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Polymeric Mach-Zehnder interferometer using serially coupled microring resonators

George T. Paloczi, Yanyi Huang, Amnon Yariv, and Shayan Mookherjea

Open Access Open Access

Abstract

We propose a novel geometry for a Mach-Zehnder interferometer in which one arm of the interferometer consists of serially coupled microresonators and the other a simple ridge waveguide. The device was fabricated in an optical polymer and its spectral characteristics were measured at telecommunications wavelengths. The serially coupled rings are modeled using a simple transfer matrix approach. Good agreement is found between the measurement and the theory.

©2003 Optical Society of America

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References

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  • Year
  • Author
  • Publication
  1. K. Oda, N. Takato, and H. Toba, “A wide-FSR double-ring resonator for optical FDM transmission systems,” IEEE J. Lightwave Tech. 9, 728–736 (1991).
    [Crossref]
  2. R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Phot. Tech. Lett. 7, 1447–1449 (1995).
    [Crossref]
  3. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filter,” IEEE J. Lightwave Tech. 15, 998–1005 (1997).
    [Crossref]
  4. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. -T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Phot. Tech. Lett. 12, 320–322 (2000).
    [Crossref]
  5. A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” IEEE J. Lightwave Tech. 20, 296–303 (2002).
    [Crossref]
  6. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled resonator optical waveguide: a proposal and analysis,” Optics Lett. 24, 711–713 (1997).
    [Crossref]
  7. Y. Xu, R. K. Lee, and A. Yariv, “Propagation and second harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide,” J. Opt. Soc. Am. B 17, 387–400 (2000).
    [Crossref]
  8. S. Mookherjea and A. Yariv, “Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides,” Phys. Rev. E 66, 046610 (2002).
    [Crossref]
  9. J. K. S. Poon, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” (submitted).
  10. A. Martinez, A. Griol, P. Sanchis, and J. Marti, “Mach-Zehnder interferometer employing coupledresonator optical waveguides,” Opt. Lett. 28, 405–407 (2003).
    [Crossref] [PubMed]
  11. M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
    [Crossref] [PubMed]
  12. K. Kawano and T. Kitoh, Introduction to optical waveguide analysis (Wiley, 2001), Chap. 4.
    [Crossref]
  13. A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electronics Lett. 36, 321–322 (2000).
    [Crossref]

2003 (1)

2002 (2)

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” IEEE J. Lightwave Tech. 20, 296–303 (2002).
[Crossref]

S. Mookherjea and A. Yariv, “Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides,” Phys. Rev. E 66, 046610 (2002).
[Crossref]

2000 (4)

Y. Xu, R. K. Lee, and A. Yariv, “Propagation and second harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide,” J. Opt. Soc. Am. B 17, 387–400 (2000).
[Crossref]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. -T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Phot. Tech. Lett. 12, 320–322 (2000).
[Crossref]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[Crossref] [PubMed]

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electronics Lett. 36, 321–322 (2000).
[Crossref]

1997 (2)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filter,” IEEE J. Lightwave Tech. 15, 998–1005 (1997).
[Crossref]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled resonator optical waveguide: a proposal and analysis,” Optics Lett. 24, 711–713 (1997).
[Crossref]

1995 (1)

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Phot. Tech. Lett. 7, 1447–1449 (1995).
[Crossref]

1991 (1)

K. Oda, N. Takato, and H. Toba, “A wide-FSR double-ring resonator for optical FDM transmission systems,” IEEE J. Lightwave Tech. 9, 728–736 (1991).
[Crossref]

Absil, P. P.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. -T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Phot. Tech. Lett. 12, 320–322 (2000).
[Crossref]

Bayindir, M.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[Crossref] [PubMed]

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filter,” IEEE J. Lightwave Tech. 15, 998–1005 (1997).
[Crossref]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filter,” IEEE J. Lightwave Tech. 15, 998–1005 (1997).
[Crossref]

Griol, A.

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filter,” IEEE J. Lightwave Tech. 15, 998–1005 (1997).
[Crossref]

Ho, P. -T.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. -T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Phot. Tech. Lett. 12, 320–322 (2000).
[Crossref]

Hryniewicz, J. V.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. -T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Phot. Tech. Lett. 12, 320–322 (2000).
[Crossref]

Huang, Y.

J. K. S. Poon, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” (submitted).

Kawano, K.

K. Kawano and T. Kitoh, Introduction to optical waveguide analysis (Wiley, 2001), Chap. 4.
[Crossref]

Kitoh, T.

K. Kawano and T. Kitoh, Introduction to optical waveguide analysis (Wiley, 2001), Chap. 4.
[Crossref]

Laine, J. -P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filter,” IEEE J. Lightwave Tech. 15, 998–1005 (1997).
[Crossref]

Lee, R. K.

Y. Xu, R. K. Lee, and A. Yariv, “Propagation and second harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide,” J. Opt. Soc. Am. B 17, 387–400 (2000).
[Crossref]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled resonator optical waveguide: a proposal and analysis,” Optics Lett. 24, 711–713 (1997).
[Crossref]

Little, B. E.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. -T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Phot. Tech. Lett. 12, 320–322 (2000).
[Crossref]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filter,” IEEE J. Lightwave Tech. 15, 998–1005 (1997).
[Crossref]

Marti, J.

Martinelli, M.

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” IEEE J. Lightwave Tech. 20, 296–303 (2002).
[Crossref]

Martinez, A.

Melloni, A.

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” IEEE J. Lightwave Tech. 20, 296–303 (2002).
[Crossref]

Mookherjea, S.

S. Mookherjea and A. Yariv, “Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides,” Phys. Rev. E 66, 046610 (2002).
[Crossref]

J. K. S. Poon, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” (submitted).

Oda, K.

K. Oda, N. Takato, and H. Toba, “A wide-FSR double-ring resonator for optical FDM transmission systems,” IEEE J. Lightwave Tech. 9, 728–736 (1991).
[Crossref]

Orta, R.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Phot. Tech. Lett. 7, 1447–1449 (1995).
[Crossref]

Ozbay, E.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[Crossref] [PubMed]

Paloczi, G. T.

J. K. S. Poon, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” (submitted).

Poon, J. K. S.

J. K. S. Poon, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” (submitted).

Sanchis, P.

Savi, P.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Phot. Tech. Lett. 7, 1447–1449 (1995).
[Crossref]

Scherer, A.

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled resonator optical waveguide: a proposal and analysis,” Optics Lett. 24, 711–713 (1997).
[Crossref]

Takato, N.

K. Oda, N. Takato, and H. Toba, “A wide-FSR double-ring resonator for optical FDM transmission systems,” IEEE J. Lightwave Tech. 9, 728–736 (1991).
[Crossref]

Tascone, R.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Phot. Tech. Lett. 7, 1447–1449 (1995).
[Crossref]

Temelkuran, B.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[Crossref] [PubMed]

Toba, H.

K. Oda, N. Takato, and H. Toba, “A wide-FSR double-ring resonator for optical FDM transmission systems,” IEEE J. Lightwave Tech. 9, 728–736 (1991).
[Crossref]

Trinchero, D.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Phot. Tech. Lett. 7, 1447–1449 (1995).
[Crossref]

Wilson, R. A.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. -T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Phot. Tech. Lett. 12, 320–322 (2000).
[Crossref]

Xu, Y.

Y. Xu, R. K. Lee, and A. Yariv, “Propagation and second harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide,” J. Opt. Soc. Am. B 17, 387–400 (2000).
[Crossref]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled resonator optical waveguide: a proposal and analysis,” Optics Lett. 24, 711–713 (1997).
[Crossref]

Yariv, A.

S. Mookherjea and A. Yariv, “Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides,” Phys. Rev. E 66, 046610 (2002).
[Crossref]

Y. Xu, R. K. Lee, and A. Yariv, “Propagation and second harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide,” J. Opt. Soc. Am. B 17, 387–400 (2000).
[Crossref]

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electronics Lett. 36, 321–322 (2000).
[Crossref]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled resonator optical waveguide: a proposal and analysis,” Optics Lett. 24, 711–713 (1997).
[Crossref]

J. K. S. Poon, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” (submitted).

Electronics Lett. (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electronics Lett. 36, 321–322 (2000).
[Crossref]

IEEE J. Lightwave Tech. (3)

K. Oda, N. Takato, and H. Toba, “A wide-FSR double-ring resonator for optical FDM transmission systems,” IEEE J. Lightwave Tech. 9, 728–736 (1991).
[Crossref]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filter,” IEEE J. Lightwave Tech. 15, 998–1005 (1997).
[Crossref]

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” IEEE J. Lightwave Tech. 20, 296–303 (2002).
[Crossref]

IEEE Phot. Tech. Lett. (2)

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. -T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Phot. Tech. Lett. 12, 320–322 (2000).
[Crossref]

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Phot. Tech. Lett. 7, 1447–1449 (1995).
[Crossref]

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

Opt. Lett. (1)

Optics Lett. (1)

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled resonator optical waveguide: a proposal and analysis,” Optics Lett. 24, 711–713 (1997).
[Crossref]

Phys. Rev. E (1)

S. Mookherjea and A. Yariv, “Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides,” Phys. Rev. E 66, 046610 (2002).
[Crossref]

Phys. Rev. Lett. (1)

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[Crossref] [PubMed]

Other (2)

K. Kawano and T. Kitoh, Introduction to optical waveguide analysis (Wiley, 2001), Chap. 4.
[Crossref]

J. K. S. Poon, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” (submitted).

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Figures (5)
Fig. 1.
Fig. 1. Schematic diagram of a CROW-MZI with one arm as a ridge waveguide of length L, with propagation constant β, and the other arm consisting of coupled microresonators, spaced by a distance d, with propagation constant βCROW . Y-branches divide and add the optical field equally between the two arms. Adiabatic tapers act as impedance matched terminations after the field couples to the first resonator, ensuring no back reflected fields.

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Fig. 2.
Fig. 2. (a) Optical microscope image of the CROW-MZI showing a total device width of approximately 1.2 mm. The identical racetrack microresonators had 50 micron straight coupling sections and 100 micron bend radii in the curved sections. (b) Angle-view SEM image of two waveguides converging into the coupling section, showing straight side-walls and indicating overall waveguide smoothness. (b) Top-view SEM image of coupling section showing 2 micron wide waveguides separated by 750 nm.

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Fig. 3.
Fig. 3. Normalized measured output power of the polymer CROW-MZI ranging over a spectral bandwidth of 50 nanometers, approximately 22 single resonator free spectral ranges.

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Fig. 4.
Fig. 4. Coupled resonator optical waveguide with N rings (N odd for the output direction as shown). The arrows signify the direction of light propagation. The matrix P represents the coupling segments and Q accounts for the phase and loss accumulated in the resonators.

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Fig. 5.
Fig. 5. Experimental data (black) and the theoretical fit (blue) based on Eq. 8. The fitting parameters used for the fit were: polarization 93% TE and 7% TM, effective indices 1.48475 for TE and 1.48555 for TM, power coupling coefficients 0.46 for TE and 0.85 for TM, and waveguide loss of 30 dB/cm.

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Equations (8)

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

( b n ′ b n + 1 ) = ( t κ − κ * t * ) ( a n ′ a n + 1 ) , ∣ t ∣ 2 + ∣ κ ∣ 2 = 1
( a n + 1 b n + 1 ) = P ( a n ′ b n ′ ) , P = 1 κ ( − t 1 − 1 t * ) .
( a n ′ b n ′ ) = Q ( a n b n ) , Q = ( 0 e − iβπR − απR e iβπR + απR 0 )
( a N + 1 b N + 1 ) = ( PQ ) N ( PQ ) N − 1 ( ⋯ ) ( PQ ) 2 P 1 ( a 0 b 0 ) = T ( a 0 b 0 ) .
T = ( A B C D ) .
b 0 a 0 = − A B , b N + 1 a 0 = C − AD B .
( a N + 1 b N + 1 ) = ( PQ ) N P ( a 0 b 0 ) .
output ∝ ∣ C − AD B + e − ( α + iβ ) L ∣ 2 .

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