Abstract

Fabry–Perot bandpass filters made of mirrors with both high- and low-Δn (refractive-index modulation) have simultaneously a broad rejection band and a narrow passband. The higher Δn’s are obtained with multilayer mirrors and the lower with Bragg gratings (BG’s). Implementation of a sampling calculation technique based on the characteristic matrix formalism used for interference coatings allows for simulation of hybrid filters constructed from multilayer mirrors and BG’s. The possible defects of hybrid filters are extensively analyzed. Bandpass filters made purely of both high- and low-Δn BG’s are also simulated. All these filters are useful for wavelength division multiplexing applications.

© 2001 Optical Society of America

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References

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    [CrossRef]
  3. J. P. Laude, “Télécommunications optiques: vers le multiplexage de longueur d’onde à trés haute densité,” Opt. Photonique 4, 36–38 (1998).
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    [CrossRef]
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    [CrossRef]
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  14. F. Bakhti, P. Sansonetti, “Design and realisation of multiple quarter-wave phase shifts UV-written bandpass filters in optical fibers,” J. Lightwave Technol. 15, 1433–1437 (1997).
    [CrossRef]

1998 (2)

J. P. Laude, “Télécommunications optiques: vers le multiplexage de longueur d’onde à trés haute densité,” Opt. Photonique 4, 36–38 (1998).

F. Lemarchand, A. Sentenac, H. Giovannini, “Increasing the angular tolerance of resonant grating filters with doubly periodic structures,” Opt. Lett. 23, 1149–1151 (1998).
[CrossRef]

1997 (1)

F. Bakhti, P. Sansonetti, “Design and realisation of multiple quarter-wave phase shifts UV-written bandpass filters in optical fibers,” J. Lightwave Technol. 15, 1433–1437 (1997).
[CrossRef]

1996 (1)

M. B. Alsous, J. Bittebierre, R. Richier, H. Ahmad, “Construction of all-fibre Nd3+ fibre lasers with multidielectric mirrors,” Pure Appl. Opt. 5, 777–790 (1996).
[CrossRef]

1995 (1)

1994 (1)

1993 (1)

1989 (1)

1982 (1)

T. Yoshino, K. Kurosawa, K. Itoh, T. Oze, “Fiber optic Fabry–Perot interferometer and its sensors applications,” IEEE J. Quantum Electron. 18, 1624–1633 (1982).
[CrossRef]

1973 (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

1948 (1)

F. Abelès, “Sur la propagation des ondes électromagnétiques dans les milieux stratifiés,” Ann. Phys. (Paris) 3, 505–520 (1948).

Abelès, F.

F. Abelès, “Sur la propagation des ondes électromagnétiques dans les milieux stratifiés,” Ann. Phys. (Paris) 3, 505–520 (1948).

Ahmad, H.

M. B. Alsous, J. Bittebierre, R. Richier, H. Ahmad, “Construction of all-fibre Nd3+ fibre lasers with multidielectric mirrors,” Pure Appl. Opt. 5, 777–790 (1996).
[CrossRef]

Alsous, M. B.

M. B. Alsous, J. Bittebierre, R. Richier, H. Ahmad, “Construction of all-fibre Nd3+ fibre lasers with multidielectric mirrors,” Pure Appl. Opt. 5, 777–790 (1996).
[CrossRef]

Amra, C.

R. Richier, C. Amra, “High-selectivity spectral multiplexers–demultiplexers usable in optical telecommunications obtained from multidielectric coatings at the end of optical fibers,” in Fiber Optics Metrology and Standards, O. D. Soares, ed., Proc. SPIE1504, 1504–1512 (1991).

Bakhti, F.

F. Bakhti, P. Sansonetti, “Design and realisation of multiple quarter-wave phase shifts UV-written bandpass filters in optical fibers,” J. Lightwave Technol. 15, 1433–1437 (1997).
[CrossRef]

Bittebierre, J.

M. B. Alsous, J. Bittebierre, R. Richier, H. Ahmad, “Construction of all-fibre Nd3+ fibre lasers with multidielectric mirrors,” Pure Appl. Opt. 5, 777–790 (1996).
[CrossRef]

Flory, F.

George, D.

A. Hamel, M. P. Mathieu, D. George, F. L. Malavieille, S. Menard, R. Richier, E. Pelletier, “Multiplexeur optique 1480/1550 nm pour amplification optique à fibre dopée,” in 12e Journées Européenes de l’Optoélectronique (ESI, Paris, 1992), pp. 22–26.

Giovannini, H.

Glenn, W. H.

Hamel, A.

A. Hamel, M. P. Mathieu, D. George, F. L. Malavieille, S. Menard, R. Richier, E. Pelletier, “Multiplexeur optique 1480/1550 nm pour amplification optique à fibre dopée,” in 12e Journées Européenes de l’Optoélectronique (ESI, Paris, 1992), pp. 22–26.

Ishihara, S.

Itoh, K.

T. Yoshino, K. Kurosawa, K. Itoh, T. Oze, “Fiber optic Fabry–Perot interferometer and its sensors applications,” IEEE J. Quantum Electron. 18, 1624–1633 (1982).
[CrossRef]

Kurosawa, K.

T. Yoshino, K. Kurosawa, K. Itoh, T. Oze, “Fiber optic Fabry–Perot interferometer and its sensors applications,” IEEE J. Quantum Electron. 18, 1624–1633 (1982).
[CrossRef]

Laude, J. P.

J. P. Laude, “Télécommunications optiques: vers le multiplexage de longueur d’onde à trés haute densité,” Opt. Photonique 4, 36–38 (1998).

Lemarchand, F.

Malavieille, F. L.

A. Hamel, M. P. Mathieu, D. George, F. L. Malavieille, S. Menard, R. Richier, E. Pelletier, “Multiplexeur optique 1480/1550 nm pour amplification optique à fibre dopée,” in 12e Journées Européenes de l’Optoélectronique (ESI, Paris, 1992), pp. 22–26.

Mathieu, M. P.

A. Hamel, M. P. Mathieu, D. George, F. L. Malavieille, S. Menard, R. Richier, E. Pelletier, “Multiplexeur optique 1480/1550 nm pour amplification optique à fibre dopée,” in 12e Journées Européenes de l’Optoélectronique (ESI, Paris, 1992), pp. 22–26.

Maythaveekulchai, N.

Menard, S.

A. Hamel, M. P. Mathieu, D. George, F. L. Malavieille, S. Menard, R. Richier, E. Pelletier, “Multiplexeur optique 1480/1550 nm pour amplification optique à fibre dopée,” in 12e Journées Européenes de l’Optoélectronique (ESI, Paris, 1992), pp. 22–26.

Metzl, G.

Minowa, J.

Morey, W. W.

Nayyer, J.

Oguri, H.

Oze, T.

T. Yoshino, K. Kurosawa, K. Itoh, T. Oze, “Fiber optic Fabry–Perot interferometer and its sensors applications,” IEEE J. Quantum Electron. 18, 1624–1633 (1982).
[CrossRef]

Pelletier, E.

A. Hamel, M. P. Mathieu, D. George, F. L. Malavieille, S. Menard, R. Richier, E. Pelletier, “Multiplexeur optique 1480/1550 nm pour amplification optique à fibre dopée,” in 12e Journées Européenes de l’Optoélectronique (ESI, Paris, 1992), pp. 22–26.

Richier, R.

M. B. Alsous, J. Bittebierre, R. Richier, H. Ahmad, “Construction of all-fibre Nd3+ fibre lasers with multidielectric mirrors,” Pure Appl. Opt. 5, 777–790 (1996).
[CrossRef]

R. Richier, C. Amra, “High-selectivity spectral multiplexers–demultiplexers usable in optical telecommunications obtained from multidielectric coatings at the end of optical fibers,” in Fiber Optics Metrology and Standards, O. D. Soares, ed., Proc. SPIE1504, 1504–1512 (1991).

A. Hamel, M. P. Mathieu, D. George, F. L. Malavieille, S. Menard, R. Richier, E. Pelletier, “Multiplexeur optique 1480/1550 nm pour amplification optique à fibre dopée,” in 12e Journées Européenes de l’Optoélectronique (ESI, Paris, 1992), pp. 22–26.

Rigneault, H.

Sansonetti, P.

F. Bakhti, P. Sansonetti, “Design and realisation of multiple quarter-wave phase shifts UV-written bandpass filters in optical fibers,” J. Lightwave Technol. 15, 1433–1437 (1997).
[CrossRef]

Sentenac, A.

Takashashi, H.

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989); H. A. Macleod, Thin Film Optical Filters (Hilger, Bristol, UK, 1986).
[CrossRef]

Yanagimachi, T.

Yariv, A.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

Yoshino, T.

T. Yoshino, K. Kurosawa, K. Itoh, T. Oze, “Fiber optic Fabry–Perot interferometer and its sensors applications,” IEEE J. Quantum Electron. 18, 1624–1633 (1982).
[CrossRef]

Zamkotsian, F.

Ann. Phys. (Paris) (1)

F. Abelès, “Sur la propagation des ondes électromagnétiques dans les milieux stratifiés,” Ann. Phys. (Paris) 3, 505–520 (1948).

Appl. Opt. (3)

IEEE J. Quantum Electron. (2)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

T. Yoshino, K. Kurosawa, K. Itoh, T. Oze, “Fiber optic Fabry–Perot interferometer and its sensors applications,” IEEE J. Quantum Electron. 18, 1624–1633 (1982).
[CrossRef]

J. Lightwave Technol. (1)

F. Bakhti, P. Sansonetti, “Design and realisation of multiple quarter-wave phase shifts UV-written bandpass filters in optical fibers,” J. Lightwave Technol. 15, 1433–1437 (1997).
[CrossRef]

Opt. Lett. (2)

Opt. Photonique (1)

J. P. Laude, “Télécommunications optiques: vers le multiplexage de longueur d’onde à trés haute densité,” Opt. Photonique 4, 36–38 (1998).

Pure Appl. Opt. (1)

M. B. Alsous, J. Bittebierre, R. Richier, H. Ahmad, “Construction of all-fibre Nd3+ fibre lasers with multidielectric mirrors,” Pure Appl. Opt. 5, 777–790 (1996).
[CrossRef]

Other (3)

R. Richier, C. Amra, “High-selectivity spectral multiplexers–demultiplexers usable in optical telecommunications obtained from multidielectric coatings at the end of optical fibers,” in Fiber Optics Metrology and Standards, O. D. Soares, ed., Proc. SPIE1504, 1504–1512 (1991).

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989); H. A. Macleod, Thin Film Optical Filters (Hilger, Bristol, UK, 1986).
[CrossRef]

A. Hamel, M. P. Mathieu, D. George, F. L. Malavieille, S. Menard, R. Richier, E. Pelletier, “Multiplexeur optique 1480/1550 nm pour amplification optique à fibre dopée,” in 12e Journées Européenes de l’Optoélectronique (ESI, Paris, 1992), pp. 22–26.

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Figures (8)

Fig. 1
Fig. 1

Diagram of a hybrid filter. In this example a multilayer filter is surrounded by two BG’s photowritten in cores of waveguides. The layers of the multilayer filter and the periods of the grating are not represented to scale.

Fig. 2
Fig. 2

Transmission of a BG for increasing number of periods (a) compared with the equivalent index N of its single period (b). On (b), where the curve is thick, N is positive and real. Where the curve is thin on (b), N is purely imaginary, and the line represents its imaginary part.

Fig. 3
Fig. 3

Transmission of an hybrid mirror (a) and of the single hybrid FP FP1H (b) as a function of the wavelength in nanometers. The transmitted peak of the FP is too narrow to be represented to the scale of Fig. 3(b). Therefore we show it at an enlarged scale.

Fig. 4
Fig. 4

Transmission of the FP2H2 filter as a function of the wavelength in nanometers. The enlarged representation shows simultaneously weak oscillations that do not significantly degrade the rejection level.

Fig. 5
Fig. 5

Chosen configuration of FP2H2 inducing perfect phases in the junctions to get resonance. For legibility, the diagram is not to scale.

Fig. 6
Fig. 6

Sensitivity of FP2H2 to a phase defect without diffraction losses. Thick curves, transmission of the filter without defect; thin curves, effect of phase defects corresponding successively to nonintegers 1.005, 1.01, 1.02, 1.03, 1.04, and 1.05 OTH in λ B /4 unity for one of the two external H layers of the multilayer inside FP2H2.

Fig. 7
Fig. 7

Simulation of the all-grating FP FP2G (thick curve). Simulation with the same parameters and a square effective-index modulation function instead of sinusoidal (thin curve), and a triangular effective-index modulation function (dashed curve).

Fig. 8
Fig. 8

Transmission of the FP2G1 filter.

Tables (1)

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Table 1 Data and Spectral Properties of the Simulated FP Filters

Equations (4)

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Ez1Z0Hz1=cosΦi sinΦnin sinΦcosΦ Ez2Z0Hz2,
M11iM12iM21M11,
N=M21M121/2,  Γ=arc cosM11.
Wp, q, r=W01+p eHnH+q eLnL+r eGnG2ZR21/2,

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