Abstract

A finite-difference time-domain full-wave vector Maxwell equation solver is coupled with a two-level-atom model to simulate the scattering of an ultrafast pulsed Gaussian beam from a finite-length, metallic lamellar grating loaded with two-level atoms. The atomic medium is taken to be resonant at or near the frequency of the incident optical radiation. The highly resonant material and grating behaviors are then combined to realize an all-optical triode at low powers and an all-optical diode at high powers. Simulation results demonstrate the operating characteristics of these triode and diode configurations.

© 1997 Optical Society of America

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  1. P. W. Smith, W. J. Tomlinson, P. J. Maloney, J.-P. Hermann, “Experimental studies of a nonlinear interface,” IEEE J. Quantum Electron. QE-17, 340–348 (1981).
    [Crossref]
  2. W. J. Tomlinson, J. P. Gordon, P. W. Smith, A. E. Kaplan, “Reflection of a Gaussian beam at a nonlinear interface,” Appl. Opt. 21, 2041–2051 (1982).
    [Crossref] [PubMed]
  3. R. W. Ziolkowski, J. B. Judkins, “Applications of discrete methods to pulse propagation in nonlinear media: self-focusing and linear-nonlinear interfaces,” Radio Sci. 28, 901–911 (1993).
    [Crossref]
  4. D. R. Andersen, J. J. Regan, “Reflection and refraction of a three-dimensional Gaussian beam at a nonlinear interface,” J. Opt. Soc. Am. A 6, 1484–1492 (1989).
    [Crossref]
  5. Y. Shibata, M. Ikeda, K. Nakashima, T. Tamamura, T. Nishida, “Optically-controlled grating switch (OG-SW),” Electron. Lett. 27, 246–247 (1991).
    [Crossref]
  6. B. E. Little, “Optical-induced spectral tuning in grating-assisted nonlinear couplers,” J. Lightwave Technol. 12, 774–783 (1994).
    [Crossref]
  7. M. H. Shih, F. S. Choa, G. J. Simonis, T. Tanbun-Ek, R. A. Logan, W. T. Tsang, “Optically controlled surface-emitting beam switches,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 67–68.
  8. H. Tsuda, T. Kurokawa, “All-optical triode device design using a nonlinear etalon and GRIN lenses,” Appl. Opt. 29, 5054–5059 (1990).
    [Crossref] [PubMed]
  9. H. Tsuda, T. Kurokawa, “Construction of an all-optical flip-flop by combination of two optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990).
    [Crossref]
  10. M Yamanishi, “Ultrafast optical processes in DC-field biased quantum well structures,” Trans. Inst. Electron. Inf. Commun. Eng. J74C-I(11), 449–457 (1991).
  11. R. W. Ziolkowski, J. M. Arnold, D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52(4), 3082–3094 (1995).
    [Crossref] [PubMed]
  12. J. B. Judkins, R. W. Ziolkowski, “Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings,” J. Opt. Soc. Am. A 12, 1974–1983 (1995).
    [Crossref]
  13. J. B. Judkins, C. W. Haggans, R. W. Ziolkowski, “Two-dimensional finite-difference time-domain simulation for rewritable optical disk surface structure design,” Appl. Opt. 35, 2477–2487 (1996).
    [Crossref] [PubMed]
  14. A. Taflove, Computational Electrodynamics (Artech House, Norwood, Mass., 1995).
  15. M. J. Barth, R. R. McLeod, R. W. Ziolkowski, “A near and far-field projection algorithm for finite-difference time-domain codes,” J. Electromagn. Waves Appl. 6, 5–18 (1992).
    [Crossref]
  16. R. Luebbers, K. S. Kunz, M. Schneider, F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation,” IEEE Trans. Antennas Propagat. AP-39, 429–433 (1991).
    [Crossref]

1996 (1)

1995 (2)

R. W. Ziolkowski, J. M. Arnold, D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52(4), 3082–3094 (1995).
[Crossref] [PubMed]

J. B. Judkins, R. W. Ziolkowski, “Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings,” J. Opt. Soc. Am. A 12, 1974–1983 (1995).
[Crossref]

1994 (1)

B. E. Little, “Optical-induced spectral tuning in grating-assisted nonlinear couplers,” J. Lightwave Technol. 12, 774–783 (1994).
[Crossref]

1993 (1)

R. W. Ziolkowski, J. B. Judkins, “Applications of discrete methods to pulse propagation in nonlinear media: self-focusing and linear-nonlinear interfaces,” Radio Sci. 28, 901–911 (1993).
[Crossref]

1992 (1)

M. J. Barth, R. R. McLeod, R. W. Ziolkowski, “A near and far-field projection algorithm for finite-difference time-domain codes,” J. Electromagn. Waves Appl. 6, 5–18 (1992).
[Crossref]

1991 (3)

R. Luebbers, K. S. Kunz, M. Schneider, F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation,” IEEE Trans. Antennas Propagat. AP-39, 429–433 (1991).
[Crossref]

Y. Shibata, M. Ikeda, K. Nakashima, T. Tamamura, T. Nishida, “Optically-controlled grating switch (OG-SW),” Electron. Lett. 27, 246–247 (1991).
[Crossref]

M Yamanishi, “Ultrafast optical processes in DC-field biased quantum well structures,” Trans. Inst. Electron. Inf. Commun. Eng. J74C-I(11), 449–457 (1991).

1990 (2)

H. Tsuda, T. Kurokawa, “All-optical triode device design using a nonlinear etalon and GRIN lenses,” Appl. Opt. 29, 5054–5059 (1990).
[Crossref] [PubMed]

H. Tsuda, T. Kurokawa, “Construction of an all-optical flip-flop by combination of two optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990).
[Crossref]

1989 (1)

1982 (1)

1981 (1)

P. W. Smith, W. J. Tomlinson, P. J. Maloney, J.-P. Hermann, “Experimental studies of a nonlinear interface,” IEEE J. Quantum Electron. QE-17, 340–348 (1981).
[Crossref]

Andersen, D. R.

Arnold, J. M.

R. W. Ziolkowski, J. M. Arnold, D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52(4), 3082–3094 (1995).
[Crossref] [PubMed]

Barth, M. J.

M. J. Barth, R. R. McLeod, R. W. Ziolkowski, “A near and far-field projection algorithm for finite-difference time-domain codes,” J. Electromagn. Waves Appl. 6, 5–18 (1992).
[Crossref]

Choa, F. S.

M. H. Shih, F. S. Choa, G. J. Simonis, T. Tanbun-Ek, R. A. Logan, W. T. Tsang, “Optically controlled surface-emitting beam switches,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 67–68.

Gogny, D. M.

R. W. Ziolkowski, J. M. Arnold, D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52(4), 3082–3094 (1995).
[Crossref] [PubMed]

Gordon, J. P.

Haggans, C. W.

Hermann, J.-P.

P. W. Smith, W. J. Tomlinson, P. J. Maloney, J.-P. Hermann, “Experimental studies of a nonlinear interface,” IEEE J. Quantum Electron. QE-17, 340–348 (1981).
[Crossref]

Hunsberger, F.

R. Luebbers, K. S. Kunz, M. Schneider, F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation,” IEEE Trans. Antennas Propagat. AP-39, 429–433 (1991).
[Crossref]

Ikeda, M.

Y. Shibata, M. Ikeda, K. Nakashima, T. Tamamura, T. Nishida, “Optically-controlled grating switch (OG-SW),” Electron. Lett. 27, 246–247 (1991).
[Crossref]

Judkins, J. B.

Kaplan, A. E.

Kunz, K. S.

R. Luebbers, K. S. Kunz, M. Schneider, F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation,” IEEE Trans. Antennas Propagat. AP-39, 429–433 (1991).
[Crossref]

Kurokawa, T.

H. Tsuda, T. Kurokawa, “Construction of an all-optical flip-flop by combination of two optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990).
[Crossref]

H. Tsuda, T. Kurokawa, “All-optical triode device design using a nonlinear etalon and GRIN lenses,” Appl. Opt. 29, 5054–5059 (1990).
[Crossref] [PubMed]

Little, B. E.

B. E. Little, “Optical-induced spectral tuning in grating-assisted nonlinear couplers,” J. Lightwave Technol. 12, 774–783 (1994).
[Crossref]

Logan, R. A.

M. H. Shih, F. S. Choa, G. J. Simonis, T. Tanbun-Ek, R. A. Logan, W. T. Tsang, “Optically controlled surface-emitting beam switches,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 67–68.

Luebbers, R.

R. Luebbers, K. S. Kunz, M. Schneider, F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation,” IEEE Trans. Antennas Propagat. AP-39, 429–433 (1991).
[Crossref]

Maloney, P. J.

P. W. Smith, W. J. Tomlinson, P. J. Maloney, J.-P. Hermann, “Experimental studies of a nonlinear interface,” IEEE J. Quantum Electron. QE-17, 340–348 (1981).
[Crossref]

McLeod, R. R.

M. J. Barth, R. R. McLeod, R. W. Ziolkowski, “A near and far-field projection algorithm for finite-difference time-domain codes,” J. Electromagn. Waves Appl. 6, 5–18 (1992).
[Crossref]

Nakashima, K.

Y. Shibata, M. Ikeda, K. Nakashima, T. Tamamura, T. Nishida, “Optically-controlled grating switch (OG-SW),” Electron. Lett. 27, 246–247 (1991).
[Crossref]

Nishida, T.

Y. Shibata, M. Ikeda, K. Nakashima, T. Tamamura, T. Nishida, “Optically-controlled grating switch (OG-SW),” Electron. Lett. 27, 246–247 (1991).
[Crossref]

Regan, J. J.

Schneider, M.

R. Luebbers, K. S. Kunz, M. Schneider, F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation,” IEEE Trans. Antennas Propagat. AP-39, 429–433 (1991).
[Crossref]

Shibata, Y.

Y. Shibata, M. Ikeda, K. Nakashima, T. Tamamura, T. Nishida, “Optically-controlled grating switch (OG-SW),” Electron. Lett. 27, 246–247 (1991).
[Crossref]

Shih, M. H.

M. H. Shih, F. S. Choa, G. J. Simonis, T. Tanbun-Ek, R. A. Logan, W. T. Tsang, “Optically controlled surface-emitting beam switches,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 67–68.

Simonis, G. J.

M. H. Shih, F. S. Choa, G. J. Simonis, T. Tanbun-Ek, R. A. Logan, W. T. Tsang, “Optically controlled surface-emitting beam switches,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 67–68.

Smith, P. W.

W. J. Tomlinson, J. P. Gordon, P. W. Smith, A. E. Kaplan, “Reflection of a Gaussian beam at a nonlinear interface,” Appl. Opt. 21, 2041–2051 (1982).
[Crossref] [PubMed]

P. W. Smith, W. J. Tomlinson, P. J. Maloney, J.-P. Hermann, “Experimental studies of a nonlinear interface,” IEEE J. Quantum Electron. QE-17, 340–348 (1981).
[Crossref]

Taflove, A.

A. Taflove, Computational Electrodynamics (Artech House, Norwood, Mass., 1995).

Tamamura, T.

Y. Shibata, M. Ikeda, K. Nakashima, T. Tamamura, T. Nishida, “Optically-controlled grating switch (OG-SW),” Electron. Lett. 27, 246–247 (1991).
[Crossref]

Tanbun-Ek, T.

M. H. Shih, F. S. Choa, G. J. Simonis, T. Tanbun-Ek, R. A. Logan, W. T. Tsang, “Optically controlled surface-emitting beam switches,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 67–68.

Tomlinson, W. J.

W. J. Tomlinson, J. P. Gordon, P. W. Smith, A. E. Kaplan, “Reflection of a Gaussian beam at a nonlinear interface,” Appl. Opt. 21, 2041–2051 (1982).
[Crossref] [PubMed]

P. W. Smith, W. J. Tomlinson, P. J. Maloney, J.-P. Hermann, “Experimental studies of a nonlinear interface,” IEEE J. Quantum Electron. QE-17, 340–348 (1981).
[Crossref]

Tsang, W. T.

M. H. Shih, F. S. Choa, G. J. Simonis, T. Tanbun-Ek, R. A. Logan, W. T. Tsang, “Optically controlled surface-emitting beam switches,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 67–68.

Tsuda, H.

H. Tsuda, T. Kurokawa, “Construction of an all-optical flip-flop by combination of two optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990).
[Crossref]

H. Tsuda, T. Kurokawa, “All-optical triode device design using a nonlinear etalon and GRIN lenses,” Appl. Opt. 29, 5054–5059 (1990).
[Crossref] [PubMed]

Yamanishi, M

M Yamanishi, “Ultrafast optical processes in DC-field biased quantum well structures,” Trans. Inst. Electron. Inf. Commun. Eng. J74C-I(11), 449–457 (1991).

Ziolkowski, R. W.

J. B. Judkins, C. W. Haggans, R. W. Ziolkowski, “Two-dimensional finite-difference time-domain simulation for rewritable optical disk surface structure design,” Appl. Opt. 35, 2477–2487 (1996).
[Crossref] [PubMed]

R. W. Ziolkowski, J. M. Arnold, D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52(4), 3082–3094 (1995).
[Crossref] [PubMed]

J. B. Judkins, R. W. Ziolkowski, “Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings,” J. Opt. Soc. Am. A 12, 1974–1983 (1995).
[Crossref]

R. W. Ziolkowski, J. B. Judkins, “Applications of discrete methods to pulse propagation in nonlinear media: self-focusing and linear-nonlinear interfaces,” Radio Sci. 28, 901–911 (1993).
[Crossref]

M. J. Barth, R. R. McLeod, R. W. Ziolkowski, “A near and far-field projection algorithm for finite-difference time-domain codes,” J. Electromagn. Waves Appl. 6, 5–18 (1992).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

H. Tsuda, T. Kurokawa, “Construction of an all-optical flip-flop by combination of two optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990).
[Crossref]

Electron. Lett. (1)

Y. Shibata, M. Ikeda, K. Nakashima, T. Tamamura, T. Nishida, “Optically-controlled grating switch (OG-SW),” Electron. Lett. 27, 246–247 (1991).
[Crossref]

IEEE J. Quantum Electron. (1)

P. W. Smith, W. J. Tomlinson, P. J. Maloney, J.-P. Hermann, “Experimental studies of a nonlinear interface,” IEEE J. Quantum Electron. QE-17, 340–348 (1981).
[Crossref]

IEEE Trans. Antennas Propagat. (1)

R. Luebbers, K. S. Kunz, M. Schneider, F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation,” IEEE Trans. Antennas Propagat. AP-39, 429–433 (1991).
[Crossref]

J. Electromagn. Waves Appl. (1)

M. J. Barth, R. R. McLeod, R. W. Ziolkowski, “A near and far-field projection algorithm for finite-difference time-domain codes,” J. Electromagn. Waves Appl. 6, 5–18 (1992).
[Crossref]

J. Lightwave Technol. (1)

B. E. Little, “Optical-induced spectral tuning in grating-assisted nonlinear couplers,” J. Lightwave Technol. 12, 774–783 (1994).
[Crossref]

J. Opt. Soc. Am. A (2)

Phys. Rev. A (1)

R. W. Ziolkowski, J. M. Arnold, D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52(4), 3082–3094 (1995).
[Crossref] [PubMed]

Radio Sci. (1)

R. W. Ziolkowski, J. B. Judkins, “Applications of discrete methods to pulse propagation in nonlinear media: self-focusing and linear-nonlinear interfaces,” Radio Sci. 28, 901–911 (1993).
[Crossref]

Trans. Inst. Electron. Inf. Commun. Eng. J74C-I(11) (1)

M Yamanishi, “Ultrafast optical processes in DC-field biased quantum well structures,” Trans. Inst. Electron. Inf. Commun. Eng. J74C-I(11), 449–457 (1991).

Other (2)

A. Taflove, Computational Electrodynamics (Artech House, Norwood, Mass., 1995).

M. H. Shih, F. S. Choa, G. J. Simonis, T. Tanbun-Ek, R. A. Logan, W. T. Tsang, “Optically controlled surface-emitting beam switches,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 67–68.

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Figures (11)

Fig. 1
Fig. 1

Basic simulation geometry for a two-level, atom-loaded diffraction grating illuminated with a pulsed Gaussian beam that can act as an optical triode or diode. These optical triode and diode configurations were studied with a two-dimensional FDTD Maxwell–Bloch simulator.

Fig. 2
Fig. 2

Equivalent transistor schematic of the optical triode.

Fig. 3
Fig. 3

Unloaded grating used to design the structure selected for the optical triode and diode studies. The resulting differential scattering factor is shown for several values of the duty factor for one grating with 11 unit cells and one with 19 unit cells.

Fig. 4
Fig. 4

Weighted differential output obtained as a function of the initial population difference ρ3i for optical triode configurations with a grating of 11 unit cells and duty factors DF = 0.05 and DF = 0.50.

Fig. 5
Fig. 5

Weighted differential output obtained as a function of the initial population difference ρ3i for optical triode configurations with ○, an 11-unit-cell grating and the 2–2–2 incident pulse; ◆, a 19-unit-cell grating and the 2–2–2 incident pulse; and ●, an 11-unit-cell grating and the 5–10–5 incident pulse. The duty factor of the grating was DF = 0.05 for all of these cases.

Fig. 6
Fig. 6

FDTD incident 5–10–5 pulse electric-field distribution at the exact time that the beam interacts with the atom-loaded diffraction grating of duty factor DF = 0.05. The angle of incidence is 19.5°. The additional lines depict the beam-center line, the normal to the grating at the point where the beam center strikes the grating, and the normal to the grating that intersects the total-field–scattered-field source boundary at the initial beam center.

Fig. 7
Fig. 7

FDTD scattered field distribution at a time after the entire 5–10–5 incident pulse given in Fig. 5 has interacted with the atom-loaded grating. The atoms are initially in their ground state characterized by ρ3i = −1.0. The pulsed beam has been reflected by this grating, with only minor distortion.

Fig. 8
Fig. 8

FDTD scattered field distribution at a time after the entire 5–10–5 incident pulse given in Fig. 5 has interacted with the atom-loaded grating. The atoms are initially in the excited state characterized by ρ3i = +0.10. The pulsed beam has been reflected strongly back into the source direction. Some of the beam leaves the grating in the reflected field direction.

Fig. 9
Fig. 9

Normalized far-field radiation pattern generated from the near-field FDTD data obtained when the 5–10–5 incident pulse is scattered from the triode configuration given in Fig. 5, when the triode is off (circled curve), which is characterized by ρ3i = −1.0, and when it is on (solid curve), which is characterized by ρ3i = +0.10. Positive (negative) angles correspond to a direction of propagation into region I (II). These radiation patterns clearly demonstrate that the grating-based triode acts as a high-fidelity switch for narrow-bandwidth incident pulses.

Fig. 10
Fig. 10

Normalized far-field patterns generated by the scattering of the 2–2–2 incident pulse from the triode configuration given in Fig. 5 obtained when the triode is both off (circled curve) and on (solid curve). Positive (negative) angles correspond to a direction of propagation into region I (II). These radiation patterns clearly demonstrate that the grating-based triode acts as a reasonably high fidelity switch, even for ultrafast, wide-bandwidth incident pulses.

Fig. 11
Fig. 11

Weighted differential output obtained as a function of the maximum amplitude Emax of the incident field for the optical diode configuration with the 2–2–2 incident pulse and a 11-unit-cell grating having a duty factor DF = 0.05.

Equations (14)

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

t H x = + 1 μ 0 z E y ,
t H z = - 1 μ 0 x E y ,
t E y = 1 0 ( z H x - x H z ) - 1 0 t P y = 1 0 ( z H x - x H z ) - N atom γ 0 T 2 ρ 1 + N atom γ ω 0 0 ρ 2 .
t ρ 1 = - 1 T 2 ρ 1 + ω 0 ρ 2 ,
t ρ 2 = - ω 0 ρ 1 - 1 T 2 ρ 2 + 2 γ E y ρ 3 ,
t ρ 3 = - 2 γ E y ρ 2 - 1 T 1 ( ρ 3 - ρ 30 ) ,
S = ( S 1 - S 2 ) S 1 + S 2 ,
WDO = - S S 2 S in ,
z 2 E y - c t 2 E y = μ 0 t 2 P y N atom γ μ 0 ω 0 2 ρ 1 ,
t 2 ρ 1 + ω 0 2 ρ 1 = - 1 T 1 t ρ 1 - ω 0 T 2 ρ 2 + 2 γ E y ω 0 ρ 3 2 γ E y ω 0 ρ 3 ,
χ ω = - ρ 3 Λ [ 1 - ( ω ω 0 ) 2 ] - 1 ,
Λ = 2 N atom γ 2 ω 0 0 .
χ ω + ρ 3 Λ 2 δ .
sin θ out = sin θ inc + m λ n ( ω ) L ,             m = 0 , ± 1 , ± 2 , ,

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