Abstract

We analyze the relationship between the bound and the free waves in the noncollinear SHG scheme, along with the vectorial conservation law for the different components arising when there are two pump beams impinging on the sample with two different incidence angles. The generated power is systematically investigated, by varying the polarization state of both fundamental beams, while absorption is included via the Herman and Hayden correction terms. The theoretical simulations, obtained for samples which are some coherence length thick show that the resulting polarization mapping is an useful tool to put in evidence the interference between bound and free waves, as well as the effect of absorption on the interference pattern.

© 2009 OSA

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    [CrossRef]
  2. N. Bloembergen and P. S. Pershan, “Light wave at the boundary of nonlinear media,” Phys. Rev. 128(2), 606–622 (1962).
    [CrossRef]
  3. J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. 41(4), 1667–1681 (1970).
    [CrossRef]
  4. V. Figà, J. Luc, B. Kulyk, M. Baitoul, and B. Sahraoui, “Characterization and investigation of NLO properties of electrodeposited polythiophenes,” J. Eur. Opt. Soc. Rapid Publ. 4, 09016–09021 (2009).
    [CrossRef]
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    [CrossRef]
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  13. S. Cattaneo and M. Kauranen, “Polarization-based identification of bulk contributions in surface nonlinear optics,” Phys. Rev. B 72, 033412/1–033412/4 (2005).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. R. Héliou, J. L. Brebner, and S. Roorda, “Role of implantation temperature on residual damage in ion-implanted 6H–SiC,” Semicond. Sci. Technol. 16(10), 836–843 (2001).
    [CrossRef]
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2009 (3)

2007 (2)

2004 (1)

S. Cattaneo, E. Vuorimaa, H. Lemmetyinen, and M. Kauranen, “Advantages of polarized two-beam second-harmonic generation in precise characterization of thin films,” J. Chem. Phys. 120(19), 9245–9252 (2004).
[CrossRef] [PubMed]

2003 (1)

2001 (1)

R. Héliou, J. L. Brebner, and S. Roorda, “Role of implantation temperature on residual damage in ion-implanted 6H–SiC,” Semicond. Sci. Technol. 16(10), 836–843 (2001).
[CrossRef]

2000 (2)

D. Faccio, V. Pruneri, and P. G. Kazansky, “Noncollinear Maker’s fringe measurements of second-order nonlinear optical layers,” Opt. Lett. 25(18), 1376–1378 (2000).
[CrossRef]

J. Rams and J. M. Cabrera, “Second harmonic generation in the strong absorption regime,” J. Mod. Opt. 47, 1659–1669 (2000).

1998 (1)

1995 (1)

1993 (1)

P. Provencher, C. Y. Côté, and M. M. Denariez-Roberge, “Surface second-harmonic susceptibility determined by noncollinear reflected second-harmonic generation,” Can. J. Phys. 71, 66–69 (1993).
[CrossRef]

1987 (1)

1980 (1)

N. Bloembergen, “Conservation laws in nonlinear optics,” J. Opt. Soc. Am. B 70(12), 1429–1436 (1980).
[CrossRef]

1970 (1)

J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. 41(4), 1667–1681 (1970).
[CrossRef]

1962 (2)

P. D. Maker, R. W. Terhume, M. Nisenhoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8(1), 21–22 (1962).
[CrossRef]

N. Bloembergen and P. S. Pershan, “Light wave at the boundary of nonlinear media,” Phys. Rev. 128(2), 606–622 (1962).
[CrossRef]

Alonzo, M.

Baitoul, M.

V. Figà, J. Luc, B. Kulyk, M. Baitoul, and B. Sahraoui, “Characterization and investigation of NLO properties of electrodeposited polythiophenes,” J. Eur. Opt. Soc. Rapid Publ. 4, 09016–09021 (2009).
[CrossRef]

Belardini, A.

Bertolotti, M.

Bloembergen, N.

N. Bloembergen, “Conservation laws in nonlinear optics,” J. Opt. Soc. Am. B 70(12), 1429–1436 (1980).
[CrossRef]

N. Bloembergen and P. S. Pershan, “Light wave at the boundary of nonlinear media,” Phys. Rev. 128(2), 606–622 (1962).
[CrossRef]

Bovino, F. A.

Brebner, J. L.

R. Héliou, J. L. Brebner, and S. Roorda, “Role of implantation temperature on residual damage in ion-implanted 6H–SiC,” Semicond. Sci. Technol. 16(10), 836–843 (2001).
[CrossRef]

Cabrera, J. M.

J. Rams and J. M. Cabrera, “Second harmonic generation in the strong absorption regime,” J. Mod. Opt. 47, 1659–1669 (2000).

Canfield, B. K.

Cattaneo, S.

Centini, M.

Chauvet, M.

Cojocaru, C.

Côté, C. Y.

P. Provencher, C. Y. Côté, and M. M. Denariez-Roberge, “Surface second-harmonic susceptibility determined by noncollinear reflected second-harmonic generation,” Can. J. Phys. 71, 66–69 (1993).
[CrossRef]

Denariez-Roberge, M. M.

P. Provencher, C. Y. Côté, and M. M. Denariez-Roberge, “Surface second-harmonic susceptibility determined by noncollinear reflected second-harmonic generation,” Can. J. Phys. 71, 66–69 (1993).
[CrossRef]

Faccio, D.

Fazio, E.

Figà, V.

V. Figà, J. Luc, B. Kulyk, M. Baitoul, and B. Sahraoui, “Characterization and investigation of NLO properties of electrodeposited polythiophenes,” J. Eur. Opt. Soc. Rapid Publ. 4, 09016–09021 (2009).
[CrossRef]

Fischer, R.

Giardina, M.

Hayden, L. M.

Héliou, R.

R. Héliou, J. L. Brebner, and S. Roorda, “Role of implantation temperature on residual damage in ion-implanted 6H–SiC,” Semicond. Sci. Technol. 16(10), 836–843 (2001).
[CrossRef]

Herman, W. N.

Herrero, R.

Jeong, M. Y.

Jerphagnon, J.

J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. 41(4), 1667–1681 (1970).
[CrossRef]

Kauranen, M.

Kazansky, P. G.

Keller, R. A.

Kim, D. C.

Kivshar, Y. S.

Krolikowski, W.

Kulyk, B.

V. Figà, J. Luc, B. Kulyk, M. Baitoul, and B. Sahraoui, “Characterization and investigation of NLO properties of electrodeposited polythiophenes,” J. Eur. Opt. Soc. Rapid Publ. 4, 09016–09021 (2009).
[CrossRef]

Kurtz, S. K.

J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. 41(4), 1667–1681 (1970).
[CrossRef]

Larciprete, M. C.

Lemmetyinen, H.

S. Cattaneo, E. Vuorimaa, H. Lemmetyinen, and M. Kauranen, “Advantages of polarized two-beam second-harmonic generation in precise characterization of thin films,” J. Chem. Phys. 120(19), 9245–9252 (2004).
[CrossRef] [PubMed]

Lim, T. K.

Luc, J.

V. Figà, J. Luc, B. Kulyk, M. Baitoul, and B. Sahraoui, “Characterization and investigation of NLO properties of electrodeposited polythiophenes,” J. Eur. Opt. Soc. Rapid Publ. 4, 09016–09021 (2009).
[CrossRef]

Maker, P. D.

P. D. Maker, R. W. Terhume, M. Nisenhoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8(1), 21–22 (1962).
[CrossRef]

Muenchausen, R. E.

N Neshev, D.

Nisenhoff, M.

P. D. Maker, R. W. Terhume, M. Nisenhoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8(1), 21–22 (1962).
[CrossRef]

Nogar, N. S.

Passaseo, A.

Pershan, P. S.

N. Bloembergen and P. S. Pershan, “Light wave at the boundary of nonlinear media,” Phys. Rev. 128(2), 606–622 (1962).
[CrossRef]

Pettazzi, F.

Provencher, P.

P. Provencher, C. Y. Côté, and M. M. Denariez-Roberge, “Surface second-harmonic susceptibility determined by noncollinear reflected second-harmonic generation,” Can. J. Phys. 71, 66–69 (1993).
[CrossRef]

Pruneri, V.

Rams, J.

J. Rams and J. M. Cabrera, “Second harmonic generation in the strong absorption regime,” J. Mod. Opt. 47, 1659–1669 (2000).

Rodríguez, F. J.

Roorda, S.

R. Héliou, J. L. Brebner, and S. Roorda, “Role of implantation temperature on residual damage in ion-implanted 6H–SiC,” Semicond. Sci. Technol. 16(10), 836–843 (2001).
[CrossRef]

Sahraoui, B.

V. Figà, J. Luc, B. Kulyk, M. Baitoul, and B. Sahraoui, “Characterization and investigation of NLO properties of electrodeposited polythiophenes,” J. Eur. Opt. Soc. Rapid Publ. 4, 09016–09021 (2009).
[CrossRef]

Saltiel, S. M.

Savage, C. M.

P. D. Maker, R. W. Terhume, M. Nisenhoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8(1), 21–22 (1962).
[CrossRef]

Scalora, M.

Sibilia, C.

Song, C.

Staliunas, K.

Tasco, V.

Terhume, R. W.

P. D. Maker, R. W. Terhume, M. Nisenhoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8(1), 21–22 (1962).
[CrossRef]

Trull, J.

Vilaseca, R.

Vuorimaa, E.

S. Cattaneo, E. Vuorimaa, H. Lemmetyinen, and M. Kauranen, “Advantages of polarized two-beam second-harmonic generation in precise characterization of thin films,” J. Chem. Phys. 120(19), 9245–9252 (2004).
[CrossRef] [PubMed]

Wang, F. X.

Appl. Opt. (1)

Can. J. Phys. (1)

P. Provencher, C. Y. Côté, and M. M. Denariez-Roberge, “Surface second-harmonic susceptibility determined by noncollinear reflected second-harmonic generation,” Can. J. Phys. 71, 66–69 (1993).
[CrossRef]

J. Appl. Phys. (1)

J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. 41(4), 1667–1681 (1970).
[CrossRef]

J. Chem. Phys. (1)

S. Cattaneo, E. Vuorimaa, H. Lemmetyinen, and M. Kauranen, “Advantages of polarized two-beam second-harmonic generation in precise characterization of thin films,” J. Chem. Phys. 120(19), 9245–9252 (2004).
[CrossRef] [PubMed]

J. Eur. Opt. Soc. Rapid Publ. (1)

V. Figà, J. Luc, B. Kulyk, M. Baitoul, and B. Sahraoui, “Characterization and investigation of NLO properties of electrodeposited polythiophenes,” J. Eur. Opt. Soc. Rapid Publ. 4, 09016–09021 (2009).
[CrossRef]

J. Mod. Opt. (1)

J. Rams and J. M. Cabrera, “Second harmonic generation in the strong absorption regime,” J. Mod. Opt. 47, 1659–1669 (2000).

J. Opt. Soc. Am. B (3)

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. (1)

N. Bloembergen and P. S. Pershan, “Light wave at the boundary of nonlinear media,” Phys. Rev. 128(2), 606–622 (1962).
[CrossRef]

Phys. Rev. Lett. (1)

P. D. Maker, R. W. Terhume, M. Nisenhoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8(1), 21–22 (1962).
[CrossRef]

Semicond. Sci. Technol. (1)

R. Héliou, J. L. Brebner, and S. Roorda, “Role of implantation temperature on residual damage in ion-implanted 6H–SiC,” Semicond. Sci. Technol. 16(10), 836–843 (2001).
[CrossRef]

Other (7)

E. D. Palik, “Gallium Arsenide (GaAs)”, in Handbook of Optical Constants of Solids, E.D. Palik, ed. (Academic Orlando, Fla., 1985).

W. J. Choyke, and E. D. Palik, “Silicon Carbide (SiC)”, in Handbook of Optical Constants of Solids, E. D. Palik, ed., (Academic Orlando, Fla., 1985).

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. Bloemer, J. W. Haus, O. G. Kosareva and V. P. Kandidov, “Role of phase matching in pulsed second harmonic generation: walk off and phase locked twin pulses in negative index media,” Phys. Rev. A 76, 033829/1–033829/12 (2007).

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905/1–113905/4 (2008).

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán and B. S. Mendoza, “Single-Beam and Enhanced Two-Beam Second-Harmonic Generation from Silicon Nanocrystals by Use of Spatially Inhomogeneous Femtosecond Pulses,” Phys. Rev. Lett. 94, 047401/1–047401/4 (2005).

S. Cattaneo and M. Kauranen, “Polarization-based identification of bulk contributions in surface nonlinear optics,” Phys. Rev. B 72, 033412/1–033412/4 (2005).

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, Berlin, 1997).

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Figures (7)

Fig. 1
Fig. 1

Scheme of noncollinear second harmonic generation.

Fig. 2
Fig. 2

Propagation angles for the collinear bound waves, α’1,B and α’2,B as a function of polarization state of the corresponding pump beam.

Fig. 3
Fig. 3

Propagation angle for the noncollinear bound wave, α’3,B as a function of polarization state of both pump beams.

Fig. 4
Fig. 4

Second harmonic intensity as a function of the polarization state of the first pump beam (φ1) and the second pump beam (φ2), calculated for a 50 μm SiC (crystal structure 6mm) slab without absorption. The polarization state of the analyzer is set to (a) p^ - and (b) s^ -, respectively.

Fig. 5
Fig. 5

Second harmonic intensity as a function of the polarization state of the first pump beam (φ1) and the second pump beam (φ2), calculated for a 50 μm SiC slab for an absorption coefficient k = 0.003 at 2ω. The polarization state of the analyzer is set to (a) p^ - and (b) s^ -, respectively.

Fig. 6
Fig. 6

Second harmonic intensity as a function of the polarization state of the first pump beam (φ1) and the second pump beam (φ2), calculated for a 50 μm SiC slab for an absorption coefficient k = 0.005 at 2ω. The polarization state of the analyzer is set to (a) p^ - and (b) s^ -, respectively.

Fig. 7
Fig. 7

Second harmonic intensity as a function of the polarization state of the first pump beam (φ1) and the second pump beam (φ2), calculated for a 50 μm GaAs slab (crystal structure 43m) under high SH absorption, i.e. k = 0.1 at 2ω. The polarization state of the analyzer is set to (a) p^ - and (b) s^ -, respectively.

Equations (8)

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

k1ωsin(α1')+k2ωsin(α2')=k3,F2ωsin(α'3,F)
k1,ω+k2ω=k3,B2ω
Pω1+ω2(α)=(512π3A1A2)(tω1)2(tω2)2Tω1+ω1P(α1,α2)sin2(ΨHH(α))+sinh2(χHH(α))ΨHH(α)2+χHH(α)2(πLλ)2(deff(α))2
δ1+δ2=(πL2)2λ[kωcos(α'1)+kωcos(α'2)+2k2ωcos(α'3,F)]
ΨHH(α)=(πL2)(2λ)[nω(α'1)cos(α'1)+nω(α'2)cos(α'2)2n2ω(α'3)cos(α'3)]
χHH(α)=(πL2)(2λ)[kωcos(α'1)+kωcos(α'2)2k2ωcos(α'3)]
deffs^=d15[sin(ϕ1)cos(ϕ2)sin(α'2)+cos(ϕ1)sin(ϕ2)sin(α'1)]deffp^=d24cos(α'3)[cos(α'1)sin(α'2)+sin(α'1)cos(α'2)]cos(ϕ1)cos(ϕ2)sin(α'3){d31sin(ϕ1)sin(ϕ2)+cos(ϕ1)cos(ϕ2)[d32cos(α'1)cos(α'2)+d33sin(α'1)sin(α'2)]}
deffs^=d14cos(ϕ1)cos(ϕ2)[cos(α'1)sin(α'2)+sin(α'1)cos(α'2)]deffp^=cos(α'3)d25{sin(ϕ1)cos(ϕ2)sin(α'2)+sin(ϕ2)cos(ϕ1)sin(α'1)}++sin(α'3)d36{sin(ϕ1)cos(ϕ2)cos(α'2)+sin(ϕ2)cos(ϕ1)cos(α'1)}

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