Abstract

Three sets of devices were simulated, designed, and laid out for fabrication in the EuroPractice shuttle program and then measured in-house after fabrication. A combination of analytical and numerical modeling is used to extract the dispersion curves that define the effective index of refraction as a function of wavelength for three different classes of silicon photonic devices, namely, micro-ring resonators, racetrack resonators, and directional couplers. The results of this phenomenological study are made plausible by the linearity of the extracted dispersion curves with wavelength over the wavelength regime of interest (S and C bands) and the use of the determined effective indices to reconstruct the measured transmission as a function of wavelength curves in close agreement with experiment. The extracted effective indices can be used to place limits on the actual fabricated values of waveguide widths, thicknesses, radii of curvature, and coupling gaps.

© 2014 Optical Society of America

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2013 (4)

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J.-M. Fedeli, H. Yu, and W. Bogaerts, “Silicon-organic hybrid electro-optical devices,” IEEE J. Sel. Top. Quantum Electron. 19, 3401413 (2013).
[CrossRef]

R. Palmer, L. Alloatti, D. Korn, P. Schindler, M. Baier, J. Bolten, T. Wahlbrink, M. Waldow, R. Dinu, W. Freude, C. Koos, and J. Leuthold, “Low power Mach-Zehnder modulator in silicon-organic hybrid technology,” IEEE Photon. Technol. Lett. 25, 1226–1229 (2013).
[CrossRef]

S. Werquin, S. Verstuyft, and P. Bienstman, “Integrated interferometric approach to solve microring resonance splitting in biosensor applications,” Opt. Express 21, 16955–16963 (2013).
[CrossRef]

X. Chen, M. Mohamed, Z. Li, L. Shang, and A. R. Mickelson, “Process variation in silicon photonic devices,” Appl. Opt. 52, 7638–7647 (2013).
[CrossRef]

2012 (3)

A. Rylyakov, C. Schow, B. Lee, W. M. J. Green, S. Assefa, F. Doany, M. Yang, J. Van Campenhout, C. V. Jahnes, J. Kash, and Y. Vlasov, “Silicon photonic switches hybrid-integrated with CMOS drivers,” IEEE J. Solid St. Circ. 47, 345–354 (2012).
[CrossRef]

L. Xu, W. Zhang, Q. Li, J. Chan, H. L. R. Lira, M. Lipson, and K. Bergman, “40-Gb/s DPSK data transmission through a silicon microring switch,” IEEE Photon. Technol. Lett. 24, 473–475 (2012).
[CrossRef]

D. Thomson, F. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B.-P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Mashanovich, and G. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24, 234–236 (2012).
[CrossRef]

2011 (5)

2010 (8)

A. Liu, L. Liao, Y. Chetrit, J. Basak, H. Nguyen, D. Rubin, and M. Paniccia, “Wavelength division multiplexing based photonic integrated circuits on silicon-on-insulator platform,” IEEE J. Sel. Top. Quantum Electron. 16, 23–32 (2010).
[CrossRef]

M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics 4, 492–494 (2010).
[CrossRef]

R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4, 495–497 (2010).
[CrossRef]

B. Guha, B. B. C. Kyotoku, and M. Lipson, “CMOS-compatible athermal silicon microring resonators,” Opt. Express 18, 3487–3493 (2010).
[CrossRef]

D. M. H. Leung, N. Kejalakshmy, B. M. A. Rahman, and K. T. V. Grattan, “Rigorous modal analysis of silicon strip nanoscale waveguides,” Opt. Express 18, 8528–8539 (2010).
[CrossRef]

S. 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, 316–324 (2010).
[CrossRef]

M. Masi, R. Orobtchouk, G. Fan, J.-M. Fedeli, and L. Pavesi, “Towards a realistic modelling of ultra-compact racetrack resonators,” J. Lightwave Technol. 28, 3233–3242 (2010).

N. Rouger, L. Chrostowski, and R. Vafaei, “Temperature effects on Silicon-on-Insulator (SOI) racetrack resonators: a coupled analytic and 2-D finite difference approach,” J. Lightwave Technol. 28, 1380–1391 (2010).
[CrossRef]

2009 (2)

C. Batten, A. Joshi, J. Orcutt, A. Khilo, B. Moss, C. W. Holzwarth, M. A. Popovic, H. Li, H. I. Smith, J. L. Hoyt, F. X. Kaertner, R. J. Ram, V. Stojanovic, and K. Asanovic, “Building many-core processor-to-DRAM networks with monolithic CMOS silicon photonics,” IEEE Micro 29, 8–21 (2009).
[CrossRef]

J. V. Campenhout, W. M. Green, S. Assefa, and Y. A. Vlasov, “Low-power, 2 × 2 silicon electro-optic switch with 110-nm bandwidth for broadband reconfigurable optical networks,” Opt. Express 17, 24020–24029 (2009).
[CrossRef]

2008 (5)

Y.-J. Quan, P.-D. Han, Q.-J. Ran, F.-P. Zeng, L.-P. Gao, and C.-H. Zhao, “A photonic wire-based directional coupler based on SOI,” Opt. Commun. 281, 3105–3110 (2008).
[CrossRef]

H.-G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nat. Photonics 2, 622–626 (2008).
[CrossRef]

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[CrossRef]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2, 737–740 (2008).
[CrossRef]

C. Li, X. Luo, and A. W. Poon, “Dual-microring-resonator electro-optic logic switches on a silicon chip,” Semicond. Sci. Technol. 23, 064010 (2008).
[CrossRef]

2007 (6)

2006 (1)

W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).
[CrossRef]

2005 (1)

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photon. Technol. Lett. 17, 585–587 (2005).
[CrossRef]

2004 (4)

Y. Vlasov and S. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12, 1622–1631 (2004).
[CrossRef]

C. Maleville and C. Mazuré, “Smart-cut technology: from 300 mm ultrathin SOI production to advanced engineered substrates,” Solid-State Electron. 48, 1055–1063 (2004).
[CrossRef]

J. Poon, J. Scheuer, S. Mookherjea, G. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103 (2004).
[CrossRef]

J. K. S. Poon, J. Scheuer, and A. Yariv, “Wavelength-selective reflector based on a circular array of coupled microring resonators,” IEEE Photon. Technol. Lett. 16, 1331–1333 (2004).
[CrossRef]

2002 (1)

R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, “Parallel-cascaded semiconductor microring resonators for high-order and wide-FSR filters,” J. Lightwave Technol. 20, 900–905 (2002).
[CrossRef]

1999 (1)

G. Cocorullo, F. Della Corte, and I. Rendina, “Temperature dependence of the thermo-optic coefficient in crystalline silicon between room temperature and 550  K at the wavelength of 1523  nm,” Appl. Phys. Lett. 74, 3338–3340 (1999).
[CrossRef]

1997 (1)

J. P. Rust, “Using randomization to break the curse of dimensionality,” Econometrica 65, 487–516 (1997).
[CrossRef]

1996 (1)

1992 (1)

G. Cocorullo and I. Rendina, “Thermo-optical modulation at 1.5  μm in silicon etalon,” Electron. Lett. 28, 83–85 (1992).
[CrossRef]

1988 (1)

1985 (1)

A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” J. Lightwave Technol. 3, 1135–1146 (1985).
[CrossRef]

1975 (1)

M. Heiblum and J. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11, 75–83 (1975).
[CrossRef]

1974 (1)

S. Sheem and J. R. Whinnery, “Guiding by single curved boundaries in integrated optics,” Wave Electron. 1, 61–68 (1974).

Absil, P. P.

R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, “Parallel-cascaded semiconductor microring resonators for high-order and wide-FSR filters,” J. Lightwave Technol. 20, 900–905 (2002).
[CrossRef]

Adam, K.

X. Wang, W. Shi, M. Hochberg, K. Adam, E. Schelew, J. Young, N. Jaeger, and L. Chrostowski, “Lithography simulation for the fabrication of silicon photonic devices with deep-ultraviolet lithography,” in 9th IEEE International Conference on Group IV Photonics (GFP), (IEEE, 2012), pp. 288–290.

Akella, V.

C. Nitta, M. Farrens, and V. Akella, “Addressing system-level trimming issues in on-chip nanophotonic networks,” in 17th IEEE International Symposium on High Performance Computer Architecture (HPCA), (IEEE, 2011), pp. 122–131.

Alic, N.

D. Thomson, F. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B.-P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Mashanovich, and G. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24, 234–236 (2012).
[CrossRef]

Alloatti, L.

R. Palmer, L. Alloatti, D. Korn, P. Schindler, M. Baier, J. Bolten, T. Wahlbrink, M. Waldow, R. Dinu, W. Freude, C. Koos, and J. Leuthold, “Low power Mach-Zehnder modulator in silicon-organic hybrid technology,” IEEE Photon. Technol. Lett. 25, 1226–1229 (2013).
[CrossRef]

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A. Rylyakov, C. Schow, B. Lee, W. M. J. Green, S. Assefa, F. Doany, M. Yang, J. Van Campenhout, C. V. Jahnes, J. Kash, and Y. Vlasov, “Silicon photonic switches hybrid-integrated with CMOS drivers,” IEEE J. Solid St. Circ. 47, 345–354 (2012).
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J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J.-M. Fedeli, H. Yu, and W. Bogaerts, “Silicon-organic hybrid electro-optical devices,” IEEE J. Sel. Top. Quantum Electron. 19, 3401413 (2013).
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Figures (9)

Fig. 1.
Fig. 1.

Schematic depictions of the devices of interest. S1 and S2 are the coupling regions; i1 and i2 are the input ports; and o1 and o2 are the output ports in the devices.

Fig. 2.
Fig. 2.

Thermal variation measurement and numerical modeling results where the temperature range is 25°C–50°C and λres1 and λres2 are the measured resonant wavelengths. (a) The micro-ring described in Fig. 1(a) has a measured thermal drift rate of 78.5pm/°C that closely agrees with the simulation result of 74.2pm/°C. (b) The racetrack described in Fig. 1(b) has a measured thermal drift rate of 89.7pm/°C, whereas the simulation result shows a drift rate of 75.2pm/°C. (c) The directional coupler described in Fig. 1(c) has a measured thermal drift rate of 116.4pm/°C and the numerical simulation shows a drift rate of about 105.8pm/°C.

Fig. 3.
Fig. 3.

Illustration of the process to find the mode number m from the (lower panel) measured resonant wavelengths and (upper panel) simulation. The simulations are carried out using foundry wafer-scale variation data. Comparing the plots, we determine m1=46 and m2=47.

Fig. 4.
Fig. 4.

Effective-index-dispersion curves extracted from measured data for a micro-ring (450 nm waveguide width, 200 nm coupling gap, and 4.975 μm radius) as sketched in Fig. 1(a). The error bar is within 0.02%.

Fig. 5.
Fig. 5.

Optical transmission measurement of a micro-ring (black line with solid circles) and its corresponding numerical model fitting (red line). The inset shows the scanning electron microscope (SEM) image of the fabricated structure. The radius of the micro-ring is 4.975 μm. Its waveguide width is 450 nm, and the gap width is 200 nm.

Fig. 6.
Fig. 6.

Effective-index-dispersion curves for the straight region (neffs) and the curved region (neffc) extracted from measured data for a racetrack (500 nm waveguide width, 130 nm coupling gap for 7 μm, and bending radius of 3 μm) as sketched in Fig. 1(b). The error bar is within 0.01%.

Fig. 7.
Fig. 7.

Optical measurement of a racetrack (black line with solid circles) and its corresponding numerical model fitting (red line). The SEM image shows the fabricated structure with 3 μm bending radius, 7 μm coupling length, and 130 nm coupling gap. The waveguide width is 450 nm.

Fig. 8.
Fig. 8.

Effective index dispersion curves for neffeneffo extracted from measured data for a directional coupler (450 nm waveguide width, 130 nm coupling gap, and 1063 μm coupling length) as sketched in Fig. 1(c). The error bar is within 0.03%.

Fig. 9.
Fig. 9.

Optical measurement of a directional coupler (black line with solid circles) and its corresponding numerical model fitting (red line). The SEM image shows part of the coupling region of the fabricated structure. Its coupling length is 1063 μm with a coupling gap of 130 nm. The waveguide width is 450 nm.

Equations (17)

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λsel=f(neff),
neff(λ)=f(w,t,Rc,g,λ;T),
(b1b2)=(rititr)(a1a2),
b=exp[αL+i·2πneffL/λ]a,
mλsel=Lcneffc(λsel),
mλsel=Lcneffc(λsel)+Lneffs(λsel),
mλsel=2L(neffe(λsel)neffo(λsel)),
nT=A+BT+CT2,
(b1df)=(r1itb1it1r1)(a1eiΦ/2eαl/2uf),
(ufb2)=(r2it2it2r2)(eiΦ/2eαl/2dfa2),
nSi(λ)=3.4277+0.1104λ2+0.041λ4,
nSiO2(λ)=1.4213+0.0856λ20.0735λ4.
mλres=2π(R+w2)neffc,
mλres=2π(R+w2)neffc+2Lneffs,
(b1b2)=(ritit*r*)(a1a2),
r=cos(Zκ2+δ2)+iδκ2+δ2sin(Zκ2+δ2),
t=κκ2+δ2sin(Zκ2+δ2),

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