Abstract

We report on the enhancement of nonlinear cross-polarized wave (XPW) generation in a one-dimensional photonic band-gap structure, which is composed of two periodic arrangements of barium-fluoride and silicon-dioxide through numerical simulations. By detuning the pump-field wavelength to the band-edge position of the photonic band-gap spectrum, the electric field at this wavelength would be resonant and then the field enhancement mechanism arises immediately. Under band-edge field enhancement condition, we found that the conversion efficiencies of XPW generation was implicitly enhanced even without phase-matched condition from the exact angle of crystallographic axis orientation.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. Y. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, 1998).
  2. N. Minkovski, G. I. Petrov, S. M. Saltiel, O. Albert, and J. Etchepare, “Nonlinear polarization rotation and orthogonal polarization generation experienced in a single-beam configuration,” J. Opt. Soc. Am. B 21(9), 1659–1664 (2004).
    [Crossref]
  3. A. Jullien, O. Albert, G. Chériaux, J. Etchepare, S. Kourtev, N. Minkovski, and S. M. Saltiel, “Two crystal arrangement to fight efficiency saturation in cross-polarized wave generation,” Opt. Express 14(7), 2760–2769 (2006).
    [Crossref] [PubMed]
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    [Crossref]
  5. S. Wicharn and P. Buranasiri, “Third-harmonic pulse generation in one-dimensional photonic crystal structures,” J. Nanophotonics 8(1), 083893 (2014).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  8. P. Buranasiri and S. Wicharn, “Efficient nonlinear cross-polarized wave conversion in photonic band-gap structure,” in Laser Congress 2018 OSA Technical Digest (Optical Society of America, 2018), paper ATu2A.13.
  9. S. Wicharn, P. Buranasiri, S. Plaipichit, and N. Reangchan, “Cross-polarized wave generation in a nonlinear hyperbolic metamaterial,” J. Phys. Conf. Ser. 1144, 012136 (2018).
    [Crossref]
  10. R. Desalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Z-scan measurements of the anisotropy of nonlinear refraction and absorption in crystals,” Opt. Lett. 18(3), 194–196 (1993).
    [Crossref] [PubMed]
  11. S. Kourtev, N. Minkovski, L. Canova, A. Jullien, O. Albert, and S. M. Saltiel, “Improved nonlinear cross-polarized wave generation in cubic crystals by optimization of the crystal orientation,” J. Opt. Soc. Am. B 26(7), 1269–1275 (2009).
    [Crossref]
  12. J. Haus, B. Y. Soon, M. Scalora, M. Bloemer, C. Bowden, C. Sibilia, and A. Zheltikov, “Spatio-temporal instabilities for counterpropagating waves in periodic media,” Opt. Express 10(2), 114–121 (2002).
    [Crossref] [PubMed]
  13. M. Weiner, Ultrafast Optics (Wiley, 2009).
  14. L. Canova, S. Kourtev, N. Minkovski, R. Lopez-Martens, O. Albert, and S. M. Saltiel, “Cross-polarized wave generation in the UV region,” Opt. Lett. 33(20), 2299–2301 (2008).
    [Crossref] [PubMed]

2018 (1)

S. Wicharn, P. Buranasiri, S. Plaipichit, and N. Reangchan, “Cross-polarized wave generation in a nonlinear hyperbolic metamaterial,” J. Phys. Conf. Ser. 1144, 012136 (2018).
[Crossref]

2014 (1)

S. Wicharn and P. Buranasiri, “Third-harmonic pulse generation in one-dimensional photonic crystal structures,” J. Nanophotonics 8(1), 083893 (2014).
[Crossref]

2013 (1)

2009 (1)

2008 (1)

2006 (1)

2004 (1)

2002 (1)

1999 (1)

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

1997 (1)

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

1993 (1)

Albert, O.

Bertolotti, M.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

Bloemer, M.

Bloemer, M. J.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Bowden, C.

Bowden, C. M.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Buranasiri, P.

S. Wicharn, P. Buranasiri, S. Plaipichit, and N. Reangchan, “Cross-polarized wave generation in a nonlinear hyperbolic metamaterial,” J. Phys. Conf. Ser. 1144, 012136 (2018).
[Crossref]

S. Wicharn and P. Buranasiri, “Third-harmonic pulse generation in one-dimensional photonic crystal structures,” J. Nanophotonics 8(1), 083893 (2014).
[Crossref]

S. Wicharn, P. Buranasiri, C. Ruttanapun, and P. Jindajitawat, “Optical parametric amplification in one-dimensional photonic bandgap structures,” Appl. Opt. 52(25), 6090–6099 (2013).
[Crossref] [PubMed]

P. Buranasiri and S. Wicharn, “Efficient nonlinear cross-polarized wave conversion in photonic band-gap structure,” in Laser Congress 2018 OSA Technical Digest (Optical Society of America, 2018), paper ATu2A.13.

Canova, L.

Centini, M.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

Chériaux, G.

D’Aguanno, G.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

Desalvo, R.

Dowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Etchepare, J.

Hagan, D. J.

Haus, J.

Haus, J. W.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Jindajitawat, P.

Jullien, A.

Kourtev, S.

Lopez-Martens, R.

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Minkovski, N.

Nefedov, I.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

Petrov, G. I.

Plaipichit, S.

S. Wicharn, P. Buranasiri, S. Plaipichit, and N. Reangchan, “Cross-polarized wave generation in a nonlinear hyperbolic metamaterial,” J. Phys. Conf. Ser. 1144, 012136 (2018).
[Crossref]

Reangchan, N.

S. Wicharn, P. Buranasiri, S. Plaipichit, and N. Reangchan, “Cross-polarized wave generation in a nonlinear hyperbolic metamaterial,” J. Phys. Conf. Ser. 1144, 012136 (2018).
[Crossref]

Ruttanapun, C.

Said, A. A.

Saltiel, S. M.

Scalora, M.

J. Haus, B. Y. Soon, M. Scalora, M. Bloemer, C. Bowden, C. Sibilia, and A. Zheltikov, “Spatio-temporal instabilities for counterpropagating waves in periodic media,” Opt. Express 10(2), 114–121 (2002).
[Crossref] [PubMed]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Sheik-Bahae, M.

Sibilia, C.

J. Haus, B. Y. Soon, M. Scalora, M. Bloemer, C. Bowden, C. Sibilia, and A. Zheltikov, “Spatio-temporal instabilities for counterpropagating waves in periodic media,” Opt. Express 10(2), 114–121 (2002).
[Crossref] [PubMed]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

Soon, B. Y.

Svirko, Y. P.

Y. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, 1998).

Van Stryland, E. W.

Viswanathan, R.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Weiner, M.

M. Weiner, Ultrafast Optics (Wiley, 2009).

Wicharn, S.

S. Wicharn, P. Buranasiri, S. Plaipichit, and N. Reangchan, “Cross-polarized wave generation in a nonlinear hyperbolic metamaterial,” J. Phys. Conf. Ser. 1144, 012136 (2018).
[Crossref]

S. Wicharn and P. Buranasiri, “Third-harmonic pulse generation in one-dimensional photonic crystal structures,” J. Nanophotonics 8(1), 083893 (2014).
[Crossref]

S. Wicharn, P. Buranasiri, C. Ruttanapun, and P. Jindajitawat, “Optical parametric amplification in one-dimensional photonic bandgap structures,” Appl. Opt. 52(25), 6090–6099 (2013).
[Crossref] [PubMed]

P. Buranasiri and S. Wicharn, “Efficient nonlinear cross-polarized wave conversion in photonic band-gap structure,” in Laser Congress 2018 OSA Technical Digest (Optical Society of America, 2018), paper ATu2A.13.

Zheltikov, A.

Zheludev, N. I.

Y. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, 1998).

Appl. Opt. (1)

J. Nanophotonics (1)

S. Wicharn and P. Buranasiri, “Third-harmonic pulse generation in one-dimensional photonic crystal structures,” J. Nanophotonics 8(1), 083893 (2014).
[Crossref]

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

J. Phys. Conf. Ser. (1)

S. Wicharn, P. Buranasiri, S. Plaipichit, and N. Reangchan, “Cross-polarized wave generation in a nonlinear hyperbolic metamaterial,” J. Phys. Conf. Ser. 1144, 012136 (2018).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (1)

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

Other (3)

P. Buranasiri and S. Wicharn, “Efficient nonlinear cross-polarized wave conversion in photonic band-gap structure,” in Laser Congress 2018 OSA Technical Digest (Optical Society of America, 2018), paper ATu2A.13.

Y. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, 1998).

M. Weiner, Ultrafast Optics (Wiley, 2009).

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Figures (4)

Fig. 1
Fig. 1 Diagram of cross-polarized wave (XPW) generation from one-dimensional photonic band-gap (1D-PBG) structure containing anisotropic nonlinearity material (BaF2). An incident pump field with linear polarization along x-axis is launched into the 1D-PBG structure and, then, a XPW field with linear polarization along y-axis is induced due to the anisotropy of nonlinear susceptibility of the nonlinear layers.
Fig. 2
Fig. 2 (a) The illustration of transmission spectrum of the PBG structure. (b) The field enhancement inside the PBG structure due to detuning wavelength of pump wave to the long-wavelength band-edge ( δ=0.044).
Fig. 3
Fig. 3 (a) Electric field distribution of incident pump pulse with Gaussian-shape at t = 0. (b) The snapshots of the generated forward and backward XPW pulses with polarization along y-axis from nonlinear XPW generation in the PBG structure. Note that the location of the 1D-PBG structure is set-up at the origin of z-axis.
Fig. 4
Fig. 4 (a) The illustration of β-dependency of conversion efficiencies of forward XPW wave from PBG structure with δ = 0.044 and from equivalent-length BaF2 bulk. (b) The illustration of β-dependency of depletion of forward Pump wave from PBG structure with δ = 0.044.

Equations (13)

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ε ^ (z,ω)= ε ^ r (ω)+i ε ^ i (ω)+2Δ ε ^ cos( 2πz Λ ),
χ (3) =[ γ 1 γ 2 2 γ 2 2 γ 3 γ 3 γ 2 γ 2 γ 3 2 γ 3 2 γ 2 γ 2 γ 1 ],
γ 1 = γ 0 [ 1 σ 2 sin 2 (2β) ], γ 2 = γ 0 [ σ 4 sin(4β) ], γ 3 = γ 0 [ σ 2 sin 2 (2β)+ 1σ 3 ], γ 0 = ω 2 2k c 2 χ xxxx (3) .
E 0 (x) = A f (x,y,z,t) e i(kzωt) + A b (x,y,z,t) e i(kz+ωt) +c.c.,
E 0 (y) = B f (x,y,z,t) e i(kzωt) + B b (x,y,z,t) e i(kz+ωt) +c.c.,
1 v g A f t = A f z + i 2k ( 2 x 2 + 2 y 2 ) A f iδ A f +iκ A b +i γ 1 [ | A f | 2 +2 | A b | 2 ] A f +i γ 2 [ A f 2 B f * +2 A f A b B f * ]+i2 γ 2 [ A f B b A b * +( | A f | 2 +2 | A b | 2 ) B f ], +i2 γ 3 [( | B f | 2 + | B b | 2 ) A f + A b B f B b * ]+i γ 3 [ B f 2 A f * +2 B f B b A b * ]i γ 2 [ | B f | 2 +2 | B b | 2 ] B f
1 v g A b t = A b z + i 2k ( 2 x 2 + 2 y 2 ) A b +iδ A b +iκ A f +i γ 1 [2 | A f | 2 + | A b | 2 ] A b +i γ 2 [ A b 2 B b * +2 A f A b B b * ]+i2 γ 2 [ A b B f A f * +( | A f | 2 +2 | A b | 2 ) B b ], +i2 γ 3 [( | B f | 2 + | B b | 2 ) A b + A f B f * B b ]+i γ 3 [ B b 2 A b * +2 B f B b A f * ]i γ 2 [2 | B f | 2 + | B b | 2 ] B b
1 v g B f t = B f z + i 2k ( 2 x 2 + 2 y 2 ) B f iδ B f +iκ B b +i γ 2 [ | A f | 2 +2 | A b | 2 ] A f +i γ 3 [ A f 2 B f * +2 A f A b B f * ]+i2 γ 3 [ A f B b A b * +( | A f | 2 +2 | A b | 2 ) B f ], i2 γ 2 [( | B f | 2 + | B b | 2 ) A f + A b B f B b * ]+i γ 2 [ B f 2 A f * +2 B f B b A b * ]i γ 1 [ | B f | 2 +2 | B b | 2 ] B f
1 v g B b t = B b z + i 2k ( 2 x 2 + 2 y 2 ) B b +iδ B b +iκ B f +i γ 2 [2 | A f | 2 + | A b | 2 ] A b +i γ 3 [ A b 2 B b * +2 A f A b B b * ]+i2 γ 3 [ A b B f A f * +( | A f | 2 +2 | A b | 2 ) B b ], i2 γ 3 [( | B f | 2 + | B b | 2 ) A b + A f B b B f * ]+i γ 2 [ B b 2 A b * +2 B f B b A f * ]i γ 1 [2 | B f | 2 + | B b | 2 ] B b
δ=k k 0 .
A f (x) (x,y,0,t)=F(x,y,t), A b (x) (x,y,L,t)= A f (y) (x,y,0,t)= A b (y) (x,y,L,t)=0.
η XPW = | B f (L) | 2 | A f (0) | 2 .
η Pump = | A f (L) | 2 | A f (0) | 2 .

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