Abstract

Second-harmonic generation of blue light in quasi-phase-matching waveguides is analyzed with respect to the linewidth of the pump radiation. From the coupled-wave equation, when the pump linewidth is small, the conversion efficiency is shown to be enhanced by a factor of 2, compared with a single-mode case. A degradation of 3 dB occurs for a linewidth of three times the acceptance bandwidth. We also analyze the influence of the pump spectrum on measurements when the frequency response of a waveguide is evaluated by tuning the fundamental wavelength or by measuring the spectrum of the generated second-harmonic radiation.

© 1991 Optical Society of America

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References

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  1. J. Webjörn, F. Laurell, and G. Arvidsson, “Fabrication of periodically domain-inverted channel waveguides in lithium niobate for second-harmonic generation,” IEEE J. Lightwave Technol. 7, 1597–1600 (1989).
    [CrossRef]
  2. J. Webjörn, F. Laurell, and G. Arvidsson, “Blue light generated by frequency doubling of laser diode light in a lithium niobate channel waveguide,” IEEE Photon. Technol. Lett. 1, 316–318 (1989).
    [CrossRef]
  3. E. J. Lim, M. M. Fejer, R. L. Byer, and W. J. Kozlovsky, “Blue light generated by frequency doubling in periodically poled lithium niobate channel waveguide,” Electron. Lett. 25, 731–732 (1989).
    [CrossRef]
  4. F. Laurell, J. Webjörn, and G. Arvidsson, “Properties of quasi-phase-matching lithium niobate waveguides,” in Integrated Photonics Research, Vol. 5 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 110–111.
  5. N. Bloembergen, Nonlinear Optics(Benjamin, New York, 1965).
  6. A. Yariv, Optical Electronics (Holt, Rhinehart & Winston, New York, 1985).
  7. F. Laurell and G. Arvidsson, “Frequency doubling in Ti:MgO:LiNbO3channel waveguides,” J. Opt. Soc. Am. B 5, 292–299 (1988).
    [CrossRef]
  8. S. Helmfrid and G. Arvidsson, “Influence of randomly varying domain lengths and nonuniform effective index on second-harmonic generation in quasi-phase-matching waveguides,” J. Opt. Soc. Am. B,  8, 797–804 (1991).
    [CrossRef]

1991 (1)

1989 (3)

J. Webjörn, F. Laurell, and G. Arvidsson, “Fabrication of periodically domain-inverted channel waveguides in lithium niobate for second-harmonic generation,” IEEE J. Lightwave Technol. 7, 1597–1600 (1989).
[CrossRef]

J. Webjörn, F. Laurell, and G. Arvidsson, “Blue light generated by frequency doubling of laser diode light in a lithium niobate channel waveguide,” IEEE Photon. Technol. Lett. 1, 316–318 (1989).
[CrossRef]

E. J. Lim, M. M. Fejer, R. L. Byer, and W. J. Kozlovsky, “Blue light generated by frequency doubling in periodically poled lithium niobate channel waveguide,” Electron. Lett. 25, 731–732 (1989).
[CrossRef]

1988 (1)

Arvidsson, G.

S. Helmfrid and G. Arvidsson, “Influence of randomly varying domain lengths and nonuniform effective index on second-harmonic generation in quasi-phase-matching waveguides,” J. Opt. Soc. Am. B,  8, 797–804 (1991).
[CrossRef]

J. Webjörn, F. Laurell, and G. Arvidsson, “Fabrication of periodically domain-inverted channel waveguides in lithium niobate for second-harmonic generation,” IEEE J. Lightwave Technol. 7, 1597–1600 (1989).
[CrossRef]

J. Webjörn, F. Laurell, and G. Arvidsson, “Blue light generated by frequency doubling of laser diode light in a lithium niobate channel waveguide,” IEEE Photon. Technol. Lett. 1, 316–318 (1989).
[CrossRef]

F. Laurell and G. Arvidsson, “Frequency doubling in Ti:MgO:LiNbO3channel waveguides,” J. Opt. Soc. Am. B 5, 292–299 (1988).
[CrossRef]

F. Laurell, J. Webjörn, and G. Arvidsson, “Properties of quasi-phase-matching lithium niobate waveguides,” in Integrated Photonics Research, Vol. 5 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 110–111.

Bloembergen, N.

N. Bloembergen, Nonlinear Optics(Benjamin, New York, 1965).

Byer, R. L.

E. J. Lim, M. M. Fejer, R. L. Byer, and W. J. Kozlovsky, “Blue light generated by frequency doubling in periodically poled lithium niobate channel waveguide,” Electron. Lett. 25, 731–732 (1989).
[CrossRef]

Fejer, M. M.

E. J. Lim, M. M. Fejer, R. L. Byer, and W. J. Kozlovsky, “Blue light generated by frequency doubling in periodically poled lithium niobate channel waveguide,” Electron. Lett. 25, 731–732 (1989).
[CrossRef]

Helmfrid, S.

Kozlovsky, W. J.

E. J. Lim, M. M. Fejer, R. L. Byer, and W. J. Kozlovsky, “Blue light generated by frequency doubling in periodically poled lithium niobate channel waveguide,” Electron. Lett. 25, 731–732 (1989).
[CrossRef]

Laurell, F.

J. Webjörn, F. Laurell, and G. Arvidsson, “Blue light generated by frequency doubling of laser diode light in a lithium niobate channel waveguide,” IEEE Photon. Technol. Lett. 1, 316–318 (1989).
[CrossRef]

J. Webjörn, F. Laurell, and G. Arvidsson, “Fabrication of periodically domain-inverted channel waveguides in lithium niobate for second-harmonic generation,” IEEE J. Lightwave Technol. 7, 1597–1600 (1989).
[CrossRef]

F. Laurell and G. Arvidsson, “Frequency doubling in Ti:MgO:LiNbO3channel waveguides,” J. Opt. Soc. Am. B 5, 292–299 (1988).
[CrossRef]

F. Laurell, J. Webjörn, and G. Arvidsson, “Properties of quasi-phase-matching lithium niobate waveguides,” in Integrated Photonics Research, Vol. 5 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 110–111.

Lim, E. J.

E. J. Lim, M. M. Fejer, R. L. Byer, and W. J. Kozlovsky, “Blue light generated by frequency doubling in periodically poled lithium niobate channel waveguide,” Electron. Lett. 25, 731–732 (1989).
[CrossRef]

Webjörn, J.

J. Webjörn, F. Laurell, and G. Arvidsson, “Fabrication of periodically domain-inverted channel waveguides in lithium niobate for second-harmonic generation,” IEEE J. Lightwave Technol. 7, 1597–1600 (1989).
[CrossRef]

J. Webjörn, F. Laurell, and G. Arvidsson, “Blue light generated by frequency doubling of laser diode light in a lithium niobate channel waveguide,” IEEE Photon. Technol. Lett. 1, 316–318 (1989).
[CrossRef]

F. Laurell, J. Webjörn, and G. Arvidsson, “Properties of quasi-phase-matching lithium niobate waveguides,” in Integrated Photonics Research, Vol. 5 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 110–111.

Yariv, A.

A. Yariv, Optical Electronics (Holt, Rhinehart & Winston, New York, 1985).

Electron. Lett. (1)

E. J. Lim, M. M. Fejer, R. L. Byer, and W. J. Kozlovsky, “Blue light generated by frequency doubling in periodically poled lithium niobate channel waveguide,” Electron. Lett. 25, 731–732 (1989).
[CrossRef]

IEEE J. Lightwave Technol. (1)

J. Webjörn, F. Laurell, and G. Arvidsson, “Fabrication of periodically domain-inverted channel waveguides in lithium niobate for second-harmonic generation,” IEEE J. Lightwave Technol. 7, 1597–1600 (1989).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. Webjörn, F. Laurell, and G. Arvidsson, “Blue light generated by frequency doubling of laser diode light in a lithium niobate channel waveguide,” IEEE Photon. Technol. Lett. 1, 316–318 (1989).
[CrossRef]

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

Other (3)

F. Laurell, J. Webjörn, and G. Arvidsson, “Properties of quasi-phase-matching lithium niobate waveguides,” in Integrated Photonics Research, Vol. 5 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 110–111.

N. Bloembergen, Nonlinear Optics(Benjamin, New York, 1965).

A. Yariv, Optical Electronics (Holt, Rhinehart & Winston, New York, 1985).

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Figures (5)

Fig. 1
Fig. 1

Solid curve: The FWHM acceptance bandwidth in nanometers for second-harmonic generation in a 10-mm-long quasi-phase-matching lithium niobate waveguide as a function of the fundamental wavelength in nanometers. Dashed curve: The corresponding relationship when birefringence phase-matching is used. Single-mode operation of the pump is assumed.

Fig. 2
Fig. 2

Second-harmonic (SH) power generated with a multimode pump as a function of pump linewidth. The output power is normalized to be 1 for a corresponding case with a single-mode pump, and the linewidth is normalized by the acceptance bandwidth of the process.

Fig. 3
Fig. 3

(a) FWHM of the phase-matching peak at a wavelength scan with a multimode pump as a function of the linewidth of the pump laser. Both the abscissa and the ordinate are given in units of the acceptance bandwidth of the process, i.e., the FWHM of the phase-matching peak at a wavelength scan with a monochromatic pump laser. (b) Ratio between the acceptance bandwidth and the width at a wavelength scan with a multimode laser as a function of the scan width normalized by the linewidth of the pump laser. This curve can be used to estimate the true bandwidth of the process when the measured width of the phase-matching peak and the linewidth of the pump laser are known.

Fig. 4
Fig. 4

Convolution of the input spectrum according to Eq. (12) as a function of Ω/ΔΩL, where ΔΩL is the linewidth of the pump laser.

Fig. 5
Fig. 5

Linewidth of the generated second-harmonic (SH) radiation in units of the corresponding linewidth when an infinitely broad pump laser is used as a function of pump linewidth in units of the acceptance bandwidth of the process. The normalization is performed in such a way that the involved widths can be expressed both in wavelengths and in frequency units.

Equations (17)

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E ( z , t ) = q = - Q Q E q ( ω ) exp [ i ( ω q t - β q ( ω ) z + Φ q ) ] , E q ( ω ) = 0 q > Q ,
d E 2 r ( 2 ω ) ( z ) d z = - i ω 0 d ( z ) n ( 2 ω ) c 0 { ( E r ( ω ) ) 2 exp [ i ( β 2 r ( 2 ω ) - 2 β r ( ω ) ) z ] × exp ( 2 i Φ r ) + 2 q = 1 Q - r E r + q ( ω ) E r - q ( ω ) exp [ i ( β 2 r ( 2 ω ) - β r + q ( ω ) - β r - q ( ω ) ) z ] × exp [ i ( Φ r + q + Φ r - q ) ] } ,
d E 2 r + 1 ( 2 ω ) ( z ) d z = - i ω 0 d ( z ) n ( 2 ω ) c 0 { 2 q = 0 Q - r - 1 E r + q + 1 ( ω ) E r - q ( ω ) exp [ i ( β 2 r + 1 ( 2 ω ) - β r + q + 1 ( ω ) - β r - q ( ω ) ) z ] exp [ i ( Φ r + q + 1 + Φ r - q ) ] } ,
E m ( 2 ω ) E m ( 2 ω ) ( l ) π n ( 2 ω ) c 0 ( E r ( ω ) ) 2 2 i d l ω 0 ,             E m ( ω ) E m ( ω ) [ ( E r ( ω ) ) 2 ] 1 / 2 .
E ^ 2 r ( 2 ω ) = { ( E ^ r ( ω ) ) 2 exp [ 2 i Φ r ] + 2 q - 1 Q - r E ^ r + q ( ω ) E ^ r - q ( ω ) × exp [ i ( Φ r + q + Φ r - q ) ] } f ( δ β 2 r ) ,
f ( δ β ) π 2 d l 0 l d ( z ) exp [ i ( 2 π / Λ + δ β ) z ] d z .
E { E ^ 2 r ( 2 ω ) 2 } = [ ( E ^ r ( ω ) ) 4 + 4 q = 1 Q - r ( E ^ r + q ( ω ) E ^ r - q ( ω ) ) 2 ] F ( δ β 2 r ) ,
E { E ^ 2 r + 1 ( 2 ω ) 2 } = 4 q = 0 Q - r - 1 ( E ^ r + q + 1 ( ω ) E ^ r - q ( ω ) ) 2 F ( δ β 2 r + 1 ) .
E { E ^ r ( 2 ω ) 2 } = 2 q = - Q Q ( E ^ r - q ( ω ) E ^ q ( ω ) ) 2 F ( δ β r ) .
1 Δ ω ,             E { E ^ r ( 2 ω , ω ) 2 } Δ ω P ^ ( 2 ω , ω ) ( r Δ ω ) ,             δ β r δ β ( r Δ ω ) .
- P ^ ( ω ) ( Ω ) d Ω = 1.
P ^ ( 2 ω ) ( Ω ) = 2 - P ^ ( ω ) ( Ω - Ω ) P ^ ( ω ) ( Ω ) d Ω F [ δ β ( Ω ) ] .
P ^ ( ω ) ( Ω ) = 3 2 2 1 Δ Ω L ( 1 - 2 Ω 2 Δ Ω L 2 ) ,
2 - P ^ ( ω ) ( Ω - Ω ) P ^ ( ω ) ( Ω ) d Ω = 12 5 1 2 Δ Ω L × ( 1 - Ω 2 Δ Ω L ) 3 [ 1 + 3 Ω 2 Δ Ω L + ( Ω 2 Δ Ω L ) 2 ] ,
F [ δ β ( Ω ) ] = sin 2 [ 1.39 ( Ω - 2 Ω 0 ) / Δ Ω B ] [ 1.39 ( Ω - 2 Ω 0 ) / Δ Ω B ] 2 .
P ^ ( 2 ω ) ( Ω ) = 12 5 1 2 Δ Ω L ( 1 - Ω 2 Δ Ω L ) 3 [ 1 + 3 Ω 2 Δ Ω L + ( Ω 2 Δ Ω L ) 2 ] sin 2 [ 1.39 ( Ω - 2 Ω 0 ) / Δ Ω B ] [ 1.39 ( Ω - 2 Ω 0 ) / Δ Ω B ] 2 .
P ^ ( 2 ω ) = - P ^ ( 2 ω ) ( Ω ) d Ω = 12 5 - 1 1 ( 1 - u ) 3 ( 1 + 3 u + u 2 ) × sin 2 ( 1.97 δ L u - 2.78 δ 0 ) ( 1.97 δ L u - 2.78 δ 0 ) 2 d u .

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