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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 25 — Dec. 10, 2007
  • pp: 17313–17322
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Coupled spiral-shaped microdisk resonators with non-evanescent asymmetric inter-cavity coupling

Xianshu Luo and Andrew W. Poon  »View Author Affiliations


Optics Express, Vol. 15, Issue 25, pp. 17313-17322 (2007)
http://dx.doi.org/10.1364/OE.15.017313


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Abstract

We study coupled spiral-shaped microdisk resonators with non-evanescent asymmetric inter-cavity coupling via seamlessly jointed notches. Our finite-difference time-domain numerical simulations reveal that the throughput-port transmissions are reciprocal between counterclockwise (CCW) and clockwise (CW) traveling-wave modes, while the drop-port transmissions and modal field distributions are input-port dependent. By introducing a slight mismatch in radii between two coupled microdisks while preserving their seamlessly jointed notches, we are able to show selectively enhanced extinction ratio for one of the split modes while suppressing the other. Our experiments using coupled spiral-shaped microdisk resonators in silicon nitride-on-silica suggest split resonances with an extinction ratio of ~20 dB using identical coupled microdisks, and an enhanced resonance extinction ratio of ~24 dB using slightly mismatched coupled microdisks. The non-evanescent coupling preserves high-Q resonances.

© 2007 Optical Society of America

1. Introduction

Coupled microresonators, e.g., coupled microdisk or microring resonators, are widely used to realize high-order filter response [1

1. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photon. Tech. Lett. 12, 320–322 (2000). [CrossRef]

], optical delay line [2

2. J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, “Transmission and group delay of microring coupled-resonator optical waveguides,” Opt. Lett. 31, 456–458 (2006). [CrossRef] [PubMed]

], and coupled resonator induced transparency [3

3. Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006). [CrossRef] [PubMed]

]. The microresonators are evanescently coupled via submicrometer gap separation. Recently [4

4. C. Li, X. Luo, and A. W. Poon, “Dual-microring-resonator electro-optic logic switches on a silicon chip,” Semicond. Sci. Technol., accepted.

], our group also studied the feasibility of electro-optic logic switching in coupled dual-microring resonator configuration. However, due to the high structural symmetry, the transmissions are independent on the waveguide input-port, implying limited device configurations and switching functionality.

2. Non-evanescent asymmetric inter-cavity coupling

Fig. 1. Schematics of the coupled spiral-shaped microdisk resonator-based filter configurations with lightwave input-coupled to the first cavity (a) counterclockwise (CCW) circulation mode, and (b) clockwise (CW) circulation mode. Insets: zoom-in schematics of the non-evanescent coupling via the joint notches. CCW circulation is preferentially confined in the first cavity and only enables a weak tail-to-tail mode spatial overlap with the second cavity. CW circulation is preferentially coupled to the second cavity due to significant mode spatial overlap [5].

Figures 1(a) and 1(b) show the schematics of the coupled spiral-shaped microdisk resonator-based filter in two input-coupling configurations, with lightwave launched from two different input-ports exciting counterclockwise (CCW) and clockwise (CW) traveling-wave modes of the first cavity. For simplicity, we refer to them as CCW and CW configurations hereafter. The structure comprises two identical spiral-shaped microdisk resonators that are seamlessly jointed at their notches, with singlemode waveguides that are evanescently side-coupled to the cavities. The spiral shape is defined in terms of the azimuthal angle dependent radius r(ϕ) as [20

20. J. Y. Lee and A. W. Poon, “Spiral-shaped microdisk resonator-based channel drop filters on a silicon nitride chip,” in Proceedings of IEEE 3rd International Conference on Group IV Photonics, (IEEE, 2006), pp.19–21.

23

23. J. Y. Lee, X. Luo, and A. W. Poon, “Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators,” Opt. Express 15, 14650–14666 (2007). [CrossRef] [PubMed]

]: r(ϕ)=r 0(1-εϕ/2π), where r 0=r(ϕ=0) and ε is a deformation parameter giving a notch junction width of r 0 ε. We wrap the side-coupled waveguides along an arc length of the microdisk in order to enhance the waveguide evanescent coupling.

The cavity light can partially transmit between the two microcavities via the notch junction. Due to the structural asymmetry, the mode spatial overlaps between the two microdisks at the notch junction are not identical between CCW and CW configurations. Insets of Fig. 1 illustrate the tail-to-tail mode spatial overlap for CCW configuration, and the more significant mode spatial overlap for CW configuration. Thus, the light transmissions from the first microdisk to the second microdisk (and likewise feedback from the second microdisk to the first microdisk) are asymmetric between CCW and CW configurations. Specifically, CCW configuration only enables weak transmissions to the second microdisk (blue dashed arrows), yet light from the second microdisk preferentially feeds back to the first microdisk CCW orbit upon traveling a round trip. This results in an asymmetric mode-field distribution between the coupled microdisks, with more intense mode-field distributions in the first microdisk. Whereas, for CW configuration, the lightwave can be preferentially transmitted to the second microdisk (red solid arrow), yet light from the second cavity is weakly coupled back (red dashed arrow). This enables more evenly distributed field intensity in the coupled microdisks.

Fig. 2. Schematic illustrations of (a)–(c) coupled spiral-shaped microresonators and (d)–(f) coupled circular-shaped microresonators upon three input-coupling configurations. I, I’, I”: input, D, D’, D”: drop-port transmissions, and T, T’, T”: throughput-port transmissions.

Hence, we see that the coupled spiral-shaped microdisk resonators have two key merits: 1) non-evanescent inter-cavity coupling is not constraint by fabricating submicrometer coupling gap; and 2) asymmetric inter-cavity coupling between different input-coupling configurations offers unique transmission characteristics that are distinct from conventional coupled microresonators.

3. 2-D FDTD simulations

Here, we numerically simulate the coupled spiral-shaped microdisk resonators using a commercial FDTD tool [25

25. FullWAVE, Rsoft Inc. Research Software, http://www.rsoftinc.com

]. We adopt identical dimensions for the coupled microdisks with r 0=5 µm, and ε=0.16. The waveguide width is 0.4 µm, with a side interaction length defined by a 36° arc, via a gap separation of 0.3 µm. We use an effective refractive index of 1.92 in order to effectively account for the vertical dimension in a silicon nitride-on-silica substrate.

Fig. 3. FDTD-simulated TE-polarized multimode (a) throughput- and (b) drop-port transmission spectra of coupled spiral-shaped microdisk filters with r 0=5 µm, ε=0.16 for CCW (blue dashed line) and CW (red solid line) configurations.

Figures 3(a)–3(b) show the simulated TE-polarized (electric field in plane) multimode throughput- and drop-port transmission spectra of the coupled identical spiral-shaped microdisk resonators for CCW and CW configurations. The two throughput-port transmission spectra overlap with each other, as expected from reciprocity relations. The corresponding drop-port transmission spectra only show identical resonance wavelengths, yet with distinct relative resonance peak heights and ERs. We attribute the lower drop-port transmission for CCW configuration to an additional radiation loss induced at the notch junction in order to balance the preferential light out-coupling for CW configuration [23

23. J. Y. Lee, X. Luo, and A. W. Poon, “Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators,” Opt. Express 15, 14650–14666 (2007). [CrossRef] [PubMed]

]. Moreover, we identify a free-spectral range (FSR) of ~45.3 nm, which is consistent with the single microdisk circumference. The resonances are split due to the strong inter-cavity coupling.

Fig. 4. FDTD-simulated steady-state mode-field patterns of the coupled spiral-shaped microdisk resonators for CCW and CW configurations at resonance wavelength of (a), (b) 1544.5 nm (resonance A) and (c), (d) 1554.1 nm (resonance B).

Here, we simulate coupled non-identical spiral-shaped microdisk resonators with radii r 1 and r 2 at the notch. In order to preserve the notch junction, the two microdisks also have slightly different spiral shapes (i.e. a slight mismatch in both their radii and ε’s). We vary the radius of the second microdisk r 2 while fixing the radius of the first microdisk. Figures 5(a)–(d) show the simulated transmission spectra of structures with (a), (b) r 2=4.8 µm (ε=0.167) and (c), (d) r 2=5.4 µm (ε=0.148), while fixing r 1=5 µm. Still, the throughput-port transmissions are reciprocal for CCW and CW configurations, while the drop-port transmissions are non-identical. The FSR in both cases are slightly differed, which is consistent with a change of average round trip path length of the two microdisks. Compared with those corresponding resonances in coupled identical spiral-shaped microdisk resonators (Fig. 3), we observe that one of the split modes is selectively enhanced while the other one is nearly suppressed. Specifically, for r 2=4.8 µm, the enhanced ER is ~25 dB for resonance C compared with ~10 dB for resonance A. Whereas, for r 2=5.4 µm, the enhanced ER is ~27 dB for resonance F compared with ~9 dB for resonance B.

Fig. 5. FDTD-simulated TE-polarized multimode transmission spectra with radius perturbations in the second microdisk for CCW and CW configurations. (a) Throughput-port, and (b) drop-port transmission spectra with r 1=5 µm and r 2=4.8 µm. (c) Throughput-port, and (d) drop-port transmission spectra with r 1=5 µm and r 2=5.4 µm.
Fig. 6. Variations of (a) resonance wavelengths, (b) extinction ratios, and (c) quality factors as a function of the radii mismatch Δr=r 2-r 1 for both split modes.

Fig. 7. FDTD-simulated steady-state mode-field patterns at resonance wavelengths of (a), (b) 1549.1 nm (resonance C), and (c), (d) 1561.9 nm (resonance D) for CCW and CW configurations with r 1=5 µm and r 2=4.8 µm.

Figures 7(a) and 7(b) show the simulated steady-state mode-field patterns at the ER enhanced resonance wavelength of 1549.1 nm (resonance C in Fig. 5(a)) for CCW and CW configurations with r 1=5 µm and r 2=4.8 µm. For CCW configuration, the mode-field intensity in the second microdisk is significantly lower than that in coupled identical microdisk resonators (see Fig. 4(a)). For CW configuration, the mode intensity distribution is less even compared with that in coupled identical microdisk resonators, with lower intensity in the second microdisk. We attribute the lower intensity in the second microdisk in part to the cavity mode mismatch between two non-identical microdisk resonators.

We see that the change in size and shape of the second microdisk modify the coupled cavity mode characteristics such as cavity loss, which affects the balance between cavity loss and waveguide coupling [26

26. A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguide,” Electron. Lett. 36, 321–322 (2000). [CrossRef]

], thus results in the change in ERs and Q values. It is also difficult to distinguish the field parities at the notch junction in coupled non-identical spiral-shaped microdisk resonators.

4. Experiments

We fabricate the coupled spiral-shaped microdisk resonator-based filters on a silicon nitrideon-silica substrate using standard silicon microelectronics processes. We use a 1.1-µm-thick silicon nitride device layer on a 1.5-µm-thick silica under-cladding layer. The device structures are defined by photolithography (i-line, 365 nm) and CF4-based reactive ion plasma etching (RIE). Figure 8(a) shows the top-view scanning electron micrograph (SEM) of the fabricated device. The measured radii for both spirals are ~20 µm. Figure 8(b) shows the cross-section of the waveguide evanescent coupling region, denoted as dash line in Fig. 8(a). The measured etch depth h is ~0.93 µm. Figures 8(c)–8(d) show the zoom-in view SEMs of the notch-coupling and waveguide evanescent-coupling regions. The notch width is ~0.4 µm. The width of the side-coupled waveguide is ~0.38 µm, and the gap spacing between the cavity sidewall and the waveguide is ~0.46 µm.

Fig. 8. (a) Top-view SEM of our fabricated device on a silicon nitride-on-silica substrate. The waveguide coupling length spans an angle of 36°. (b) Cross-section view SEM of the evanescent coupling region. h~0.93 µm. (c)–(d) Zoom-in view SEMs of the notch-coupling region and the lateral evanescent-coupling region. r 0~20 µm, ε~0.02, w~0.38 µm, and g~0.46 µm.

Figure 9 shows the measured TE-polarized transmission spectra for coupled identical and non-identical spiral-shaped microdisk resonators. The experimental setup follows standard passive wavelength scanning measurements and has been detailed elsewhere [23

23. J. Y. Lee, X. Luo, and A. W. Poon, “Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators,” Opt. Express 15, 14650–14666 (2007). [CrossRef] [PubMed]

]. Figure 9(a) shows the measured throughput-port multimode transmission spectra for CCW and CW configurations. We observe essentially identical throughput-port transmission spectra, suggesting reciprocal transmissions. The transmission spectra suggest pronounced split resonances with large ERs, although it is difficult to differentiate a split mode in a multimode cavity. We label two of the possible split resonances as modes A and B, each displays a Q ~6,500. We measure a FSR of ~9.1 nm, which is consistent with a single microcavity circumference. The measured highest Q is ~15,000, which means our coupled spiral-shaped microdisk resonators preserve high-Q modes [18

18. G. D. Chern, G. E. Fernandes, R. K. Chang, Q. Song, L. Xu, M. Kneissl, and N. M. Johnson, “High-Q-preserving coupling between a spiral and a semicircle µ-cavity,” Opt. Lett. 32, 1093–1095 (2007). [CrossRef] [PubMed]

].

Fig. 9. Measured TE-polarized transmission spectra for (a)–(b) coupled identical spiral-shaped microdisk resonators, and (c)–(d) coupled non-identical spiral-shaped microdisk resonators. (a) Throughput-port and (b) drop-port multimode transmission spectra for fabricated device with r 0=20 µm, ε=0.02. (c) Throughput-port and (d) drop-port multimode transmission spectra for fabricated device with r 1=20 µm, ε=0.02 and r 2=19.8 µm, ε=0.0202.

We also fabricate coupled non-identical spiral-shaped microdisk resonators with radius and shape perturbations in the second microdisk. Figures 9(c)–9(d) show the measured transmission spectra for a device with r 1=20 µm, r 2=19.8 µm for CCW and CW configurations. We observe that the throughput-port transmission spectra are essentially identical as expected from reciprocity relations, whereas the drop-port transmission spectra exhibit essentially the same set of resonance modes but display more pronounced variations in their resonance ERs. The measured highest Q is ~13,500, which is slightly lower than the case of coupled identical microdisks.

The transmission spectra here suggest that one of the split resonances is selectively enhanced in ER. For instance, it is conceivable that split resonances A and B in coupled identical spiral-shaped microdisk resonators (Fig. 9(a)) become resonance C in coupled non-identical spiral-shaped microdisk resonators (Fig. 9(c)), with reduced Q (reduced from ~6,500 to ~3,500) and enhanced ER (enhanced from ~20 dB to ~24 dB). There is, however, no significant FSR expansion or resonance wavelength shifts as compared with the case of coupled identical microdisks, due to the small difference between the two cavities.

5. Conclusion

Acknowledgements

This work was substantially supported by a grant from the Research Grants Council of The Hong Kong Special Administrative Region, China (Project No. 618506). X. Luo acknowledges the fellowship support from the NANO program of HKUST.

References and Links

1.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photon. Tech. Lett. 12, 320–322 (2000). [CrossRef]

2.

J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, “Transmission and group delay of microring coupled-resonator optical waveguides,” Opt. Lett. 31, 456–458 (2006). [CrossRef] [PubMed]

3.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006). [CrossRef] [PubMed]

4.

C. Li, X. Luo, and A. W. Poon, “Dual-microring-resonator electro-optic logic switches on a silicon chip,” Semicond. Sci. Technol., accepted.

5.

X. Luo, J. Y. Lee, and A. W. Poon, “Coupled spiral-shaped microdisk resonators with asymmetric non-evanescent coupling,” in Proceedings of IEEE 4th International Conference on Group IV Photonics, (IEEE, 2007), pp.19–21.

6.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillar,” Appl. Phys. Lett. 83, 1710–1712 (2003). [CrossRef]

7.

M. Kneissl, M. Teepe, N. Miyashita, N. M. Johnson, G. D. Chern, and R. K. Chang, “Current-injection spiral-shaped microcavity disk laser diodes with unidirectional emission,” Appl. Phys. Lett. 84, 2485–2487 (2004). [CrossRef]

8.

T. Ben-Messaoud and J. Zyss, “Unidirectional laser emission from polymer-based spiral microdisks,” Appl. Phys. Lett. 86, 241110 (2005). [CrossRef]

9.

A. Fujii, T. Nishimura, Y. Yoshida, K. Yoshino, and M. Ozaki, “Unidirectional laser emission from spiral microcavity utilizing conducting polymer,” Jap. J. Appl. Phys. 44, L1091–L1093 (2005). [CrossRef]

10.

A. Fujii, T. Takashima, N. Tsujimoto, T. Nakao, Y. Yoshida, and M. Ozaki, “Fabrication and unidirectional laser emission properties of asymmetric microdisks based on poly(p-phenylenevinylene) derivative,” Jap. J. Appl. Phys. 45, L833–L836 (2006). [CrossRef]

11.

N. Tsujimoto, T. Takashima, T. Nakao, K. Masuyama, A. Fujii, and M. Ozaki, “Laser emission from spiral-shaped microdisc with waveguide of conducting polymer,” J. Phys. D: Appl. Phys. 40, 1669–1672 (2007). [CrossRef]

12.

R. M. Audet, M. A. Belkin, J. A. Fan, F. Capasso, E. Narimanov, D. Bour, S. Corzine, J. Zhu, and G. Höfler, “Current injection spiral-shaped chaotic microcavity quantum cascade lasers,” in Conference on Lasers and Electro-Optics 2007, (IEEE and Optical Society of America, 2007), paper CTuE4.

13.

A. Tulek and Z. V. Vardeny, “Unidirectional laser emission from π-conjugated polymer microcavities with broken symmetry,” Appl. Phys. Lett. 90, 161106 (2007). [CrossRef]

14.

S. Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C. M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004). [CrossRef] [PubMed]

15.

T. Y. Kwon, S. Y. Lee, M. S. Kurdoglyan, S. Rim, C. M. Kim, and Y. J. Park, “Lasing modes in a spiral-shaped dielectric microcavity,” Opt. Lett. 31, 1250–1252 (2006). [CrossRef] [PubMed]

16.

C. M. Kim, S. Y. Lee, J. W. Ryu, T. Y. Kwon, S. Rim, J. Lee, and J. Cho, “Characteristics of lasing modes in a spiral-shaped microcavity,” Prog. Theor. Phys. Suppl. 166, 112–118 (2007). [CrossRef]

17.

R. K. Chang, G. E. Fernandes, and M. Kneissl, “The quest for uni-directionality with WGMs in µ-Lasers: coupled oscillators and amplifiers,” in Proceedings of 8th International Conference on Transparent Optical Networks, (IEEE, 2006), 1, pp. 47–51.

18.

G. D. Chern, G. E. Fernandes, R. K. Chang, Q. Song, L. Xu, M. Kneissl, and N. M. Johnson, “High-Q-preserving coupling between a spiral and a semicircle µ-cavity,” Opt. Lett. 32, 1093–1095 (2007). [CrossRef] [PubMed]

19.

J. Y. Lee and A. W. Poon, “Spiral micropillar resonator-based unidirectional channel drop filters,” in Proceedings of 8th International Conference on Transparent Optical Networks, (IEEE, 2006), 1, pp. 62–65.

20.

J. Y. Lee and A. W. Poon, “Spiral-shaped microdisk resonator-based channel drop filters on a silicon nitride chip,” in Proceedings of IEEE 3rd International Conference on Group IV Photonics, (IEEE, 2006), pp.19–21.

21.

A. W. Poon, J. Y. Lee, and C. Chan, “Spiral microdisk resonator-based channel filters on a silicon chip: probing the out-of-plane scattering spectra,” in Proceedings of International Symposium on Biophotonics, Nanophotonics and Metamaterials, (IEEE, 2006), pp.234–239.

22.

J. Y. Lee, X. Luo, and A. W. Poon, “Spiral-shaped microdisk resonator channel drop/add filters: asymmetry in modal distributions,” in Conference on Lasers and Electro-Optics 2007, (IEEE and Optical Society of America, 2007), paper JThD116.

23.

J. Y. Lee, X. Luo, and A. W. Poon, “Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators,” Opt. Express 15, 14650–14666 (2007). [CrossRef] [PubMed]

24.

M. Born and E. Wolf, Principles of Optics, 7th edition (Cambridge, Cambridge University Press, 1999), pp.724–726.

25.

FullWAVE, Rsoft Inc. Research Software, http://www.rsoftinc.com

26.

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguide,” Electron. Lett. 36, 321–322 (2000). [CrossRef]

27.

L. Zhou and A. W. Poon, “Silicon electro-optic modulators using p-i-n diodes embedded 10-micron-diameter microdisk resonators,” Opt. Express 14, 6851–6857 (2006). [CrossRef] [PubMed]

28.

C. Li, L. Zhou, and A. W. Poon, “Silicon microring carrier-injection-based modulators/switches with tunable extinction ratios and OR-logic switching by using waveguide cross-coupling,” Opt. Express 15, 5069–5076 (2007). [CrossRef] [PubMed]

OCIS Codes
(230.3990) Optical devices : Micro-optical devices
(230.5750) Optical devices : Resonators

ToC Category:
Rings, Disks, and Other Cavities

History
Original Manuscript: October 8, 2007
Revised Manuscript: November 29, 2007
Manuscript Accepted: November 29, 2007
Published: December 10, 2007

Virtual Issues
Physics and Applications of Microresonators (2007) Optics Express

Citation
Xianshu Luo and Andrew W. Poon, "Coupled spiral-shaped microdisk resonators with non-evanescent asymmetric inter-cavity coupling," Opt. Express 15, 17313-17322 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-25-17313


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References

  1. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, "Higher order filter response in coupled microring resonators," IEEE Photon. Tech. Lett. 12, 320-322 (2000). [CrossRef]
  2. J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, "Transmission and group delay of microring coupled-resonator optical waveguides," Opt. Lett. 31, 456-458 (2006). [CrossRef] [PubMed]
  3. Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96, 123901 (2006). [CrossRef] [PubMed]
  4. C. Li, X. Luo, and A. W. Poon, "Dual-microring-resonator electro-optic logic switches on a silicon chip," Semicond. Sci. Technol., accepted.
  5. X. Luo, J. Y. Lee and A. W. Poon, "Coupled spiral-shaped microdisk resonators with asymmetric non-evanescent coupling," in Proceedings of IEEE 4th International Conference on Group IV Photonics, (IEEE, 2007), pp.19 - 21.
  6. G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, "Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillar," Appl. Phys. Lett. 83, 1710 - 1712 (2003). [CrossRef]
  7. M. Kneissl, M. Teepe, N. Miyashita, N. M. Johnson, G. D. Chern, and R. K. Chang, "Current-injection spiral-shaped microcavity disk laser diodes with unidirectional emission," Appl. Phys. Lett. 84, 2485 - 2487 (2004). [CrossRef]
  8. T. Ben-Messaoud and J. Zyss, "Unidirectional laser emission from polymer-based spiral microdisks," Appl. Phys. Lett. 86, 241110 (2005). [CrossRef]
  9. A. Fujii, T. Nishimura, Y. Yoshida, K. Yoshino, and M. Ozaki, "Unidirectional laser emission from spiral microcavity utilizing conducting polymer," Jap. J. Appl. Phys. 44, L1091-L1093 (2005). [CrossRef]
  10. A. Fujii, T. Takashima, N. Tsujimoto, T. Nakao, Y. Yoshida, and M. Ozaki, "Fabrication and unidirectional laser emission properties of asymmetric microdisks based on poly(p-phenylenevinylene) derivative," Jap. J. Appl. Phys. 45, L833-L836 (2006). [CrossRef]
  11. N. Tsujimoto, T. Takashima, T. Nakao, K. Masuyama, A. Fujii, and M. Ozaki, "Laser emission from spiral-shaped microdisc with waveguide of conducting polymer," J. Phys. D: Appl. Phys. 40, 1669-1672 (2007). [CrossRef]
  12. R. M. Audet, M. A. Belkin, J. A. Fan, F. Capasso, E. Narimanov, D. Bour, S. Corzine, J. Zhu, and G. Höfler, "Current injection spiral-shaped chaotic microcavity quantum cascade lasers," in Conference on Lasers and Electro-Optics 2007, (IEEE and Optical Society of America, 2007), paper CTuE4.
  13. A. Tulek and Z. V. Vardeny, "Unidirectional laser emission from π-conjugated polymer microcavities with broken symmetry," Appl. Phys. Lett. 90, 161106 (2007). [CrossRef]
  14. S. Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C. M. Kim, "Quasiscarred resonances in a spiral-shaped microcavity," Phys. Rev. Lett. 93, 164102 (2004). [CrossRef] [PubMed]
  15. T. Y. Kwon, S. Y. Lee, M. S. Kurdoglyan, S. Rim, C. M. Kim, and Y. J. Park, "Lasing modes in a spiral-shaped dielectric microcavity," Opt. Lett. 31, 1250 - 1252 (2006). [CrossRef] [PubMed]
  16. C. M. Kim, S. Y. Lee, J. W. Ryu, T. Y. Kwon, S. Rim, J. Lee, and J. Cho, "Characteristics of lasing modes in a spiral-shaped microcavity," Prog. Theor. Phys.Suppl. 166, 112-118 (2007). [CrossRef]
  17. R. K. Chang, G. E. Fernandes, and M. Kneissl, "The quest for uni-directionality with WGMs in μ-Lasers: coupled oscillators and amplifiers," in Proceedings of 8th International Conference on Transparent Optical Networks, (IEEE, 2006), 1, pp. 47-51.
  18. G. D. Chern, G. E. Fernandes, R. K. Chang, Q. Song, L. Xu, M. Kneissl, and N. M. Johnson, "High-Q-preserving coupling between a spiral and a semicircle μ-cavity," Opt. Lett. 32, 1093-1095 (2007). [CrossRef] [PubMed]
  19. J. Y. Lee and A. W. Poon, "Spiral micropillar resonator-based unidirectional channel drop filters," in Proceedings of 8th International Conference on Transparent Optical Networks, (IEEE, 2006), 1, pp. 62-65.
  20. J. Y. Lee and A. W. Poon, "Spiral-shaped microdisk resonator-based channel drop filters on a silicon nitride chip," in Proceedings of IEEE 3rd International Conference on Group IV Photonics, (IEEE, 2006), pp.19 - 21.
  21. A. W. Poon, J. Y. Lee, and C. Chan, "Spiral microdisk resonator-based channel filters on a silicon chip: probing the out-of-plane scattering spectra," in Proceedings of International Symposium on Biophotonics, Nanophotonics and Metamaterials, (IEEE, 2006), pp.234 - 239.
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