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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 17 — Aug. 26, 2013
  • pp: 20041–20051
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Design and analysis of ultra-compact EO polymer modulators based on hybrid plasmonic microring resonators

Fei Lou, Daoxin Dai, Lars Thylen, and Lech Wosinski  »View Author Affiliations


Optics Express, Vol. 21, Issue 17, pp. 20041-20051 (2013)
http://dx.doi.org/10.1364/OE.21.020041


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Abstract

Ultra-compact EO polymer modulators based on hybrid plasmonic microring resonators are proposed, simulated and analyzed. Comparing with Si slot microring modulator, hybrid plasmonic microring modulator shows about 6-times enhancement of the figure of merit when the bending radius is around 510 nm, due to its much larger intrinsic quality factor in sub-micron radius range. Influences of the EO polymer height and Si height on the device’s performance are analyzed and optimal design is given. When operating with a bias of 3.6V, the proposed device has optical modulation amplitude of 0.8 and insertion loss of about 1 dB. The estimated power consumption is about 5 fJ/bit at100 GHz.

© 2013 Optical Society of America

1. Introduction

Optical interconnects are envisaged as a promising way to break through the physical limits of electronic circuits in microprocessors, and enable the future continuation of Moore’s law. Significant challenges emerge in the efforts to seamlessly integrate electronic and photonic circuits on a single silicon platform, since photonic components generally have larger footprint than their electronic counterparts. Plasmonics, by localizing energy around the metal-dielectric interfaces, can enable light confinement beyond the diffraction limit and has the potential to bridge the size mismatch between optical and electrical components [1

1. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]

, 2

2. R. Zia, J. A. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006). [CrossRef]

]. In recent years, various kinds of plasmonic waveguides with high confinement were investigated including v-groove waveguide [3

3. D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30(10), 1186–1188 (2005). [CrossRef] [PubMed]

], periodic metal chain waveguide [4

4. P. Holmström, L. Thylén, and A. Bratkovsky, “Composite metal/quantum-dot nanoparticle-array waveguides with compensated loss,” Appl. Phys. Lett. 97(7), 073110 (2010). [CrossRef]

], metal-insulator-metal waveguide [5

5. L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13(17), 6645–6650 (2005). [CrossRef] [PubMed]

], but in all cases the propagation length is limited to the order of few micrometers due to inherent energy dissipation in metals. The recently proposed hybrid plasmonic waveguide is a novel option to realize light confinement in nano scale as well as relatively long propagation distance [6

6. M. Z. Alam, J. Meier, J. S. Aitchison, and M. Mojahedi, “Super mode propagation in low index medium,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JThD112.

9

9. Z. Wang, D. Dai, Y. Shi, G. Somesfalean, P. Holmstrom, L. Thylen, S. He, and L. Wosinski, “Experimental Realization of a Low-loss Nano-scale Si Hybrid Plasmonic Waveguide,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JThA017. [CrossRef]

]. Functional elements to compose photonic integrated circuits have been theoretically proposed and experimentally demonstrated based on hybrid plasmonic waveguides, such as lasers [10

10. R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009). [CrossRef] [PubMed]

12

12. D. Costantini, L. Greusard, A. Bousseksou, Y. De Wilde, B. Habert, F. Marquier, J.-J. Greffet, F. Lelarge, J. Decobert, G.-H. Duan, and R. Colombelli, “A hybrid plasmonic semiconductor laser,” Appl. Phys. Lett. 102(10), 101106 (2013). [CrossRef]

], couplers [13

13. F. Lou, Z. Wang, D. Dai, L. Thylen, and L. Wosinski, “Experimental demonstration of ultra-compact directional couplers based on silicon hybrid plasmonic waveguides,” Appl. Phys. Lett. 100(24), 241105 (2012). [CrossRef]

15

15. Q. Li, Y. Song, G. Zhou, Y. Su, and M. Qiu, “Asymmetric plasmonic-dielectric coupler with short coupling length, high extinction ratio, and low insertion loss,” Opt. Lett. 35(19), 3153–3155 (2010). [CrossRef] [PubMed]

], polarization beam splitters [16

16. F. Lou, D. Dai, and L. Wosinski, “Ultracompact polarization beam splitter based on a dielectric-hybrid plasmonic-dielectric coupler,” Opt. Lett. 37(16), 3372–3374 (2012). [CrossRef] [PubMed]

18

18. M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “Compact and silicon-on-insulator-compatible hybrid plasmonic TE-pass polarizer,” Opt. Lett. 37(1), 55–57 (2012). [CrossRef] [PubMed]

], etc. Using free-carrier dispersion effect in silicon, hybrid plasmonic metal-oxide-semiconductor (MOS) type modulators were also developed [19

19. J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9(2), 897–902 (2009). [CrossRef] [PubMed]

, 20

20. S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Theoretical investigation of silicon MOS-type plasmonic slot waveguide based MZI modulators,” Opt. Express 18(26), 27802–27819 (2010). [CrossRef] [PubMed]

]. However, the relatively weak free-carrier dispersion effect of silicon limits the overall modulation performance and requires demanding power consumption. On the other hand, recent endeavors show great promises of EO polymers as an alternative to Si as an active modulating material. State-of-the art polymers exhibit an electro-optic coefficient r33 approaching 500 pm/V while keeping negligible optical losses [21

21. L. R. Dalton, B. Robinson, A. Jen, P. Ried, B. Eichinger, P. Sullivan, A. Akelaitis, D. Bale, M. Haller, J. Luo, S. Liu, Y. Liao, K. Firestone, N. Bhatambrekar, S. Bhattacharjee, J. Sinness, S. Hammond, N. Buker, R. Snoeberger, M. Lingwood, H. Rommel, J. Amend, S.-H. Jang, A. Chen, and W. Steier, “Electro-optic coefficients of 500 pm/V and beyond for organic materials,” Proc. SPIE 5935, 593502 (2005). [CrossRef]

, 22

22. S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010). [CrossRef]

]; highly reliable and stable EO polymer modulators with a speed larger than 100 Gb/s have been commercially available already [23

23. R. Dinu, D. Jin, G. Yu, B. Chen, D. Huang, H. Chen, A. Barklund, E. Miller, C. Wei, and J. Vemagiri, “Environmental stress testing of electro-optic polymer modulators,” J. Lightwave Technol. 27(11), 1527–1532 (2009). [CrossRef]

, 24

24. D. Jin, H. Chen, A. Barklund, J. Mallari, G. Yu, E. Miller, and R. Dinu, “EO polymer modulators reliability study,” Proc. SPIE 7599, 75990H (2010). [CrossRef]

]. To merge the advantages of EO polymers with nano scale plasmonics, plasmonic modulators based on EO polymers have been proposed [25

25. W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9(12), 4403–4411 (2009). [CrossRef] [PubMed]

28

28. Z. Wu, R. L. Nelson, J. W. Haus, and Q. Zhan, “Plasmonic electro-optic modulator design using a resonant metal grating,” Opt. Lett. 33(6), 551–553 (2008). [CrossRef] [PubMed]

]. Unfortunately, these devices have issues of either high insertion loss [25

25. W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9(12), 4403–4411 (2009). [CrossRef] [PubMed]

], or large footprint [26

26. M. Xu, F. Li, T. Wang, J. Wu, L. Lu, L. Zhou, and Y. Su, “Design of an Electro-Optic Modulator Based on a Silicon-Plasmonic Hybrid Phase Shifter,” J. Lightwave Technol. 31(8), 1170–1177 (2013). [CrossRef]

, 27

27. X. Sun, L. Zhou, X. Li, Z. Hong, and J. Chen, “Design and analysis of a phase modulator based on a metal-polymer-silicon hybrid plasmonic waveguide,” Appl. Opt. 50(20), 3428–3434 (2011). [CrossRef] [PubMed]

], or CMOS incompatibility [28

28. Z. Wu, R. L. Nelson, J. W. Haus, and Q. Zhan, “Plasmonic electro-optic modulator design using a resonant metal grating,” Opt. Lett. 33(6), 551–553 (2008). [CrossRef] [PubMed]

].

The remainder of the paper is organized as follows. Section 2 investigates the figure of merit (FOM) of a HP microring modulator with sub-micron radius and compares its performance with a Si slot microring modulator. Section 3 analyzes the dependence of the modulator’s properties on device parameters and provides useful guidelines to reach optimal design. Section 4 discusses the device’s insertion loss, modulation speed, power consumption, fabrication process and other issues. Conclusions are made in Section 5.

2. Hybrid plasmonic microring modulators with sub-micron radius

Figure 1(a)
Fig. 1 (a) Schematic diagram of the proposed hybrid plasmonic microring modulator. Cross-sectional view along the (b) xy and (c) xz planes of the Ez field distributions of a resonant mode at 1550 nm, with an azimuthal number of 6. The bending radius is R = 542 nm.
shows the schematic diagram of the proposed hybrid plasmonic microring modulator consisting of an EO polymer (EOP) ring with a radius of R and a width of W sandwiched between a silver ring and a silicon ring with the same radii and widths. The heights of EOP, Ag and Si layers are HEOP, HAg and HSi, respectively. Microwave field is applied between Ag cap and the bottom Si layer, and the refractive index of EOP can be changed through ultra-fast EO effects; correspondingly, the cavity can be switched between on- and off- resonance mode at a given frequency, resulting in the modulation of transmission power if an access waveguide is placed aside. For simplicity, the silicon thin strip used to electrically connect Si core with the other metal electrode [33

33. J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010). [CrossRef] [PubMed]

35

35. L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon technology,” Opt. Express 19(12), 11841–11851 (2011). [CrossRef] [PubMed]

] (not shown in Fig. 1(a)) is not considered in this study. Sufficient conductivity of Si can be achieved by Arsenic doping while introducing negligible losses [36

36. C. Koos, J. Brosi, M. Waldow, W. Freude, and J. Leuthold, “Silicon-on-insulator modulators for next-generation 100 Gbit/s-Ethernet,” Proc. European Conf. on Optical Communication (ECOC), Paper P056 (2007). [CrossRef]

]. Note that the losses introduced by a moderate doping level of 1017 to 1018 cm−3 are typically on an order of 1/cm [37

37. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]

], while the metal absorption losses are on an order of 102/cm [9

9. Z. Wang, D. Dai, Y. Shi, G. Somesfalean, P. Holmstrom, L. Thylen, S. He, and L. Wosinski, “Experimental Realization of a Low-loss Nano-scale Si Hybrid Plasmonic Waveguide,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JThA017. [CrossRef]

,13

13. F. Lou, Z. Wang, D. Dai, L. Thylen, and L. Wosinski, “Experimental demonstration of ultra-compact directional couplers based on silicon hybrid plasmonic waveguides,” Appl. Phys. Lett. 100(24), 241105 (2012). [CrossRef]

] in hybrid plasmonic waveguides. A key merit for a ring-based modulator is the driving voltage required to shift the cavity resonance by the 3dB bandwidth distance (V3dB) [38

38. J. Takayesu, M. Hochberg, T. Baehr-Jones, E. Chan, G. Wang, P. Sullivan, Y. Liao, J. Davies, L. Dalton, A. Scherer, and W. Krug, “A Hybrid Electrooptic Microring Resonator-Based 1×4×1 ROADM for Wafer Scale Optical Interconnects,” J. Lightwave Technol. 27(4), 440–448 (2009). [CrossRef]

]. The proposed EOP microring modulator has several important characteristics. The Q-factor of the cavity represents the 3dB bandwidth of the resonance and is given by Q = λ0/Δλ3dB where λ0 is 1550 nm. The tuning efficiency is denoted by Γ=ΔλRes/ΔnEOP, describing the resonance shift per unit change of EOP’s index. To characterize the effective modulation by switching the cavity in and out of resonance by changing the EOP index, figure of merit (FOM) can be defined as
FOM=Qλ0Γ=ΔλResΔλ3dB1ΔnEOP,
(1)
which describes the effective resonance tuning per unit change of nEOP. One can readily see that V3dB is inversely proportional to FOM. A higher FOM enables a lower driving voltage as well as power consumption. In the following investigations, a three-dimensional (3D) finite- difference-time-domain method (FDTD) is used for numerical simulations. The mesh sizes employed in 3D-FDTD simulations are 5 nm in xyz directions. HAg is fixed at 100 nm, which is thick enough to prevent the electric field from penetrating through the metal. A moderate width of 300 nm is chosen as the waveguide width, which on one hand can ensure single-mode operation as well as low device capacitance, and on the other is wide enough so that the inner surface of the ring hardly influences on the bending-waveguide’s mode in the sub-micron-radius range [39

39. D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, “Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides,” Opt. Express 19(24), 23671–23682 (2011). [CrossRef] [PubMed]

]. By analyzing the temporal decay of the cavity’s field, the resonant frequency and the corresponding Q-factor can be deduced. Figures 1(b) and 1(c) show the Ez field distributions of a resonant mode with a wavelength of 1550 nm and an azimuthal number of 6 along the xy and xz cross-sectional plane. Here, the microring radius is 542 nm and HEOP and HSi are 30 nm and 400 nm, respectively. One can see that in such hybrid plasmonic waveguides, light is highly localized in the low-index EOP layer between the metal cap and the high-index Si, which is similar to the confinement in a Si slot waveguide [33

33. J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010). [CrossRef] [PubMed]

36

36. C. Koos, J. Brosi, M. Waldow, W. Freude, and J. Leuthold, “Silicon-on-insulator modulators for next-generation 100 Gbit/s-Ethernet,” Proc. European Conf. on Optical Communication (ECOC), Paper P056 (2007). [CrossRef]

, 40

40. R. Sun, P. Dong, N. N. Feng, C. Y. Hong, J. Michel, M. Lipson, and L. Kimerling, “Horizontal single and multiple slot waveguides: optical transmission at λ = 1550 nm,” Opt. Express 15(26), 17967–17972 (2007). [CrossRef] [PubMed]

]. The refractive indices of Si, SiO2 and EOP are 3.455, 1.46 and 1.65 in this study, and silver is modeled by the Drude model as εAg(ω)p2/(ω2+jγω)which is fitted by the experimental data by Johnson and Christy [41

41. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

].

The intrinsic quality factors of HP microrings and Si slot microrings as functions of bending radii are shown in Fig. 2
Fig. 2 Quality factors of Si slot microrings and HP microrings as functions of bending radius. QSlot and QHP are shown by the left Y axis and the ratio between QHP and QSlot is shown by the right Y axis.
. The radii are carefully chosen to enable a resonant wavelength at 1550 ± 10 nm. The Si horizontal slot waveguide which also supports a TM-polarized mode is used for a fair comparison. It has the same width as 300 nm and is composed by introducing a 30 nm EOP slot in the middle of a 400 nm high Si waveguide. As one can see from Fig. 2, the quality factor of the HP microring QHP is much higher than that of the Si slot microring QSlot when the radius is in sub-micron region, and the ratio between QHP and QSlot can be as large as 8.5 when the bending radius is around 510 nm. The enhancement of Q-factor evaluated by QHP/QSlotis attributed to the advantage of hybrid plasmonic waveguide which has a more compact mode confinement than dielectric waveguides [6

6. M. Z. Alam, J. Meier, J. S. Aitchison, and M. Mojahedi, “Super mode propagation in low index medium,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JThD112.

8

8. D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17(19), 16646–16653 (2009). [CrossRef] [PubMed]

], and the radiation loss of an ultra-sharp plasmonic bend can be much smaller as a result [29

29. F. Lou, L. Thylen, and L. Wosinski, “Hybrid plasmonic microdisk resonators for optical interconnect applications,” Proc. SPIE 8781, 87810X (2013). [CrossRef]

,39

39. D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, “Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides,” Opt. Express 19(24), 23671–23682 (2011). [CrossRef] [PubMed]

]. The quality factor of the hybrid plasmonic cavity asymptotically approaches the value of about 1760 when the radius increases further. The reason is that when radius is large enough, Qrad which is determined by the radiation loss of sharp bends is much larger than Qabs which originates from the absorption loss due to the energy dissipation in metals; considering that the intrinsic quality factor is governed by 1/QHP=1/Qrad+1/Qabs [42

42. S.-H. Kwon, “Deep subwavelength plasmonic whispering-gallery-mode cavity,” Opt. Express 20(22), 24918–24924 (2012). [CrossRef] [PubMed]

], QHPapproximately equalsQabswhich is only dependent on the waveguide geometry as a result.

Next, resonance shifts ΔλRes of the HP microring and Si slot microring with the change of EOP’s index ΔnEOP are studied. For HP cavity with radius of 542 nm and Si slot cavity with radius of 583 nm, ΔλRes as functions of ΔnEOP are shown in Fig. 3(a)
Fig. 3 (a) Tuning efficiencies of Si Slot microring and HP microring. (b) Enhancement of FOM by HP microring as a function of bending radius.
. By calculating the slopes of the linear curves, tuning efficiencies of two cavities can be determined as ΓSlot182nmandΓHP134nm, respectively. Note that the radii are chosen so that the cavity resonances are at 1550 nm when ΔnEOP = 0 for fair comparison. It’s worth mentioning that tuning efficiencies of both cavities are almost independent on the radius variations; more simulation results indicate that Γ changes less than 4% in the studied radius range. This can be explained by looking into the definition of tuning efficiency as Γ=ΔλResΔnEOP=λ0neffΔneffΔnEOP, where neff is the effective index of the bending-waveguide, and ΔneffΔnEOP describes the effective index change per unit change of EOP index which is linearly proportional to the overlap integral of optical field with the EOP slot expressed as [33

33. J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010). [CrossRef] [PubMed]

]
Ov=EOPSlotn|E|2dxdydzZ0Re(E×H)dxdydz,
(2)
where Z0 is the impedance of free space. When decreasing the bending radius, since peak of the field density of the fundamental mode would shift more towards the outer perimeter of the ring, unit change of EOP index would result in smaller change of effective index based on Eq. (2); on the other hand, neff would also decrease due to larger amount of radiation field [39

39. D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, “Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides,” Opt. Express 19(24), 23671–23682 (2011). [CrossRef] [PubMed]

]. Hence, influences of radius variations on Ov and neff counteract and Γ as the ratio between these two factors is insensitive to radius variations. Using Eq. (1), FOM of HP microring and Si slot microring can be calculated, and the enhancement of FOM by HP microring is shown in Fig. 3(b). One can see that FOM can be significantly enhanced by HP microring due to its much larger quality factor. The maximum FOM enhancement is about 6 when R is around 510 nm.

3. Optimal design of a hybrid plasmonic microring modulator

In this section, the influences of parameters including EOP slot height HEOP and silicon height HSi on the performance of the HP microring modulator will be investigated. In the first study, HEOP varies from 20 nm to 100 nm at a step of 10 nm, and HSi is fixed at either 400 nm or 300 nm. Note that such value is close to the optimal HSi which can neither be too large for single mode operation and decent tuning efficiency nor too small for proper waveguide performance, as will be discussed later in this section. The bending radii of the cavities are chosen around 550 nm. In this sub-micron radius range, the enhancement of FOM by hybrid plasmonic microring is maximal as discussed in Section 2. The selected radii can enable a resonance at 1550 nm and the azimuthal order M is 6 for all the cases. Figure 4(a)
Fig. 4 (a) Quality factors and tuning efficiencies of HP microrings as functions of EOP slot height; the silicon height is either 400 nm or 300 nm. (b) Figure of merits of HP microrings as functions of EOP slot height.
shows the quality factors and tuning efficiencies of the HP microring as functions of EOP slot height. One can see that when the EOP height increases from 20 nm to 100 nm, Q of microring with HSi = 300 nm increases at first, then drops and approaches a lower limit; while Q for HSi = 400 nm increases continuously to an upper limit. The above-mentioned limits in fact equal to the quality factors of HP microrings with infinite EOP height which can be regarded as pure-dielectric microrings. Different tendencies of the curves result from combined effects of radiation loss and absorption loss. Looking into the tuning efficiencies as shown in Fig. 4(a), however, one can see that Γ decreases significantly when increasing the EOP slot height for both cases. This is because when the slot height increases, although the slot area is larger, the enhancement of electrical field in the slot region decreases dramatically. The overall integral of electrical field with the slot area decreases, which can be calculated by Eq. (2), and the tuning efficiencies drop correspondingly. Figure of merits as defined in Eq. (1) are also evaluated, as shown in Fig. 4(b). One can see that there is an optimal EOP slot height for both Si heights when the FOM can be maximized. The optimal EOP height is a tradeoff between large quality factor and high tuning efficiency. For both silicon heights of 400 nm and 300 nm, the optimal EOP slot heights are around 30 nm. The results also show the degree of FOM’s deterioration due to the variation of EOP slot thickness. One can see from Fig. 4(b) that for both cases, when HEOP doubles from 30 nm to 60 nm, FOM drops by less than 20%.

4. Discussion

The proposed hybrid plasmonic modulators can be realized following a similar process as in Ref [9

9. Z. Wang, D. Dai, Y. Shi, G. Somesfalean, P. Holmstrom, L. Thylen, S. He, and L. Wosinski, “Experimental Realization of a Low-loss Nano-scale Si Hybrid Plasmonic Waveguide,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JThA017. [CrossRef]

]. with several modifications and additional steps [34

34. M. Gould, T. Baehr-Jones, R. Ding, S. Huang, J. Luo, A. K.-Y. Jen, J. M. Fedeli, M. Fournier, and M. Hochberg, “Silicon-polymer hybrid slot waveguide ring-resonator modulator,” Opt. Express 19(5), 3952–3961 (2011). [CrossRef] [PubMed]

, 35

35. L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon technology,” Opt. Express 19(12), 11841–11851 (2011). [CrossRef] [PubMed]

, 38

38. J. Takayesu, M. Hochberg, T. Baehr-Jones, E. Chan, G. Wang, P. Sullivan, Y. Liao, J. Davies, L. Dalton, A. Scherer, and W. Krug, “A Hybrid Electrooptic Microring Resonator-Based 1×4×1 ROADM for Wafer Scale Optical Interconnects,” J. Lightwave Technol. 27(4), 440–448 (2009). [CrossRef]

]. Firstly, microring and waveguide geometries are patterned on a SOI wafer by lithography and etching. Then, shallow-etched grating couplers for in and out coupling are patterned similarly. Subsequently, the sample is doped by ion implantation, followed by the definition of bottom contact through a metal evaporation and liftoff process. After that, the EO polymers are spin-coated as the slot layer of hybrid plasmonic waveguide. Note that the thickness of the slot layer can be controlled by using different spin-coating recipes [9

9. Z. Wang, D. Dai, Y. Shi, G. Somesfalean, P. Holmstrom, L. Thylen, S. He, and L. Wosinski, “Experimental Realization of a Low-loss Nano-scale Si Hybrid Plasmonic Waveguide,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JThA017. [CrossRef]

], aided by etching-back processes. After that, another liftoff process is done to deposit the noble metal which serves as part of the hybrid plasmonic waveguide as well as top contact. A thin layer of insulator with low-conductivity may be deposited before coating the noble metal to decrease the leakage current [22

22. S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010). [CrossRef]

]. Note that before device operation, the polymer should be effectively poled by applying high electric field through the defined contacts.

The deterioration of the device’s performance due to the fabrication errors can also be evaluated from the study in Section 3. As one can see from Fig. 4(b), when EOP thickness increases from the optimal 30 nm to 100 nm, FOM drops to about 57% of the maximal value. In practical fabrications, such larger slots can be employed to pursue a higher poling efficiency as well as in-slot r33. On the other hand, when Silicon height of the HP waveguide varies 100 nm from the optimal design, FOM decreases by about 15% only, as shown in Fig. 5(c). Other characteristics as insertion loss and extinction ratio of the proposed device would not deteriorate much given that the microring operates still around critical coupling condition.

5. Conclusions

Ultra-compact hybrid plasmonic microring modulators based on E-O polymers are proposed and analyzed. Comparisons have been made with traditional Si slot microring modulator when the bending radius is at sub-micron scale. Enhancement of figure of merit by hybrid plasmonic microring can be as large as 6 when radius is around 510 nm, due to the increased intrinsic quality factor. Optimal EO polymer height and Si height are investigated, and the design guidelines are given. A modulation voltage of 3.6 V can shift the cavity resonance by 3dB bandwidth. The corresponding optical modulation amplitude and insertion loss are 0.8 and 0.97 dB, respectively. The power consumption is about 5 fJ/bit at a modulation frequency of 100 GHz. The proposed device can find potential use in high-speed, small footprint, low-power-consumption modulation applications.

Acknowledgment

The work described in this paper was partly supported by the Swedish Research Council (VR) through its Linnæus Center of Excellence ADOPT and proj. VR-621-2010-4379. Constructive discussion with Dr. Petter Holmström is also acknowledged.

References and links

1.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]

2.

R. Zia, J. A. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006). [CrossRef]

3.

D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30(10), 1186–1188 (2005). [CrossRef] [PubMed]

4.

P. Holmström, L. Thylén, and A. Bratkovsky, “Composite metal/quantum-dot nanoparticle-array waveguides with compensated loss,” Appl. Phys. Lett. 97(7), 073110 (2010). [CrossRef]

5.

L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13(17), 6645–6650 (2005). [CrossRef] [PubMed]

6.

M. Z. Alam, J. Meier, J. S. Aitchison, and M. Mojahedi, “Super mode propagation in low index medium,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JThD112.

7.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008). [CrossRef]

8.

D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17(19), 16646–16653 (2009). [CrossRef] [PubMed]

9.

Z. Wang, D. Dai, Y. Shi, G. Somesfalean, P. Holmstrom, L. Thylen, S. He, and L. Wosinski, “Experimental Realization of a Low-loss Nano-scale Si Hybrid Plasmonic Waveguide,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JThA017. [CrossRef]

10.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009). [CrossRef] [PubMed]

11.

K. Ding, M. T. Hill, Z. C. Liu, L. J. Yin, P. J. van Veldhoven, and C. Z. Ning, “Record performance of electrical injection sub-wavelength metallic-cavity semiconductor lasers at room temperature,” Opt. Express 21(4), 4728–4733 (2013). [CrossRef] [PubMed]

12.

D. Costantini, L. Greusard, A. Bousseksou, Y. De Wilde, B. Habert, F. Marquier, J.-J. Greffet, F. Lelarge, J. Decobert, G.-H. Duan, and R. Colombelli, “A hybrid plasmonic semiconductor laser,” Appl. Phys. Lett. 102(10), 101106 (2013). [CrossRef]

13.

F. Lou, Z. Wang, D. Dai, L. Thylen, and L. Wosinski, “Experimental demonstration of ultra-compact directional couplers based on silicon hybrid plasmonic waveguides,” Appl. Phys. Lett. 100(24), 241105 (2012). [CrossRef]

14.

Y. Song, J. Wang, Q. Li, M. Yan, and M. Qiu, “Broadband coupler between silicon waveguide and hybrid plasmonic waveguide,” Opt. Express 18(12), 13173–13179 (2010). [CrossRef] [PubMed]

15.

Q. Li, Y. Song, G. Zhou, Y. Su, and M. Qiu, “Asymmetric plasmonic-dielectric coupler with short coupling length, high extinction ratio, and low insertion loss,” Opt. Lett. 35(19), 3153–3155 (2010). [CrossRef] [PubMed]

16.

F. Lou, D. Dai, and L. Wosinski, “Ultracompact polarization beam splitter based on a dielectric-hybrid plasmonic-dielectric coupler,” Opt. Lett. 37(16), 3372–3374 (2012). [CrossRef] [PubMed]

17.

J. Chee, S. Zhu, and G. Q. Lo, “CMOS compatible polarization splitter using hybrid plasmonic waveguide,” Opt. Express 20(23), 25345–25355 (2012). [CrossRef] [PubMed]

18.

M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “Compact and silicon-on-insulator-compatible hybrid plasmonic TE-pass polarizer,” Opt. Lett. 37(1), 55–57 (2012). [CrossRef] [PubMed]

19.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9(2), 897–902 (2009). [CrossRef] [PubMed]

20.

S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Theoretical investigation of silicon MOS-type plasmonic slot waveguide based MZI modulators,” Opt. Express 18(26), 27802–27819 (2010). [CrossRef] [PubMed]

21.

L. R. Dalton, B. Robinson, A. Jen, P. Ried, B. Eichinger, P. Sullivan, A. Akelaitis, D. Bale, M. Haller, J. Luo, S. Liu, Y. Liao, K. Firestone, N. Bhatambrekar, S. Bhattacharjee, J. Sinness, S. Hammond, N. Buker, R. Snoeberger, M. Lingwood, H. Rommel, J. Amend, S.-H. Jang, A. Chen, and W. Steier, “Electro-optic coefficients of 500 pm/V and beyond for organic materials,” Proc. SPIE 5935, 593502 (2005). [CrossRef]

22.

S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett. 96(24), 243311 (2010). [CrossRef]

23.

R. Dinu, D. Jin, G. Yu, B. Chen, D. Huang, H. Chen, A. Barklund, E. Miller, C. Wei, and J. Vemagiri, “Environmental stress testing of electro-optic polymer modulators,” J. Lightwave Technol. 27(11), 1527–1532 (2009). [CrossRef]

24.

D. Jin, H. Chen, A. Barklund, J. Mallari, G. Yu, E. Miller, and R. Dinu, “EO polymer modulators reliability study,” Proc. SPIE 7599, 75990H (2010). [CrossRef]

25.

W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9(12), 4403–4411 (2009). [CrossRef] [PubMed]

26.

M. Xu, F. Li, T. Wang, J. Wu, L. Lu, L. Zhou, and Y. Su, “Design of an Electro-Optic Modulator Based on a Silicon-Plasmonic Hybrid Phase Shifter,” J. Lightwave Technol. 31(8), 1170–1177 (2013). [CrossRef]

27.

X. Sun, L. Zhou, X. Li, Z. Hong, and J. Chen, “Design and analysis of a phase modulator based on a metal-polymer-silicon hybrid plasmonic waveguide,” Appl. Opt. 50(20), 3428–3434 (2011). [CrossRef] [PubMed]

28.

Z. Wu, R. L. Nelson, J. W. Haus, and Q. Zhan, “Plasmonic electro-optic modulator design using a resonant metal grating,” Opt. Lett. 33(6), 551–553 (2008). [CrossRef] [PubMed]

29.

F. Lou, L. Thylen, and L. Wosinski, “Hybrid plasmonic microdisk resonators for optical interconnect applications,” Proc. SPIE 8781, 87810X (2013). [CrossRef]

30.

X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express 20(3), 2507–2515 (2012). [CrossRef] [PubMed]

31.

H. M. G. Wassel, D. Dai, M. Tiwari, J. K. Valamehr, L. Theogarajan, J. Dionne, F. T. Chong, and T. Sherwood, “Opportunities and Challenges of Using Plasmonic Components in Nanophotonic Architectures,” IEEE J. Emer. Sel. Top. Circuits Systems 2(2), 154–168 (2012). [CrossRef]

32.

K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Dynamic Stabilization of a Microring Modulator Under Thermal Perturbation,” Proc. Optical Fiber Communication Conference (Optical Society of America, 2012), paper OW4F.2. [CrossRef]

33.

J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010). [CrossRef] [PubMed]

34.

M. Gould, T. Baehr-Jones, R. Ding, S. Huang, J. Luo, A. K.-Y. Jen, J. M. Fedeli, M. Fournier, and M. Hochberg, “Silicon-polymer hybrid slot waveguide ring-resonator modulator,” Opt. Express 19(5), 3952–3961 (2011). [CrossRef] [PubMed]

35.

L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon technology,” Opt. Express 19(12), 11841–11851 (2011). [CrossRef] [PubMed]

36.

C. Koos, J. Brosi, M. Waldow, W. Freude, and J. Leuthold, “Silicon-on-insulator modulators for next-generation 100 Gbit/s-Ethernet,” Proc. European Conf. on Optical Communication (ECOC), Paper P056 (2007). [CrossRef]

37.

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]

38.

J. Takayesu, M. Hochberg, T. Baehr-Jones, E. Chan, G. Wang, P. Sullivan, Y. Liao, J. Davies, L. Dalton, A. Scherer, and W. Krug, “A Hybrid Electrooptic Microring Resonator-Based 1×4×1 ROADM for Wafer Scale Optical Interconnects,” J. Lightwave Technol. 27(4), 440–448 (2009). [CrossRef]

39.

D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, “Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides,” Opt. Express 19(24), 23671–23682 (2011). [CrossRef] [PubMed]

40.

R. Sun, P. Dong, N. N. Feng, C. Y. Hong, J. Michel, M. Lipson, and L. Kimerling, “Horizontal single and multiple slot waveguides: optical transmission at λ = 1550 nm,” Opt. Express 15(26), 17967–17972 (2007). [CrossRef] [PubMed]

41.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

42.

S.-H. Kwon, “Deep subwavelength plasmonic whispering-gallery-mode cavity,” Opt. Express 20(22), 24918–24924 (2012). [CrossRef] [PubMed]

43.

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004). [CrossRef]

44.

X. Wang, C. Y. Lin, S. Chakravarty, J. Luo, A. K.-Y. Jen, and R. T. Chen, “Effective in-device r33 of 735 pm/V on electro-optic polymer infiltrated silicon photonic crystal slot waveguides,” Opt. Lett. 36(6), 882–884 (2011). [CrossRef] [PubMed]

45.

R. Ding, T. Baehr-Jones, W. Kim, A. Spott, M. Fournier, J. Fedeli, S. Huang, J. Luo, A. K.-Y. Jen, L. Dalton, and M. Hochberg, “Sub-Volt Silicon-Organic Electro-optic Modulator With 500 MHz Bandwidth,” J. Lightwave Technol. 29(8), 1112–1117 (2011). [CrossRef]

OCIS Codes
(250.2080) Optoelectronics : Polymer active devices
(250.5300) Optoelectronics : Photonic integrated circuits
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optoelectronics

History
Original Manuscript: May 31, 2013
Revised Manuscript: July 25, 2013
Manuscript Accepted: August 4, 2013
Published: August 19, 2013

Citation
Fei Lou, Daoxin Dai, Lars Thylen, and Lech Wosinski, "Design and analysis of ultra-compact EO polymer modulators based on hybrid plasmonic microring resonators," Opt. Express 21, 20041-20051 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-20041


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References

  1. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010). [CrossRef]
  2. R. Zia, J. A. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today9(7-8), 20–27 (2006). [CrossRef]
  3. D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett.30(10), 1186–1188 (2005). [CrossRef] [PubMed]
  4. P. Holmström, L. Thylén, and A. Bratkovsky, “Composite metal/quantum-dot nanoparticle-array waveguides with compensated loss,” Appl. Phys. Lett.97(7), 073110 (2010). [CrossRef]
  5. L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express13(17), 6645–6650 (2005). [CrossRef] [PubMed]
  6. M. Z. Alam, J. Meier, J. S. Aitchison, and M. Mojahedi, “Super mode propagation in low index medium,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JThD112.
  7. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008). [CrossRef]
  8. D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express17(19), 16646–16653 (2009). [CrossRef] [PubMed]
  9. Z. Wang, D. Dai, Y. Shi, G. Somesfalean, P. Holmstrom, L. Thylen, S. He, and L. Wosinski, “Experimental Realization of a Low-loss Nano-scale Si Hybrid Plasmonic Waveguide,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JThA017. [CrossRef]
  10. R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009). [CrossRef] [PubMed]
  11. K. Ding, M. T. Hill, Z. C. Liu, L. J. Yin, P. J. van Veldhoven, and C. Z. Ning, “Record performance of electrical injection sub-wavelength metallic-cavity semiconductor lasers at room temperature,” Opt. Express21(4), 4728–4733 (2013). [CrossRef] [PubMed]
  12. D. Costantini, L. Greusard, A. Bousseksou, Y. De Wilde, B. Habert, F. Marquier, J.-J. Greffet, F. Lelarge, J. Decobert, G.-H. Duan, and R. Colombelli, “A hybrid plasmonic semiconductor laser,” Appl. Phys. Lett.102(10), 101106 (2013). [CrossRef]
  13. F. Lou, Z. Wang, D. Dai, L. Thylen, and L. Wosinski, “Experimental demonstration of ultra-compact directional couplers based on silicon hybrid plasmonic waveguides,” Appl. Phys. Lett.100(24), 241105 (2012). [CrossRef]
  14. Y. Song, J. Wang, Q. Li, M. Yan, and M. Qiu, “Broadband coupler between silicon waveguide and hybrid plasmonic waveguide,” Opt. Express18(12), 13173–13179 (2010). [CrossRef] [PubMed]
  15. Q. Li, Y. Song, G. Zhou, Y. Su, and M. Qiu, “Asymmetric plasmonic-dielectric coupler with short coupling length, high extinction ratio, and low insertion loss,” Opt. Lett.35(19), 3153–3155 (2010). [CrossRef] [PubMed]
  16. F. Lou, D. Dai, and L. Wosinski, “Ultracompact polarization beam splitter based on a dielectric-hybrid plasmonic-dielectric coupler,” Opt. Lett.37(16), 3372–3374 (2012). [CrossRef] [PubMed]
  17. J. Chee, S. Zhu, and G. Q. Lo, “CMOS compatible polarization splitter using hybrid plasmonic waveguide,” Opt. Express20(23), 25345–25355 (2012). [CrossRef] [PubMed]
  18. M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “Compact and silicon-on-insulator-compatible hybrid plasmonic TE-pass polarizer,” Opt. Lett.37(1), 55–57 (2012). [CrossRef] [PubMed]
  19. J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett.9(2), 897–902 (2009). [CrossRef] [PubMed]
  20. S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Theoretical investigation of silicon MOS-type plasmonic slot waveguide based MZI modulators,” Opt. Express18(26), 27802–27819 (2010). [CrossRef] [PubMed]
  21. L. R. Dalton, B. Robinson, A. Jen, P. Ried, B. Eichinger, P. Sullivan, A. Akelaitis, D. Bale, M. Haller, J. Luo, S. Liu, Y. Liao, K. Firestone, N. Bhatambrekar, S. Bhattacharjee, J. Sinness, S. Hammond, N. Buker, R. Snoeberger, M. Lingwood, H. Rommel, J. Amend, S.-H. Jang, A. Chen, and W. Steier, “Electro-optic coefficients of 500 pm/V and beyond for organic materials,” Proc. SPIE5935, 593502 (2005). [CrossRef]
  22. S. Huang, T.-D. Kim, J. Luo, S. K. Hau, Z. Shi, X.-H. Zhou, H.-L. Yip, and A. K.-Y. Jen, “Highly efficient electro-optic polymers through improved poling using a thin TiO2-modified transparent electrode,” Appl. Phys. Lett.96(24), 243311 (2010). [CrossRef]
  23. R. Dinu, D. Jin, G. Yu, B. Chen, D. Huang, H. Chen, A. Barklund, E. Miller, C. Wei, and J. Vemagiri, “Environmental stress testing of electro-optic polymer modulators,” J. Lightwave Technol.27(11), 1527–1532 (2009). [CrossRef]
  24. D. Jin, H. Chen, A. Barklund, J. Mallari, G. Yu, E. Miller, and R. Dinu, “EO polymer modulators reliability study,” Proc. SPIE7599, 75990H (2010). [CrossRef]
  25. W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett.9(12), 4403–4411 (2009). [CrossRef] [PubMed]
  26. M. Xu, F. Li, T. Wang, J. Wu, L. Lu, L. Zhou, and Y. Su, “Design of an Electro-Optic Modulator Based on a Silicon-Plasmonic Hybrid Phase Shifter,” J. Lightwave Technol.31(8), 1170–1177 (2013). [CrossRef]
  27. X. Sun, L. Zhou, X. Li, Z. Hong, and J. Chen, “Design and analysis of a phase modulator based on a metal-polymer-silicon hybrid plasmonic waveguide,” Appl. Opt.50(20), 3428–3434 (2011). [CrossRef] [PubMed]
  28. Z. Wu, R. L. Nelson, J. W. Haus, and Q. Zhan, “Plasmonic electro-optic modulator design using a resonant metal grating,” Opt. Lett.33(6), 551–553 (2008). [CrossRef] [PubMed]
  29. F. Lou, L. Thylen, and L. Wosinski, “Hybrid plasmonic microdisk resonators for optical interconnect applications,” Proc. SPIE8781, 87810X (2013). [CrossRef]
  30. X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express20(3), 2507–2515 (2012). [CrossRef] [PubMed]
  31. H. M. G. Wassel, D. Dai, M. Tiwari, J. K. Valamehr, L. Theogarajan, J. Dionne, F. T. Chong, and T. Sherwood, “Opportunities and Challenges of Using Plasmonic Components in Nanophotonic Architectures,” IEEE J. Emer. Sel. Top. Circuits Systems2(2), 154–168 (2012). [CrossRef]
  32. K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Dynamic Stabilization of a Microring Modulator Under Thermal Perturbation,” Proc. Optical Fiber Communication Conference (Optical Society of America, 2012), paper OW4F.2. [CrossRef]
  33. J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express18(16), 16902–16928 (2010). [CrossRef] [PubMed]
  34. M. Gould, T. Baehr-Jones, R. Ding, S. Huang, J. Luo, A. K.-Y. Jen, J. M. Fedeli, M. Fournier, and M. Hochberg, “Silicon-polymer hybrid slot waveguide ring-resonator modulator,” Opt. Express19(5), 3952–3961 (2011). [CrossRef] [PubMed]
  35. L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon technology,” Opt. Express19(12), 11841–11851 (2011). [CrossRef] [PubMed]
  36. C. Koos, J. Brosi, M. Waldow, W. Freude, and J. Leuthold, “Silicon-on-insulator modulators for next-generation 100 Gbit/s-Ethernet,” Proc. European Conf. on Optical Communication (ECOC), Paper P056 (2007). [CrossRef]
  37. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron.23(1), 123–129 (1987). [CrossRef]
  38. J. Takayesu, M. Hochberg, T. Baehr-Jones, E. Chan, G. Wang, P. Sullivan, Y. Liao, J. Davies, L. Dalton, A. Scherer, and W. Krug, “A Hybrid Electrooptic Microring Resonator-Based 1×4×1 ROADM for Wafer Scale Optical Interconnects,” J. Lightwave Technol.27(4), 440–448 (2009). [CrossRef]
  39. D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, “Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides,” Opt. Express19(24), 23671–23682 (2011). [CrossRef] [PubMed]
  40. R. Sun, P. Dong, N. N. Feng, C. Y. Hong, J. Michel, M. Lipson, and L. Kimerling, “Horizontal single and multiple slot waveguides: optical transmission at λ = 1550 nm,” Opt. Express15(26), 17967–17972 (2007). [CrossRef] [PubMed]
  41. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
  42. S.-H. Kwon, “Deep subwavelength plasmonic whispering-gallery-mode cavity,” Opt. Express20(22), 24918–24924 (2012). [CrossRef] [PubMed]
  43. W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron.40(10), 1511–1518 (2004). [CrossRef]
  44. X. Wang, C. Y. Lin, S. Chakravarty, J. Luo, A. K.-Y. Jen, and R. T. Chen, “Effective in-device r33 of 735 pm/V on electro-optic polymer infiltrated silicon photonic crystal slot waveguides,” Opt. Lett.36(6), 882–884 (2011). [CrossRef] [PubMed]
  45. R. Ding, T. Baehr-Jones, W. Kim, A. Spott, M. Fournier, J. Fedeli, S. Huang, J. Luo, A. K.-Y. Jen, L. Dalton, and M. Hochberg, “Sub-Volt Silicon-Organic Electro-optic Modulator With 500 MHz Bandwidth,” J. Lightwave Technol.29(8), 1112–1117 (2011). [CrossRef]

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