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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 4 — Feb. 13, 2012
  • pp: 4225–4231
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Thermo-optic characteristics and switching power limit of slow-light photonic crystal structures on a silicon-on-insulator platform

Manjit Chahal, George K. Celler, Yogesh Jaluria, and Wei Jiang  »View Author Affiliations


Optics Express, Vol. 20, Issue 4, pp. 4225-4231 (2012)
http://dx.doi.org/10.1364/OE.20.004225


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Abstract

Employing a semi-analytic approach, we study the influence of key structural and optical parameters on the thermo-optic characteristics of photonic crystal waveguide (PCW) structures on a silicon-on-insulator (SOI) platform. The power consumption and spatial temperature profile of such structures are given as explicit functions of various structural, thermal and optical parameters, offering physical insight not available in finite-element simulations. Agreement with finite-element simulations and experiments is demonstrated. Thermal enhancement of the air-bridge structure is analyzed. The practical limit of thermo-optic switching power in slow light PCWs is discussed, and the scaling with key parameters is analyzed. Optical switching with sub-milliwatt power is shown viable.

© 2012 OSA

1. Introduction

Silicon photonics benefits from the wealth of experience and the infrastructure of the Si electronics industry, and the compatibility of Si photonic circuits with CMOS electronics allows for mass production of low cost integrated photonic/electronic circuits [1

1. R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006). [CrossRef]

,2

2. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006). [CrossRef]

]. Silicon-on-insulator (SOI) substrates [3

3. G. K. Celler and S. Cristoloveanu, “Frontiers of silicon-on-insulator,” J. Appl. Phys. 93(9), 4955–4978 (2003). [CrossRef]

] are an attractive medium for making silicon photonic integrated circuits (PICs). For Si PICs, switching and modulation devices are indispensable components. Thermo-optic effect is one of the preferred options for optical switching in compact SOI photonic devices. Photonic crystal structures can be incorporated into these devices to help shrink the interaction length based on the slow light effect [4

4. M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004). [CrossRef] [PubMed]

]. In recent research, thermo-optic switching and modulation in ultra-compact photonic crystal structures have been studied [5

5. E. A. Camargo, H. M. H. Chong, and R. M. De La Rue, “2D Photonic crystal thermo-optic switch based on AlGaAs/GaAs epitaxial structure,” Opt. Express 12(4), 588–592 (2004). [CrossRef] [PubMed]

10

10. Y. Cui, K. Liu, D. L. MacFarlane, and J.-B. Lee, “Thermo-optically tunable silicon photonic crystal light modulator,” Opt. Lett. 35(21), 3613–3615 (2010). [CrossRef] [PubMed]

]. However, the performance of these structures varies widely. For example, the power consumption of most of these structures ranges from 2mW to tens of milliwatts. As these structures vary widely in their size, design, and the group velocity of light, it is not always clear what physical factors are crucial to their performance. A theory that can describe the thermo-optic characteristics of an SOI photonic crystal structure as explicit functions of various parameters is desired. Note that the understanding of such thermo-optic characteristics could also help control the thermo-optic effect in photonic crystal electro-optic modulators and other active devices [11

11. L. Gu, W. Jiang, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007). [CrossRef]

13

13. J. Pan, Y. Huo, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. H. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett. 92(10), 103114 (2008). [CrossRef]

].

A photonic crystal thermo-optic device on an SOI chip comprises structural components whose scales differ by orders of magnitude, such as small holes of ~200nm in diameter and thick substrates of hundreds of microns. Simulations of such a multi-scale structure can be time-consuming and challenging. Such simulations may be performed for a small number of structures. However they are not efficient for systematically studying a large ensemble of structures in which many parameters such as the hole diameter and the buried-oxide thickness vary over a large range. Here we develop an efficient and accurate approach to analyze the thermo-optic characteristics of an SOI photonic crystal structure. The effective thermal conductivity κeff for a silicon photonic crystal slab is determined through the lateral thermal spreading length. Physical properties such as the spatial temperature profile and the power consumption required to induce a π phase shift can be described semi-analytically based on a quasi-1D model with numerically determined κeff. The results agree well with 3D simulations based on the finite element method (FEM). The theoretical results also explain the low switching power observed in an air-bridge structure [6

6. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]

]. The analytic formulas offer insight into the key factors governing the thermo-optic characteristics of SOI photonic crystal structures.

2. Analysis of SOI photonic crystal thermo-optic structures

Figure 1
Fig. 1 Configurations of Si active PCW structures. (a) SOI; (b) Air-bridge (membrane).
illustrates two common configurations of active photonic crystal waveguide (PCW) structures on an SOI wafer. A heat source of width W and length L is assumed to be embedded in the top silicon layer. Such a heat source can be formed by a lightly doped (e.g. ~1014cm−3) Si strip surrounded by a relatively highly doped (e.g. ~1017cm−3) silicon on both sides [6

6. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]

]. Passing current laterally through this structure produces concentrated ohmic heating in the center strip.

The heat conduction process in a photonic crystal slab can be effectively modeled by that of an equivalent hole-free homogeneous slab with an effective thermal conductivity κeff. This is valid because the temperature varies spatially on a scale much larger than the typical photonic crystal lattice constant a. To determine κeff, the heat transfer process is simulated using the finite element method for one period of the PCW structure, as shown in the inset of Fig. 2
Fig. 2 Temperature profiles in the top Si layer of a PCW (center: x = 0) for various hole radii and in a homogenized slab with κeff(r). Inset: 3D temperature profile in a PCW with r/a = 0.25. One period of the PCW along the y axis is shown.
. The thicknesses of the top Si layer and buried oxide layer are tSi = 250 nm and tox = 2 μm respectively. The hexagonal lattice has a lattice constant a = 400nm. The simulations indicate that the vertical temperature variation in the top Si layer and the in-plane temperature variation in each unit cell are small. The temperature of the top Si layer varies significantly only along the x axis, as plotted in Fig. 2. Outside the heater (centered at x = 0), it closely follows an exponential form
T(x)exp[(|x|W/2)/Xspr(r)],for|x|>W/2,
(1)
where Xspr(r) is the thermal spreading length. For an unpatterned SOI structure, it is given by [14

14. V. M. N. Passaro, F. Magno, and A. V. Tsarev, “Investigation of thermo-optic effect and multi-reflector tunable filter/multiplexer in SOI waveguides,” Opt. Express 13(9), 3429–3437 (2005). [CrossRef] [PubMed]

,15

15. L. T. Su, J. E. Chung, D. A. Antoniadis, K. E. Goodson, and M. I. Flik, “Measurement and modeling of self-heating in SOI nMOSFETS,” IEEE Trans. Electron. Dev. 41(1), 69–75 (1994). [CrossRef]

]
Xspr=XSi=[tSitoxκSi/κox]1/2,
(2)
where κSi and κox are the thermal conductivities of silicon and SiO2 respectively (values from Ref [14

14. V. M. N. Passaro, F. Magno, and A. V. Tsarev, “Investigation of thermo-optic effect and multi-reflector tunable filter/multiplexer in SOI waveguides,” Opt. Express 13(9), 3429–3437 (2005). [CrossRef] [PubMed]

].).

For a photonic crystal slab, Xspr(r) depends on the hole radius r and it can be obtained from an exponential fit of the lateral temperature profile in the slab. The effective thermal conductivity of a Si photonic crystal slab can then be calculated from

κeff(r)=κoxXspr2(r)/(tSitox).
(3)

The values of κeff/κSi and Xspr determined from the plots are given in Table 1

Table 1. Values of Xspr(r) and κeff(r) for Various Hole Sizes

table-icon
View This Table
. To further verify the results, homogenized slab structures with the tabulated κeff(r) are simulated, with all other parameters unchanged. The lateral temperature profile in the homogenized slab is generally in good agreement (within 6%) with that of the original photonic crystal slab, as shown in Fig. 2.

For an SOI structure, the heat conduction can generally be described by a quasi-1D model predicated on the vertical heat conduction in the buried oxide [14

14. V. M. N. Passaro, F. Magno, and A. V. Tsarev, “Investigation of thermo-optic effect and multi-reflector tunable filter/multiplexer in SOI waveguides,” Opt. Express 13(9), 3429–3437 (2005). [CrossRef] [PubMed]

,15

15. L. T. Su, J. E. Chung, D. A. Antoniadis, K. E. Goodson, and M. I. Flik, “Measurement and modeling of self-heating in SOI nMOSFETS,” IEEE Trans. Electron. Dev. 41(1), 69–75 (1994). [CrossRef]

]. Note that the thermal spreading increases the effective heat flux cross-section to Aeff = L[W + 2Xspr]. For the photonic crystal structure in Fig. 1(a), this model yields
Q=κoxL[W+2Xspr(r)](ΔTox/tox),
(4)
where Q is the heat transfer rate (equal to the heating power in steady state) and ΔTox the temperature difference between the top and bottom of the oxide at x = 0. To verify Eq. (4), 3D FEM steady-state simulations are performed for an SOI chip having a homogenized top layer with κeff (Fig. 3
Fig. 3 ΔTox/Q vs. waveguide length L (for tox=2μm). Inset: 3D temperature distribution in a chip obtained from finite element simulation for a PCW structure having tSi=250nm, W=400nm, tox=2μm, κeff(r=0.25a) on a 200μm×200μm substrate with a thickness of 100μm.
inset). The absence of small holes significantly mitigates the difficulty in mesh generation for multi-scale structures, and reduces the simulation time significantly.

Due to the small thermal conductivity and natural convection coefficient of air [16

16. Y. Jaluria, Natural Convection Heat and Mass Transfer (Pergamon Press, Oxford, UK, 1980).

], the heat dissipation from the top and side surfaces of the chip is negligible, hence adiabatic boundary conditions are used for the top and side surfaces [7

7. M. T. Tinker and J.-B. Lee, “Thermal and optical simulation of a photonic crystal light modulator based on the thermo-optic shift of the cut-off frequency,” Opt. Express 13(18), 7174–7188 (2005). [CrossRef] [PubMed]

,17

17. M. Iodice, G. Mazzi, and L. Sirleto, “Thermo-optical static and dynamic analysis of a digital optical switch based on amorphous silicon waveguide,” Opt. Express 14(12), 5266–5278 (2006). [CrossRef] [PubMed]

]. The bottom surface is kept at 300 K. The simulated ΔTox per unit heating power Q and the results based on Eq. (4) agree well (within 3%), as shown in Fig. 3 for various lengths of the heat source.

3. Thermo-optic characteristics and switching power for SOI and air-bridge structures

To study the thermo-optic characteristics, we note that the phase shift induced in a PCW is given by [4

4. M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004). [CrossRef] [PubMed]

]
Δϕ=2πΔnσLng/(nλ),
(5)
where ng is the group index of the mode, λ the wavelength, and σ the fraction of the mode energy stored in the region where the refractive index change ∆n = (dn/dT)∆T occurs. By virtue of Eqs. (4) and (5), the power required to induce a phase shift of π for a structure in Fig. 1(a) is given by

Qπ=nλκox[W+2Xspr(r)]/[2σtoxng(dn/dT)].
(6)

BecauseXspr~tox, the power Qπ actually scales as 1/tox for heater width W<<Xspr. Figure 4
Fig. 4 Qπ vs. group index (ng) for r/a = 0.25 for an SOI PCW structure (for various tox), and the estimated 3dB-propagation-loss length for a membrane PCW structure. Inset: The thermal enhancement for a membrane PCW with tox = 2μm.
shows the results for σ = 0.9, λ = 1.55μm and dn/dT = 1.86 × 10−4 K−1 with different values of oxide layer thickness. For ng = 60, r/a = 0.25 and tox = 2μm, Qπ is less than 2.5mW.

This approach can also be applied to an air-bridge (membrane) structure shown in Fig. 1(b). Here the heat conduction consists of two steps in series: (1) the lateral heat conduction in the suspended membrane; and (2) the quasi-1D heat conduction in the SOI region. Based on the continuity of heat flux, one readily finds for the left (or right) half membrane
Qmembrane/2=κeffLtSi(ΔT)membrane(ΔT)edgeWmembrane/2=κoxLXSi(ΔT)edgetox,
(7)
where Wmembrane is the membrane width, XSi is given by Eq. (2), (ΔT)membrane is the membrane temperature rise evaluated at the PCW core and (∆T)edge at the membrane edge. Eliminating (∆T)edge, we find

Qmembrane=κoxL(2XSi)(ΔT)membranetoxκeff(r)XSiκeff(r)XSi+κSiWmembrane/2,
(8)

For the same power Q, the membrane structure may enhance the temperature rise by a factor

(ΔT)membrane(ΔT)SOIXspr(r)XSiκeff(r)XSi+κSiWmembrane/2κeff(r)XSi.
(9)

Correspondingly, Qπ of the membrane structure is reduced by this factor. The enhancement factors obtained from Eq. (9) agree very well (within 6%) with the simulation results, as shown in Fig. 4 inset. Based on Fig. 4, the attainable power consumption for a Si air-bridge PCW thermo-optic Mach-Zehnder switch is estimated between 1~2mW for ng~60 and tox = 2μm, which agrees well with the experimental result [6

6. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]

].

4. Discussions

The scaling of the thermo-optic characteristics of an SOI photonic crystal structure with various parameters is of significant interest in device design. The analytic formulas enable us to study such scaling over a wide parameter range. The heater location is an important factor in determining the power consumption. Here we consider two options: in the PCW core [6

6. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]

], at the lateral edge of the PCW [8

8. L. Gu, W. Jiang, X. Chen, and R. T. Chen, “Thermooptically tuned photonic crystal waveguide silicon-on-insulator Mach-Zehnder interferometers,” IEEE Photon. Technol. Lett. 19(5), 342–344 (2007). [CrossRef]

]. The temperature profile given in Eq. (1) shows that the temperature rise in the silicon layer decreases exponentially with the lateral distance from the heater. Compared to a heater embedded exactly in the PCW core, a heat source located at Δx = 6μm from the core has an efficiency reduction by exp(−6μm/Xspr)≈0.3~0.4 for r/a = 0.25~0.35. The buried oxide thickness is another crucial factor. Generally, a thicker oxide is preferred for lower power consumption according to Eqs. (6) and (8). However, the thermal time constant of an SOI chip increases with the oxide thickness. Therefore, some trade-off must be made in realistic device design to balance power consumption and speed. For the membrane structure, the enhancement factor in Eq. (9) is found to weaken the scaling of Qπ with tox due to XSi ~tox. Thus, Qπ scales slower than tox1/2, particularly for a large Wmembrane. Ultimately, the reduction of Qπ based on the slow light effect is limited by optical loss, which increases with ng. The optical loss of a PCW can be attributed to a number of factors, such as random variation of hole positions due to fabrication tolerances, sidewall roughness, and the input/output coupling. The random variation of the hole positions in fabricated PCWs can be controlled to be within a small range (<1nm) with high-end e-beam lithography tools [18

18. E. Dulkeith, S. J. McNab, and Y. A. Vlasov, “Mapping the optical properties of slab-type two-dimensional photonic crystal waveguides,” Phys. Rev. B 72(11), 115102 (2005). [CrossRef]

]; and the corresponding loss is usually small. Sidewall roughness of the holes depends on the lithography tool, resist, and etching process and is more difficult to control. Such roughness could induce substantial loss at large ng. The estimated PCW length for 3dB propagation loss is plotted against ng in Fig. 4 based on theoretical calculations with experimentally achievable rms roughness σ = 3nm and correlation length lc = 40nm [19

19. W. Song, R. A. Integlia, and W. Jiang, “Slow light loss due to roughness in photonic crystal waveguides: An analytic approach,” Phys. Rev. B 82(23), 235306 (2010). [CrossRef]

]. To further address the effect of the input/output coupling loss, we consider two prior experiments [6

6. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]

,20

20. C.-Y. Lin, X. Wang, S. Chakravarty, B. S. Lee, W.-C. Lai, and R. T. Chen, “Wideband group velocity independent coupling into slow light silicon photonic crystal waveguide,” Appl. Phys. Lett. 97(18), 183302 (2010). [CrossRef]

]. In an earlier experiment [6

6. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]

], the insertion loss of well-fabricated PCWs is about 10~13dB at ng~110 for L = 50μm and 250μm and shows weak dependence on the PCW lengths. This indicates that most of the observed loss is due to input/output coupling [6

6. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]

]. A more recent experiment based on group index tapering has shown that the coupling loss can be significantly reduced throughout the spectrum of the defect-mode, including the slow light region near the band edge [20

20. C.-Y. Lin, X. Wang, S. Chakravarty, B. S. Lee, W.-C. Lai, and R. T. Chen, “Wideband group velocity independent coupling into slow light silicon photonic crystal waveguide,” Appl. Phys. Lett. 97(18), 183302 (2010). [CrossRef]

]. To summarize, with the best fabrication tools and best design, optical loss due to random hole position variation and input/output coupling can be very small, but the roughness induced loss [19

19. W. Song, R. A. Integlia, and W. Jiang, “Slow light loss due to roughness in photonic crystal waveguides: An analytic approach,” Phys. Rev. B 82(23), 235306 (2010). [CrossRef]

] (especially the backscattering loss, which scales roughly as ng2) will be a primary limiting factor. Hence the roughness-induced loss (including backscattering and out-of-plane scattering loss) is considered in Fig. 4 to explore the limit of Qπ in connection with ng. Considering all the factors discussed above, a practical lower limit of Qπ is estimated on the order of 0.5mW for a reasonable tox~5μm, L~10μm, and ng~110. Our calculation also shows that for ng~60, Qπ already enters the sub-milliwatt regime for the tox~5μm case.

It should be noted that this theory indicates that many factors are insignificant. For example, Qπ is insensitive to the choice of the heater width W as long as W<<2Xspr(~12μm). Also, Qπ varies only ~20% for the typical radius range of r/a = 0.25~0.35. Note that typical silicon photonic crystal waveguides used for the 1550nm communications window have a = 380nm to 440nm. As the lattice constant is much smaller than the scale of temperature variation (a<<Xspr), this approach works well for this range of a. For a given lattice structure, when a and r vary simultaneously while maintaining a fixed ratio of r/a, Xspr is essentially invariant. Note that the power Qπ given above is for switching and steadily holding a state. This is pertinent for most optical switching applications that require holding a switching state steadily over an extended period. The thermal time constant of an SOI structure is τ~tox2ρoxcox/κox (~μs for tox = 1~2μm), where ρox is the density and cox the specific heat capacity of SiO2. Our simulations confirm that τ is relatively insensitive to the details of a photonic crystal structure. Although the heating transient can be shortened [7

7. M. T. Tinker and J.-B. Lee, “Thermal and optical simulation of a photonic crystal light modulator based on the thermo-optic shift of the cut-off frequency,” Opt. Express 13(18), 7174–7188 (2005). [CrossRef] [PubMed]

,14

14. V. M. N. Passaro, F. Magno, and A. V. Tsarev, “Investigation of thermo-optic effect and multi-reflector tunable filter/multiplexer in SOI waveguides,” Opt. Express 13(9), 3429–3437 (2005). [CrossRef] [PubMed]

], the overall performance of a switch over an extended period is limited primarily by Qπ and τ given above. The effect of the temperature drop in the substrate is less than 10% for all cases we simulated. Note that κeff used in this work is obtained based on the structured “porosity” of materials within the framework of classical heat transfer theory, neglecting quantum mechanical effects such as phonon scattering in a periodic structure [21

21. C. M. Reinke, M. F. Su, B. L. Davis, B. Kim, M. I. Hussein, Z. C. Leseman, R. H. Olsson-III, and I. El-Kady, “Thermal conductivity prediction of nanoscale phononic crystal slabs using a hybrid lattice dynamics-continuum mechanics technique,” AIP Advances 1(4), 041403 (2011). [CrossRef]

]. When quantum effects are considered, most formulas in this work remain useful, except κeff values from quantum mechanical calculations will be used.

5. Summary

In conclusion, the thermo-optic characteristics of active photonic crystal structures on an SOI platform are investigated semi-analytically. The power consumption Qπ and spatial temperature profile are given as explicit functions of structural, thermal, and optical parameters. The results agree well with FEM simulations and also explain the low switching power in air-bridge structures. The scaling of Qπ with key physical parameters is analyzed. The practical limit of Qπ is estimated on the sub-milliwatt level considering all key factors.

Acknowledgments

We are grateful to Dr. S. R. McAfee for helpful discussions. This work is supported in part by AFOSR MURI Grant No. FA9550-08-1-0394 (G. Pomrenke) and a Rutgers ECE Graduate Fellowship (for M.C.).

References and links

1.

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006). [CrossRef]

2.

B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006). [CrossRef]

3.

G. K. Celler and S. Cristoloveanu, “Frontiers of silicon-on-insulator,” J. Appl. Phys. 93(9), 4955–4978 (2003). [CrossRef]

4.

M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004). [CrossRef] [PubMed]

5.

E. A. Camargo, H. M. H. Chong, and R. M. De La Rue, “2D Photonic crystal thermo-optic switch based on AlGaAs/GaAs epitaxial structure,” Opt. Express 12(4), 588–592 (2004). [CrossRef] [PubMed]

6.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005). [CrossRef] [PubMed]

7.

M. T. Tinker and J.-B. Lee, “Thermal and optical simulation of a photonic crystal light modulator based on the thermo-optic shift of the cut-off frequency,” Opt. Express 13(18), 7174–7188 (2005). [CrossRef] [PubMed]

8.

L. Gu, W. Jiang, X. Chen, and R. T. Chen, “Thermooptically tuned photonic crystal waveguide silicon-on-insulator Mach-Zehnder interferometers,” IEEE Photon. Technol. Lett. 19(5), 342–344 (2007). [CrossRef]

9.

D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Ultracompact and low-power optical switch based on silicon photonic crystals,” Opt. Lett. 33(2), 147–149 (2008). [CrossRef] [PubMed]

10.

Y. Cui, K. Liu, D. L. MacFarlane, and J.-B. Lee, “Thermo-optically tunable silicon photonic crystal light modulator,” Opt. Lett. 35(21), 3613–3615 (2010). [CrossRef] [PubMed]

11.

L. Gu, W. Jiang, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007). [CrossRef]

12.

L. Gu, W. Jiang, X. Chen, and R. T. Chen, “Physical mechanism of p-i-n diode based photonic crystal silicon electrooptic modulators for gigahertz operation,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1132–1139 (2008). [CrossRef]

13.

J. Pan, Y. Huo, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. H. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett. 92(10), 103114 (2008). [CrossRef]

14.

V. M. N. Passaro, F. Magno, and A. V. Tsarev, “Investigation of thermo-optic effect and multi-reflector tunable filter/multiplexer in SOI waveguides,” Opt. Express 13(9), 3429–3437 (2005). [CrossRef] [PubMed]

15.

L. T. Su, J. E. Chung, D. A. Antoniadis, K. E. Goodson, and M. I. Flik, “Measurement and modeling of self-heating in SOI nMOSFETS,” IEEE Trans. Electron. Dev. 41(1), 69–75 (1994). [CrossRef]

16.

Y. Jaluria, Natural Convection Heat and Mass Transfer (Pergamon Press, Oxford, UK, 1980).

17.

M. Iodice, G. Mazzi, and L. Sirleto, “Thermo-optical static and dynamic analysis of a digital optical switch based on amorphous silicon waveguide,” Opt. Express 14(12), 5266–5278 (2006). [CrossRef] [PubMed]

18.

E. Dulkeith, S. J. McNab, and Y. A. Vlasov, “Mapping the optical properties of slab-type two-dimensional photonic crystal waveguides,” Phys. Rev. B 72(11), 115102 (2005). [CrossRef]

19.

W. Song, R. A. Integlia, and W. Jiang, “Slow light loss due to roughness in photonic crystal waveguides: An analytic approach,” Phys. Rev. B 82(23), 235306 (2010). [CrossRef]

20.

C.-Y. Lin, X. Wang, S. Chakravarty, B. S. Lee, W.-C. Lai, and R. T. Chen, “Wideband group velocity independent coupling into slow light silicon photonic crystal waveguide,” Appl. Phys. Lett. 97(18), 183302 (2010). [CrossRef]

21.

C. M. Reinke, M. F. Su, B. L. Davis, B. Kim, M. I. Hussein, Z. C. Leseman, R. H. Olsson-III, and I. El-Kady, “Thermal conductivity prediction of nanoscale phononic crystal slabs using a hybrid lattice dynamics-continuum mechanics technique,” AIP Advances 1(4), 041403 (2011). [CrossRef]

OCIS Codes
(130.4815) Integrated optics : Optical switching devices
(130.5296) Integrated optics : Photonic crystal waveguides
(230.5298) Optical devices : Photonic crystals
(130.4110) Integrated optics : Modulators

ToC Category:
Photonic Crystals

History
Original Manuscript: December 15, 2011
Revised Manuscript: January 26, 2012
Manuscript Accepted: January 27, 2012
Published: February 6, 2012

Citation
Manjit Chahal, George K. Celler, Yogesh Jaluria, and Wei Jiang, "Thermo-optic characteristics and switching power limit of slow-light photonic crystal structures on a silicon-on-insulator platform," Opt. Express 20, 4225-4231 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-4225


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