Abstract

We theoretically investigate second-harmonic generation in extremely narrow, subwavelength semiconductor and dielectric waveguides. We discuss a guiding mechanism characterized by the inhibition of diffraction and the suppression of cutoff limits in the context of a light trapping phenomenon that sets in under conditions of general phase and group velocity mismatch between the fundamental and the generated harmonic.

© 2012 Optical Society of America

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References

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  1. N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
    [CrossRef]
  2. M. Mlejnek, E. M. Wright, J. V. Moloney, and N. Bloembergen, Phys. Rev. Lett. 83, 2934 (1999).
    [CrossRef]
  3. V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, Waves Random Complex Media 20, 319 (2010).
    [CrossRef]
  4. V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, Phys. Rev. A 76, 033829 (2007).
    [CrossRef]
  5. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
    [CrossRef]
  6. M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, Phys. Rev. Lett. 101, 113905 (2008).
    [CrossRef]
  7. V. Roppo, J. V. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, Appl. Phys. Lett. 98, 111105 (2011).
    [CrossRef]
  8. E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, Opt. Express 17, 3141 (2009).
    [CrossRef]
  9. V. Roppo, N. Akozbek, D. de Ceglia, M. A. Vincenti, and M. Scalora, J. Opt. Soc. Am. B 28, 2888 (2011).
    [CrossRef]
  10. V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, Opt. Lett. 36, 1809 (2011).
    [CrossRef]
  11. E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).
  12. D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983).
    [CrossRef]
  13. M. Scalora and M. E. Crenshaw, Opt. Commun. 108, 191 (1994).
    [CrossRef]
  14. One way to express the visibility of the fields can be V=(Imax−Imin)/(Imax+Imin), where Imax is the peak value and Imax is the lower value between the two peaks.

2011

2010

V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, Waves Random Complex Media 20, 319 (2010).
[CrossRef]

2009

2008

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef]

2007

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, Phys. Rev. A 76, 033829 (2007).
[CrossRef]

1999

M. Mlejnek, E. M. Wright, J. V. Moloney, and N. Bloembergen, Phys. Rev. Lett. 83, 2934 (1999).
[CrossRef]

1994

M. Scalora and M. E. Crenshaw, Opt. Commun. 108, 191 (1994).
[CrossRef]

1983

D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983).
[CrossRef]

1962

N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

1961

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Akozbek, N.

V. Roppo, J. V. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, Appl. Phys. Lett. 98, 111105 (2011).
[CrossRef]

V. Roppo, N. Akozbek, D. de Ceglia, M. A. Vincenti, and M. Scalora, J. Opt. Soc. Am. B 28, 2888 (2011).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Alonzo, M.

Aspnes, D. E.

D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983).
[CrossRef]

Belardini, A.

Bertolotti, M.

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, Opt. Express 17, 3141 (2009).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Bloembergen, N.

M. Mlejnek, E. M. Wright, J. V. Moloney, and N. Bloembergen, Phys. Rev. Lett. 83, 2934 (1999).
[CrossRef]

N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Bloemer, M. J.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Centini, M.

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, Opt. Express 17, 3141 (2009).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Chauvet, M.

Cojocaru, C.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, Opt. Lett. 36, 1809 (2011).
[CrossRef]

V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, Waves Random Complex Media 20, 319 (2010).
[CrossRef]

Crenshaw, M. E.

M. Scalora and M. E. Crenshaw, Opt. Commun. 108, 191 (1994).
[CrossRef]

de Ceglia, D.

V. Roppo, N. Akozbek, D. de Ceglia, M. A. Vincenti, and M. Scalora, J. Opt. Soc. Am. B 28, 2888 (2011).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Fazio, E.

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, Opt. Express 17, 3141 (2009).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef]

Foreman, J. V.

V. Roppo, J. V. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, Appl. Phys. Lett. 98, 111105 (2011).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef]

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Haus, J. W.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Kandidov, V. P.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Kosareva, O. G.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Mlejnek, M.

M. Mlejnek, E. M. Wright, J. V. Moloney, and N. Bloembergen, Phys. Rev. Lett. 83, 2934 (1999).
[CrossRef]

Moloney, J. V.

M. Mlejnek, E. M. Wright, J. V. Moloney, and N. Bloembergen, Phys. Rev. Lett. 83, 2934 (1999).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

Pershan, P. S.

N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Pettazzi, F.

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, Opt. Express 17, 3141 (2009).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef]

Raineri, F.

Raj, R.

Roppo, V.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, Opt. Lett. 36, 1809 (2011).
[CrossRef]

V. Roppo, N. Akozbek, D. de Ceglia, M. A. Vincenti, and M. Scalora, J. Opt. Soc. Am. B 28, 2888 (2011).
[CrossRef]

V. Roppo, J. V. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, Appl. Phys. Lett. 98, 111105 (2011).
[CrossRef]

V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, Waves Random Complex Media 20, 319 (2010).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Sagnes, I.

Scalora, M.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, Opt. Lett. 36, 1809 (2011).
[CrossRef]

V. Roppo, N. Akozbek, D. de Ceglia, M. A. Vincenti, and M. Scalora, J. Opt. Soc. Am. B 28, 2888 (2011).
[CrossRef]

V. Roppo, J. V. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, Appl. Phys. Lett. 98, 111105 (2011).
[CrossRef]

V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, Waves Random Complex Media 20, 319 (2010).
[CrossRef]

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, Opt. Express 17, 3141 (2009).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, Phys. Rev. A 76, 033829 (2007).
[CrossRef]

M. Scalora and M. E. Crenshaw, Opt. Commun. 108, 191 (1994).
[CrossRef]

Sibilia, C.

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, Opt. Express 17, 3141 (2009).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Studna, A. A.

D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983).
[CrossRef]

Trull, J.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, Opt. Lett. 36, 1809 (2011).
[CrossRef]

V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, Waves Random Complex Media 20, 319 (2010).
[CrossRef]

Vilaseca, R.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, Opt. Lett. 36, 1809 (2011).
[CrossRef]

V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, Waves Random Complex Media 20, 319 (2010).
[CrossRef]

Vincenti, M. A.

V. Roppo, J. V. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, Appl. Phys. Lett. 98, 111105 (2011).
[CrossRef]

V. Roppo, N. Akozbek, D. de Ceglia, M. A. Vincenti, and M. Scalora, J. Opt. Soc. Am. B 28, 2888 (2011).
[CrossRef]

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Wright, E. M.

M. Mlejnek, E. M. Wright, J. V. Moloney, and N. Bloembergen, Phys. Rev. Lett. 83, 2934 (1999).
[CrossRef]

Appl. Phys. Lett.

V. Roppo, J. V. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, Appl. Phys. Lett. 98, 111105 (2011).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

M. Scalora and M. E. Crenshaw, Opt. Commun. 108, 191 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Phys. Rev. A

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Phys. Rev. B

D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983).
[CrossRef]

Phys. Rev. Lett.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef]

M. Mlejnek, E. M. Wright, J. V. Moloney, and N. Bloembergen, Phys. Rev. Lett. 83, 2934 (1999).
[CrossRef]

Waves Random Complex Media

V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, Waves Random Complex Media 20, 319 (2010).
[CrossRef]

Other

One way to express the visibility of the fields can be V=(Imax−Imin)/(Imax+Imin), where Imax is the peak value and Imax is the lower value between the two peaks.

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

Supplementary Material (2)

» Media 1: MOV (775 KB)     
» Media 2: MOV (587 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

(a) Sketch of the waveguide and excitation scheme. A nonlinear channel is created in a linear background material. The linear properties of the entire sample are assumed to be those of GaP; (b) dispersion relation of GaP from [12].

Fig. 2.
Fig. 2.

(Media 1). Propagation snapshot of an FF pulse (|E|2, norm. units) impinging on the structure in Fig. 1(a). FF and SH are tuned in the transparent spectral region of the material. The generated SH is composed of (1) the HOM component that walks off and lags behind the FF pulse; (2) the INH component that locks to the FF pulse; (3) the portion that spills out in the linear region thanks to diffraction and is not bound to the pump.

Fig. 3.
Fig. 3.

(a) SH power k space spectrum (arb. units) of the snapshot in Fig. 2. The FF (not shown) has a k vector in the forward direction (FD) at kFF=kωnω=2πωnω=14.74μm1. The SH k spectrum has three k-components: (1) the HOM component in the FD with kHOM-SH=2π2ωn2ω=32.85μm1; (2) the INH component in the FD with kINH-SH=2kωnω=4πωnω=28.9μm1; (3) the portion that spills out in the linear region with kHOM-SH=32.85μm1. (b) SH power k space spectrum (arb. units) of the snapshot in Fig. 4. FF (not shown) has k vector in the FD at the value kFF=kωnω=27.5μm1. The SH k spectrum is now composed only by the INH k component with kINH-SH=2kωnω=54.9μm1.

Fig. 4.
Fig. 4.

Same as Fig. 1 (|E|2, norm. units) but now the SH is tuned in the absorption spectral region of the medium. All the generated portions of the SH are absorbed, but the INH component travels locked to the FF pulse.

Fig. 5.
Fig. 5.

(Media 2) Propagation snapshot of a generated SH signal (Poynting vector, z component norm. units) when an FF pulse impinges on a linear material having two ultra-narrow, adjacent waveguides. The negative value outside the waveguide region is a clear indication of strong confinement.

Metrics