Abstract

We propose a new device configuration that incorporates a nested ring with a Mach-Zehnder interferometer. The nested ring is analogous to a dual-bus coupled ring resonator, with the ends of the two buses connected to form a semi-closed loop. With proper design of the length of the U-shaped loop, as well as the coupling coefficient between the ring and the waveguide, the device is capable of generating a box-shaped spectral response. This is shown to be mainly due to the double-Fano resonances that arise from constructive interference between the nested ring and the outer loop. The device is simple in that it requires only one ring, and unique in that it harnesses a pair of Fano resonances to generate a reasonably box-like filter response. The analysis is based on the transfer matrix formalism, and compared and verified with the FDTD simulations.

©2007 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  12. C. K. Madsen and J. H. Zhao, Optical filter design and analysis: A signal processing approach (Wiley, New York, 1999).
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    [Crossref]
  14. C. Y. Chao and L. J. Guo, “Reduction of surface scattering loss in polymer mirorings using thermal-reflow technique,“ IEEE Photon. Technol. Lett. 16,1498–1500 (2004).
    [Crossref]
  15. J. Niehusmann, A. Vörckel, P. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, “Ultrahigh-quality-factor silicon-on-insulator microring resonator,“ Opt. Lett. 29,2861–2863 (2004).
    [Crossref]

2006 (1)

S. Darmawan and M. K. Chin, “Critical coupling, oscillation, reflection and transmission in optical waveguide-ring resonator systems,“ J. Opt. Soc. Am. B. 23,834–841 (2006).
[Crossref]

2005 (3)

2004 (6)

J. Heebner, N. Lepeshkin, A. Schweinsberg, G. Wicks, R. Boyd, R. Grover, and P. Ho, “Enhanced linear and nonlinear optical phase response of AlGaAs microring resonators,“ Opt. Lett. 29,769–771 (2004).
[Crossref] [PubMed]

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,“ IEEE Photon. Technol. Lett. 16,2263–2265 (2004).
[Crossref]

C. Y. Chao and L. J. Guo, “Reduction of surface scattering loss in polymer mirorings using thermal-reflow technique,“ IEEE Photon. Technol. Lett. 16,1498–1500 (2004).
[Crossref]

J. Niehusmann, A. Vörckel, P. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, “Ultrahigh-quality-factor silicon-on-insulator microring resonator,“ Opt. Lett. 29,2861–2863 (2004).
[Crossref]

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,“ IEEE Photon. Technol. Lett. 14,483–485 (2004).
[Crossref]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,“ Nature. 431,1081–1084 (2004).
[Crossref] [PubMed]

2002 (1)

D. G. Rabus, M. Hamacher, U Troppenz, and H. Heidrich, “Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP-InP,“ IEEE J. Sel. Top. Quantum Electron. 8,1405–1410 (2002).
[Crossref]

2001 (1)

2000 (1)

1995 (1)

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

Absil, P.

Absil, P. P.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,“ IEEE Photon. Technol. Lett. 16,2263–2265 (2004).
[Crossref]

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,“ Nature. 431,1081–1084 (2004).
[Crossref] [PubMed]

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,“ Nature. 431,1081–1084 (2004).
[Crossref] [PubMed]

Bolivar, P. H.

Boyd, R.

Boyd, R. W.

Chao, C. Y.

C. Y. Chao and L. J. Guo, “Reduction of surface scattering loss in polymer mirorings using thermal-reflow technique,“ IEEE Photon. Technol. Lett. 16,1498–1500 (2004).
[Crossref]

Chin, M. K.

S. Darmawan and M. K. Chin, “Critical coupling, oscillation, reflection and transmission in optical waveguide-ring resonator systems,“ J. Opt. Soc. Am. B. 23,834–841 (2006).
[Crossref]

Y. M. Landobasa, S. Darmawan, and M. K. Chin, “Matrix analysis of 2-D micro-resonator lattice optical filters,“ IEEE J. Quantum Electron. 41,1410–1418 (2005).
[Crossref]

Chu, S.

Chu, S. T.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,“ IEEE Photon. Technol. Lett. 16,2263–2265 (2004).
[Crossref]

Darmawan, S.

S. Darmawan and M. K. Chin, “Critical coupling, oscillation, reflection and transmission in optical waveguide-ring resonator systems,“ J. Opt. Soc. Am. B. 23,834–841 (2006).
[Crossref]

Y. M. Landobasa, S. Darmawan, and M. K. Chin, “Matrix analysis of 2-D micro-resonator lattice optical filters,“ IEEE J. Quantum Electron. 41,1410–1418 (2005).
[Crossref]

DeRose, G.

Gill, D.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,“ IEEE Photon. Technol. Lett. 16,2263–2265 (2004).
[Crossref]

Green, W.

Grover, R.

Guo, L. J.

C. Y. Chao and L. J. Guo, “Reduction of surface scattering loss in polymer mirorings using thermal-reflow technique,“ IEEE Photon. Technol. Lett. 16,1498–1500 (2004).
[Crossref]

Hamacher, M.

D. G. Rabus, M. Hamacher, U Troppenz, and H. Heidrich, “Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP-InP,“ IEEE J. Sel. Top. Quantum Electron. 8,1405–1410 (2002).
[Crossref]

Heebner, J.

Heebner, J. E.

Heidrich, H.

D. G. Rabus, M. Hamacher, U Troppenz, and H. Heidrich, “Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP-InP,“ IEEE J. Sel. Top. Quantum Electron. 8,1405–1410 (2002).
[Crossref]

Henschel, W.

Ho, P.

Hryniewicz, J.

Hryniewicz, J. V.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,“ IEEE Photon. Technol. Lett. 16,2263–2265 (2004).
[Crossref]

Johnson, F. G.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,“ IEEE Photon. Technol. Lett. 16,2263–2265 (2004).
[Crossref]

King, O.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,“ IEEE Photon. Technol. Lett. 16,2263–2265 (2004).
[Crossref]

Kurz, H.

Landobasa, Y. M.

Y. M. Landobasa, S. Darmawan, and M. K. Chin, “Matrix analysis of 2-D micro-resonator lattice optical filters,“ IEEE J. Quantum Electron. 41,1410–1418 (2005).
[Crossref]

Lee, R.

Lepeshkin, N.

Li, X.

Lipson, M.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,“ Nature. 431,1081–1084 (2004).
[Crossref] [PubMed]

Little, B.

Little, B. E.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,“ IEEE Photon. Technol. Lett. 16,2263–2265 (2004).
[Crossref]

Lu, Y.

Madsen, C. K.

C. K. Madsen and J. H. Zhao, Optical filter design and analysis: A signal processing approach (Wiley, New York, 1999).

Niehusmann, J.

Orta, R.

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

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,“ Nature. 431,1081–1084 (2004).
[Crossref] [PubMed]

Rabus, D. G.

D. G. Rabus, M. Hamacher, U Troppenz, and H. Heidrich, “Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP-InP,“ IEEE J. Sel. Top. Quantum Electron. 8,1405–1410 (2002).
[Crossref]

Savi, P.

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

Scherer, A.

Schweinsberg, A.

Seiferth, F.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,“ IEEE Photon. Technol. Lett. 16,2263–2265 (2004).
[Crossref]

Tascone, R.

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

Trakalo, M.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,“ IEEE Photon. Technol. Lett. 16,2263–2265 (2004).
[Crossref]

Trinchero, D.

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

Troppenz, U

D. G. Rabus, M. Hamacher, U Troppenz, and H. Heidrich, “Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP-InP,“ IEEE J. Sel. Top. Quantum Electron. 8,1405–1410 (2002).
[Crossref]

Van, V.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,“ IEEE Photon. Technol. Lett. 16,2263–2265 (2004).
[Crossref]

Vörckel, A.

Wahlbrink, T.

Wang, P.

Wicks, G.

Yao, J.

Yariv, A.

Zhao, J. H.

C. K. Madsen and J. H. Zhao, Optical filter design and analysis: A signal processing approach (Wiley, New York, 1999).

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

Y. M. Landobasa, S. Darmawan, and M. K. Chin, “Matrix analysis of 2-D micro-resonator lattice optical filters,“ IEEE J. Quantum Electron. 41,1410–1418 (2005).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

D. G. Rabus, M. Hamacher, U Troppenz, and H. Heidrich, “Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP-InP,“ IEEE J. Sel. Top. Quantum Electron. 8,1405–1410 (2002).
[Crossref]

IEEE Photon. Technol. Lett. (3)

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,“ IEEE Photon. Technol. Lett. 16,2263–2265 (2004).
[Crossref]

C. Y. Chao and L. J. Guo, “Reduction of surface scattering loss in polymer mirorings using thermal-reflow technique,“ IEEE Photon. Technol. Lett. 16,1498–1500 (2004).
[Crossref]

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,“ IEEE Photon. Technol. Lett. 14,483–485 (2004).
[Crossref]

IEEE. Photon. Technol. Lett. (1)

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

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

S. Darmawan and M. K. Chin, “Critical coupling, oscillation, reflection and transmission in optical waveguide-ring resonator systems,“ J. Opt. Soc. Am. B. 23,834–841 (2006).
[Crossref]

Nature. (1)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,“ Nature. 431,1081–1084 (2004).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (4)

Other (1)

C. K. Madsen and J. H. Zhao, Optical filter design and analysis: A signal processing approach (Wiley, New York, 1999).

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Figures (12)

Fig. 1.
Fig. 1. (a). Single-bus and dual-bus coupled ring resonator; (b) The NRR. The dashed line refers to the outer feedback arm with a length of Lv = v(2πR) where R is the radius of the inner-ring.

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Fig. 2.
Fig. 2. The effect of r on the phase response of NRR (a = 1; v = 1.5).

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Fig. 3.
Fig. 3. Two different periodicities for the case of (a) v = m and (b) v = m-1/2 (a = 1).

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Fig. 4.
Fig. 4. The NRR transmission showing the critical coupling (a = 0.95) and (b) the oscillation (a = 1.1) conditions for the case v = 5.5, and for various values of r. The corresponding pole-zero diagrams and the contour plots of TNRR on the r-δ plane are shown on the right. The zeros are red, the poles are blue, and the arrows indicate the direction of movement as r is increased from 0 to 1. The dashed lines in the contour plots correspond to the transmission curves.

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Fig. 5.
Fig. 5. Schematic of a nested-ring MZI.

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Fig. 6.
Fig. 6. The bar transmission of NRMZI for various r values, showing the double Fano resonances giving rise to a box-like transmission profile (a = 1; v = 1.5).

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Fig. 7.
Fig. 7. Left: The build-up factor of the inner (B 31) and the outer loop (B 61) of NRR. Right: The corresponding bar transmission of NRMZI (a = 1; v = 1.5). The r value is varied showing 3 different modes of operation: (i) MZI-like mode; (ii) Box-like NRMZI mode; (iii) Lorentzian DBRR mode.

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Fig. 8.
Fig. 8. The build-up factor for two cases of v values (a = 1; r = 0.65), showing a more evenly distributed build-up factor when v = m or v = m-1/2, and chirped build-up factor when v ≠ m or v ≠ m-1/2.

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Fig. 9.
Fig. 9. (a). The optimized “box-shaped” response for various combinations of r and v for a single-stage NRMZI, assuming a =1. (b) The bar transmission of a cascaded NRMZI showing suppressed sidelobes (v = 1.5; r = 0.65). The inset shows the double-stage NRMZI configuration.

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Fig. 10.
Fig. 10. Comparison between the 2-D FDTD simulation and the analytic transfer matrix formalism (for the case v = 1) in terms of: (a) The outer-loop build-up factor B 61 and the inner-loop build-up factor B 31. The insets show the field distributions at three different points of the spectrum as indicated. (b) The bar transmission of NRMZI. The inset show the field distribution where the inner ring is on resonance (B 31 is maximum).

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Fig. 11.
Fig. 11. The effect of loss on a single-stage NRMZI (v = 1.5).

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Fig. 12.
Fig. 12. The NRMZI sensitivity to a 50-nm length deviations in: (a) the length Lv variations of NRMZI around v = 1 assuming balanced bare MZI; (b) the length variations in the lower arm of MZI assuming v = 1. All parameters not mentioned in the legends are extracted from Fig. 10(b).

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Equations (13)

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

ρ = r − a exp ( iδ ) 1 − ra exp ( iδ ) , R = ∣ ρ ∣ 2 = r 2 − 2 ar cos δ + a 2 1 − 2 ar cos δ + a 2 r 2
φ = − tan − 1 ( a sin δ r − a cos δ ) + tan − 1 ( ra sin δ 1 − ra sin δ )
ρ = r ( 1 − a exp ( iδ ) ) 1 − r 2 a exp ( iδ ) , R = ∣ ρ ∣ 2 = r 2 − 2 ar 2 cos δ + r 2 a 2 1 − 2 ar 2 cos δ + a 2 r 4
t = − κ 2 a exp ( iδ 2 ) 1 − r 2 a exp ( iδ ) , T = ∣ t ∣ 2 = κ 4 a 1 − 2 ar 2 cos δ + a 2 r 4
φ ρ = π − tan − 1 ( a sin δ 1 − a cos δ ) + tan − 1 ( r 2 a sin δ 1 − r 2 a cos δ )
φ t = π + δ 2 + tan − 1 ( r 2 a sin δ 1 − r 2 a cos δ )
t NRR = t + ρ 2 a v e ivδ ( 1 + ta v e ivδ + … . ) = ( t + ( ρ 2 − t 2 ) a v e ivδ ) ( 1 − ta v e ivδ )
= − κ 2 ae iδ 2 + r 2 a v e ivδ − a v + 1 e i ( v + 1 ) δ 1 − r 2 ae iδ + κ 2 a v + 1 2 e i ( v + 1 2 ) δ
t NRR = t { 1 − ∣ t ∣ − 1 exp [ i ( vδ + φ t ) ] } 1 − ∣ t ∣ exp ( i [ vδ + φ t ] ) = exp ( iϕ NRR )
φ load = − tan − 1 ( sin ( vδ + φ t ) ∣ t ∣ − cos ( vδ + φ t ) ) + tan − 1 ( ∣ t ∣ sin ( vδ + φ t ) 1 − ∣ t ∣ cos ( v δ + φ t ) )
T bar = sin 2 { ( φ NRR − vδ ) 2 } T cross = cos 2 { ( φ NRR − vδ ) 2 }
B 31 = ∣ E 3 E 1 ∣ 2 = ∣ iκ ( 1 + a v + 1 2 e i ( v + 1 2 ) δ ) 1 − r 2 ae iδ + κ 2 a v + 1 2 e i ( v + 1 2 ) δ ∣ 2
B 61 = ∣ E 6 E 1 ∣ 2 = ∣ r ( 1 − ae iδ ) 1 − r 2 ae iδ + κ 2 a v + 1 2 e i ( v + 1 2 ) δ ∣ 2

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