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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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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)

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( 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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