Abstract

We present a numerical study of a two dimensional all-optical switching device which consists of two crossed waveguides and a nonlinear photonic band-gap structure in the center. The switching mechanism is based on a dynamic shift of the photonic band edge by means of a strong pump pulse and is modeled on the basis of a two dimensional finite volume time domain method. With our arrangement we find a pronounced optical switching effect in which due to the cross-waveguide geometry the overlay of the probe beam by a pump pulse is significantly reduced.

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References

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  1. E. Yablonovitch, "Photonic band-gap structures," J. Opt. Soc. Am. B 10, 283-295 (1993).
    [CrossRef]
  2. John D. Joannopoulos, R. D. Meade, Joshua N. Winn, Photonic Crystals, (Princeton University Press, Princeton, NJ, 1995).
  3. P. Tran, "Optical switching with a nonlinear photonic Crystal: a numerical study," Opt. Lett. 21, 1138-1140 (1996).
    [CrossRef] [PubMed]
  4. M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical Limiting and Switching of Ultrashort Pulses in Nonlinear Photonic Band Gap Materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
    [CrossRef] [PubMed]
  5. S. V. Polstyanko, R. Dyczij-Edlinger, and J. F. Lee Lee, "Full vectorial analysis of a nonlinear slab waveguide based on the nonlinear hybrid vector finite-element method," Opt. Lett. 21, 98-100 (1996).
    [CrossRef] [PubMed]
  6. A. Reineix and B. Jecko, "A new photonic band gap equivalent model using finite difference time domain method," Ann. Telecommun. 51 656-662 (1996).
  7. S. Scholz (Ph. D Thesis, University of Stuttgart, 1999).
  8. P. M. Goorjian and A. Taflove, "Direct time integration of Maxwell's equations in nonlinear dispersive media for propagation and scattering of femtosecond electromagnetic solitons," Opt. Lett. 17, 180 (1992).
    [CrossRef] [PubMed]
  9. J. D. Jackson, Classical Electrodynamics, (John Wiley & Sons, Inc., NJ, 1975).

Other (9)

E. Yablonovitch, "Photonic band-gap structures," J. Opt. Soc. Am. B 10, 283-295 (1993).
[CrossRef]

John D. Joannopoulos, R. D. Meade, Joshua N. Winn, Photonic Crystals, (Princeton University Press, Princeton, NJ, 1995).

P. Tran, "Optical switching with a nonlinear photonic Crystal: a numerical study," Opt. Lett. 21, 1138-1140 (1996).
[CrossRef] [PubMed]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical Limiting and Switching of Ultrashort Pulses in Nonlinear Photonic Band Gap Materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef] [PubMed]

S. V. Polstyanko, R. Dyczij-Edlinger, and J. F. Lee Lee, "Full vectorial analysis of a nonlinear slab waveguide based on the nonlinear hybrid vector finite-element method," Opt. Lett. 21, 98-100 (1996).
[CrossRef] [PubMed]

A. Reineix and B. Jecko, "A new photonic band gap equivalent model using finite difference time domain method," Ann. Telecommun. 51 656-662 (1996).

S. Scholz (Ph. D Thesis, University of Stuttgart, 1999).

P. M. Goorjian and A. Taflove, "Direct time integration of Maxwell's equations in nonlinear dispersive media for propagation and scattering of femtosecond electromagnetic solitons," Opt. Lett. 17, 180 (1992).
[CrossRef] [PubMed]

J. D. Jackson, Classical Electrodynamics, (John Wiley & Sons, Inc., NJ, 1975).

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Figures (7)

Figure 1.
Figure 1.

Transmission versus frequency for a one-dimensional multilayer structure. The multilayer structure consists of 29 layers with a low dielectric constant ϵl of 1.0 and a high dielectric constant ϵh of 2.0 (green curve) and 2.1 (blue curve), respectively. The width of one layer is d = λ 0/(4 ∙ ), where = 1.21 is the averaged index of refraction of two consecutive layers. The arrow indicates the frequency fprobe = 0.8745 ∙ c/λ 0 of the probe beam, where c is the speed of light.

Figure 2.
Figure 2.

Schematic representation of the geometry of the nonlinear photonic band-gap switch. On the left, there is the inlet of the probe beam, on the bottom the inlet of the pump pulse. The boundaries are perfectly conducting. Besides the finite extension in y-direction, the multilayer structure in the center corresponds to the multilayer structure described in Fig. 1. In addition, we have a Kerr nonlinearity of χ 3 = 0.001 in the layers with the high dielectric constant (blue stripes).

Figure 3.
Figure 3.

Snapshot of the probe beam with ϵh = 2.0. The frequency is adjusted to f = fprobe .

Figure 4.
Figure 4.

Snapshot of the probe beam with ϵh = 2.1. The frequency is adjusted to f = fprobe .

Figure 5.
Figure 5.

Snapshot of the pump pulse at the time when its maximum passes the nonlinear photonic band-gap structure.

Figure 6.
Figure 6.

Snapshot of the induced nonlinear dielectric constant ϵnl .

Figure 7.
Figure 7.

Animation of the switching process. The animation at the left shows the spatio-temporal variation of the energy density of the probe beam. The sequence at the right visualizes the dynamically changing spatial distribution of the (nonlinear) dielectric constant. [Media 1]

Equations (11)

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1 c t D z = x H y y H x
1 c t B x = y E z
1 c t B y = x E z
x B x + y B y = 0 ,
D z = ϵ · E z + χ 3 · E z 3 = ϵ nl · E z .
w = 1 2 ( E z D z + B x 2 + B y 2 ) .
t V + x F x + y F y = 0
G V n + 1 dv = G V n dv t n t n + 1 O ( G ) F · d o ,
D z = A · sin ( k y y ) · sin ( k x x ωt + ϕ x )
B x = A · k y c ω · cos ( k y y ) · cos ( k x x · ωt + ϕ x )
B y = A · k x c ω · sin ( k y y ) · sin ( k x x · ωt + ϕ x ) ,

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