Abstract

A new type of resonant, waveguided, 2×2 cross-connect optical filter is proposed and synthesized using a microwave filter analog. The optical passbands of the device are determined using 2D scattering matrix theory and the desired response is generated via a synthesis for a combined singly and doubly terminated circuit. This synthesis realizes the microring coupling coefficients necessary for maximally flat infrared spectral response. Closed-form analytical solutions are presented. Devices containing two, four, and six microrings were investigated.

© 2005 Optical Society of America

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References

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  1. S. T. Chu, B.E. Little, W. Pan, T. Kaneko and Y. Kokubun, �??An Eight-Channel Add-Drop Filter Using Vertically Coupled Microring Resonators over a Cross Grid, �?? IEEE Photon Technol. Lett. 11, 691-693, (1999).
    [CrossRef]
  2. S. T. Chu, B.E. Little, W. Pan, T. Kaneko and Y. Kokubun, �?? Second-Order Filter Response from Parallel Coupled Glass Microring Resonators,�?? IEEE Photon Technol. Lett. 11,1426-1428, (1999).
    [CrossRef]
  3. Y. Kokubun, T. Kato, S.T. Chu, �??Box-Like Response of Microring Resonator Filter by Stacked Double-Ring Geometry,�?? IEICE Trans. Electron. E85-C,1018-1024, (2000).
  4. W. K. Burns and A. F. Milton, �??Waveguides Transitions and Junctions,�?? in Guided-Wave Optoelectronics-Second Edition, T. Tamir, ed. (Springer-Verlag, Brooklyn, New York, 1990).
    [CrossRef]
  5. Y. Yanagase, S. Suzuki, Y. Kokubun, S. T. Chu, �??Box-Like Filter Response and Expansion of FSR by a Vertically Triple Coupled Microring Resonator Filter,�?? J. Lightwave Technol. 20, 1525-1529, (2002).
    [CrossRef]
  6. S. J. Emelett and R. A. Soref, �??Design and Simulation of Silicon Microring Optical Routing Switches,�?? J. Lightwave Technol. 23, 1800-1807, (2005).
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  7. G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance Matching Networks and Coupling Structures (McGraw-Hill, New York 1964), Chap. 4, 8, 11, 14.
  8. R. E. Collins, Foundations for Microwave Engineering (McGraw-Hill, New York 1966).
  9. S. B. Cohn, �??Direct-Coupled-Resonator Filters,�?? Proc. IRE. 187-195, Feb. (1957).
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  10. A. Melloni and M. Martinelli, �??Synthesis of Direct-Coupled-Resonators Bandpass Filters for WDM Systems,�?? J. Lightwave Technol. 20, 296-303, (2002).
    [CrossRef]
  11. C. K . Madsen and G. Lenz, �??Optical All-Pass Filters for Phase Response Design with Applications for Dispersion Compensation,�?? IEEE Photon. Technol. Lett. 10, 994-996, (1998).
    [CrossRef]
  12. C. K . Madsen J.H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley & Sons, New York 1999).
  13. R. Grover, Indium Phosphide based optical micro-ring resonators. Ph.D.thesis, Univ. of Maryland, College Park, Maryland, U.S.A., (2003), <a href= " http://www.enee.umd.edu/research/microphotonics.">http://www.enee.umd.edu/research/microphotonics.<a/>
  14. B.E. Little, S.T. Chu, H.A. Haus, J. Foresi and J.-P Laine, �??Microring resonator channel dropping filters,�?? J. Lightwave Technol. 15, 998-1005, (1992).
    [CrossRef]

IEEE Photon Technol. Lett. (2)

S. T. Chu, B.E. Little, W. Pan, T. Kaneko and Y. Kokubun, �??An Eight-Channel Add-Drop Filter Using Vertically Coupled Microring Resonators over a Cross Grid, �?? IEEE Photon Technol. Lett. 11, 691-693, (1999).
[CrossRef]

S. T. Chu, B.E. Little, W. Pan, T. Kaneko and Y. Kokubun, �?? Second-Order Filter Response from Parallel Coupled Glass Microring Resonators,�?? IEEE Photon Technol. Lett. 11,1426-1428, (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

C. K . Madsen and G. Lenz, �??Optical All-Pass Filters for Phase Response Design with Applications for Dispersion Compensation,�?? IEEE Photon. Technol. Lett. 10, 994-996, (1998).
[CrossRef]

IEICE Trans. Electron. (1)

Y. Kokubun, T. Kato, S.T. Chu, �??Box-Like Response of Microring Resonator Filter by Stacked Double-Ring Geometry,�?? IEICE Trans. Electron. E85-C,1018-1024, (2000).

J. Lightwave Technol. (4)

Proc. IRE Feb. 1957 (1)

S. B. Cohn, �??Direct-Coupled-Resonator Filters,�?? Proc. IRE. 187-195, Feb. (1957).
[CrossRef]

Other (5)

C. K . Madsen J.H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley & Sons, New York 1999).

R. Grover, Indium Phosphide based optical micro-ring resonators. Ph.D.thesis, Univ. of Maryland, College Park, Maryland, U.S.A., (2003), <a href= " http://www.enee.umd.edu/research/microphotonics.">http://www.enee.umd.edu/research/microphotonics.<a/>

G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance Matching Networks and Coupling Structures (McGraw-Hill, New York 1964), Chap. 4, 8, 11, 14.

R. E. Collins, Foundations for Microwave Engineering (McGraw-Hill, New York 1966).

W. K. Burns and A. F. Milton, �??Waveguides Transitions and Junctions,�?? in Guided-Wave Optoelectronics-Second Edition, T. Tamir, ed. (Springer-Verlag, Brooklyn, New York, 1990).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Dual Microring Cross-Connect System. A signal enters at input EI , propagates down bus guide of width 2w to the bus-ring interaction region, and couples to ring 1 of radius R1 . The remaining uncoupled signal continues down bus guide to the through-port, ET . The coupled light propagates and resonates in ring 1, whose fields are dictated by Eqs. (i)(vi), and couples to ring 2 of radius R2 . The signal, which couples to ring 2, propagates and resonates in ring 2, whose fields are governed by (vii)–(viii). The signal then returns to ring 1, selectively couples to the drop guide, and finally exits the system via the drop guide ED .

Fig. 2.
Fig. 2.

Characteristic wavelength spectral response. The normalized through- and drop- port optical output power response of the cross-connect displays the general properties of the system. The quantities a and -a represent the desired half-width normalized wavelengths at Am while b and -b are the half-width at half maximum. The waveform shape is novel, as are the power asymptotes away from λ0 .

Fig. 3.
Fig. 3.

Schematic of the cross-connect microring resonator prototype bandpass filter. The horizontal box represents the doubly terminated circuit, while the circuit vertically enclosed depicts the singly terminated filter in the hybrid synthesis. The first impedance inverters of both circuits are displayed as dotted boxes because they are not static in the filter synthesis. The physical positions of the two bus guides are understood to be located on both far ends of the horizontal box, but are not illustrated.

Fig. 4.
Fig. 4.

Depiction of regular orders of N=2, 4, and 6 or pair order η=0, 1, and 2 cross-grid systems.

Fig. 5.
Fig. 5.

A comparison of the passband characteristics for a system which consists of N=2, 4, and 6 rings. These through-port responses were obtained from the results of the synthesis prescribed in Eq. (12). A more box-like response is observed as N is increased.

Fig. 6.
Fig. 6.

The drop-port of the N=2, 4, and 6 cross-connect filter. The ability to specifically dictate the separation of the two central peaks is clearly displayed for pair order 0, 1, and 2. It is noteworthy that the displayed N=4, or η=1, response represents the highest order of peaks with the highest order of symmetry. In order to obtain the respective through-port responses, this figure is simply inverted and is displayed in the inset. It is understood that the value a is the half width of the desired response.

Fig. 7.
Fig. 7.

The through-port responses of several N=2 filters with different linewidths and percentages of loss. The specifics of each device appear in Table 2.

Fig. 8.
Fig. 8.

Detailed view of the responses depicted in Fig. 7. These responses, which coincide with Table 2, demonstrate the ability of the synthesis to realize a response that is subject to a desired linewidth and percentage of loss. These specific parameters and many others were used, along with the more box-like response displayed in Fig. 5, to add to validity of the synthesis.

Fig. 9.
Fig. 9.

Tolerances of the dual-microring cross-connect filter. Structure 2 is displayed along with 5 and 10% deviations from the prescribed value of κ 2, as is presented in Table 2.

Tables (4)

Tables Icon

Table 1(a). Coupling coefficients and of N=2, 4, and 6 systems.

Tables Icon

Table 1(b). Drop-port peaks wavelengths of N=2, 4, and 6 systems.

Tables Icon

Table 2. Response parameters utilized in Figs. 7 and 8.

Tables Icon

Appendix Glossary of Symbols

Equations (42)

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E T = j κ a E r 1 f + τ a E I
E D = j κ aa E r 1 d
E T E I 2 = A α τ a + A Φ Γ a Γ b τ aa A ( τ a + κ a 2 τ aa + τ a 2 τ aa ) τ b A α A ( 1 + τ a τ aa ) τ b + A Φ τ a τ aa Γ b 2
E D E I 2 = A κ a κ aa ( A Φ Γ b + A α τ b 2 ) A α A ( 1 + τ a τ aa ) τ b + A Φ τ a τ aa Γ b 2
A = exp ( α r L 2 + j ω T r )
A = exp ( α r L 4 + j ω T r 2 )
A α = exp ( α r L )
A α = exp ( α r L 2 )
A Φ = exp ( 2 j ω T r )
A Φ = exp ( j ω T r )
Γ a , b = ( κ a , b 2 + τ a , b 2 ) .
K 1 S = π B 2 g 1 S F S R 1
K q S = π B 2 g q S g q 1 S F S R q F S R q 1
K N + 1 S = π B 2 g N + 1 S F S R N = 0
g 1 S = a 1 S ε N
g q S = a q S a q 1 S c q 1 S g q 1 S ε N
g N + 1 S =
a q S = sin π 2 ( 2 q 1 ) N
c q S = cos 2 ( π q 2 N )
Δ λ λ 0 2 2 π c Δ ω .
K 1 D = π B 2 g 1 D F S R 1
K q D = π B 2 g q D g q 1 D F S R q F S R q 1
K N + 1 D = π B 2 g N + 1 D F S R N
g q D = 2 a q D ε N
a q D = sin π 2 ( 2 q 1 ) N
g 1 D = 2 a 1 D ε N D = 2 a 1 D ε
g 2 F = 1 2 N + η a 2 S a 1 S c 1 S g 1 S ε 1 + 1 N
g 3 F = 1 N a 3 S a 2 S c 2 S g 2 S ε 2 N
g 4 F = 2 N + 1 10 2 a 4 S a 3 S c 3 S g 3 S ε 2 N
g 5 F = 1 N a 5 S a 4 S c 4 S g 4 S ε 2 N
g N F = N 2 N + η a N S a N 1 S c N 1 S g N 1 S ε 2 N
g N + 1 F =
g 1 D = 2 a 1 D ε
g 2 F = 1 4 a 2 S a 1 D c 1 S g 1 D ε 3 2
g 3 F =
K 1 D = π B 2 g 1 D F S R 1
K 2 F = π B 2 g 2 F g 1 D F S R 2 F S R 1
K 3 F = π B 2 g 3 F F S R 2 = 0
a 1 D = sin π 2
a 2 S = sin 3 π 4
c 1 S = cos 2 π 4 .
κ q = 2 K q K q 2 + 1

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