequency mixing laser,” J. Opt. Soc. Am. B 18, 646–656 (2001).
    [CrossRef]
  12. X.-Y. Chen, Z.-D. Luo, and Y.-D. Huang, “Modeling of the self-sum-frequency-mixing laser,” Chin. Phys. Lett. 18, 230–232 (2001).
    [CrossRef]
  13. G. I. Edwands and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
    [CrossRef]
  14. H. Y. Shen and H. Su, “Operating conditions of continuous wave simultaneous dual wavelength laser in neodymium host crystals,” J. Appl. Phys. 86, 6647–6651 (1999).
    [CrossRef]

2001 (3)

J. Capmany, “Simultaneous generation of red, green, and blue continuous-wave laser radiation in Nd3+-doped aperiodically poled lithium niobate,” Appl. Phys. Lett. 78, 144–146 (2001).
[CrossRef]

X.-Y. Chen, Z.-D. Luo, and Y.-D. Huang, “Modeling of the self-sum-frequency mixing laser,” J. Opt. Soc. Am. B 18, 646–656 (2001).
[CrossRef]

X.-Y. Chen, Z.-D. Luo, and Y.-D. Huang, “Modeling of the self-sum-frequency-mixing laser,” Chin. Phys. Lett. 18, 230–232 (2001).
[CrossRef]

2000 (3)

D. Jaque, S. A. Sanz-Garcia, J. Capmany, and J. Garcia Sole, “Continuous wave laser radiation at 693 nm from LiNbO3:ZnO:Nd3+ nonlinear laser crystal,” Appl. Phys. B 70, 483–486 (2000).
[CrossRef]

J. Capmany, V. Bermudez, D. Callejo, J. Garcia Sole, and E. Dieguez, “Continuous wave simultaneous multi-self-frequency conversion in Nd3+-doped aperiodically poled bulk lithium niobate,” Appl. Phys. Lett. 76, 1225–1227 (2000).
[CrossRef]

J. Capmany, E. Montoya, V. Bermudez, D. Callejo, E. Dieguez, and L. E. Bausa, “Self-frequency doubling in Yb3+ doped periodically poled LiNbO3:MgO bulk crystal,” Appl. Phys. Lett. 76, 1374–1376 (2000).
[CrossRef]

1999 (1)

H. Y. Shen and H. Su, “Operating conditions of continuous wave simultaneous dual wavelength laser in neodymium host crystals,” J. Appl. Phys. 86, 6647–6651 (1999).
[CrossRef]

1997 (1)

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

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

1986 (1)

1984 (1)

G. I. Edwands and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

1982 (1)

N. B. Ming, J. F. Hong, and D. Feng, “The growth striations and ferroelectric domain structures in Czochralski-grown LiNbO3 single crystals,” J. Mater. Sci. 17, 1663–1670 (1982).
[CrossRef]

1980 (1)

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, “Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains,” Appl. Phys. Lett. 37, 607–609 (1980).
[CrossRef]

1962 (1)

I. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Armstrong, I. A.

I. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Bausa, L. E.

J. Capmany, E. Montoya, V. Bermudez, D. Callejo, E. Dieguez, and L. E. Bausa, “Self-frequency doubling in Yb3+ doped periodically poled LiNbO3:MgO bulk crystal,” Appl. Phys. Lett. 76, 1374–1376 (2000).
[CrossRef]

Bermudez, V.

J. Capmany, E. Montoya, V. Bermudez, D. Callejo, E. Dieguez, and L. E. Bausa, “Self-frequency doubling in Yb3+ doped periodically poled LiNbO3:MgO bulk crystal,” Appl. Phys. Lett. 76, 1374–1376 (2000).
[CrossRef]

J. Capmany, V. Bermudez, D. Callejo, J. Garcia Sole, and E. Dieguez, “Continuous wave simultaneous multi-self-frequency conversion in Nd3+-doped aperiodically poled bulk lithium niobate,” Appl. Phys. Lett. 76, 1225–1227 (2000).
[CrossRef]

Bloembergen, N.

I. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

T. Y. Fan, A. Cordova-Plaza, M. J. F. Digonnet, R. L. Byer, and H. J. Shaw, “Nd:MgO:LiNbO3 spectrscopy and laser devices,” J. Opt. Soc. Am. B 3, 140–147 (1986).
[CrossRef]

Callejo, D.

J. Capmany, V. Bermudez, D. Callejo, J. Garcia Sole, and E. Dieguez, “Continuous wave simultaneous multi-self-frequency conversion in Nd3+-doped aperiodically poled bulk lithium niobate,” Appl. Phys. Lett. 76, 1225–1227 (2000).
[CrossRef]

J. Capmany, E. Montoya, V. Bermudez, D. Callejo, E. Dieguez, and L. E. Bausa, “Self-frequency doubling in Yb3+ doped periodically poled LiNbO3:MgO bulk crystal,” Appl. Phys. Lett. 76, 1374–1376 (2000).
[CrossRef]

Capmany, J.

J. Capmany, “Simultaneous generation of red, green, and blue continuous-wave laser radiation in Nd3+-doped aperiodically poled lithium niobate,” Appl. Phys. Lett. 78, 144–146 (2001).
[CrossRef]

J. Capmany, V. Bermudez, D. Callejo, J. Garcia Sole, and E. Dieguez, “Continuous wave simultaneous multi-self-frequency conversion in Nd3+-doped aperiodically poled bulk lithium niobate,” Appl. Phys. Lett. 76, 1225–1227 (2000).
[CrossRef]

J. Capmany, E. Montoya, V. Bermudez, D. Callejo, E. Dieguez, and L. E. Bausa, “Self-frequency doubling in Yb3+ doped periodically poled LiNbO3:MgO bulk crystal,” Appl. Phys. Lett. 76, 1374–1376 (2000).
[CrossRef]

D. Jaque, S. A. Sanz-Garcia, J. Capmany, and J. Garcia Sole, “Continuous wave laser radiation at 693 nm from LiNbO3:ZnO:Nd3+ nonlinear laser crystal,” Appl. Phys. B 70, 483–486 (2000).
[CrossRef]

Chen, X.-Y.

X.-Y. Chen, Z.-D. Luo, and Y.-D. Huang, “Modeling of the self-sum-frequency mixing laser,” J. Opt. Soc. Am. B 18, 646–656 (2001).
[CrossRef]

X.-Y. Chen, Z.-D. Luo, and Y.-D. Huang, “Modeling of the self-sum-frequency-mixing laser,” Chin. Phys. Lett. 18, 230–232 (2001).
[CrossRef]

Cordova-Plaza, A.

Dieguez, E.

J. Capmany, E. Montoya, V. Bermudez, D. Callejo, E. Dieguez, and L. E. Bausa, “Self-frequency doubling in Yb3+ doped periodically poled LiNbO3:MgO bulk crystal,” Appl. Phys. Lett. 76, 1374–1376 (2000).
[CrossRef]

J. Capmany, V. Bermudez, D. Callejo, J. Garcia Sole, and E. Dieguez, “Continuous wave simultaneous multi-self-frequency conversion in Nd3+-doped aperiodically poled bulk lithium niobate,” Appl. Phys. Lett. 76, 1225–1227 (2000).
[CrossRef]

Digonnet, M. J. F.

Ducuing, J.

I. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Edwands, G. I.

G. I. Edwands and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

Fan, T. Y.

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Feng, D.

N. B. Ming, J. F. Hong, and D. Feng, “The growth striations and ferroelectric domain structures in Czochralski-grown LiNbO3 single crystals,” J. Mater. Sci. 17, 1663–1670 (1982).
[CrossRef]

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, “Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains,” Appl. Phys. Lett. 37, 607–609 (1980).
[CrossRef]

Hong, J. F.

N. B. Ming, J. F. Hong, and D. Feng, “The growth striations and ferroelectric domain structures in Czochralski-grown LiNbO3 single crystals,” J. Mater. Sci. 17, 1663–1670 (1982).
[CrossRef]

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, “Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains,” Appl. Phys. Lett. 37, 607–609 (1980).
[CrossRef]

Huang, Y.-D.

X.-Y. Chen, Z.-D. Luo, and Y.-D. Huang, “Modeling of the self-sum-frequency mixing laser,” J. Opt. Soc. Am. B 18, 646–656 (2001).
[CrossRef]

X.-Y. Chen, Z.-D. Luo, and Y.-D. Huang, “Modeling of the self-sum-frequency-mixing laser,” Chin. Phys. Lett. 18, 230–232 (2001).
[CrossRef]

Jaque, D.

D. Jaque, S. A. Sanz-Garcia, J. Capmany, and J. Garcia Sole, “Continuous wave laser radiation at 693 nm from LiNbO3:ZnO:Nd3+ nonlinear laser crystal,” Appl. Phys. B 70, 483–486 (2000).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Lawrence, M.

G. I. Edwands and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

Luo, Z.-D.

X.-Y. Chen, Z.-D. Luo, and Y.-D. Huang, “Modeling of the self-sum-frequency-mixing laser,” Chin. Phys. Lett. 18, 230–232 (2001).
[CrossRef]

X.-Y. Chen, Z.-D. Luo, and Y.-D. Huang, “Modeling of the self-sum-frequency mixing laser,” J. Opt. Soc. Am. B 18, 646–656 (2001).
[CrossRef]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Ming, N. B.

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

N. B. Ming, J. F. Hong, and D. Feng, “The growth striations and ferroelectric domain structures in Czochralski-grown LiNbO3 single crystals,” J. Mater. Sci. 17, 1663–1670 (1982).
[CrossRef]

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, “Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains,” Appl. Phys. Lett. 37, 607–609 (1980).
[CrossRef]

Montoya, E.

J. Capmany, E. Montoya, V. Bermudez, D. Callejo, E. Dieguez, and L. E. Bausa, “Self-frequency doubling in Yb3+ doped periodically poled LiNbO3:MgO bulk crystal,” Appl. Phys. Lett. 76, 1374–1376 (2000).
[CrossRef]

Pershan, P. S.

I. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Sanz-Garcia, S. A.

D. Jaque, S. A. Sanz-Garcia, J. Capmany, and J. Garcia Sole, “Continuous wave laser radiation at 693 nm from LiNbO3:ZnO:Nd3+ nonlinear laser crystal,” Appl. Phys. B 70, 483–486 (2000).
[CrossRef]

Shaw, H. J.

Shen, H. Y.

H. Y. Shen and H. Su, “Operating conditions of continuous wave simultaneous dual wavelength laser in neodymium host crystals,” J. Appl. Phys. 86, 6647–6651 (1999).
[CrossRef]

Sole, J. Garcia

D. Jaque, S. A. Sanz-Garcia, J. Capmany, and J. Garcia Sole, “Continuous wave laser radiation at 693 nm from LiNbO3:ZnO:Nd3+ nonlinear laser crystal,” Appl. Phys. B 70, 483–486 (2000).
[CrossRef]

J. Capmany, V. Bermudez, D. Callejo, J. Garcia Sole, and E. Dieguez, “Continuous wave simultaneous multi-self-frequency conversion in Nd3+-doped aperiodically poled bulk lithium niobate,” Appl. Phys. Lett. 76, 1225–1227 (2000).
[CrossRef]

Su, H.

H. Y. Shen and H. Su, “Operating conditions of continuous wave simultaneous dual wavelength laser in neodymium host crystals,” J. Appl. Phys. 86, 6647–6651 (1999).
[CrossRef]

Wang, Y. N.

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, “Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains,” Appl. Phys. Lett. 37, 607–609 (1980).
[CrossRef]

Yang, Y. S.

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, “Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains,” Appl. Phys. Lett. 37, 607–609 (1980).
[CrossRef]

Yang, Z.

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, “Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains,” Appl. Phys. Lett. 37, 607–609 (1980).
[CrossRef]

Zhu, J. S.

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, “Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains,” Appl. Phys. Lett. 37, 607–609 (1980).
[CrossRef]

Zhu, S. N.

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

Zhu, Y. Y.

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

Appl. Phys. B (1)

D. Jaque, S. A. Sanz-Garcia, J. Capmany, and J. Garcia Sole, “Continuous wave laser radiation at 693 nm from LiNbO3:ZnO:Nd3+ nonlinear laser crystal,” Appl. Phys. B 70, 483–486 (2000).
[CrossRef]

Appl. Phys. Lett. (4)

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, “Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains,” Appl. Phys. Lett. 37, 607–609 (1980).
[CrossRef]

J. Capmany, “Simultaneous generation of red, green, and blue continuous-wave laser radiation in Nd3+-doped aperiodically poled lithium niobate,” Appl. Phys. Lett. 78, 144–146 (2001).
[CrossRef]

J. Capmany, V. Bermudez, D. Callejo, J. Garcia Sole, and E. Dieguez, “Continuous wave simultaneous multi-self-frequency conversion in Nd3+-doped aperiodically poled bulk lithium niobate,” Appl. Phys. Lett. 76, 1225–1227 (2000).
[CrossRef]

J. Capmany, E. Montoya, V. Bermudez, D. Callejo, E. Dieguez, and L. E. Bausa, “Self-frequency doubling in Yb3+ doped periodically poled LiNbO3:MgO bulk crystal,” Appl. Phys. Lett. 76, 1374–1376 (2000).
[CrossRef]

Chin. Phys. Lett. (1)

X.-Y. Chen, Z.-D. Luo, and Y.-D. Huang, “Modeling of the self-sum-frequency-mixing laser,” Chin. Phys. Lett. 18, 230–232 (2001).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

J. Appl. Phys. (1)

H. Y. Shen and H. Su, “Operating conditions of continuous wave simultaneous dual wavelength laser in neodymium host crystals,” J. Appl. Phys. 86, 6647–6651 (1999).
[CrossRef]

J. Mater. Sci. (1)

N. B. Ming, J. F. Hong, and D. Feng, “The growth striations and ferroelectric domain structures in Czochralski-grown LiNbO3 single crystals,” J. Mater. Sci. 17, 1663–1670 (1982).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Quantum Electron. (1)

G. I. Edwands and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

Phys. Rev. (1)

I. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Science (1)

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

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Figures (6)

Fig. 1
Fig. 1

Model of random period errors (see text of Subsection 3.A).

Fig. 2
Fig. 2

Value of χQ for 1st-order QPM SSFM in Nd:APLN crystal versus the deviation from the nominal operating point, δΔkL. Tunning curves with random period errors and with linearly tapered period errors are shown.

Fig. 3
Fig. 3

Value of dQ for 1st-order QPM of SFD (or SHG) in Nd:APLN crystal versus the practical fundamental wavelength.

Fig. 4
Fig. 4

Calculated output powers at dual wavelengths 1084 and 1372 nm as a function of absorbed pump power.

Fig. 5
Fig. 5

Calculated output powers of the visible lasers simultaneously generated at 686, 605, 542, 482, 441, and 372 nm as functions of the absorbed pump power in a single Nd:APLN crystal.

Fig. 6
Fig. 6

Simulated spectrum of the relative laser intensity in the visible.

Tables (2)

Tables Icon

Table 1 Cavity parameters for the Oscillation of Dual-Wavelength Fundamental Lasers in a Nd:APLN Crystal

Tables Icon

Table 2 Calculated Values of χQ and dQ and Output Power of the Six Visible Lasers in the Nd:APLN Crystal

Equations (75)

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

p(r, z)=p0 exp(-1/2αpz)exp(-r2/wp2),
1(r, z)=10 exp(-r2/w12),
d2(r, z)dz=iω2χeff (z)2cn2p(r, z)1(r, z)exp(-iΔkz),
Δkk2-kp-k1=πlc,
lc=λ12 λ1λp(n2-np)+(n2-n1)-1
d2(r, z)dz=Aχeff (z)exp[-(iΔk+1/2αp)z],
w2=wpw1(wp2+w12)2
A=iω22cn2p010 exp(-r2/w22).
2(r, L)=A 0L χeff (z)exp[-(iΔk+1/2αp)z]dz.
2(r, L)=Aχeff L1-exp(-1/2αpL)1/2αpL.
2=-2Ag1χeffiΔk+1/2αp k=1N exp(-iϕk-αpzk/2),
2=iAg1χQL1-exp(-1/2αpL)1/2αpL=2,ideal1-exp(-1/2αpL)1/2αpL,
2,ideal=iAg1χQL.
22,ideal=1N k=1N exp(-iϕk-αpzk/2)1L 0L exp(-iϕ(z)-1/2αpz)dz,
2=2,idealB(δΔk),
B(δΔk)=1-exp[-(iδΔk+1/2αp)L](iδΔk+1/2αp)L.
2=iAg1χQL sin cδΔkL2exp-i δΔkL2.
2=2(r, L)=Aχeff LG(Δk),
G(Δk)=1L 0L g(z)exp[-(iΔk+1/2αp)z]dz.
g(z)=n=- Gn exp(iknz),
kn=2πnΛ.
Gn=1Λ 0Λ g(ξ)exp(-iknξ)dξ=2πn sin(πnD)exp(-iπnD),
2=AχeffL n=- GnB(Δk-kn).
2=-iAχQLB(Δk-km),
km=2πmΛ=πlc=Δk0.
P2=120cn2 02π0|2(r, L)|2rdrdϕ=0ω2216 |10|2|p0|2cn2χQ2L2|B(δΔk)|2πw22.
Pp0=0cnp|p0|2 πwp24,
Pc=0cn1|10|2 πw124.
P2=KPp0Pc,
K=4ω02χQ2L2|B(δΔk)|20c3npn1n2π(w12+wp2).
P2,nonideal=KPp0Pc,
K=4ω02χQ2L20c3npn1n2π(w12+wp2),
χQχQ=P2,nonidealP2,ideal1/2=22,ideal=1N k=1N exp(-iϕk-αpzk/2)1L 0L exp-iϕ(z)-12αpzdz.
Pc=πw12Is4q 2G2δL-ln R1R2+2KPp0Pp0-1,
q=1-0.92 wp2wp2+w12,
G=2σeτfλ1[1-exp(-αpL)]πhc(wp2+w12;
Pf=(1-R2)Pc,
PSSFM=KPcPp0T.
Pth=πhc(wp2+w12)(2δL-ln R1R2)4σeτfλ1[1-exp(-αpL)]-2πhc(wp2+w12)K.
d2(r, z)dz=Adeff (z)exp(-iΔkz),
A=iω1102cn2 exp(-r2/w22);
Δkk2-2k1=πlc,
2(r, L)=A 0L deff (z)exp(-iΔkz)dz.
2=i2Ag1deffΔk k=1N exp(-iϕk).
2,ideal=iAg1dQL,
22,ideal=1N k=1N exp(-iϕk)1L 0L exp[-iϕ(z)]dz.
2=-iAdQL sin cδΔkL2exp-i δΔkL2,
P2=120cn2 02π0|2(r, L)|2rdrdϕ=8ω12dQ2L2 sin c12δΔk20c3n12n2πw12Pc2.
P2,ideal=KSHGPc2,
KSHG=8ω12dQ2L20c3n12n2πw12.
P2,nonideal=KSHGPc2,
KSHG=8ω12dQ2L20c3n12n2πw12,
dQdQ=P2,nonidealP2,ideal1/2=22,ideal=1N k=1N exp(-iϕk)1L 0L exp[-iϕ(z)]dz.
Pc=πw12Is4q 2G2δL-ln R1R2+2KSHGPcPp0-1.
Pf=(1-R2)Pc,
PSFD=KSHGPc2T.
Pth=πhc(wp2+w12)(2δL-ln R1R2)4σeτfλ1[1-exp(-αpL)].
ˆ21L 0L exp[-iϕ(z)]dz1L 0L exp-12αpzdz=1-exp(-1/2αpL)1/2αpL 1L 0L exp[-iϕ(z)]dz.
ηˆrandom=|ˆ2|2=(χQ/χQ)2=1-exp(-1/2αpL)1/2αpL2 2D2{F2-S2+SD+e-S[(S2-F2)cos(F)-2FS sin(F)]},
Δlj=ΔlN j-N2.
ϕk=πΔl2Nlc[k(k+1)-Nk]+δΔkzk,0.
ϕ(z)=πΔl2Nlc zmlc2-(N-1)zmlc+δΔkz.
ϕ(z)=πΔlN2lc zL2-zL+δΔkL zL.
ξ=12 NΔllc,ν=δΔkL2πξ2,
t=2ξzL-1-ν2
ϕ(t)=π2t2-π2ξ2(1-ν)2.
ˆ21L 0L exp-iϕ(z)-12αpzdz=expi π2ξ2(1-ν)2-14αpL(1-ν)2ξ×-ξ(1-ν)ξ(1+ν) exp-i π2t2-αpL4ξtdt.
ηˆtaper=|ˆ2|2=χQχQ2=exp-14αpL(1-ν)2ξ×-ξ(1-ν)ξ(1+ν) exp-i π2t2-αpL4ξtdt2.
ˆ2=expi π2ξ2(1-ν)22ξ -ξ(1-ν)ξ(1+ν) exp-i π2t2dt=expi π2ξ2(1-ν)22ξ{C[ξ(1+ν)]+C[ξ(1-ν)]-iS[ξ(1+ν)]-iS[ξ(1-ν]},
ηˆtaper=|ˆ2|2=dQdQ2=14ξ2 -ξ(1-ν)ξ(1+ν) exp-i π2t2dt2=(1/4ξ2){C[ξ(1+ν)]+C[ξ(1-ν)]-iS[ξ(1+ν)]-iS[ξ(1-ν]}2,
C(x)=0x cosπ2t2dt,S(x)=0x sinπ2t2dt.
wc=λLπ g1-g1/4,g=1-LR;
ne(λ)2=4.5820+0.09921λ2-0.21092-0.02194λ2,
PSFM=4ω02χQ2L20c3n3n1n2π(wc12+wc22)Pc(1084)Pc(1372)T.
PSHG=8ωp2dQ2L20c3np2n2πwp2Pp02T.

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