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Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators: Reply
Optics Express, Vol. 16, Issue 8, pp. 5876-5877 (2008)
http://dx.doi.org/10.1364/OE.16.005876
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Abstract
We respond to the comment [Opt. Express 16, to be published (2008)] J. Wiersig, on our recent work reporting on the reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators [J. Y. Lee et al., Opt. Express, 15 (22), 14650 (2007)].
© 2008 Optical Society of America
The purpose of this letter is to respond to the comment of J. Wiersig [1] directed to our original paper [2] describing the reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators. While we thank the author for taking an interest in and providing an extended discussion on this subject, we must clarify here that our methodology and conclusions in [2] remain valid and are not contradicting the numerical studies presented in [1].
J. Wiersig, “Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiralshaped microdisk resonators: Comment,” Opt. Express , to be published. [PubMed]
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) http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14650. [CrossRef] [PubMed]
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) http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14650. [CrossRef] [PubMed]
J. Wiersig, “Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiralshaped microdisk resonators: Comment,” Opt. Express , to be published. [PubMed]
Our original paper [2] presented comprehensive experimental and numerical studies on waveguide-coupled spiral-shaped microdisk resonators. Based on (i) transmission measurements (Fig. 2), (ii) out-of-plane scattering measurements (Figs. 3–4), and (iii) numerical simulations (Figs. 5–9), we concluded that waveguide-coupled spiral-shaped microdisk resonators exhibit identical resonance wavelengths and quality factors (Q’s) with asymmetric modal distributions in clockwise (CW) and counterclockwise (CCW) traveling waves. The traveling waves were selectively excited by input coupling light from either an evanescently coupled waveguide at the cavity sidewall or a directly coupled waveguide seamlessly jointed at the spiral notch. The modal distributions depend on the input coupling direction and coupling mechanism. It is worth mentioning that our measurements imposed a spectral resolution of 0.02 nm, while our spectra simulations imposed a spectral resolution of 0.09 nm.
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) http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14650. [CrossRef] [PubMed]
In the comment [1], the author found two non-degenerate modes displaying similar modal distributions by numerically solving eigenmodes in a spiral-shaped microdisk resonator without coupled waveguides. This is a useful result as it explicitly shows the possible existence of non-degenerate modes in spiral-shaped microresonators. Should non-degenerate modes with similar degree of mode splitting exist in our waveguide-coupled microresonators, our spectral resolutions in both experiments and numerical simulations would have forbidden us from resolving the split modes.
J. Wiersig, “Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiralshaped microdisk resonators: Comment,” Opt. Express , to be published. [PubMed]
However, the comment [1] and our original work [2] are not necessarily contradicting. While possible non-degenerate modes can display similar modal distributions, our observations focus on the CW and CCW traveling-wave resonances which we selectively excited via waveguide coupling. Our observed field patterns are with identical resonance wavelength (as a result of reciprocity), are traveling in opposite directions (selectively launched from the different ports of the coupled waveguides), and are displaying distinguishable features (Figs. 3–4 for experiments and Figs. 6, 7, 9 for simulations). In passing, we mention that our simulations in [2] adopted radius r0
=10 µm and deformation parameter ε=0.04 as detailed in our original paper, not r0
=9.6 µm as suggested in [1].
J. Wiersig, “Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiralshaped microdisk resonators: Comment,” Opt. Express , to be published. [PubMed]
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) http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14650. [CrossRef] [PubMed]
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) http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14650. [CrossRef] [PubMed]
J. Wiersig, “Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiralshaped microdisk resonators: Comment,” Opt. Express , to be published. [PubMed]
In conclusion, we believe that the reciprocal transmissions and the corresponding asymmetric field patterns in waveguide-coupled spiral-shaped microdisk resonators reported in our original work [2] are reasonable. In particular, the spectra measurements should provide relevant experimental inputs to further understanding resonances and unidirectional lasing in spiral-shaped microdisk resonators [3]. Although we are fully aware of the fact that the side-coupled and notch-coupled waveguides can perturb the boundary condition from that of an isolated spiral-shaped microresonator, the waveguide coupling is a necessary device feature to turn the microresonator into practical on-chip devices for signal processing functionalities, as exemplified in some most recent work [4–6].
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) http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14650. [CrossRef] [PubMed]
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]
X. Luo and A. W. Poon, “Coupled spiral-shaped microdisk resonators with non-evanescent asymmetric inter-cavity coupling,” Opt. Express 15, 17313–17322 (2007), http://www.opticsinfobase.org/abstract.cfm?id=148395. [CrossRef] [PubMed]
References and links
J. Wiersig, “Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiralshaped microdisk resonators: Comment,” Opt. Express , to be published. [PubMed] | |
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) http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14650. [CrossRef] [PubMed] | |
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] | |
X. Luo and A. W. Poon, “Coupled spiral-shaped microdisk resonators with non-evanescent asymmetric inter-cavity coupling,” Opt. Express 15, 17313–17322 (2007), http://www.opticsinfobase.org/abstract.cfm?id=148395. [CrossRef] [PubMed] | |
X. Luo, C. Li, and A. W. Poon, “Double-notch-shaped microdisk resonator-based devices in silicon-oninsulator,” accepted by Conference on Lasers and Electro-Optics 2008, (IEEE and Optical Society of America, 2008), San Jose, CA, USA. | |
G. E. Fernandes, L. Guyot, G. D. Chern, M. Kneissl, N. M. Johnson, Q. Song, L. Xu, and R. K. Chang, “Wavelength and intensity switching in directly coupled semiconductor microdisk lasers,” Opt. Lett. 33, 605–607 (2008). [CrossRef] [PubMed] |
OCIS Codes
(230.3990) Optical devices : Micro-optical devices
(230.5750) Optical devices : Resonators
ToC Category:
Optical Devices
History
Original Manuscript: March 19, 2008
Revised Manuscript: April 9, 2008
Manuscript Accepted: April 9, 2008
Published: April 11, 2008
Citation
Xianshu Luo, Hui Chen, and Andrew W. Poon, "Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators: Reply," Opt. Express 16, 5876-5877 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-8-5876
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References
- J. Wiersig, "Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators: Comment," Opt. Express, to be published. [PubMed]
- 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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14650. [CrossRef] [PubMed]
- 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]
- X. Luo and A. W. Poon, "Coupled spiral-shaped microdisk resonators with non-evanescent asymmetric inter-cavity coupling," Opt. Express 15, 17313-17322 (2007), http://www.opticsinfobase.org/abstract.cfm?id=148395. [CrossRef] [PubMed]
- X. Luo, C. Li, and A. W. Poon, "Double-notch-shaped microdisk resonator-based devices in silicon-on-insulator," accepted by Conference on Lasers and Electro-Optics 2008, (IEEE and Optical Society of America, 2008), San Jose, CA, USA.
- G. E. Fernandes, L. Guyot, G. D. Chern, M. Kneissl, N. M. Johnson, Q. Song, L. Xu, and R. K. Chang, "Wavelength and intensity switching in directly coupled semiconductor microdisk lasers," Opt. Lett. 33, 605-607 (2008). [CrossRef] [PubMed]
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