Abstract

We derived a recursion formula for the reflectance of the stratified and phase-shifted volume index gratings. The characteristics of the reflectance spectra of the stratified and phase-shifted volume index gratings were studied based on the recursion formula. It is shown that narrow bandwidth transparency peaks appear within the stop-band of the reflectance spectrum of the volume index gratings due to the intervention of the homogeneous buffer layers that induce the phase-shifts between neighboring volume index gratings. The spectral positions of the transparency peaks can be shifted within the stop-band by controlling the phase-shift, i.e., the buffer layer thickness. The described properties may find applications in addressable band-pass filter, switching, wavelength division multiplexing, and de-multiplexing. The dispersion near the transparency peaks of the stratified and phase-shifted volume index grating is found to be sharply enhanced as compared to the uniform volume index gratings. Significantly enhanced control on the group velocity of light by several orders of magnitude while keeping high transmittance is demonstrated in the stratified and phase-shifted volume index grating.

© 2007 Optical Society of America

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2006

2005

2003

S. Khorasani and K. Mehrany, "Differential transfer-matrix method for solution of one-dimensional linear nonhomogeneous optical sturctures," J. Opt. Soc. Am. B 20, 91-96 (2003).
[CrossRef]

A. D’Orazio, M. De Sario, V. Petruzzelli, and F. Prudenzano, "Photonic band gap filter for wavelength division multiplexer," Opt. Express 11, 230-239 (2003).
[CrossRef] [PubMed]

Y. Lai, W. Zhang, L. Zhang, J. A. R. Williams, and I. Bennion, "Optically tumable fiber grating transmission filters," Opt. Lett. 28, 2446-2448 (2003).
[CrossRef] [PubMed]

V. M. Petrov, C. Caraboue, J. Petter, T. Tschudi, V. V. Bryksin, and M. P. Petrov, "A dynamic narrow-band tunable optical filter," Appl. Phys. B 76, 41-44 (2003).
[CrossRef]

S. Khorasani and A. Adibi, "New analytical approach for computation of band structure in one-dimensional periodic media," Opt. Commun. 216, 439-451 (2003).
[CrossRef]

J. J. Monzón, T. Yonte, and L. L. Sánchez-Soto, "Charcterizing the reflectance of periodic layered media," Opt. Commun. 218, 43-47 (2003).
[CrossRef]

2002

I. S. Nefedov and S. A. Tretyakov, "Photonic band gap structure containing metamaterial with negative permittivity and permeability," Phys. Rev. E 66, 036611-1-4 (2002).
[CrossRef]

S. Longhi, M. Marano, P. Laporta, O. Svelto, and M. Belmonte, "Propagation, manipulation, and control of picosecond optical pulses at 1.5 μm in fiber Bragg gratings," J. Opt. Soc. Am B 19, 2742-2757 (2002).
[CrossRef]

J. Liu, B. Shi, D. Zhao, and X. Wang, "Optical delay in defective photonic bandgap structures," J. Opt. A: Pure Appl. Opt. 4, 636-639 (2002).
[CrossRef]

Ch. Martinez, S. Magne, and P. Ferdinand, "Apodized fiber Bragg gratings manufactured with the phase plate process," Appl. Opt. 41, 1733-1740 (2002).
[CrossRef] [PubMed]

2000

S. H. Lin, K. Y. Hsu, and P. Yeh, "Experimental observation of the slowdown of optical beams by a volume-index grating in a photorefractive LiNbO3 crystal," Opt. Lett. 25, 1582-1584 (2000).
[CrossRef]

M. McCall, "On the application of coupled mode theory for modeling fiber Bragg gratings," J. Lightwave Technol. 18, 236-242 (2000).
[CrossRef]

S. Zhu, N. Liu, H. Zheng, and H. Chen, "Time delay of light propagation through defect modes of one-dimensional photonic band-gap structures," Opt. Commun. 174, 139-144 (2000).
[CrossRef]

M. A. Rodriguez, M. S. Malcuit, and J. J. Butler, "Transmission properties of refrective index-shifted Bragg gratings," Opt. Commun. 177, 251-257 (2000).
[CrossRef]

1999

1997

L. Wei and J. W. Y. Lit, "Phase-Shifted Bragg Grating Filters with Symmetrical Structures," J. Lightwave Technol. 15, 1405-1410 (1997).
[CrossRef]

F. Bakhti and P. Sansonetti, "Design and Realization of Multiple Quater-Wave Phase-Shifts UV-Written Bandpass Filter in Optical Fibers," J. Lightwave Technol. 15, 1433-1437 (1997).
[CrossRef]

1996

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, and R. P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss," Phys. Rev. E 54, R1078-R1081 (1996).
[CrossRef]

1995

R. Zengerle and O. Leminger, "Phase-shifted Bragg-Grating Filters with Improved Transmission Characteristics," J. Lightwave Technol. 13, 2354-2358 (1995).
[CrossRef]

Y. Painchaud, A. Chandonnet, and J. Lauzon, "Chirped fibre gratings produced by tilting the fibre," Electron. Lett. 31, 171-172 (1995).
[CrossRef]

B. Malo, S. Thériault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, "Apodised in-fibre Bragg grating reflectors photoimprinted using a phase mask," Electron. Lett. 31, 223-225 (1995).
[CrossRef]

1994

1992

1988

1987

1986

R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, "Narrowband grating resonator filters in InGaAsP/InP waveguides," Appl. Phys. Lett. 49, 125-127 (1986).
[CrossRef]

1982

Adibi, A.

S. Khorasani and A. Adibi, "New analytical approach for computation of band structure in one-dimensional periodic media," Opt. Commun. 216, 439-451 (2003).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal and S. Radic, "Phase-Shifted Fiber Bragg Gratings and their Application for Wavelength Demultiplexing," IEEE Photon. Technol. Lett. 6, 995-997 (1994).
[CrossRef]

Albert, J.

B. Malo, S. Thériault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, "Apodised in-fibre Bragg grating reflectors photoimprinted using a phase mask," Electron. Lett. 31, 223-225 (1995).
[CrossRef]

Alferness, R. C.

R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, "Narrowband grating resonator filters in InGaAsP/InP waveguides," Appl. Phys. Lett. 49, 125-127 (1986).
[CrossRef]

Bakhti, F.

F. Bakhti and P. Sansonetti, "Design and Realization of Multiple Quater-Wave Phase-Shifts UV-Written Bandpass Filter in Optical Fibers," J. Lightwave Technol. 15, 1433-1437 (1997).
[CrossRef]

Belmonte, M.

S. Longhi, M. Marano, P. Laporta, O. Svelto, and M. Belmonte, "Propagation, manipulation, and control of picosecond optical pulses at 1.5 μm in fiber Bragg gratings," J. Opt. Soc. Am B 19, 2742-2757 (2002).
[CrossRef]

Bendickson, J. M.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, and R. P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss," Phys. Rev. E 54, R1078-R1081 (1996).
[CrossRef]

Bennion, I.

Bette, S.

Bilodeau, F.

B. Malo, S. Thériault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, "Apodised in-fibre Bragg grating reflectors photoimprinted using a phase mask," Electron. Lett. 31, 223-225 (1995).
[CrossRef]

Birge, J. R.

Bjorklund, G. C.

Bloemer, M. J.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, and R. P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss," Phys. Rev. E 54, R1078-R1081 (1996).
[CrossRef]

Bowden, C. M.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, and R. P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss," Phys. Rev. E 54, R1078-R1081 (1996).
[CrossRef]

Bryksin, V. V.

V. M. Petrov, C. Caraboue, J. Petter, T. Tschudi, V. V. Bryksin, and M. P. Petrov, "A dynamic narrow-band tunable optical filter," Appl. Phys. B 76, 41-44 (2003).
[CrossRef]

Buhl, L. L.

R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, "Narrowband grating resonator filters in InGaAsP/InP waveguides," Appl. Phys. Lett. 49, 125-127 (1986).
[CrossRef]

Butler, J. J.

M. A. Rodriguez, M. S. Malcuit, and J. J. Butler, "Transmission properties of refrective index-shifted Bragg gratings," Opt. Commun. 177, 251-257 (2000).
[CrossRef]

Capmany, J.

Caraboue, C.

V. M. Petrov, C. Caraboue, J. Petter, T. Tschudi, V. V. Bryksin, and M. P. Petrov, "A dynamic narrow-band tunable optical filter," Appl. Phys. B 76, 41-44 (2003).
[CrossRef]

Caucheteur, C.

Chandonnet, A.

Y. Painchaud, A. Chandonnet, and J. Lauzon, "Chirped fibre gratings produced by tilting the fibre," Electron. Lett. 31, 171-172 (1995).
[CrossRef]

Chen, H.

S. Zhu, N. Liu, H. Zheng, and H. Chen, "Time delay of light propagation through defect modes of one-dimensional photonic band-gap structures," Opt. Commun. 174, 139-144 (2000).
[CrossRef]

D’Orazio, A.

De Sario, M.

De Vré, R.

Divino, M. D.

R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, "Narrowband grating resonator filters in InGaAsP/InP waveguides," Appl. Phys. Lett. 49, 125-127 (1986).
[CrossRef]

Ferdinand, P.

Flynn, R. J.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, and R. P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss," Phys. Rev. E 54, R1078-R1081 (1996).
[CrossRef]

Fork, R. L.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, and R. P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss," Phys. Rev. E 54, R1078-R1081 (1996).
[CrossRef]

Garcia-Olcina, R.

Hesselink, L.

Hill, K. O.

B. Malo, S. Thériault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, "Apodised in-fibre Bragg grating reflectors photoimprinted using a phase mask," Electron. Lett. 31, 223-225 (1995).
[CrossRef]

Hsu, K. Y.

Johnson, D. C.

B. Malo, S. Thériault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, "Apodised in-fibre Bragg grating reflectors photoimprinted using a phase mask," Electron. Lett. 31, 223-225 (1995).
[CrossRef]

Johnson, R. V.

Joyner, C. H.

R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, "Narrowband grating resonator filters in InGaAsP/InP waveguides," Appl. Phys. Lett. 49, 125-127 (1986).
[CrossRef]

Kärtner, F. X.

Kelly, P. K.

Khorasani, S.

S. Khorasani and K. Mehrany, "Differential transfer-matrix method for solution of one-dimensional linear nonhomogeneous optical sturctures," J. Opt. Soc. Am. B 20, 91-96 (2003).
[CrossRef]

S. Khorasani and A. Adibi, "New analytical approach for computation of band structure in one-dimensional periodic media," Opt. Commun. 216, 439-451 (2003).
[CrossRef]

Koshiba, M.

Lai, Y.

Laporta, P.

S. Longhi, M. Marano, P. Laporta, O. Svelto, and M. Belmonte, "Propagation, manipulation, and control of picosecond optical pulses at 1.5 μm in fiber Bragg gratings," J. Opt. Soc. Am B 19, 2742-2757 (2002).
[CrossRef]

Lauzon, J.

Y. Painchaud, A. Chandonnet, and J. Lauzon, "Chirped fibre gratings produced by tilting the fibre," Electron. Lett. 31, 171-172 (1995).
[CrossRef]

Leavitt, R. P.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, and R. P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss," Phys. Rev. E 54, R1078-R1081 (1996).
[CrossRef]

Ledbetter, H. S.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, and R. P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss," Phys. Rev. E 54, R1078-R1081 (1996).
[CrossRef]

Lee, Ch. M.

Leminger, O.

R. Zengerle and O. Leminger, "Phase-shifted Bragg-Grating Filters with Improved Transmission Characteristics," J. Lightwave Technol. 13, 2354-2358 (1995).
[CrossRef]

Lin, S. H.

Lit, J. W. Y.

L. Wei and J. W. Y. Lit, "Phase-Shifted Bragg Grating Filters with Symmetrical Structures," J. Lightwave Technol. 15, 1405-1410 (1997).
[CrossRef]

Liu, J.

J. Liu, B. Shi, D. Zhao, and X. Wang, "Optical delay in defective photonic bandgap structures," J. Opt. A: Pure Appl. Opt. 4, 636-639 (2002).
[CrossRef]

Liu, N.

S. Zhu, N. Liu, H. Zheng, and H. Chen, "Time delay of light propagation through defect modes of one-dimensional photonic band-gap structures," Opt. Commun. 174, 139-144 (2000).
[CrossRef]

Longhi, S.

S. Longhi, M. Marano, P. Laporta, O. Svelto, and M. Belmonte, "Propagation, manipulation, and control of picosecond optical pulses at 1.5 μm in fiber Bragg gratings," J. Opt. Soc. Am B 19, 2742-2757 (2002).
[CrossRef]

Magne, S.

Malcuit, M. S.

M. A. Rodriguez, M. S. Malcuit, and J. J. Butler, "Transmission properties of refrective index-shifted Bragg gratings," Opt. Commun. 177, 251-257 (2000).
[CrossRef]

Malo, B.

B. Malo, S. Thériault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, "Apodised in-fibre Bragg grating reflectors photoimprinted using a phase mask," Electron. Lett. 31, 223-225 (1995).
[CrossRef]

Marano, M.

S. Longhi, M. Marano, P. Laporta, O. Svelto, and M. Belmonte, "Propagation, manipulation, and control of picosecond optical pulses at 1.5 μm in fiber Bragg gratings," J. Opt. Soc. Am B 19, 2742-2757 (2002).
[CrossRef]

Martinez, Ch.

Martyak, M. J. R.

R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, "Narrowband grating resonator filters in InGaAsP/InP waveguides," Appl. Phys. Lett. 49, 125-127 (1986).
[CrossRef]

McCall, M.

Mégret, P.

Mehrany, K.

Moerner, W. E.

Monzón, J. J.

J. J. Monzón, T. Yonte, and L. L. Sánchez-Soto, "Charcterizing the reflectance of periodic layered media," Opt. Commun. 218, 43-47 (2003).
[CrossRef]

Nefedov, I. S.

I. S. Nefedov and S. A. Tretyakov, "Photonic band gap structure containing metamaterial with negative permittivity and permeability," Phys. Rev. E 66, 036611-1-4 (2002).
[CrossRef]

Nordin, G. P.

Painchaud, Y.

Y. Painchaud, A. Chandonnet, and J. Lauzon, "Chirped fibre gratings produced by tilting the fibre," Electron. Lett. 31, 171-172 (1995).
[CrossRef]

Petrov, M. P.

V. M. Petrov, C. Caraboue, J. Petter, T. Tschudi, V. V. Bryksin, and M. P. Petrov, "A dynamic narrow-band tunable optical filter," Appl. Phys. B 76, 41-44 (2003).
[CrossRef]

Petrov, V. M.

V. M. Petrov, C. Caraboue, J. Petter, T. Tschudi, V. V. Bryksin, and M. P. Petrov, "A dynamic narrow-band tunable optical filter," Appl. Phys. B 76, 41-44 (2003).
[CrossRef]

Petruzzelli, V.

Petter, J.

V. M. Petrov, C. Caraboue, J. Petter, T. Tschudi, V. V. Bryksin, and M. P. Petrov, "A dynamic narrow-band tunable optical filter," Appl. Phys. B 76, 41-44 (2003).
[CrossRef]

Piket-May, M.

Prudenzano, F.

Radic, S.

G. P. Agrawal and S. Radic, "Phase-Shifted Fiber Bragg Gratings and their Application for Wavelength Demultiplexing," IEEE Photon. Technol. Lett. 6, 995-997 (1994).
[CrossRef]

Reinhardt, S. B.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, and R. P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss," Phys. Rev. E 54, R1078-R1081 (1996).
[CrossRef]

Rodriguez, M. A.

M. A. Rodriguez, M. S. Malcuit, and J. J. Butler, "Transmission properties of refrective index-shifted Bragg gratings," Opt. Commun. 177, 251-257 (2000).
[CrossRef]

Sakuda, K.

Sales, S.

Sánchez-Soto, L. L.

J. J. Monzón, T. Yonte, and L. L. Sánchez-Soto, "Charcterizing the reflectance of periodic layered media," Opt. Commun. 218, 43-47 (2003).
[CrossRef]

Sansonetti, P.

F. Bakhti and P. Sansonetti, "Design and Realization of Multiple Quater-Wave Phase-Shifts UV-Written Bandpass Filter in Optical Fibers," J. Lightwave Technol. 15, 1433-1437 (1997).
[CrossRef]

Scalora, M.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, and R. P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss," Phys. Rev. E 54, R1078-R1081 (1996).
[CrossRef]

Shi, B.

J. Liu, B. Shi, D. Zhao, and X. Wang, "Optical delay in defective photonic bandgap structures," J. Opt. A: Pure Appl. Opt. 4, 636-639 (2002).
[CrossRef]

Silence, S. M.

Stankus, J. J.

Svelto, O.

S. Longhi, M. Marano, P. Laporta, O. Svelto, and M. Belmonte, "Propagation, manipulation, and control of picosecond optical pulses at 1.5 μm in fiber Bragg gratings," J. Opt. Soc. Am B 19, 2742-2757 (2002).
[CrossRef]

Takimoto, N.

Tanguay, A. R.

Thériault, S.

B. Malo, S. Thériault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, "Apodised in-fibre Bragg grating reflectors photoimprinted using a phase mask," Electron. Lett. 31, 223-225 (1995).
[CrossRef]

Thylén, L

Thylén, L.

Tocci, M. D.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, and R. P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss," Phys. Rev. E 54, R1078-R1081 (1996).
[CrossRef]

Tretyakov, S. A.

I. S. Nefedov and S. A. Tretyakov, "Photonic band gap structure containing metamaterial with negative permittivity and permeability," Phys. Rev. E 66, 036611-1-4 (2002).
[CrossRef]

Tschudi, T.

V. M. Petrov, C. Caraboue, J. Petter, T. Tschudi, V. V. Bryksin, and M. P. Petrov, "A dynamic narrow-band tunable optical filter," Appl. Phys. B 76, 41-44 (2003).
[CrossRef]

Tsuji, Y.

Wang, X.

J. Liu, B. Shi, D. Zhao, and X. Wang, "Optical delay in defective photonic bandgap structures," J. Opt. A: Pure Appl. Opt. 4, 636-639 (2002).
[CrossRef]

Wei, L.

L. Wei and J. W. Y. Lit, "Phase-Shifted Bragg Grating Filters with Symmetrical Structures," J. Lightwave Technol. 15, 1405-1410 (1997).
[CrossRef]

Williams, J. A. R.

Wuilpart, M.

Yamada, M.

Yeh, P.

Yevick, D.

Yonte, T.

J. J. Monzón, T. Yonte, and L. L. Sánchez-Soto, "Charcterizing the reflectance of periodic layered media," Opt. Commun. 218, 43-47 (2003).
[CrossRef]

Zengerle, R.

R. Zengerle and O. Leminger, "Phase-shifted Bragg-Grating Filters with Improved Transmission Characteristics," J. Lightwave Technol. 13, 2354-2358 (1995).
[CrossRef]

Zhang, L.

Zhang, W.

Zhao, D.

J. Liu, B. Shi, D. Zhao, and X. Wang, "Optical delay in defective photonic bandgap structures," J. Opt. A: Pure Appl. Opt. 4, 636-639 (2002).
[CrossRef]

Zheng, H.

S. Zhu, N. Liu, H. Zheng, and H. Chen, "Time delay of light propagation through defect modes of one-dimensional photonic band-gap structures," Opt. Commun. 174, 139-144 (2000).
[CrossRef]

Zhu, S.

S. Zhu, N. Liu, H. Zheng, and H. Chen, "Time delay of light propagation through defect modes of one-dimensional photonic band-gap structures," Opt. Commun. 174, 139-144 (2000).
[CrossRef]

Appl. Opt.

Appl. Phys. B

V. M. Petrov, C. Caraboue, J. Petter, T. Tschudi, V. V. Bryksin, and M. P. Petrov, "A dynamic narrow-band tunable optical filter," Appl. Phys. B 76, 41-44 (2003).
[CrossRef]

Appl. Phys. Lett.

R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, "Narrowband grating resonator filters in InGaAsP/InP waveguides," Appl. Phys. Lett. 49, 125-127 (1986).
[CrossRef]

Electron. Lett.

Y. Painchaud, A. Chandonnet, and J. Lauzon, "Chirped fibre gratings produced by tilting the fibre," Electron. Lett. 31, 171-172 (1995).
[CrossRef]

B. Malo, S. Thériault, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, "Apodised in-fibre Bragg grating reflectors photoimprinted using a phase mask," Electron. Lett. 31, 223-225 (1995).
[CrossRef]

IEEE Photon. Technol. Lett.

G. P. Agrawal and S. Radic, "Phase-Shifted Fiber Bragg Gratings and their Application for Wavelength Demultiplexing," IEEE Photon. Technol. Lett. 6, 995-997 (1994).
[CrossRef]

J. Lightwave Technol.

R. Zengerle and O. Leminger, "Phase-shifted Bragg-Grating Filters with Improved Transmission Characteristics," J. Lightwave Technol. 13, 2354-2358 (1995).
[CrossRef]

L. Wei and J. W. Y. Lit, "Phase-Shifted Bragg Grating Filters with Symmetrical Structures," J. Lightwave Technol. 15, 1405-1410 (1997).
[CrossRef]

F. Bakhti and P. Sansonetti, "Design and Realization of Multiple Quater-Wave Phase-Shifts UV-Written Bandpass Filter in Optical Fibers," J. Lightwave Technol. 15, 1433-1437 (1997).
[CrossRef]

M. McCall, "On the application of coupled mode theory for modeling fiber Bragg gratings," J. Lightwave Technol. 18, 236-242 (2000).
[CrossRef]

Y. Tsuji, M. Koshiba, and N. Takimoto, "Finite element beam propagation method for anisotropic optical waveguides," J. Lightwave Technol. 17, 723-728 (1999).
[CrossRef]

P. K. Kelly and M. Piket-May, "Propagation characteristics for a one-dimensional grounded finite height finite length electromagnetic crystal," J. Lightwave Technol. 17, 2008-2012 (1999).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

J. Liu, B. Shi, D. Zhao, and X. Wang, "Optical delay in defective photonic bandgap structures," J. Opt. A: Pure Appl. Opt. 4, 636-639 (2002).
[CrossRef]

J. Opt. Soc. Am B

S. Longhi, M. Marano, P. Laporta, O. Svelto, and M. Belmonte, "Propagation, manipulation, and control of picosecond optical pulses at 1.5 μm in fiber Bragg gratings," J. Opt. Soc. Am B 19, 2742-2757 (2002).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

S. Khorasani and A. Adibi, "New analytical approach for computation of band structure in one-dimensional periodic media," Opt. Commun. 216, 439-451 (2003).
[CrossRef]

J. J. Monzón, T. Yonte, and L. L. Sánchez-Soto, "Charcterizing the reflectance of periodic layered media," Opt. Commun. 218, 43-47 (2003).
[CrossRef]

M. A. Rodriguez, M. S. Malcuit, and J. J. Butler, "Transmission properties of refrective index-shifted Bragg gratings," Opt. Commun. 177, 251-257 (2000).
[CrossRef]

S. Zhu, N. Liu, H. Zheng, and H. Chen, "Time delay of light propagation through defect modes of one-dimensional photonic band-gap structures," Opt. Commun. 174, 139-144 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, and R. P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss," Phys. Rev. E 54, R1078-R1081 (1996).
[CrossRef]

I. S. Nefedov and S. A. Tretyakov, "Photonic band gap structure containing metamaterial with negative permittivity and permeability," Phys. Rev. E 66, 036611-1-4 (2002).
[CrossRef]

Other

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 1995).

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Figures (8)

Fig. 1.
Fig. 1.

The structure of the SPVIG.

Fig. 2.
Fig. 2.

Reflectance spectra of a SG (red) and a 2-layer SPVIG (green). The grating parameters for both cases are Λ = 0.5 μm and n1 = 4 ×10-4. Other parameters are set to be D = 3 mm, d = 2.25 μm and n0 = 1.55, respectively. The thickness of the SG is 6 mm for comparison.

Fig. 3.
Fig. 3.

The reflectance spectra of the SPVIGs with N=3 (a) and N=10 (b), respectively. The parameters for both cases are set to be n0 = 1.55, n1 = 4×10-4, D = 2 mm, Λ = 0.5 μm, and d = 2.25 μm, respectively.

Fig. 4.
Fig. 4.

Shift of the transparency wavelength within the stop-band by controlling the thickness of the buffer layer in a 2-layer SPVIG. The thicknesses of the buffer layers are 2.15, 2.25 and 2.35 μm for the red, green and blue curves, respectively. Other parameters are the same for three curves: n0 = 1.55, n1 = 4×10-4, D = 3 mm, and Λ = 0.5 μm, respectively.

Fig. 5.
Fig. 5.

The periodical transparency peaks at the Bragg-matched wavelength λ0 = 1.55 μm with the variation of the phase-shift 2k0d induced by the buffer layer in a 2-layer SPVIG, where n0 = 1.55, D = 3 mm, Λ = 0.5 μm and n1 = 4×10-4, respectively.

Fig. 6.
Fig. 6.

The group velocity and the transmittance T of the light incident normally onto a 2-layer SPVIG (a) and a SG (b), respectively. The blue curves and the green curves are for the group velocity and the transmittance, respectively. The Bragg-matched wavelength is set to be 1.55 μm. The parameters for the 2-layer SPVIG are set to be n0 = 1.55, D = 1.46 mm, d = 0.25 μm, Λ = 0.5 μm and n1 = 4×10-4, respectively. The grating parameters for the SG are the same as those of the SPVIG, and the thickness of the SG is equal to 2D+d.

Fig. 7.
Fig. 7.

The group delays τg of a 2-layer SPVIG (blue curve) and a SG (green curve) versus the variation of D. The wavelength is set at Bragg-matched and is at 1.55 μm. The parameters for the 2-layer SPVIG are set to be n0 = 1.55, d = 0.25 μm, Λ = 0.5 mm and n1 = 4×10-4, respectively. The thickness of the SG is equal to 2D+d.

Fig. 8.
Fig. 8.

The group delay tg of a 2-layer SPVIG versus the phase variation 2k0d induced by the buffer layer. The wavelength is set to be Bragg-matched at 1.55 μm. The parameters for the 2-layer SPVIG are set to be n0 = 1.55, D = 2 mm, Λ = 0.5 μm and n1 = 4×10-4, respectively.

Equations (24)

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2 E ( x ) x 2 + [ ω c n ( x ) ] 2 E ( x ) = 0 ,
E 1 ( x ) = A 1 ( x ) e i k 0 x + B 1 ( x ) e i k 0 x ,
A 1 ( x ) x = B 1 ( x ) e i Δ kx ,
B 1 ( x ) x = A 1 ( x ) e i Δ kx ,
A 1 ( x ) = ( A 1 ( 0 ) cosh ( sx ) + C 1 sinh ( sx ) ) e i Δ kx 2 ,
B 1 ( x ) = i k e i Δ kx A 1 ( x ) x ,
r 1 = B 1 ( 0 ) A 1 ( 0 ) = sinh ( sD ) s cosh ( sD ) i ( Δ k 2 ) sinh ( sD ) .
A 1 ( D ) e i k 0 d = A 2 ( D + d ) ,
B 1 ( D ) = B 2 ( D + d ) e i k 0 d ,
C 1 = r N cosh ( sD ) e i Δ kD + 2 i k 0 d + i Δ k 2 cosh ( sD ) s sinh ( sD ) r N sinh ( sD ) e i Δ kD + 2 i k 0 d i Δ k 2 sinh ( sD ) + s cosh ( sD ) A 1 ( 0 ) .
r N + 1 = B 1 ( 0 ) A 1 ( 0 ) = s r N cosh ( sD ) e i Δ kD + 2 i k 0 d + i Δ k 2 r N sinh ( sD ) e i Δ kD + 2 i k 0 d + sinh ( sD ) r N sinh ( sD ) e i Δ kD + 2 i k 0 d i Δ k 2 sinh ( sD ) + s cosh ( sD ) .
r 2 = sinh ( sD ) ( 1 + s cosh ( sD ) + i Δ k 2 sinh ( sD ) s cosh ( sD ) i Δ k 2 sinh ( sD ) e i Δ kD + i 2 k 0 d ) κ 2 sinh 2 ( sD ) s cosh ( sD ) i Δk 2 sinh ( sD ) e i Δ kD + i 2 k 0 d + s cosh ( sD ) i Δ k 2 sinh ( sD ) .
r 2 = sinh ( sD ) ( 1 + e i 2 k 0 d ) κ 2 sinh 2 ( sD ) s cosh ( sD ) e i 2 k 0 d + s cosh ( sD ) .
ν g = ν p ( Δ k 2 ) 2 κ 2 cosh 2 ( sD ) ( Δ k 2 ) 2 κ 2 sinh ( sD ) sD cosh ( sD ) ,
Φ = 2 π Λ D + 2 k 0 d + arctan ( sinh 2 ( sD ) sin φ + sin γ cos γ sinh ( 2 sD ) sinh 2 ( sD ) cos φ + sin 2 γ cosh 2 ( sD ) cos 2 γ sinh 2 ( sD ) ) .
ν g = ( 2 D + d ) ( Φ ω ) 1 .
E 2 ( x ) = A 2 ( x ) e i k 0 ( x ( D + d ) ) + B 2 ( x ) e i k 0 ( x ( D + d ) ) ,
A 2 ( x ) = ( A 2 ( D + d ) cosh ( s ( x ( D + d ) ) ) + C 2 sinh ( s ( x ( D + d ) ) ) e i Δ k ( x ( D + d ) ) 2 ,
B 2 ( x ) = i κ e i Δ k ( x ( D + d ) ) A 2 ( x ) ( x ) .
C 2 = 1 s ( i κ B 1 ( D ) e i k 0 d + i Δ k 2 A 1 ( D ) e i k 0 d ) .
E 2 ( 2 D + d ) = A 2 ( 2 D + d ) e i k 0 D ,
A 2 ( 2 D + d ) = s 2 κ 2 A 1 ( 0 ) ARe iAIm e i k 0 d e i Δ kD ,
ARe = sinh 2 ( sD ) cos φ + sin 2 γ cosh 2 ( sD ) cos 2 γ sinh 2 ( sD )
AIm = sinh 2 ( sD ) sin φ + cos γ sin γ sinh ( 2 sD ) ,

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