Abstract

A pump–probe optical switching mechanism that uses a nonlinear chiral photonic bandgap structure is proposed. The switching is achieved by shifting the bandgap of the structure; the chirality permits the use of the same frequency for the pump and the probe beam. The pump beam is never transmitted, so there is no discrimination problem. A new extension of the finite-difference time-domain technique is developed to simulate the propagation of an electromagnetic wave in a Kerr nonlinear chiral medium.

© 1999 Optical Society of America

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References

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  1. For a review, see H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, Orlando, 1985).
  2. S. R. Firberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. W. Smith, “Femtosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13, 904 (1988).
    [CrossRef]
  3. J. U. Kang, G. I. Stegeman, and J. S. Aichison, “One-dimensional spatial soliton dragging, trapping, and all-optical switching in AlGaAs waveguides,” Opt. Lett. 21, 189–191 (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. P. Tran, “Optical limiting and switching of short pulses by use of a nonlinear photonic bandgap structure with a defect,” J. Opt. Soc. Am. B 14, 2589–2595 (1997).
    [CrossRef]
  6. M. A. Krumbugel, J. N. Sweetser, D. N. Fittinghoff, K. W. DeLong, and R. Trebino, “Ultrafast optical switching by use of fully phase-matched cascaded second-order nonlinearities in a polarization-gate geometry,” Opt. Lett. 22, 245–247 (1997).
    [CrossRef] [PubMed]
  7. R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).
    [CrossRef] [PubMed]
  8. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in Isotropic Media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).
  9. G. Mur, “Absorbing boundary conditions for finite-difference approximation of the time-domain electromagnetic field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 1073–1077 (1981).
    [CrossRef]
  10. G. Maxein, H. Keller, B. M. Novak, and R. Zentel, “Opalescent cholesteric networks from chiral polyisocyanates in polystyrene,” Adv. Mater. 3, 341–345 (1998).
    [CrossRef]

1998 (1)

G. Maxein, H. Keller, B. M. Novak, and R. Zentel, “Opalescent cholesteric networks from chiral polyisocyanates in polystyrene,” Adv. Mater. 3, 341–345 (1998).
[CrossRef]

1997 (2)

1996 (2)

1994 (1)

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]

1988 (1)

1981 (1)

G. Mur, “Absorbing boundary conditions for finite-difference approximation of the time-domain electromagnetic field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 1073–1077 (1981).
[CrossRef]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in Isotropic Media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

Aichison, J. S.

Baek, Y.

Baumann, I.

Bloemer, M. J.

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]

Bowden, C. M.

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]

DeLong, K. W.

Dowling, J. P.

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]

Firberg, S. R.

Fittinghoff, D. N.

Kang, J. U.

Keller, H.

G. Maxein, H. Keller, B. M. Novak, and R. Zentel, “Opalescent cholesteric networks from chiral polyisocyanates in polystyrene,” Adv. Mater. 3, 341–345 (1998).
[CrossRef]

Krijnen, G.

Krumbugel, M. A.

Maxein, G.

G. Maxein, H. Keller, B. M. Novak, and R. Zentel, “Opalescent cholesteric networks from chiral polyisocyanates in polystyrene,” Adv. Mater. 3, 341–345 (1998).
[CrossRef]

Mur, G.

G. Mur, “Absorbing boundary conditions for finite-difference approximation of the time-domain electromagnetic field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 1073–1077 (1981).
[CrossRef]

Novak, B. M.

G. Maxein, H. Keller, B. M. Novak, and R. Zentel, “Opalescent cholesteric networks from chiral polyisocyanates in polystyrene,” Adv. Mater. 3, 341–345 (1998).
[CrossRef]

Scalora, M.

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]

Schiek, R.

Sfez, B. G.

Silberberg, Y.

Smith, P. W.

Sohler, W.

Stegeman, G. I.

Sweetser, J. N.

Tran, P.

Trebino, R.

Weiner, A. M.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in Isotropic Media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

Zentel, R.

G. Maxein, H. Keller, B. M. Novak, and R. Zentel, “Opalescent cholesteric networks from chiral polyisocyanates in polystyrene,” Adv. Mater. 3, 341–345 (1998).
[CrossRef]

Adv. Mater. (1)

G. Maxein, H. Keller, B. M. Novak, and R. Zentel, “Opalescent cholesteric networks from chiral polyisocyanates in polystyrene,” Adv. Mater. 3, 341–345 (1998).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in Isotropic Media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

IEEE Trans. Electromagn. Compat. (1)

G. Mur, “Absorbing boundary conditions for finite-difference approximation of the time-domain electromagnetic field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 1073–1077 (1981).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

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]

Other (1)

For a review, see H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, Orlando, 1985).

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Figures (5)

Fig. 1
Fig. 1

Plot of the transmission as a function of frequency near the lower band edge of a chiral photonic bandgap structure (inset). The solid curve corresponds to the fast mode, and the dashed curve corresponds to the slow mode.

Fig. 2
Fig. 2

Plot of the intensity distribution of the fast (solid curve) and the slow (dashed curve) pulse after launching each toward the chiral photonic bandgap structure and integrating for a time cT=300λ0.

Fig. 3
Fig. 3

Schematic of the optical switch. The probe (signal) beam is the fast pulse, and the pump (control) beam is the slow pulse. The solid line at the output end is the probe beam when the pump beam is not present. When the pump beam is present, the probe beam is reflected (dashed line at the input end).

Fig. 4
Fig. 4

Plot of the transmission and the reflection from a nonlinear chiral photonic bandgap structure of the fast (probe) pulse for three field strength of the slow (pump) pulse. The integration time is the same as for Fig. 2.

Fig. 5
Fig. 5

Plot of the transmission and the reflection from a nonlinear chiral photonic bandgap structure of the pump and the probe pulses when the field strength of the pump is 14.14.

Equations (11)

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D=¯·E+χ|E|2E
¯=x000iβ0-iβ.
1cBt=-×E,
1cDt=×B,
Dy=Ey+iβEz+χ(|Ey|2+|Ez|2)Ey,
Dz=Ez-iβEy+χ(|Ey|2+|Ez|2)Ez.
E1=12(Ey+iEz),
E2=12(Ey-iEz).
q[(+q)2-β2]2-χ(|Dy|2+|Dz|2)[(+q)2+β2]
+4χβ Im(DyDz*)(+q)=0.
E(x, t)=(yˆ+izˆ)E0 exp{-iω0/c[ct-0(x-x0)]-[ct-0(x-x0)]2(Δω/c)2/2},

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