Abstract

We numerically investigate the response of a quadratically nonlinear channel waveguide for second-harmonic generation, in which the insertion of a localized phase discontinuity allows the simple implementation of directional nonreciprocity in the fundamental-frequency transmission.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Assanto, “Quadratic cascading: effects and applications,” in Beam Shaping and Control with Nonlinear Optics, F. Kajzar and R. Reinisch, eds. (Plenum, New York, 1997), p. 341.
  2. G. I. Stegeman, D. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691 (1996).
    [CrossRef]
  3. H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded second-order processes in β-barium borate,” Appl. Phys. Lett. 63, 2472 (1993).
    [CrossRef]
  4. K. Gallo, G. Assanto, and G. I. Stegeman, “Efficient wavelength shifting over the erbium amplifier bandwidth via cascaded second order processes in lithium niobate waveguides,” Appl. Phys. Lett. 71, 1020 (1997).
    [CrossRef]
  5. A. Arbore, O. Marco, and M. M. Fejer, “Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings,” Opt. Lett. 22, 865 (1997).
    [CrossRef] [PubMed]
  6. C. G. Treviño-Palacios, G. I. Stegeman, and P. Baldi, “Spatial nonreciprocity in waveguide second-order processes,” Opt. Lett. 21, 1442 (1996).
    [CrossRef] [PubMed]
  7. C. G. Treviño-Palacios, “Novel effects in waveguide second-harmonic generation,” Ph.D. dissertation (University of Central Florida, Orlando, Fla., 1998).
  8. M. M. Fejer, G. A. Magel, D. H. Jundt, and L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631 (1992).
    [CrossRef]
  9. G. Assanto, K. Gallo, and C. Conti, “Plane and guided-wave effects and devices via quadratic cascading,” in Advanced Photonics with Second-Order Optically Nonlinear Processes, A. Boardman, ed. (Kluwer Academic, Boston, Mass., to be published).
  10. G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. Van Stryland, “Coherent interactions for all-optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673 (1995).
    [CrossRef]
  11. G. Imeshev, M. Proctor, and M. M. Fejer, “Phase correction in double-pass quasi-phase-matched second-harmonic generation with a wedged crystal,” Opt. Lett. 23, 165 (1998).
    [CrossRef]
  12. M. Cha, “Cascaded phase shift and intensity modulation in aperiodic quasi-phase-matched gratings,” Opt. Lett. 23, 250 (1998).
    [CrossRef]

1998 (2)

1997 (2)

K. Gallo, G. Assanto, and G. I. Stegeman, “Efficient wavelength shifting over the erbium amplifier bandwidth via cascaded second order processes in lithium niobate waveguides,” Appl. Phys. Lett. 71, 1020 (1997).
[CrossRef]

A. Arbore, O. Marco, and M. M. Fejer, “Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings,” Opt. Lett. 22, 865 (1997).
[CrossRef] [PubMed]

1996 (2)

C. G. Treviño-Palacios, G. I. Stegeman, and P. Baldi, “Spatial nonreciprocity in waveguide second-order processes,” Opt. Lett. 21, 1442 (1996).
[CrossRef] [PubMed]

G. I. Stegeman, D. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

1995 (1)

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. Van Stryland, “Coherent interactions for all-optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

1993 (1)

H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded second-order processes in β-barium borate,” Appl. Phys. Lett. 63, 2472 (1993).
[CrossRef]

1992 (1)

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

Arbore, A.

Assanto, G.

K. Gallo, G. Assanto, and G. I. Stegeman, “Efficient wavelength shifting over the erbium amplifier bandwidth via cascaded second order processes in lithium niobate waveguides,” Appl. Phys. Lett. 71, 1020 (1997).
[CrossRef]

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. Van Stryland, “Coherent interactions for all-optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

Baldi, P.

Banfi, G. P.

H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded second-order processes in β-barium borate,” Appl. Phys. Lett. 63, 2472 (1993).
[CrossRef]

Byer, L.

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

Cha, M.

Fejer, M. M.

Gallo, K.

K. Gallo, G. Assanto, and G. I. Stegeman, “Efficient wavelength shifting over the erbium amplifier bandwidth via cascaded second order processes in lithium niobate waveguides,” Appl. Phys. Lett. 71, 1020 (1997).
[CrossRef]

Hagan, D.

G. I. Stegeman, D. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Imeshev, G.

Jundt, D. H.

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

Magel, G. A.

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

Marco, O.

Proctor, M.

Sheik-Bahae, M.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. Van Stryland, “Coherent interactions for all-optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

Stegeman, G. I.

K. Gallo, G. Assanto, and G. I. Stegeman, “Efficient wavelength shifting over the erbium amplifier bandwidth via cascaded second order processes in lithium niobate waveguides,” Appl. Phys. Lett. 71, 1020 (1997).
[CrossRef]

G. I. Stegeman, D. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

C. G. Treviño-Palacios, G. I. Stegeman, and P. Baldi, “Spatial nonreciprocity in waveguide second-order processes,” Opt. Lett. 21, 1442 (1996).
[CrossRef] [PubMed]

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. Van Stryland, “Coherent interactions for all-optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

Tan, H.

H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded second-order processes in β-barium borate,” Appl. Phys. Lett. 63, 2472 (1993).
[CrossRef]

Tomaselli, A.

H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded second-order processes in β-barium borate,” Appl. Phys. Lett. 63, 2472 (1993).
[CrossRef]

Torner, L.

G. I. Stegeman, D. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Treviño-Palacios, C. G.

Van Stryland, E.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. Van Stryland, “Coherent interactions for all-optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

Appl. Phys. Lett. (2)

H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded second-order processes in β-barium borate,” Appl. Phys. Lett. 63, 2472 (1993).
[CrossRef]

K. Gallo, G. Assanto, and G. I. Stegeman, “Efficient wavelength shifting over the erbium amplifier bandwidth via cascaded second order processes in lithium niobate waveguides,” Appl. Phys. Lett. 71, 1020 (1997).
[CrossRef]

IEEE J. Quantum Electron. (2)

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

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. Van Stryland, “Coherent interactions for all-optical signal processing via quadratic nonlinearities,” IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

Opt. Lett. (4)

Opt. Quantum Electron. (1)

G. I. Stegeman, D. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Other (3)

G. Assanto, “Quadratic cascading: effects and applications,” in Beam Shaping and Control with Nonlinear Optics, F. Kajzar and R. Reinisch, eds. (Plenum, New York, 1997), p. 341.

G. Assanto, K. Gallo, and C. Conti, “Plane and guided-wave effects and devices via quadratic cascading,” in Advanced Photonics with Second-Order Optically Nonlinear Processes, A. Boardman, ed. (Kluwer Academic, Boston, Mass., to be published).

C. G. Treviño-Palacios, “Novel effects in waveguide second-harmonic generation,” Ph.D. dissertation (University of Central Florida, Orlando, Fla., 1998).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Sketch of the investigated geometry: a waveguide of length L is formed by two phase-matched segments of lengths L1 and L2, respectively, separated by a small region that introduces a phase variation Δφ on the relative phase 2φω-φ2ω between fundamental and second-harmonic fields. The arrows indicate nominal forward and backward propagation directions, respectively.

Fig. 2
Fig. 2

Evolution of the normalized fundamental-frequency (a) power |Aω(ζ)|2 and (b) phase φω(ζ)/π versus propagation distance in a waveguide with L1=0.1L and Δφ=0.2π, for a given excitation |Γ|2=15. Solid (dashed) curves refer to forward (backward) propagation. Notice that the backward field amplitude is nearly unaffected by the localized phase jump.

Fig. 3
Fig. 3

Tω+ versus excitation |Γ|2 for various dephasings Δφ (solid curves). Here L1=0.1L. The dashed curves refer to two backward cases, with Δφ=0.2π and Δφ=π. Varying Δφ has a minor effect on Tω- for sufficiently large excitations. The dots refer to the case of a linearly chirped QPM grating (see the conclusive remarks in the text).

Fig. 4
Fig. 4

Forward fundamental transmittance Tω+ versus dephasing Δφ/π for L1=0.1L and |Γ|2=15.

Fig. 5
Fig. 5

Contour map of rejection r=Tω+(Tω+-Tω-)/(Tω++Tω-) versus excitation |Γ|2 and dephasing Δφ/π for L1=0.1L: values approaching unity indicate regions where the device operates as an ideal diode.

Equations (9)

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

dAωdζ=-iΓAω*A2ω exp(-iΔkζ),
dA2ωdζ=-iΓ*Aω2 exp(+iΔkζ),
θ(l1+δ)=θ(l1)+Δφ,
Aω(l1+δ)=Aω(l1)
A2ω(l1+δ)=A2ω(l1)exp(-iΔφ),
intheforwardcase,
Aω(l1)=Aω(l1+δ),
A2ω(l1)=A2ω(l1+δ)exp(-iΔφ)
inthebackwardcase.

Metrics