Abstract

We have realized a first optical filter composed of optical delay lines and couplers that has a periodic response with respect to wavelength, whereas a conventional optical filter is known to have a periodic response to relative optical frequency. This new filter can be constructed by using a phase-generating coupler (PGC) that supplies the optical delay lines with a wavelength-dependent nonlinear phase. The PGC, which is also composed of optical delay lines and couplers, can simultaneously provide a desired phase and an arbitrary amplitude coupling ratio. We applied our transformation method to a conventional Mach–Zehnder interferometer (MZI) as an example of an optical frequency filter and converted it to an optical wavelength filter. We fabricated the designed MZI on a silica-based planar lightwave circuit and successfully realized what is believed to be the first MZI with a uniform wavelength period.

© 2004 Optical Society of America

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  1. L. F. Stokes, M. Chodorow, and H. J. Shaw, Opt. Lett. 7, 288 (1982).
    [CrossRef] [PubMed]
  2. B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, Proc. IEEE 72, 909 (1984).
    [CrossRef]
  3. K. P. Jackson, G. Xiao, and H. J. Shaw, Electron. Lett. 22, 1335 (1986).
    [CrossRef]
  4. K. Jinguji and M. Kawachi, J. Lightwave Technol. 13, 73 (1995).
    [CrossRef]
  5. K. Oda, N. Takato, H. Toba, and K. Nosu, J. Lightwave Technol. 6, 1016 (1988).
    [CrossRef]
  6. N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, IEEE J. Sel. Areas Commun. 8, 1120 (1990).
    [CrossRef]
  7. C. Kostrzewa and K. Petermann, IEEE Photon. Technol. Lett. 7, 902 (1995).
    [CrossRef]
  8. M. Kuznetsov, J. Lightwave Technol. 12, 226 (1994).
    [CrossRef]
  9. K. Sasayama, M. Okuno, and K. Habara, J. Lightwave Technol. 12, 664 (1994).
    [CrossRef]
  10. K. Jinguji, N. Takato, Y. Hida, T. Kitoh, and M. Kawachi, J. Lightwave Technol. 14, 2301 (1996).
    [CrossRef]
  11. K. Okamoto, Fundamentals of Optical Waveguides (Academic, New York, 2000).
  12. T. Mizuno, T. Kitoh, M. Ishii, Y. Inoue, T. Saida, M. Itoh, T. Shibata, and Y. Hibino, IEEE Photon. Technol. Lett. 15, 239 (2003).
    [CrossRef]

2003 (1)

T. Mizuno, T. Kitoh, M. Ishii, Y. Inoue, T. Saida, M. Itoh, T. Shibata, and Y. Hibino, IEEE Photon. Technol. Lett. 15, 239 (2003).
[CrossRef]

1996 (1)

K. Jinguji, N. Takato, Y. Hida, T. Kitoh, and M. Kawachi, J. Lightwave Technol. 14, 2301 (1996).
[CrossRef]

1995 (2)

K. Jinguji and M. Kawachi, J. Lightwave Technol. 13, 73 (1995).
[CrossRef]

C. Kostrzewa and K. Petermann, IEEE Photon. Technol. Lett. 7, 902 (1995).
[CrossRef]

1994 (2)

M. Kuznetsov, J. Lightwave Technol. 12, 226 (1994).
[CrossRef]

K. Sasayama, M. Okuno, and K. Habara, J. Lightwave Technol. 12, 664 (1994).
[CrossRef]

1990 (1)

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, IEEE J. Sel. Areas Commun. 8, 1120 (1990).
[CrossRef]

1988 (1)

K. Oda, N. Takato, H. Toba, and K. Nosu, J. Lightwave Technol. 6, 1016 (1988).
[CrossRef]

1986 (1)

K. P. Jackson, G. Xiao, and H. J. Shaw, Electron. Lett. 22, 1335 (1986).
[CrossRef]

1984 (1)

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, Proc. IEEE 72, 909 (1984).
[CrossRef]

1982 (1)

Chodorow, M.

Goodman, J. W.

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, Proc. IEEE 72, 909 (1984).
[CrossRef]

Habara, K.

K. Sasayama, M. Okuno, and K. Habara, J. Lightwave Technol. 12, 664 (1994).
[CrossRef]

Hibino, Y.

T. Mizuno, T. Kitoh, M. Ishii, Y. Inoue, T. Saida, M. Itoh, T. Shibata, and Y. Hibino, IEEE Photon. Technol. Lett. 15, 239 (2003).
[CrossRef]

Hida, Y.

K. Jinguji, N. Takato, Y. Hida, T. Kitoh, and M. Kawachi, J. Lightwave Technol. 14, 2301 (1996).
[CrossRef]

Inoue, Y.

T. Mizuno, T. Kitoh, M. Ishii, Y. Inoue, T. Saida, M. Itoh, T. Shibata, and Y. Hibino, IEEE Photon. Technol. Lett. 15, 239 (2003).
[CrossRef]

Ishii, M.

T. Mizuno, T. Kitoh, M. Ishii, Y. Inoue, T. Saida, M. Itoh, T. Shibata, and Y. Hibino, IEEE Photon. Technol. Lett. 15, 239 (2003).
[CrossRef]

Itoh, M.

T. Mizuno, T. Kitoh, M. Ishii, Y. Inoue, T. Saida, M. Itoh, T. Shibata, and Y. Hibino, IEEE Photon. Technol. Lett. 15, 239 (2003).
[CrossRef]

Jackson, K. P.

K. P. Jackson, G. Xiao, and H. J. Shaw, Electron. Lett. 22, 1335 (1986).
[CrossRef]

Jinguji, K.

K. Jinguji, N. Takato, Y. Hida, T. Kitoh, and M. Kawachi, J. Lightwave Technol. 14, 2301 (1996).
[CrossRef]

K. Jinguji and M. Kawachi, J. Lightwave Technol. 13, 73 (1995).
[CrossRef]

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, IEEE J. Sel. Areas Commun. 8, 1120 (1990).
[CrossRef]

Kawachi, M.

K. Jinguji, N. Takato, Y. Hida, T. Kitoh, and M. Kawachi, J. Lightwave Technol. 14, 2301 (1996).
[CrossRef]

K. Jinguji and M. Kawachi, J. Lightwave Technol. 13, 73 (1995).
[CrossRef]

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, IEEE J. Sel. Areas Commun. 8, 1120 (1990).
[CrossRef]

Kitoh, T.

T. Mizuno, T. Kitoh, M. Ishii, Y. Inoue, T. Saida, M. Itoh, T. Shibata, and Y. Hibino, IEEE Photon. Technol. Lett. 15, 239 (2003).
[CrossRef]

K. Jinguji, N. Takato, Y. Hida, T. Kitoh, and M. Kawachi, J. Lightwave Technol. 14, 2301 (1996).
[CrossRef]

Kominato, T.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, IEEE J. Sel. Areas Commun. 8, 1120 (1990).
[CrossRef]

Kostrzewa, C.

C. Kostrzewa and K. Petermann, IEEE Photon. Technol. Lett. 7, 902 (1995).
[CrossRef]

Kuznetsov, M.

M. Kuznetsov, J. Lightwave Technol. 12, 226 (1994).
[CrossRef]

Mizuno, T.

T. Mizuno, T. Kitoh, M. Ishii, Y. Inoue, T. Saida, M. Itoh, T. Shibata, and Y. Hibino, IEEE Photon. Technol. Lett. 15, 239 (2003).
[CrossRef]

Moslehi, B.

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, Proc. IEEE 72, 909 (1984).
[CrossRef]

Nosu, K.

K. Oda, N. Takato, H. Toba, and K. Nosu, J. Lightwave Technol. 6, 1016 (1988).
[CrossRef]

Oda, K.

K. Oda, N. Takato, H. Toba, and K. Nosu, J. Lightwave Technol. 6, 1016 (1988).
[CrossRef]

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Academic, New York, 2000).

Okuno, M.

K. Sasayama, M. Okuno, and K. Habara, J. Lightwave Technol. 12, 664 (1994).
[CrossRef]

Petermann, K.

C. Kostrzewa and K. Petermann, IEEE Photon. Technol. Lett. 7, 902 (1995).
[CrossRef]

Saida, T.

T. Mizuno, T. Kitoh, M. Ishii, Y. Inoue, T. Saida, M. Itoh, T. Shibata, and Y. Hibino, IEEE Photon. Technol. Lett. 15, 239 (2003).
[CrossRef]

Sasayama, K.

K. Sasayama, M. Okuno, and K. Habara, J. Lightwave Technol. 12, 664 (1994).
[CrossRef]

Shaw, H. J.

K. P. Jackson, G. Xiao, and H. J. Shaw, Electron. Lett. 22, 1335 (1986).
[CrossRef]

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, Proc. IEEE 72, 909 (1984).
[CrossRef]

L. F. Stokes, M. Chodorow, and H. J. Shaw, Opt. Lett. 7, 288 (1982).
[CrossRef] [PubMed]

Shibata, T.

T. Mizuno, T. Kitoh, M. Ishii, Y. Inoue, T. Saida, M. Itoh, T. Shibata, and Y. Hibino, IEEE Photon. Technol. Lett. 15, 239 (2003).
[CrossRef]

Stokes, L. F.

Sugita, A.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, IEEE J. Sel. Areas Commun. 8, 1120 (1990).
[CrossRef]

Takato, N.

K. Jinguji, N. Takato, Y. Hida, T. Kitoh, and M. Kawachi, J. Lightwave Technol. 14, 2301 (1996).
[CrossRef]

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, IEEE J. Sel. Areas Commun. 8, 1120 (1990).
[CrossRef]

K. Oda, N. Takato, H. Toba, and K. Nosu, J. Lightwave Technol. 6, 1016 (1988).
[CrossRef]

Toba, H.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, IEEE J. Sel. Areas Commun. 8, 1120 (1990).
[CrossRef]

K. Oda, N. Takato, H. Toba, and K. Nosu, J. Lightwave Technol. 6, 1016 (1988).
[CrossRef]

Tur, M.

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, Proc. IEEE 72, 909 (1984).
[CrossRef]

Xiao, G.

K. P. Jackson, G. Xiao, and H. J. Shaw, Electron. Lett. 22, 1335 (1986).
[CrossRef]

Electron. Lett. (1)

K. P. Jackson, G. Xiao, and H. J. Shaw, Electron. Lett. 22, 1335 (1986).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, IEEE J. Sel. Areas Commun. 8, 1120 (1990).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

C. Kostrzewa and K. Petermann, IEEE Photon. Technol. Lett. 7, 902 (1995).
[CrossRef]

T. Mizuno, T. Kitoh, M. Ishii, Y. Inoue, T. Saida, M. Itoh, T. Shibata, and Y. Hibino, IEEE Photon. Technol. Lett. 15, 239 (2003).
[CrossRef]

J. Lightwave Technol. (5)

M. Kuznetsov, J. Lightwave Technol. 12, 226 (1994).
[CrossRef]

K. Sasayama, M. Okuno, and K. Habara, J. Lightwave Technol. 12, 664 (1994).
[CrossRef]

K. Jinguji, N. Takato, Y. Hida, T. Kitoh, and M. Kawachi, J. Lightwave Technol. 14, 2301 (1996).
[CrossRef]

K. Jinguji and M. Kawachi, J. Lightwave Technol. 13, 73 (1995).
[CrossRef]

K. Oda, N. Takato, H. Toba, and K. Nosu, J. Lightwave Technol. 6, 1016 (1988).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, Proc. IEEE 72, 909 (1984).
[CrossRef]

Other (1)

K. Okamoto, Fundamentals of Optical Waveguides (Academic, New York, 2000).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic diagram of a proposed MZI with PGCs. (b) Configuration of our novel MZI.

Fig. 2
Fig. 2

Calculated wavelength dependence of (top) the amplitude coupling ratio and (bottom) the phase created by our PGC.

Fig. 3
Fig. 3

Calculated transmission spectra of (top) the conventional MZI and (bottom) the MZI with a wavelength period of 40 nm designed with our proposed method.

Fig. 4
Fig. 4

Measured transmission spectra of the proposed MZI with 40-nm wavelength periodicity fabricated with silica-based PLC technology.

Equations (8)

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

Xω=q=0Nxq exp-jqΔLωc,
Xλ=q=0Nxq exp-j2πqΔL/λ-Ψλ,
Ψλ=ΔL+δLλ+λΔλ-m2+λcΔλ.
ΨλΔL+δLλc-m2+-ΔL+δLλc2+1Δλ×λ-λc+q2-1qΔL+δLλ-λcqλcq+1.
Sn=Hnz-Fn*zFnzHn*z,=cos θn,Mn+1-j sin θn,Mn+1-j sin θn,Mn+1cos θn,Mn+1×p=Mn1cos θn,p exp-jπδln,p/λ-j sin θn,p exp-jπδln,p/λ-j sin θn,p expjπδln,p/λcos θn,p expjπδln,p/λ,
Φλ=arg-F1*z+argF2z-argH1*z-argH2*z/2π.
Φλ=arg-F*z-argH*z/π.
Ψλ0.3-λ-λc+17λ-λc2-11λ-λc3.

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