Abstract

Coupling induced effects are higher order effects inherent in waveguide evanescent coupling that are known to spectrally distort optical performances of integrated optics devices formed by coupled resonators. We present both numerical and experimental studies of coupling-induced phase shift in various basic integrated optics devices. Rigorous finite difference time domain simulations and systematic experimental characterizations of different basic structures were conducted for more accurate parameter extraction, where it can be observed that coupling induced wave vector may change sign at the increasing gap separation. The devices characterized in this work were fabricated by CMOS-process 193nm Deep UV (DUV) lithography in silicon-on-insulator (SOI) technology.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Popovic, C. Manolatou, and M. R. Watts, “Coupling-induced resonance frequency shifts in coupled dielectric multi-cavity filters,” Opt. Express 14(3), 1208–1222 (2006).
    [CrossRef] [PubMed]
  2. Q. Li, M. Soltani, A. H. Atabaki, S. Yegnanarayanan, and A. Adibi, “Quantitative modeling of coupling-induced resonance frequency shift in microring resonators,” Opt. Express 17(26), 23474–23487 (2009).
    [CrossRef] [PubMed]
  3. Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
    [CrossRef] [PubMed]
  4. S. Darmawan, L. Y. Tobing, and T. Mei, “Coupling-induced phase shift in a microring-coupled Mach-Zehnder interferometer,” Opt. Lett. 35(2), 238–240 (2010).
    [CrossRef] [PubMed]
  5. L. Y. M. Tobing, P. Dumon, R. Baets, and M. K. Chin, “Boxlike filter response based on complementary photonic bandgaps in two-dimensional microresonator arrays,” Opt. Lett. 33(21), 2512–2514 (2008).
    [CrossRef] [PubMed]
  6. K. Oda, N. Takato, H. Toba, K. Nosu, and J. Lightwave, “A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems,” J. LightwaveTechnol. 6, 1016–1023 (1988).
  7. M. Kohtoku, S. Oku, Y. Kadota, Y. Shibata, and Y. Yoshikuni, “200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interferometer with a ring resonator,” IEEE Photon. Technol. Lett. 12(9), 1174–1176 (2000).
    [CrossRef]
  8. 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(10), 2263–2265 (2004).
    [CrossRef]
  9. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, 1991).
  10. URL, http://www.epixfab.eu .
  11. S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
    [CrossRef]
  12. L. Y. Mario, S. Darmawan, and M. K. Chin, “Asymmetric Fano resonance and bistability for high extinction ratio, large modulation depth, and low power switching,” Opt. Express 14(26), 12770–12781 (2006).
    [CrossRef] [PubMed]
  13. E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express 14(9), 3853–3863 (2006).
    [CrossRef] [PubMed]
  14. J. D. Doménech, P. Muñoz, and J. Capmany, “Transmission and group-delay characterization of coupled resonator optical waveguide apodized through the longitudinal offset technique,” Opt. Lett. 36(2), 136–138 (2011).
    [CrossRef] [PubMed]
  15. A. Yariv, Optical Electronics in Modern Communication, 5th ed. (Oxford, 1997).
  16. URL, http://www.rsoftdesign.com/ .
  17. A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
    [CrossRef]

2011 (1)

2010 (2)

S. Darmawan, L. Y. Tobing, and T. Mei, “Coupling-induced phase shift in a microring-coupled Mach-Zehnder interferometer,” Opt. Lett. 35(2), 238–240 (2010).
[CrossRef] [PubMed]

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
[CrossRef]

2009 (1)

2008 (1)

2006 (3)

2004 (1)

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(10), 2263–2265 (2004).
[CrossRef]

2002 (1)

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
[CrossRef]

2000 (2)

M. Kohtoku, S. Oku, Y. Kadota, Y. Shibata, and Y. Yoshikuni, “200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interferometer with a ring resonator,” IEEE Photon. Technol. Lett. 12(9), 1174–1176 (2000).
[CrossRef]

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

1988 (1)

K. Oda, N. Takato, H. Toba, K. Nosu, and J. Lightwave, “A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems,” J. LightwaveTechnol. 6, 1016–1023 (1988).

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(10), 2263–2265 (2004).
[CrossRef]

Adibi, A.

Atabaki, A. H.

Baets, R.

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
[CrossRef]

L. Y. M. Tobing, P. Dumon, R. Baets, and M. K. Chin, “Boxlike filter response based on complementary photonic bandgaps in two-dimensional microresonator arrays,” Opt. Lett. 33(21), 2512–2514 (2008).
[CrossRef] [PubMed]

Bogaerts, W.

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
[CrossRef]

Capmany, J.

Chin, M. K.

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(10), 2263–2265 (2004).
[CrossRef]

Darmawan, S.

Doménech, J. D.

Dulkeith, E.

Dumon, P.

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
[CrossRef]

L. Y. M. Tobing, P. Dumon, R. Baets, and M. K. Chin, “Boxlike filter response based on complementary photonic bandgaps in two-dimensional microresonator arrays,” Opt. Lett. 33(21), 2512–2514 (2008).
[CrossRef] [PubMed]

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(10), 2263–2265 (2004).
[CrossRef]

Green, W. M. 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(10), 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(10), 2263–2265 (2004).
[CrossRef]

Kadota, Y.

M. Kohtoku, S. Oku, Y. Kadota, Y. Shibata, and Y. Yoshikuni, “200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interferometer with a ring resonator,” IEEE Photon. Technol. Lett. 12(9), 1174–1176 (2000).
[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(10), 2263–2265 (2004).
[CrossRef]

Kohtoku, M.

M. Kohtoku, S. Oku, Y. Kadota, Y. Shibata, and Y. Yoshikuni, “200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interferometer with a ring resonator,” IEEE Photon. Technol. Lett. 12(9), 1174–1176 (2000).
[CrossRef]

Lee, R. K.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Li, Q.

Li, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Lightwave, J.

K. Oda, N. Takato, H. Toba, K. Nosu, and J. Lightwave, “A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems,” J. LightwaveTechnol. 6, 1016–1023 (1988).

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(10), 2263–2265 (2004).
[CrossRef]

Manolatou, C.

Mario, L. Y.

Mei, T.

Muñoz, P.

Nosu, K.

K. Oda, N. Takato, H. Toba, K. Nosu, and J. Lightwave, “A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems,” J. LightwaveTechnol. 6, 1016–1023 (1988).

Oda, K.

K. Oda, N. Takato, H. Toba, K. Nosu, and J. Lightwave, “A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems,” J. LightwaveTechnol. 6, 1016–1023 (1988).

Oku, S.

M. Kohtoku, S. Oku, Y. Kadota, Y. Shibata, and Y. Yoshikuni, “200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interferometer with a ring resonator,” IEEE Photon. Technol. Lett. 12(9), 1174–1176 (2000).
[CrossRef]

Popovic, M.

Schares, L.

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(10), 2263–2265 (2004).
[CrossRef]

Selvaraja, S. K.

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
[CrossRef]

Shibata, Y.

M. Kohtoku, S. Oku, Y. Kadota, Y. Shibata, and Y. Yoshikuni, “200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interferometer with a ring resonator,” IEEE Photon. Technol. Lett. 12(9), 1174–1176 (2000).
[CrossRef]

Soltani, M.

Takato, N.

K. Oda, N. Takato, H. Toba, K. Nosu, and J. Lightwave, “A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems,” J. LightwaveTechnol. 6, 1016–1023 (1988).

Toba, H.

K. Oda, N. Takato, H. Toba, K. Nosu, and J. Lightwave, “A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems,” J. LightwaveTechnol. 6, 1016–1023 (1988).

Tobing, L. Y.

Tobing, L. Y. M.

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(10), 2263–2265 (2004).
[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(10), 2263–2265 (2004).
[CrossRef]

Van Thourhout, D.

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
[CrossRef]

Vlasov, Y. A.

Watts, M. R.

Xia, F.

Xu, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
[CrossRef]

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Yegnanarayanan, S.

Yoshikuni, Y.

M. Kohtoku, S. Oku, Y. Kadota, Y. Shibata, and Y. Yoshikuni, “200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interferometer with a ring resonator,” IEEE Photon. Technol. Lett. 12(9), 1174–1176 (2000).
[CrossRef]

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

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

M. Kohtoku, S. Oku, Y. Kadota, Y. Shibata, and Y. Yoshikuni, “200-GHz FSR periodic multi/demultiplexer with flattened transmission and rejection band by using a Mach-Zehnder interferometer with a ring resonator,” IEEE Photon. Technol. Lett. 12(9), 1174–1176 (2000).
[CrossRef]

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(10), 2263–2265 (2004).
[CrossRef]

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
[CrossRef]

J. LightwaveTechnol. (1)

K. Oda, N. Takato, H. Toba, K. Nosu, and J. Lightwave, “A wide-band guided-wave periodic multi/demultiplexer with a ring resonator for optical FDM transmission systems,” J. LightwaveTechnol. 6, 1016–1023 (1988).

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Other (4)

A. Yariv, Optical Electronics in Modern Communication, 5th ed. (Oxford, 1997).

URL, http://www.rsoftdesign.com/ .

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, 1991).

URL, http://www.epixfab.eu .

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

The fabricated (a) Ring-enhanced Mach-Zehnder Interferometer (REMZI), (b) 3dB multimode interferometer (MMI), and (c) ring resonator side coupled to two bus waveguides (1R2B) devices.

Fig. 2
Fig. 2

The schematic of MZI for phase extraction.

Fig. 3
Fig. 3

The simulation of coupling coefficients as a function of wavelength for different coupler lengths and gap separations.

Fig. 4
Fig. 4

(a) The induced phase shift as a function of coupler length and gap separation. The wavelength at which the phase is extracted is ~1564.9nm (for 200nm), ~1576.2nm (for 300nm), and ~1576.5nm (for 400nm). (b) The coupling induced phase wavevector as a function of gap separation.

Fig. 5
Fig. 5

The simulation strategy for 1R2B when it is (a) coupled and (b) uncoupled. For the coupled case, the drop transmission is normalized with respect to the input spectrum. For the uncoupled case, the intra-cavity field is normalized with respect to the input spectrum. (c) Induced phase shift in 1R2B as a function of coupler length for three different gaps. The resonance wavelength shift is measured from three resonance orders. Each point represents the average resonance shift and its standard deviation.

Fig. 6
Fig. 6

(a) The input/output curved gratings. (b) The waveguide loss characterization in spiral structures in three different SOI samples: (left) the PECVD SiO2 coated, (middle) the i-line resist coated, and (right) bare silicon.

Fig. 7
Fig. 7

(a) The measured drop transmissions of 1R2B structures for 300nm gap separation. Each measurement is offset by 10dB from each other. (b) Linearized coupling coefficients in different gap separations.

Fig. 8
Fig. 8

Beating length and phase offset for different gap separations.

Fig. 9
Fig. 9

(a) The schematic of MZI based on different MMI geometries. (b) Experimental measurements of Bar and Cross MMI transmissions for different MMI lengths. (c) Measured MMI phase imbalances for different MMI lengths.

Fig. 10
Fig. 10

The measured Bar transmissions and their best fittings for 6μm coupler length for different gap separations.

Fig. 11
Fig. 11

(a) The measurements of coupling induced phase shift for different gap separations and upper claddings. The PECVD was done at 300C with 600nm nominal thickness. The 2 points in 200nm gap in the first two panels are excluded because the measured coupling is too strong, which renders the curve-fitting no longer accurate. This is also the case for the rightmost panel for 400nm gap when the coupling is far too weak. (b) The phase slope as a function of gap separation for the three samples.

Tables (3)

Tables Icon

Table 1 SiO2 (PECVD Coated)

Tables Icon

Table 2 i-Line Resist Coated

Equations (10)

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

d dz [ A 1 A 2 ]=i[ β 1 + k 11 k 12 k 21 β 2 + k 22 ][ A 1 A 2 ]
[ A 1 (L) A 2 (L) ]=exp(i β ¯ L)M[ A 1 (0) A 2 (0) ],
M=[ cos(sL)+i Δ β ˜ 2s sin(sL) i k 12 s sin(sL) i k 21 s sin(sL) cos(sL)i Δ β ˜ 2s sin(sL) ].
M=[ rexp(i ϕ r ) it it rexp(i ϕ r ) ],
ϕ r = sin 1 ( T B / T C ) [( t 2 r 2 )/(2rt)] 2 1+( T B / T C ) ,
D= a (1 r 2 ) 2 1+ a 2 r 4 2a r 2 cosδ ,
1 D = (1a r 2 ) 2 +4a r 2 cosδ a (1 r 2 ) 2 = (1a r 2 ) 2 a (1 r 2 ) 2 + 4 r 2 (1 r 2 ) 2 cosδ,
r=cos( π L C 2 L π (g) + ϕ 0 (g) ), t=sin( π L C 2 L π (g) + ϕ 0 (g) ),
ϕ MMI =2 tan 1 T B / T C .
T BAR = 1 4 | t r exp(i ϕ CIPS )exp(i ϕ MMI ) | 2 , T CROSS = 1 4 | t r exp(i ϕ CIPS )+exp(i ϕ MMI ) | 2 ,

Metrics