D. Bachman, A. Tsay, and V. Van, “Realization of a fourth-order pseudo-elliptic microring filter with negative coupling on SOI,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2014, Paper SM3G.7.

A. Tsay and V. Van, “Field coupling method for the direct synthesis of 2-D microring resonator networks,” IEEE J. Quantum Electron., vol. 48, no. 10, pp. 1314–1321, 2012.

I. Chremmos and N. Uzunoglu, “Propagation in a directional coupler of parallel microring coupled-resonator optical waveguides,” Opt. Commun., vol. 281, pp. 3381–3389, 2008.

V. Van, “Synthesis of elliptic optical filters using mutually coupled microring resonators,” J. Lightw. Technol., vol. 25, no. 2, pp. 584–590, 2007.

F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Exp., vol. 15, pp. 11934–11941, 2007.

T. Barwicz, M. A. Popovic, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” J. Lightw. Technol., vol. 24, no. 5, pp. 2207–2218, 2006.

V. Van, “Circuit-based method for synthesizing serially-coupled microring filters,” J. Lightw. Technol., vol. 24, no. 7, pp. 2912–2919, 2006.

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., vol. 16, no. 10, pp. 2263–2265, 2004.

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightw. Technol., vol. 20, no. 2, pp. 296–303, 2002.

R. J. Cameron, “General coupling matrix synthesis methods for Chebyshev filtering functions,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 4, pp. 433–442, 1999.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine “Microring resonator channel dropping filters,” J. Lightw. Technol., vol. 15, no. 6, pp. 998–1005, 1997.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photon. Technol. Lett., vol. 7, no. 12, pp. 1447–1449, 1995.

B. J. Bennett, “A new filter synthesis technique—The hourglass,” IEEE Trans. Circuits Syst., vol. 35, no. 12, pp. 1469–1477, 1988.

A. E. Atia, A. E. Williams, and R. W. Newcomb, “Narrow-band multiple-coupled cavity synthesis,” IEEE Trans. Circuits Syst., vol. CAS-21, no. 5, pp. 649–655, 1974.

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., vol. 16, no. 10, pp. 2263–2265, 2004.

A. E. Atia, A. E. Williams, and R. W. Newcomb, “Narrow-band multiple-coupled cavity synthesis,” IEEE Trans. Circuits Syst., vol. CAS-21, no. 5, pp. 649–655, 1974.

D. Bachman, A. Tsay, and V. Van, “Realization of a fourth-order pseudo-elliptic microring filter with negative coupling on SOI,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2014, Paper SM3G.7.

T. Barwicz, M. A. Popovic, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” J. Lightw. Technol., vol. 24, no. 5, pp. 2207–2218, 2006.

M. A. Popovic, T. Barwicz, P. T. Rakich, M. S. Dahlem, C. W. Holzwarth, F. Gan, L. Socci, M. R. Watts, H. I. Smith, F. X. Kartner, and E. P. Ippen, “Experimental demonstration of loop-coupled microring resonators for optimally sharp optical filters,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2008, Paper CTuNND.

V. Belevitch, Classical Network Theory. San Francisco, CA, USA: Holden-Day, 1968.

B. J. Bennett, “A new filter synthesis technique—The hourglass,” IEEE Trans. Circuits Syst., vol. 35, no. 12, pp. 1469–1477, 1988.

R. J. Cameron, “General coupling matrix synthesis methods for Chebyshev filtering functions,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 4, pp. 433–442, 1999.

I. Chremmos and N. Uzunoglu, “Propagation in a directional coupler of parallel microring coupled-resonator optical waveguides,” Opt. Commun., vol. 281, pp. 3381–3389, 2008.

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., vol. 16, no. 10, pp. 2263–2265, 2004.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine “Microring resonator channel dropping filters,” J. Lightw. Technol., vol. 15, no. 6, pp. 998–1005, 1997.

M. A. Popovic, T. Barwicz, P. T. Rakich, M. S. Dahlem, C. W. Holzwarth, F. Gan, L. Socci, M. R. Watts, H. I. Smith, F. X. Kartner, and E. P. Ippen, “Experimental demonstration of loop-coupled microring resonators for optimally sharp optical filters,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2008, Paper CTuNND.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine “Microring resonator channel dropping filters,” J. Lightw. Technol., vol. 15, no. 6, pp. 998–1005, 1997.

M. A. Popovic, T. Barwicz, P. T. Rakich, M. S. Dahlem, C. W. Holzwarth, F. Gan, L. Socci, M. R. Watts, H. I. Smith, F. X. Kartner, and E. P. Ippen, “Experimental demonstration of loop-coupled microring resonators for optimally sharp optical filters,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2008, Paper CTuNND.

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., vol. 16, no. 10, pp. 2263–2265, 2004.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine “Microring resonator channel dropping filters,” J. Lightw. Technol., vol. 15, no. 6, pp. 998–1005, 1997.

M. A. Popovic, T. Barwicz, P. T. Rakich, M. S. Dahlem, C. W. Holzwarth, F. Gan, L. Socci, M. R. Watts, H. I. Smith, F. X. Kartner, and E. P. Ippen, “Experimental demonstration of loop-coupled microring resonators for optimally sharp optical filters,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2008, Paper CTuNND.

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., vol. 16, no. 10, pp. 2263–2265, 2004.

T. Barwicz, M. A. Popovic, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” J. Lightw. Technol., vol. 24, no. 5, pp. 2207–2218, 2006.

M. A. Popovic, T. Barwicz, P. T. Rakich, M. S. Dahlem, C. W. Holzwarth, F. Gan, L. Socci, M. R. Watts, H. I. Smith, F. X. Kartner, and E. P. Ippen, “Experimental demonstration of loop-coupled microring resonators for optimally sharp optical filters,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2008, Paper CTuNND.

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., vol. 16, no. 10, pp. 2263–2265, 2004.

M. A. Popovic, T. Barwicz, P. T. Rakich, M. S. Dahlem, C. W. Holzwarth, F. Gan, L. Socci, M. R. Watts, H. I. Smith, F. X. Kartner, and E. P. Ippen, “Experimental demonstration of loop-coupled microring resonators for optimally sharp optical filters,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2008, Paper CTuNND.

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., vol. 16, no. 10, pp. 2263–2265, 2004.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine “Microring resonator channel dropping filters,” J. Lightw. Technol., vol. 15, no. 6, pp. 998–1005, 1997.

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., vol. 16, no. 10, pp. 2263–2265, 2004.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine “Microring resonator channel dropping filters,” J. Lightw. Technol., vol. 15, no. 6, pp. 998–1005, 1997.

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightw. Technol., vol. 20, no. 2, pp. 296–303, 2002.

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightw. Technol., vol. 20, no. 2, pp. 296–303, 2002.

A. E. Atia, A. E. Williams, and R. W. Newcomb, “Narrow-band multiple-coupled cavity synthesis,” IEEE Trans. Circuits Syst., vol. CAS-21, no. 5, pp. 649–655, 1974.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photon. Technol. Lett., vol. 7, no. 12, pp. 1447–1449, 1995.

T. Barwicz, M. A. Popovic, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” J. Lightw. Technol., vol. 24, no. 5, pp. 2207–2218, 2006.

M. A. Popovic, “Sharply-defined optical filters and dispersionless delay lines based on loop-coupled resonators and ‘negative’ coupling”, presented at the Conf. Lasers and Electro-Optics, Baltimore, MD, USA, 2007, paper CThP6.

M. A. Popovic, T. Barwicz, P. T. Rakich, M. S. Dahlem, C. W. Holzwarth, F. Gan, L. Socci, M. R. Watts, H. I. Smith, F. X. Kartner, and E. P. Ippen, “Experimental demonstration of loop-coupled microring resonators for optimally sharp optical filters,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2008, Paper CTuNND.

T. Barwicz, M. A. Popovic, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” J. Lightw. Technol., vol. 24, no. 5, pp. 2207–2218, 2006.

M. A. Popovic, T. Barwicz, P. T. Rakich, M. S. Dahlem, C. W. Holzwarth, F. Gan, L. Socci, M. R. Watts, H. I. Smith, F. X. Kartner, and E. P. Ippen, “Experimental demonstration of loop-coupled microring resonators for optimally sharp optical filters,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2008, Paper CTuNND.

F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Exp., vol. 15, pp. 11934–11941, 2007.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photon. Technol. Lett., vol. 7, no. 12, pp. 1447–1449, 1995.

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., vol. 16, no. 10, pp. 2263–2265, 2004.

F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Exp., vol. 15, pp. 11934–11941, 2007.

T. Barwicz, M. A. Popovic, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” J. Lightw. Technol., vol. 24, no. 5, pp. 2207–2218, 2006.

M. A. Popovic, T. Barwicz, P. T. Rakich, M. S. Dahlem, C. W. Holzwarth, F. Gan, L. Socci, M. R. Watts, H. I. Smith, F. X. Kartner, and E. P. Ippen, “Experimental demonstration of loop-coupled microring resonators for optimally sharp optical filters,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2008, Paper CTuNND.

M. A. Popovic, T. Barwicz, P. T. Rakich, M. S. Dahlem, C. W. Holzwarth, F. Gan, L. Socci, M. R. Watts, H. I. Smith, F. X. Kartner, and E. P. Ippen, “Experimental demonstration of loop-coupled microring resonators for optimally sharp optical filters,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2008, Paper CTuNND.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photon. Technol. Lett., vol. 7, no. 12, pp. 1447–1449, 1995.

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., vol. 16, no. 10, pp. 2263–2265, 2004.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photon. Technol. Lett., vol. 7, no. 12, pp. 1447–1449, 1995.

D. Bachman, A. Tsay, and V. Van, “Realization of a fourth-order pseudo-elliptic microring filter with negative coupling on SOI,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2014, Paper SM3G.7.

A. Tsay and V. Van, “Field coupling method for the direct synthesis of 2-D microring resonator networks,” IEEE J. Quantum Electron., vol. 48, no. 10, pp. 1314–1321, 2012.

I. Chremmos and N. Uzunoglu, “Propagation in a directional coupler of parallel microring coupled-resonator optical waveguides,” Opt. Commun., vol. 281, pp. 3381–3389, 2008.

D. Bachman, A. Tsay, and V. Van, “Realization of a fourth-order pseudo-elliptic microring filter with negative coupling on SOI,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2014, Paper SM3G.7.

A. Tsay and V. Van, “Field coupling method for the direct synthesis of 2-D microring resonator networks,” IEEE J. Quantum Electron., vol. 48, no. 10, pp. 1314–1321, 2012.

V. Van, “Synthesis of elliptic optical filters using mutually coupled microring resonators,” J. Lightw. Technol., vol. 25, no. 2, pp. 584–590, 2007.

V. Van, “Circuit-based method for synthesizing serially-coupled microring filters,” J. Lightw. Technol., vol. 24, no. 7, pp. 2912–2919, 2006.

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., vol. 16, no. 10, pp. 2263–2265, 2004.

F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Exp., vol. 15, pp. 11934–11941, 2007.

T. Barwicz, M. A. Popovic, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” J. Lightw. Technol., vol. 24, no. 5, pp. 2207–2218, 2006.

M. A. Popovic, T. Barwicz, P. T. Rakich, M. S. Dahlem, C. W. Holzwarth, F. Gan, L. Socci, M. R. Watts, H. I. Smith, F. X. Kartner, and E. P. Ippen, “Experimental demonstration of loop-coupled microring resonators for optimally sharp optical filters,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2008, Paper CTuNND.

A. E. Atia, A. E. Williams, and R. W. Newcomb, “Narrow-band multiple-coupled cavity synthesis,” IEEE Trans. Circuits Syst., vol. CAS-21, no. 5, pp. 649–655, 1974.

F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Exp., vol. 15, pp. 11934–11941, 2007.

A. Tsay and V. Van, “Field coupling method for the direct synthesis of 2-D microring resonator networks,” IEEE J. Quantum Electron., vol. 48, no. 10, pp. 1314–1321, 2012.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photon. Technol. Lett., vol. 7, no. 12, pp. 1447–1449, 1995.

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., vol. 16, no. 10, pp. 2263–2265, 2004.

A. E. Atia, A. E. Williams, and R. W. Newcomb, “Narrow-band multiple-coupled cavity synthesis,” IEEE Trans. Circuits Syst., vol. CAS-21, no. 5, pp. 649–655, 1974.

B. J. Bennett, “A new filter synthesis technique—The hourglass,” IEEE Trans. Circuits Syst., vol. 35, no. 12, pp. 1469–1477, 1988.

R. J. Cameron, “General coupling matrix synthesis methods for Chebyshev filtering functions,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 4, pp. 433–442, 1999.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine “Microring resonator channel dropping filters,” J. Lightw. Technol., vol. 15, no. 6, pp. 998–1005, 1997.

T. Barwicz, M. A. Popovic, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” J. Lightw. Technol., vol. 24, no. 5, pp. 2207–2218, 2006.

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightw. Technol., vol. 20, no. 2, pp. 296–303, 2002.

V. Van, “Circuit-based method for synthesizing serially-coupled microring filters,” J. Lightw. Technol., vol. 24, no. 7, pp. 2912–2919, 2006.

V. Van, “Synthesis of elliptic optical filters using mutually coupled microring resonators,” J. Lightw. Technol., vol. 25, no. 2, pp. 584–590, 2007.

I. Chremmos and N. Uzunoglu, “Propagation in a directional coupler of parallel microring coupled-resonator optical waveguides,” Opt. Commun., vol. 281, pp. 3381–3389, 2008.

F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Exp., vol. 15, pp. 11934–11941, 2007.

M. A. Popovic, T. Barwicz, P. T. Rakich, M. S. Dahlem, C. W. Holzwarth, F. Gan, L. Socci, M. R. Watts, H. I. Smith, F. X. Kartner, and E. P. Ippen, “Experimental demonstration of loop-coupled microring resonators for optimally sharp optical filters,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2008, Paper CTuNND.

D. Bachman, A. Tsay, and V. Van, “Realization of a fourth-order pseudo-elliptic microring filter with negative coupling on SOI,” presented at the Conf. on Lasers and Electro-Optics, San Jose, CA, USA, 2014, Paper SM3G.7.

M. A. Popovic, “Sharply-defined optical filters and dispersionless delay lines based on loop-coupled resonators and ‘negative’ coupling”, presented at the Conf. Lasers and Electro-Optics, Baltimore, MD, USA, 2007, paper CThP6.

V. Belevitch, Classical Network Theory. San Francisco, CA, USA: Holden-Day, 1968.