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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 3 — Jan. 31, 2011
  • pp: 2417–2425
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Micro-resonator with metallic mirrors coupled to a bus waveguide

Steve Zamek, Liang Feng, Mercedeh Khajavikhan, Dawn T. H. Tan, Maurice Ayache, and Yeshaiahu Fainman  »View Author Affiliations


Optics Express, Vol. 19, Issue 3, pp. 2417-2425 (2011)
http://dx.doi.org/10.1364/OE.19.002417


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Abstract

We demonstrate a micro-resonator based on a channel waveguide terminated with metallic mirrors side coupled to a bus waveguide. Transmission through such a resonant structure implemented in a silicon-on-insulator platform is investigated theoretically and demonstrated experimentally. The resonator is 13.4 μm long, exhibits an unloaded Q-factor of ∼2100, and a free spectral range of 21 nm around the wavelength of 1.55 μm.

© 2011 Optical Society of America

1. Introduction

Optical micro-resonators are promising candidates for miniaturization of free-space and fiber-based devices. Such resonators have sparked enormous interest due to the advantages they offer in the areas of biochemical sensing [1

1. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

], chip-scale interconnects [2

2. S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1(5), 293–296 (2007). [CrossRef]

], sub-wavelength lasers [3

3. A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33(11), 1261–1263 (2008). [CrossRef] [PubMed]

,4

4. M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4(6), 395–399 (2010). [CrossRef]

], signal processing [5

5. L. Zhang and A. E. Willner, “Microresonators for Communication and Signal Processing Applications”, in Photonic Microresonator Research and Applications, I. Chremmos, O. Schwelb, and N. Uzunoglu, eds, (Springer2010), pp. 485–505. [CrossRef]

], and communications [6

6. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]

]. The silicon on insulator (SOI) platform is especially appealing as it offers (1) strong confinement of light due to high index contrast between silicon and the oxide, (2) ready integration of photonics with microelectronics, and (3) high-volume production, leveraging the existing CMOS fabrication infrastructure [7

7. L. Pavesi and D. J. Lockwood, eds., Silicon Photonics, (Springer2004), pp. 51–84.

]. Examples of recently studied silicon based micro-resonators include microrings [8

8. B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10(4), 549–551 (1998). [CrossRef]

10

10. Q. Xu and M. Lipson, “Carrier-induced optical bistability in silicon ring resonators,” Opt. Lett. 31(3), 341–343 (2006). [CrossRef] [PubMed]

], microdisks [11

11. P. Koonath, T. Indukuri, and B. Jalali, “Add-drop filters utilizing vertically coupled microdisk resonators in silicon,” Appl. Phys. Lett. 86(9), 091102 (2005). [CrossRef]

, 12

12. A. Morand, Y. Zhang, B. Martin, K. Phan Huy, D. Amans, P. Benech, J. Verbert, E. Hadji, and J. M. Fédéli, “Ultra-compact microdisk resonator filters on SOI substrate,” Opt. Express 14(26), 12814–12821 (2006). [CrossRef] [PubMed]

], and cavities with distributed Bragg reflectors (DBRs) [13

13. H.-C. Kim, K. Ikeda, and Y. Fainman, “Tunable transmission resonant filter and modulator with vertical gratings,” J. Lightwave Technol. 25(5), 1147–1151 (2007). [CrossRef]

, 14

14. H.-C. Kim, K. Ikeda, and Y. Fainman, “Resonant waveguide device with vertical gratings,” Opt. Lett. 32(5), 539–541 (2007). [CrossRef] [PubMed]

].

Fig. 1 (a) Schematic of the studied device. (b) Illustration of the formalism used to construct the analytical model.

2. Description of the device

A schematic of the device is shown in Fig. 1a. SOI platform was used to realize Si waveguides resting on a SiO2 substrate. The resonator is based on a channel silicon waveguide with a cross-section identical to the cross section of the bus waveguide. The resonator’s waveguide is terminated with two metallic plates, creating a cavity. The resonator is side coupled to a channel (bus) waveguide. The upper cladding of the device is silicon dioxide, which is not shown on Fig. 1a for clarity. The resonator’s length, Lr, is the distance between the mirrors, and Lc is the length of the coupling region, where the gap between the two waveguides is uniform (LrLc).

When an optical mode propagates in the bus waveguide, some of its energy will couple into the resonator by the mechanism of co-directional evanescent coupling [23

23. A. Yariv, Optical Electronics, 3d Ed. (Holt, Rinehart and Winston1985), ch. 13.7, p. 432.

]. It will further circulate in the resonator, reflecting off the mirrors. Assuming low coupling between the two waveguides, this will generally have a negligible effect, with most of the power transmitted through the bus waveguide. If the resonance condition is satisfied, even a small coupling will cause a buildup of an intense field in the resonator. Some of this field will couple back into the bus resonator and will destructively interfere with the incident mode propagating in the waveguide. As we show below, at resonance this effect can result in an appreciable dip in the transmission spectrum and strong reflection back into the bus waveguide.

3. Analytical Model

Analytical approaches for the analysis of waveguide-coupled resonators include rigorous solution of four coupled modes equations [24

24. R. Kazarinov, C. Henry, and N. Olsson, “Narrow Band Resonant Optical Reflectors and Resonant Optical Transformers for Laser Stabilization and Wavelength Division Multiplexing,” IEEE J. Quantum Electron. 23(9), 1419–1425 (1987). [CrossRef]

], coupling of modes in time [25

25. H. A. Haus and Y. Lai, “Theory of Cascaded Quarter Wave Shifted Distributed Feedback Resonators,” IEEE J. Quantum Electron. 28(1), 205–213 (1992). [CrossRef]

], and scattering-theory formalism [27

27. 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(5 5 Pt B), 7389–7404 (2000). [CrossRef] [PubMed]

]. Here we took an approach based on multiple reflections model, analogous to the one used for the analysis of Fabry-Perot interferometer. The advantage of this model is simplicity and an insight into the features of the transmission spectrum.

The formalism is illustrated in Fig. 1b. A mode with amplitude Ei is launched into the input port of the bus waveguide, as shown in the figure. Some part of it, a, couples into the resonator, while part b propagates to the output port. The mode coupled into the resonator with amplitude aEi, will undergo multiple reflections, while in each cycle some of it (a) will couple back into the bus waveguide. The coefficients a and b can be obtained from the coupled mode theory [23

23. A. Yariv, Optical Electronics, 3d Ed. (Holt, Rinehart and Winston1985), ch. 13.7, p. 432.

]: a = −isin(κLc)exp(iβLr) and b = cos(κLc)exp(iβLr). Similarly to the derivation of a transmission through a Fabry-Perot interferometer [17

17. H. A. Haus, Waves and Fields in Optoelectronics, (Prentice Hall1984), ch. 8.3, pp. 226–8 and 243.

], the output field Et is given by an infinite sum of the fields coupled out from the resonator into the output port Et=Eiar0(b2r02+b2r02b2r02+)a. The transmission coefficient, t = Et/Ei is easily obtained as
t=(1e2iβLRR)cos(κLc)exp(iβLr)1cos2(κLc)exp(2iβLr)R
(1)
where κ is the coupling coefficient between the two waveguides, Lc and Lr, are the lengths of the coupling section and the resonator (as shown in Fig. 1a), β is the wave number of the guided mode, and R = r02 is the reflectance of the mirror. The expression in Eq. (1) was confirmed with 2D simulations based on the Finite Element Method (FEM). In these simulations we considered a TE-mode, 200 nm wide waveguide, side-coupled to a resonator with the coupling coefficient of κ = 560 cm−1. Three resonators with Lc = Lr = 5,10, and 15μm, terminated with mirrors with reflectivity R = 0.95 were simulated and full agreement between Eq. (1) and the simulation results was obtained.

It is interesting to notice, that the two Q-factors associated with the coupling and the mirror losses are both dependent on the resonator length, but in an opposite manner, as shown in Fig. 2a. For extremely short cavities the coupling is negligible and the Q-factor is dominated by the mirror losses. For long cavities, the coupling happens over a longer length, leading to a larger mode decay rate, and the Q-factor is dominated by the coupling. To confirm the results obtained in Eqs. (4) and (5) we performed 2D FEM simulations as shown in Figs. 2b–d. The Q-factors were calculated from the eigenmodes found from the simulations, with the simulation results shown in Fig. 2a by black cross-marks. Good agreement between simulations and analytical results was found, confirming the validity of our model.

Fig 2 Confirmation of the model. (a) Q-factors as a function of normalized length of the resonator L/λ calculated from Eqs 4 and 5. Q-factor associated with the external coupling (QC), mirror losses (Q0), and the total Q-factor (QT) are shown by broken blue, dashed black, and solid black correspondingly. The black cross-marks show FEM simulation results of the coupled resonator. (b–d) Electric field |Ez| distribution as obtained from FEM simulations for L/λ=0.22, 1.33, and 3.54 (where L=Lr=Lc). All simulation used TE polarization with the following parameters: mirror reflectivity R=0.98, normalized coupling coefficient κλ=0.114, normalized separation distance between the resonator and the bus waveguide G/λ=0.26, and normalized thickness of the waveguides d/λ=0.13.

Another important characteristic of the coupled micro-resonator, is the extinction ratio (ER). ER is defined as the ratio of the transmittance in the pass-band to the one on the resonance. To derive it, we should notice here that at resonance exp(2iβLr) = 1 in Eq. (1). This happens when βLr = πm, where m is an integer describing the longitudinal mode number. Exactly in the middle between two resonances βLr = π(m + 0.5) and therefore exp(2iβLr) = −1 By substitution of these two into Eq. (1), the ratio between the two transmittances can be calculated and the ER is found:
ER=[1+R1R1Rcos2(κLc)1+Rcos2(κLc)]2
(6)

It is interesting to notice that for no coupling between the resonator and the bus waveguide, i.e. κ = 0, ER approaches 1, as anticipated. This case is equivalent to a straight waveguide, for which the transmission equals 1 over the entire spectrum above the waveguide’s cutoff frequency. On the other hand, when the reflectivity R approaches 1, the ER tends to infinity. From this discussion it becomes evident that the coupling loss must predominate over the internal resonator loss to achieve high ER.

4. Design

As a proof-of-concept, we designed a micro-resonator coupled to a bus waveguide, based on channel Si waveguides with SiO2 cladding, terminated with Au mirrors. To do so, we used a SOI wafer with top silicon thickness of 250nm and thermal oxide layer ∼3 μm thick. The design was carried out in the following steps. First we analyzed the reflectance of the mirror for different waveguide widths. Having set the width of the guide, we chose the length of the resonator as a tradeoff between the unloaded Q-factor, Q0, and the FSR. For the chosen waveguide cross section and resonator’s length, we analyzed the coupling coefficient and the external Q-factor QC, as a function of the separation distance between the resonator and the bus waveguide. This distance was set to obtain the desired extinction ratio in the transmission spectrum.

Reflectance of a mirror was analyzed for the basic TE-like mode of the waveguide as a function of its width, W, based on three dimensional (3D) FEM simulations, in a configuration shown in Fig. 3a. For most waveguide geometries, the decay length of the optical mode into the cladding is only several hundreds of nanometers or less. Therefore a mirror that extends sufficiently into the cladding behaves as an infinite metallic plate for any practical purpose. For the gold we used dielectric constant ɛ = −132-12.7i at the wavelength of 1.55 μm [30

30. E. D. Palik, ed., Handbook of Optical Constants of Solids, (Academic1985), p. 294.

]. The obtained reflectance R is shown in Fig. 3b by a solid black line. The total loss, 1-R, is composed of the material loss in the metal and scattering due to the waveguide discontinuity introduced by the mirror. The relative contribution of scattering to the total loss is shown by broken blue line on the same figure.

Fig. 3 Theoretical investigation of the micro-resonator. (a) Schematic of an Au mirror inserted into a Si waveguide. (b) Mirror’s reflectance, R, (solid black) and the ratio of scattering loss to the total loss (broken blue) as a function of guide’s width, W. An inset shows the considered cross-section of the waveguide. The shaded area corresponds to W below 150nm, for which the results are inaccurate due to the high numerical error of FEM, associated with low mode confinement. (c) Effective and group index, ne and ng, as a function of waveguide’s width, W. (d) Coupling coefficient, κ, as a function of the gap, G, between the guides, for the geometry shown in the inset. All results pertain to TE-like mode and a wavelength of λ = 1.55µm.

To understand the result we consider two extremes. In the first extreme, W approaches zero, the mode is poorly confined, and most of the power flows in the cladding. This case resembles reflection of a plane wave normally incident onto the Au-SiO2 interface, for which the reflectance equals ∼0.975. In the other extreme, where W is sufficiently large, the mode is strongly confined to the core of the waveguide, and the reflectance approaches ∼0.95, which is the reflectance at the Au-Si interface. For W = 280 nm, the reflectance reaches its minimum value of ∼0.78, associated with strong scattering. For this geometry most of the loss is attributed to the scattering, as shown by the broken blue line in Fig. 3b. A width W = 400 nm was chosen to provide both high reflectance R = 0.9, and high group index ng = 4.27, as shown in Figs. 3b and 3c.

The length of the resonator, LR, is a tradeoff between the Free Spectral Range (FSR) and the Q-factor. The FSR is given by λ2/2Lrng [22

22. S. Zamek, A. Mizrahi, L. Feng, A. Simic, and Y. Fainman, “On-chip waveguide resonator with metallic mirrors,” Opt. Lett. 35(4), 598–600 (2010). [CrossRef] [PubMed]

]. We chose the length to be Lr = 13.4 μm, leading to FSR of 21 nm, making it possible to observe several resonant lines with the setup described below. Such length resulted in an unloaded Q-factor of Q0 = 2100 at the wavelength of λ = 1.55 μm, as given by Eq. (2). The total Q-factor is dominated by the external Q-factor, Qc, which is calculated below.

5. Fabrication

The step-by-step fabrication process is illustrated in Fig. 4. We first used electron beam lithography (EBL) to pattern Hydrogen SilsesQuioxane (HSQ) resist on a SOI wafer. The created pattern was used as a mask for dry etching of silicon, resulting in Si waveguides on top of a SiO2 layer. The residual HSQ was removed by 10 sec wet etching in a diluted (1:10) buffered oxide etch (1:6 BOE solution). A layer of polymethyl methacrylate (PMMA) resist was patterned on top using an overlay EBL. The patterned PMMA was used as a mask for the second dry etching of silicon, and a successive dry etching of silicon dioxide, opening gaps for the mirrors in the Si waveguides. Electron beam evaporation of gold with a consecutive liftoff in acetone left gold plugs inserted into the Si waveguide. This created a resonator composed of a Si waveguide side coupled to a bus waveguide as shown in Fig. 5a. A layer of SiO2 with a thickness of 2 μm was deposited on top using plasma-enhanced chemical vapor deposition (PECVD). The fabricated device and its parameters are shown in Fig. 5a.

Fig. 4 Conceptual illustration of the fabrication process. The two panes show two different cross-sections of the device (XY in the upper pane and ZY in the lower pane, as shown). The dimensions are not up to scale.
Fig. 5 Experimental results. (a) Micrograph obtained with a scanning electron microscope (SEM) of the fabricated device right after the lift-off and prior to the deposition of top cladding with PECVD. The device is tilted at 45 degrees with respect to the imaging axis. (b) Experimental (red dots) and simulated (solid black) transmission spectra of TE-like mode of the fabricated device in dB.

6. Experiment

To measure the transmission spectrum we used a telecom-grade linearly polarized tunable laser source. Its output was coupled into an on-chip waveguide through a tapered polarization maintaining fiber. The fiber was affixed to a 5-axis mechanical stage to allow precise alignment between the fiber and the waveguide. The output port of the waveguide was imaged through a polarizer onto the detector, connected to a power meter. The polarizer was set to pass the electric field parallel to the plane of the sample, to efficiently excite TE-like mode of the waveguide. The reading of the power meter was recorded as the wavelength of the source was scanned in steps of 20 pm. The obtained power spectrum of the transmission through the bus waveguide is plotted in Fig. 5b by red dots. The solid black curve shows the analytical result as calculated from Eq. (1) for the parameters used in the design.

The obtained transmission spectrum exhibits several interesting features. First, it shows a ripple of approximately 2 dB, which is a result of interference created by mode reflection off the cleaved facets of the waveguide. Second, it shows a FSR∼21 nm, which is in agreement with the analytical prediction. The ER grows towards longer wavelengths, due to poorer mode confinement and larger coupling between the two waveguides. The experimentally obtained extinction ratio ER∼10 dB is significantly lower than the analytical value (∼20 dB). This is due to several factors, listed here in the order of their significance: mirror reflectivity R∼0.8 lower than anticipated (∼0.9) due to fabrication imperfections, smaller coupling coefficient κ (∼1200cm−1 instead of 1400cm−1) due to narrower waveguides, depolarization of the mode due to the coupling between TE- and TM-like modes at waveguide bends and perturbations created by the mirrors, reduced refractive index of the upper cladding created by PECVD process, and polarization extinction ratio in the excitation of the waveguide by a tapered fiber. To summarize, the fabricated device exhibited QC = 360 instead of 300 (by design) and Q0 = 900 instead of 2100, providing a total Q-factor of 260. According to these parameters, the insertion loss is ∼0.7dB as estimated from Eq. (1).

The mirror quality, which is the dominant factor among those listed above, is compromised by the roughness, tilt, and conformity to the waveguide facet. The roughness is introduced in the dry-etching of Si through a mask of PMMA, with its typical values on the order of ∼10 nm peak-to-peak. The roughness of the deposited metal is significantly increased outside of the silicon waveguide due to the lift-off process. However the rough surface of metal is believed to play minor role as most of the power flows in the Si waveguide, where the roughness is minimal since no contact between metal and the resist was established. The tilt of the mirror is about 7 degrees as estimated from the SEM images. This tilt is due to the shadowing of the evaporated metal by the PMMA resist.

7. Discussion

The described fabrication process can be improved to reduce the roughness and the tilt of the mirror. Evaporation of metal at an angle can be done to reduce the tilt and to increase the conformity of the mirror to the waveguide. PMMA can be replaced with other resists that offer higher sidewall smoothness. Adding post-fabrication processing, such as rapid thermal annealing, can smooth the mirrors’ rough surface. Also other fabrication techniques can be investigated.

High mirror reflectivity R is critical to obtain high finesse, narrow resonance line width, and high extinction ratio, desirable in many applications. Our design was constrained by the height of the Si waveguide (250 nm), set by the availability of SOI wafers. In practice, the guide cross section can be optimized to achieve reflectivity of 0.95, as suggested by Fig. 3b. Even higher reflectivity (up to 0.975) can be obtained on the expense of mode confinement by significantly decreasing the cross section of the waveguide, and pushing the mode out into the cladding, as suggested by the same figure. Nevertheless, the inherent material loss limits the reflectivity to ∼97.5%, corresponding to the maximum finesse of ∼120. Such losses do not exist in DBRs, whose reflectivity approaches unity for a sufficiently large number of periods.

The reflectivity of metallic mirrors cannot compete with the conventional DBRs. Nor can the resonator achieve the Q-factors of the state-of-the-art resonators with small mode volumes [3

3. A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33(11), 1261–1263 (2008). [CrossRef] [PubMed]

,32

32. K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal microcavity,” Appl. Phys. Lett. 83(10), 1915 (2003). [CrossRef]

35

35. K. Preston and M. Lipson, “Slot waveguides with polycrystalline silicon for electrical injection,” Opt. Express 17(3), 1527–1534 (2009). [CrossRef] [PubMed]

]. The major strength of metallic mirrors, however, rests with their ability to provide reasonably high reflectivity over a broad band of wavelengths and low polarization sensitivity. In addition, the optical skin depth in metal is on the order of 10 nm, so that a very thin layer of metal is sufficient to achieve the desired reflectivity. Hence the proposed metallic mirrors can attain extremely small footprints, by an order of magnitude smaller than those of a typical DBR. DBR’s smallest feature size is in the deep sub-micron regime and requires a high degree of fabrication accuracy. Metallic mirrors, in contrast, impose no such constraints and exhibit low sensitivity to fabrication imperfections.

8. Summary

To summarize, we demonstrated a micro-resonator based on silicon waveguide terminated with metallic mirrors. The mirrors are compact and highly reflective. The geometry was optimized to achieve an unloaded Q-factor of 2100 for a resonator 13.4 μm long. Its measured transmission spectrum was in good agreement with the developed analytical model. The device may be used to construct high-order inline filters, spectrum shapers, true-time delays, modulators, channel add-drop multiplexers, and biochemical sensors.

Acknowledgments

This work was supported by the Defense Advanced Research Projects Agency (DARPA), the National Science Foundation (NSF), the NSF Center for Integrated Access Networks (CIAN), the Cymer Corporation, and the U.S. Army Research Office. The fabrication was performed at UCSB Nanofab and UCSD Nano3 facilities. The authors wish to thank Bill Mitchell from UCSB and Nano3 staff for their technical support. Steve Zamek thanks Adam Zamek for inspiring discussions.

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A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

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M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4(6), 395–399 (2010). [CrossRef]

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A. B. Buckman, Guided Wave Photonics, (Saunder College Publishing1992), pp. 149–154.

32.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal microcavity,” Appl. Phys. Lett. 83(10), 1915 (2003). [CrossRef]

33.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81(5), 1110–1113 (1998). [CrossRef]

34.

Y.-F. Xiao, C.-L. Zou, B.-B. Li, Y. Li, C.-H. Dong, Z.-F. Han, and Q. Gong, “High-Q Exterior Whispering-Gallery Modes in a Metal-Coated Microresonator,” Phys. Rev. Lett. 105(15), 153902 (2010). [CrossRef]

35.

K. Preston and M. Lipson, “Slot waveguides with polycrystalline silicon for electrical injection,” Opt. Express 17(3), 1527–1534 (2009). [CrossRef] [PubMed]

OCIS Codes
(230.5750) Optical devices : Resonators
(130.7408) Integrated optics : Wavelength filtering devices

ToC Category:
Integrated Optics

History
Original Manuscript: December 7, 2010
Revised Manuscript: December 19, 2010
Manuscript Accepted: December 23, 2010
Published: January 25, 2011

Citation
Steve Zamek, Liang Feng, Mercedeh Khajavikhan, Dawn T. H. Tan, Maurice Ayache, and Yeshaiahu Fainman, "Micro-resonator with metallic mirrors coupled to a bus waveguide," Opt. Express 19, 2417-2425 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-3-2417


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