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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 22 — Oct. 29, 2007
  • pp: 14650–14666
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Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators

Jonathan Y. Lee, Xianshu Luo, and Andrew W. Poon  »View Author Affiliations


Optics Express, Vol. 15, Issue 22, pp. 14650-14666 (2007)
http://dx.doi.org/10.1364/OE.15.014650


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Abstract

We report transmission spectra and mode-field distributions of a waveguide-coupled spiral-shaped microdisk resonator on a silicon nitride-on-silica substrate. Our measured and simulated transmission spectra reveal reciprocal transmissions between clockwise and counterclockwise traveling-waves of such microcavity that lacks mirror symmetry. Our measured out-of-plane scattering intensity distributions and simulated steady-state mode-field patterns, however, indicate asymmetric modal distributions that depend on the sense of lightwave circulations and the input-coupling mechanisms. We discuss implications of the observed reciprocal transmissions with asymmetric modal distributions to unidirectional lasing from spiral-shaped microcavities reported in the literature.

© 2007 Optical Society of America

1. Introduction

Micrometer-scale ring or disk resonators, with their key merits of high-Q modes, compact size, and accessibility with optical waveguides, have long been regarded as promising microlaser cavities and wavelength-selective filter components in large-scale-integrated photonic circuits [1–3

1. R. K. Chang and A. J. Campillo, eds. Optical Processes in Microcavities (World Scientific, Singapore, 1996). [CrossRef]

]. However, one major shortcoming of microring/disk laser cavities is that clockwise (CW) and counterclockwise (CCW) traveling-wave modes are degenerate. The degeneracy between CW and CCW traveling-wave modes results in undesirable bidirectional emissions from waveguide-coupled microresonator lasers, as recently reported by Fang et al., [4

4. A. W. Fang, R. Jones, H. Park, O. Cohen, O. Raday, M. J. Paniccia, and J. E. Bowers, “Integrated AlGaInAs-silicon evanescent racetrack laser and photodetector,” Opt. Express 15, 2315–2322 (2007). [CrossRef] [PubMed]

] on racetrack-shaped microring lasers. In order to obtain unidirectionality from ring lasers, conventional wisdom employs selective feedback to only one traveling-wave mode, which consequently lases and unidirectionally emits [5

5. A. E. Siegman, Lasers (University Science Books, 1986), pp. 532–538.

]. For waveguide ring lasers, selective feedback approach for unidirectional lasing has been demonstrated by using asymmetric waveguide structures including S-waveguides [6–7

6. J. P. Hohimer, G. A. Vawter, and D. C. Craft, “Unidirectional operation in a semiconductor ring diode laser,” Appl. Phys. Lett. 62, 1185–1187 (1993). [CrossRef]

], tapered waveguides [8

8. J. J. Liang, S. T. Lau, M. H. Leary, and J. M. Ballantyne, “Unidirectional operation of waveguide diode ring lasers,” Appl. Phys. Lett. 70, 1192–1194 (1997). [CrossRef]

], and spiral waveguides [9

9. H. Cao, C. Liu, H. Ling, H. Deng, M. Benavidez, V. A. Smagley, and R. B. Caldwell, “Frequency beating between monolithically integrated semiconductor ring lasers,” Appl. Phys. Lett. 86, 041101 (2005). [CrossRef]

].

Alternatively, Chern et al. [10

10. 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]

] in their pioneering work demonstrated unidirectional lasing from a spiral-shaped micropillar, which was believed to lift the degeneracy between CW and CCW traveling-wave modes due to the lack of mirror symmetry in the cavity shape.

Unidirectional lasing emission was observed to be non-evanescently out-coupled from the spiral notch. Later experiments by a number of independent research groups confirmed the unidirectional lasing from spiral-shaped micropillar/disk lasers [11–17

11. 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]

] using various material systems (III-V semiconductors [11

11. 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]

, 16

16. 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.

], polymer [12–15

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

, 17

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

]), quantum well structures, and pumping techniques. Recently, optical switching mechanism based on high-Q-preserving direct non-evanescent coupling between a spiral-shaped microdisk laser and a semicircle microdisk amplifier has also been proposed and demonstrated [21–22

21. R. K. Chang, G. E. Fernandes, and M. Kneissl, “The Quest for Uni-Directionality with WGMs in u-Lasers: Coupled Oscillators and Amplifiers,” in Proceedings of 8th International Conference on Transparent Optical Networks, (IEEE, 2006), 1, pp. 47–51.

].

2. Wavelength-selective filter configurations, device fabrications, and experimental setup

Figures 1(a)–(c) depict the schematics of the waveguide-coupled spiral-shaped microdisk resonator-based wavelength-selective filter configurations. The filter comprises a spiral-shaped microdisk, a single-mode waveguide that is seamlessly butt-coupled to the spiral notch, and another single-mode waveguide that is evanescently side-coupled to the cavity [23–26

23. 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.

]. Lightwave can be in/out-coupled to the microdisk non-evanescently via the notch-waveguide or evanescently from the side-coupled waveguide. The spiral shape is defined as [24

24. 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.

]:

r(ϕ)=r0(1ε2πϕ)
(1)

where r 0 is the spiral radius at azimuthal angle ϕ = 0, and e is the deformation parameter. The radius mismatch of r 0 ε at ϕ = 2π defines the spiral notch width and the notch-waveguide width. The notch-waveguide and the side-coupled waveguide do not necessarily have the same width, thus enabling the non-evanescent and evanescent coupling to be separately optimized.

The filter functionality depends on from which waveguide-port the lightwave is input-coupled. The evanescently in-coupled CCW traveling-waves do not favor out-coupling to the notch-waveguide, and thus the microdisk can act as a notch filter (Fig. 1(a)). In contrast, the evanescently in-coupled CW traveling-waves favor partial transmission to the notch-waveguide, and thus the microdisk can act as a drop filter (Fig. 1(b)). Moreover, the non-evanescently in-coupled CCW traveling-waves also do not favor out-coupling to the notch-waveguide upon a cavity round trip, yet the cavity mode field can be evanescently out-coupled to the side-coupled waveguide. We refer to this configuration as add-only filter. The non-evanescent coupling via the notch junction offers a potentially efficient coupling to the spiral-shaped microdisk resonances, without imposing the technologically-challenging constraint for fabricating an evanescent coupling gap.

We fabricate the spiral-shaped microdisk filters on a silicon nitride-on-silica substrate using standard silicon microelectronics processes. In brief, a bulk silicon wafer is first thermally oxidized to form a 1.5-μm-thick silica under-cladding layer. A 1.0-μm-thick low-stress silicon nitride device layer is then deposited using low-pressure chemical-vapor deposition (LPCVD). The device structures are defined by photolithography (i-line, 365 nm) and CF4-based reactive ion plasma etching (RIE). The etch depth is ~0.9 μm.

Figure 1(d) shows the scanning electron micrograph (SEM) of the spiral-shaped microdisk filter. We adopt ro = 25 μm and ε = 0.016. The small ε value gives a notch size of 0.4 μm for single-mode notch-waveguide coupling. Insets show the zoom-in view SEMs of the evanescent-coupling region and the notch junction. The side-coupled waveguide width is ~450 nm while the notch-waveguide width is ~400 nm. The gap spacing between the cavity sidewall and the side-coupled waveguide (and between the cavity sidewall and the notch-waveguide) is ~300 nm limited by our lithography.

Figure 1(e) schematically depicts the experimental setup. We use an external-cavity wavelength-tunable diode laser with wavelength tuning range between 1505 nm and 1585 nm (spectral resolution of 20 pm). Laser light is coupled into a polarization-maintaining (PM) single-mode (SM) lensed-fiber for end-firing to the waveguide. The lensed-fiber output spot diameter is ~2.5 μm, which approximately matches the waveguide tapered end-face. The waveguide is out-coupled to another lensed-fiber. We lock-in detect the transmission spectra of notch/drop/add-only filters by separately in-coupling to the three waveguide ports. The inset shows the optical micrograph of the filter. The notch-waveguide has a 180°-bend (with a large 50-μm radius of curvature) towards the throughput-port direction. This enables throughput measurements for add-only filter, and enables measurements of both throughput-and drop-port spectra in the same output direction for drop filter. For each in-coupling configuration, we also collect the out-of-plane scattering intensities near the spiral notch junction and the evanescent-coupling region by linearly scanning a third lensed-fiber at a height of a few μm above the cavity top surface.

Fig. 1. (a)–(c) Schematics of the spiral-shaped microdisk resonator-based filter configurations. The configurations assume different wavelength-selective filter functionalities depending on the input-coupling port. (a) Notch filter: the arrows depict the evanescently in-coupled CCW traveling-waves that do not favor out-coupling to the notch-waveguide. (b) Drop filter: the arrows depict the evanescently in-coupled CW traveling-waves that favor partial transmission to the notch-waveguide. (c) Add-only filter: the arrows depict the non-evanescently in-coupled CCW traveling-waves that do not favor out-coupling to the notch-waveguide. The throughput-port transmissions (labeled with “*”) of notch and drop filters are reciprocal related. The drop-port transmission of drop filter and the throughput-port transmission of add-only filter (labeled with “**”) are also reciprocal related. (d) SEM of the fabricated spiral-shaped microdisk filter in silicon nitride. The two red circles denote the evanescent-coupling region and the notch junction. The coordinates define the fiber scanning directions for the out-of-plane scattering measurements. Left inset: zoom-in view SEM of the evanescent-coupling region. Right inset: zoom-in view SEM of the notch junction. (e) Schematic of the experimental setup for transmission and out-of-plane scattering measurements of the three filter configurations. Bottom inset: optical micrograph of the spiral-shaped microdisk filter with arrows denoting the three filter operations.

3. Transmission spectra measurements

We identify a free spectral range (FSR) of ~7.2 nm, which is consistent with the spiral microdisk circumference. This suggests that the resonance lightwave is guided along the microcavity rim in round-trips as in WG modes. The observed highest Q value is ~12,000 with an extinction ratio (ER) exceeding 5 dB. We estimate Q values from the measured spectra using the relationship Q = λ0/∆λ, where λ0 is the resonance wavelength and Δλ, is the estimated 3-dB-linewidth. However, as resonances in waveguide-coupled microresonator transmission spectra typically exhibit asymmetric line shapes [31

31. S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80, 908–910 (2002). [CrossRef]

], our Q estimations from the transmission spectra can be skewed by the line shapes.

Fig. 2. (a) Measured TE-polarized throughput-port transmission spectra of notch (blue line) and drop (green line) filters. The multimode spectra show essentially identical spectral features, suggesting reciprocal transmissions between the evanescently in-coupled CCW and CW traveling-waves. (b) Measured TE-polarized drop-port transmission spectrum of drop filter (green line) and throughput-port spectrum of add-only filter (red line). The multimode spectra essentially overlap albeit with some mismatches. Most of the modal features in (a) find corresponding resonances in (b). The waveguide transmission intensity is normalized to the input-coupling lensed-fiber transmission intensity.

The observation of reciprocal transmissions in a spiral-shaped microdisk resonator is significant, though may not be surprising in hindsight. The observed reciprocal transmissions can be expected from reciprocity relations [27–30

27. R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004). [CrossRef]

]. In essence, reciprocity relations mean that light transmissions are preserved by interchanging positions of the source and the detector in a linear dielectric media with symmetric permittivity tensors [27

27. R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004). [CrossRef]

]. Reciprocity relations have been proven in stratified media [28

28. M. Nieto-Vesperinas and E. Wolf, “Generalized Stokes reciprocity relations for scattering from dielectric objects of arbitrary shape,” J. Opt. Soc. Am. A. 3, 2038 – 2046 (1986). [CrossRef]

], in scattering from dielectric objects of arbitrary shapes [28

28. M. Nieto-Vesperinas and E. Wolf, “Generalized Stokes reciprocity relations for scattering from dielectric objects of arbitrary shape,” J. Opt. Soc. Am. A. 3, 2038 – 2046 (1986). [CrossRef]

, 29

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

], and in one-dimensional Fabry-Perot cavities [30

30. G. S. Agarwal and S. Dutta Gupta, “Reciprocity relations for reflected amplitudes,” Opt. Lett. 27, 1205 – 1207 (2002). [CrossRef]

]. Hence, it is conceivable that the transmissions of the passive silicon nitride waveguide-coupled spiral microdisk resonator follow reciprocity relations. To our knowledge, this is the first report on reciprocity relations in two-dimensional microdisk resonators in a linear dielectric medium.

Furthermore, the concept of reciprocity relations provides a new insight in understanding the spiral-shaped microdisk cavity CW and CCW traveling-waves. Reciprocal transmissions with identical resonance spectra and identical quality factors imply that CW and CCW traveling-wave modes encounter identical total cavity loss. The total cavity loss in a spiral-shaped microdisk with direct-coupled waveguide comprise (i) out-coupling via the notch-waveguide, (ii) diffraction and scattering at the notch junction, (iii) distributed cavity loss along the cavity sidewall (including curved sidewall diffraction, refraction, and roughness-induced scattering), and (iv) material absorption. Given CW traveling-wave modes can preferentially out-couple via the notch-waveguide, the loss from (ii) and (iii) should therefore be relatively lower. In contrast, CCW traveling-wave modes can see relatively higher loss from (ii) and/or (iii) in order to balance the relatively lower loss from (i). We remark that scattering at the notch junction and along the cavity sidewall may result in cross-coupling between CCW and CW traveling-wave modes. While a large distributed cavity loss can be originated from a less confined traveling-wave orbit (e.g. a quasiscarred three-bounce mode [18

18. 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]

]).

4. Out-of-plane scattering spectra measurements

Fig. 3. Measured out-of-plane scattering spectra near the notch junction region for (a) notch, (b) drop, and (c) add-only filters. (d) Light scattering spectra near the notch junction (x = 50 μm, y = -5 μm). The estimated Q values are labeled. We see no clear evidence for distinct Q values between CW and CCW traveling-wave modes. (e) Measured throughout- and drop-port transmission spectra of drop filter for reference. (f)-(g) Light scattering intensity profiles at resonances of (f) 1552.06 nm, and (g) 1553.02 nm. The profiles suggest input-port dependent modal distributions. The intensity profile width is estimated by the distance between the 5% of the maximum intensity and the cavity rim.

Figures 3(a)–(c) show the averaged out-of-plane scattering spectra near the notch junction in the x-direction (centered at y = -5 μm) for notch, drop, and add-only filters. The spatial scanning spans from x = 39 μm (11 μm inward from the notch at x = 50 μm) to slightly outside the notch junction. The scattering intensity is normalized to the input-coupling lensed-fiber transmission intensity. For all three filter configurations, the spatial profiles reveal similarly pronounced scattering intensities in the neighborhood of the notch junction (x ≈ 50 μm). This suggests that CCW and CW traveling-waves encounter similar out-of-plane scattering at the notch junction, regardless of the evanescent or non-evanescent input-coupling.

Figure 3(d) depicts the measured light scattering spectra at the notch junction (x = 50 μm). Figure 3(e) shows the measured throughput- and drop-port transmission spectra of drop filter for reference (see Fig. 2). The light scattering spectra and the transmission spectra exhibit the same resonance wavelengths at 1552.06 nm and 1553.02 nm. The estimated Q values from the scattering spectra of notch filter marginally differ from those estimated for drop filter. We note that the difference in the estimated Q values here is similar to that between CW and CCW traveling-wave modes in circular microdisk resonators in our control experiments (data not shown). Thus, our light scattering measurements near the notch junction reveal no evidence beyond tolerance that CW and CCW traveling-wave modes see different Q’s or total cavity loss. We are not able to estimate the Q values from the add-only filter scattering spectrum due to the asymmetric broadened line shapes.

Fig. 4. Measured out-of-plane scattering spectra near the evanescent-coupling region for (a) notch, (b) drop, and (c) add-only filters. The intensity profiles display distinct spatial and spectral features among the three filter configurations, and also from those near the notch junction. (d) Light scattering spectra near the evanescent-coupling region (x = 0 μm, y = 0 μm). The estimated Q values are labeled. (e) Measured throughout- and drop-port transmission spectra of drop filter for reference. (f)-(g) Light scattering intensity profiles at resonances of (f) 1552.06 nm, and (g) 1553.02 nm. The profiles suggest input-port dependent modal distributions.

5. FDTD simulations

5.1 Simulated transmission spectra

Fig. 5. (a) FDTD-simulated TE-polarized throughput-port transmission spectra of notch (blue dashed line) and drop (green line) filters. The multimode spectra overlap with each other, indicating reciprocal transmissions. The resonances within a FSR are labeled as A1, B1, C1, D1, E1, F1, G1, and H1. (b) FDTD-simulated TE-polarized drop-filter drop-port transmission spectrum (green line) and add-only filter throughput-port transmission spectrum (red dashed line). The multimode transmission spectra are identical, with corresponding resonances in the throughput-port transmission spectra in (a).

5.2 Simulated cavity internal-field spectra near the notch junction and the evanescent-coupling region

We simulate the cavity internal-field spectra near the notch junction and the evanescent-coupling region. We integrate the cavity fields over a square area of 1.2 μm × 1.2 μm, which is approximately in scale with the lensed-fiber field-of-view relative to the actual cavity size. We choose the wavelength range of 1531 nm – 1537 nm, spanning resonances H1 and A2. The integrated internal-field intensity is normalized to the input-field intensity.

Fig. 6. FDTD-simulated cavity internal-field spectra along the x-direction near the notch junction for (a) notch, (b) drop, and (c) add-only filters. (d) Simulated internal-field spectra at the notch junction (x = 19 μm, y = 0 μm). (e) Simulated drop-filter throughput- and drop-port transmission spectra for reference. (f), (g) Simulated internal-field intensity profiles at resonances (f) H1 (1532.72 nm), and (g) A2 (1535.13 nm). The intensity profile width is estimated by the distance between the 5% of the maximum intensity and the cavity rim.

Figure 6(d) depicts the simulated cavity internal-field spectra at the notch junction (x = 19 μm). We find the same resonance H1 (1532.72 nm) as in the transmission spectra shown in Fig. 6(e). Yet, resonance A2 (1535.13 nm) cannot be discerned from the cavity internal-field spectra due to the pulse-excitation-induced multimode line-shape broadening. The estimated Q values at resonance H1 are essentially identical for drop and add-only filters, and thus suggest no evidence that CW and CCW traveling-wave modes see non-reciprocal total cavity losses.

Fig. 7. FDTD-simulated internal-field spectra along the x-direction near the evanescent coupling region for (a) notch-, (b) drop-, and (c) add-only filters. (d) Simulated internal-field spectra near the side-coupled waveguide (x = 1 μm, y = 0 μm). (e) Simulated drop-filter throughput- and drop-port transmission spectra for reference. (f)-(g) Simulated internal-field intensity profiles at resonances (f) H1 (1532.72 nm), and (g) A2 (1535.13 nm). The intensity profile width is estimated by the distance between the 5% of the maximum intensity and the cavity rim.

We therefore conclude that our simulated reciprocal transmission spectra, along with input-port-dependent cavity internal-field spectra near the notch junction and the evanescent-coupling region, are consistent with our measurements. We find no evidence that CW and CCW traveling-wave modes display different Q’s.

5.3 Simulated input-coupling field patterns

In order to gain further insights to the input-coupling dependence, we simulate the input-coupling field patterns. Figures 8(a)–(c) show the FDTD-simulated TE-polarized input-coupling H-field patterns at wavelength of 1512.52 nm (resonance A1) for each filter configuration. We consider only the input-coupling side of the cavity in the computation window by truncating the other half by a perfectly matched layer (PML). The evanescently in-coupled field patterns for notch and drop filters display essentially identical Gaussian beam-like profiles (due to the curved sidewall focusing effect). While the non-evanescently in-coupled field pattern for add-only filter shows that the lightwave is diffracted at the notch junction.

Fig. 8. FDTD-simulated TE-polarized input-coupling H-field patterns at wavelength of 1512.52 nm (resonance A1), and the corresponding spatial Fourier transforms, for (a), (d) notch filter, (b), (e) drop filter, and (c), (f) add-only filter. The Fourier transform is applied over the dashed rectangular windows depicted in (a)-(c). Only the Fourier component amplitudes above the half-maximum are shown in (d)-(f).

5.4 Simulated mode-field patterns

Fig. 9. FDTD-simulated TE-polarized steady-state resonance mode H-field patterns for notch (left column), drop (center column), and add-only (right column) filters. (a)-(c) resonance A1, (d)-(f) resonance H1, and (g)-(i) resonance A2.

6. Discussion

We also confirm that the reciprocal transmissions remain valid in both experimental measurements (within tolerance) and numerical simulations for large-ε waveguide-coupled spiral-shaped microdisks, with up to ε = 0.16 for experiments and ε = 0.20 for simulations (data not shown). We conduct the experiments on the same chip as the ε = 0.016 devices reported here.

Hence, based on this work, we offer our interpretations to unidirectional lasing from spiral-shaped microcavities as follows: Given the same total cavity losses (the same Q’s) between CCW and CW traveling-wave modes, we expect CCW traveling-wave modes see larger distributed losses along the cavity rim and/or diffraction/scattering losses at the notch junction than CW traveling-wave modes in order to balance CW traveling-wave mode direct out-coupling losses (see Sec. 3). As scattering along the cavity rim and diffraction/scattering at the notch junction can result in cross-coupling between CCW and CW traveling-wave modes, it is thus conceivable that the CCW-to-CW cross-coupling can exceed the CW-to-CCW cross-coupling, resulting in selective feedback to unidirectional lasing in CW traveling-wave modes that enable out-coupling via the spiral notch. Our proposal is much similar to the conventional selective feedback approach to obtaining unidirectionality from ring lasers [5

5. A. E. Siegman, Lasers (University Science Books, 1986), pp. 532–538.

]. Further experiments on silicon waveguide-coupled spiral-shaped microdisks exploiting silicon Raman gain [34

34. H. Chen, J. Y. Lee, A. W. Poon, and H. K. Tsang, “Non-evanescently pumped Raman silicon lasers using spiral-shaped microdisks,” in Conference on Lasers and Electro-Optics 2007, (IEEE and Optical Society of America, 2007), paper JThD114. [CrossRef]

] are in progress in order to test our hypothesis.

7. Conclusion

Our experiments and numerical simulations of a waveguide-coupled spiral-shaped microdisk resonator have revealed reciprocal throughput-port transmissions between the evanescently in-coupled clockwise (CW) and counterclockwise (CCW) traveling-waves, and also between the evanescently in-coupled CW traveling-wave drop-port transmission and the non-evanescently in-coupled CCW traveling-wave throughput-port transmission. The reciprocal transmissions suggest that CW and CCW traveling-wave modes see the same cavity Q’s, and thus reciprocal total cavity losses. This observation is, however, inconsistent with the general belief that CW and CCW traveling-wave modes in a spiral-shaped microdisk see different total cavity losses.

Spiral-shaped microdisks with non-evanescent resonance coupling points to a possible paradigm shift in microresonator-based device designs from conventional microresonators that impose evanescent coupling. One implication is that spiral-shaped microdisk silicon Raman lasers can be non-evanescently pumped through the spiral notch from a seamlessly butt-coupled waveguide, and the unidirectional lasing emission can then be out-coupled evanescently or non-evanescently [34

34. H. Chen, J. Y. Lee, A. W. Poon, and H. K. Tsang, “Non-evanescently pumped Raman silicon lasers using spiral-shaped microdisks,” in Conference on Lasers and Electro-Optics 2007, (IEEE and Optical Society of America, 2007), paper JThD114. [CrossRef]

].

Acknowledgements

We thank Prof. Richard K. Chang of Yale University for his foresight on spiral-shaped microresonators; Prof. Vahid Sandoghdar of Eldgenössische Technische Hochschule (ETH) Zürich for his suggestion on probing the out-of-plane scattering by a scanning fiber. X. Luo acknowledges the fellowship support from the NANO program of HKUST. This work was substantially supported by a grant from the Research Grants Council of The Hong Kong Special Administrative Region, China (Project No. 618506).

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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]

15.

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]

16.

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.

17.

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

18.

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]

19.

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]

20.

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

21.

R. K. Chang, G. E. Fernandes, and M. Kneissl, “The Quest for Uni-Directionality with WGMs in u-Lasers: Coupled Oscillators and Amplifiers,” in Proceedings of 8th International Conference on Transparent Optical Networks, (IEEE, 2006), 1, pp. 47–51.

22.

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]

23.

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.

24.

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.

25.

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.

26.

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. [CrossRef]

27.

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004). [CrossRef]

28.

M. Nieto-Vesperinas and E. Wolf, “Generalized Stokes reciprocity relations for scattering from dielectric objects of arbitrary shape,” J. Opt. Soc. Am. A. 3, 2038 – 2046 (1986). [CrossRef]

29.

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

30.

G. S. Agarwal and S. Dutta Gupta, “Reciprocity relations for reflected amplitudes,” Opt. Lett. 27, 1205 – 1207 (2002). [CrossRef]

31.

S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80, 908–910 (2002). [CrossRef]

32.

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

33.

E. E. Narimanov and V. A. Podolskiy, “Dynamical localization in spiral microlasers with unidirectional emission,” in Conference on Lasers and Electro-Optics 2004, (IEEE and Optical Society of America, 2004), paper IThI5.

34.

H. Chen, J. Y. Lee, A. W. Poon, and H. K. Tsang, “Non-evanescently pumped Raman silicon lasers using spiral-shaped microdisks,” in Conference on Lasers and Electro-Optics 2007, (IEEE and Optical Society of America, 2007), paper JThD114. [CrossRef]

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

ToC Category:
Optical Devices

History
Original Manuscript: June 18, 2007
Revised Manuscript: September 3, 2007
Manuscript Accepted: October 5, 2007
Published: October 23, 2007

Citation
Jonathan Y. Lee, Xianshu Luo, and Andrew 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/oe/abstract.cfm?URI=oe-15-22-14650


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References

  1. R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996). [CrossRef]
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  3. P. R. Romeo, J. Van Campenhout, P. Regreny, A. Kazmierczak, C. Seassal, X. Letartre, G. Hollinger, D. Van Thourhout, R. Baets, J. M. Fedeli, and L. Di Cioccio, "Heterogeneous integration of electrically driven microdisk based laser sources for optical interconnects and photonic ICs," Opt. Express 14, 3864-3871 (2006). [CrossRef]
  4. A. W. Fang, R. Jones, H. Park, O. Cohen, O. Raday, M. J. Paniccia, and J. E. Bowers, "Integrated AlGaInAs-silicon evanescent racetrack laser and photodetector," Opt. Express 15, 2315-2322 (2007). [CrossRef] [PubMed]
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  8. J. J. Liang, S. T. Lau, M. H. Leary, and J. M. Ballantyne, "Unidirectional operation of waveguide diode ring lasers," Appl. Phys. Lett. 70, 1192-1194 (1997). [CrossRef]
  9. H. Cao, C. Liu, H. Ling, H. Deng, M. Benavidez, V. A. Smagley, and R. B. Caldwell, "Frequency beating between monolithically integrated semiconductor ring lasers," Appl. Phys. Lett. 86, 041101 (2005). [CrossRef]
  10. 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]
  11. 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]
  12. T. Ben-Messaoud and J. Zyss, "Unidirectional laser emission from polymer-based spiral microdisks," Appl. Phys. Lett. 86, 241110 (2005). [CrossRef]
  13. A. Fujii, T. Nishimura, Y. Yoshida, K. Yoshino, and M. Ozaki, "Unidirectional laser emission from spiral microcavity utilizing conducting polymer," Jpn. J. Appl. Phys. 44, L1091-L1093 (2005). [CrossRef]
  14. 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," Jpn. J. Appl. Phys. 45, L833-L836 (2006). [CrossRef]
  15. 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 40, 1669-1672 (2007). [CrossRef]
  16. 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.
  17. A. Tulek and Z. V. Vardeny, "Unidirectional laser emission from π-conjugated polymer microcavities with broken symmetry," Appl. Phys. Lett. 90, 161106 (2007). [CrossRef]
  18. 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]
  19. 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]
  20. 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.sSuppl. 166, 112-118 (2007). [CrossRef]
  21. 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.
  22. 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]
  23. 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.
  24. 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.
  25. 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.
  26. 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. [CrossRef]
  27. R. J. Potton, "Reciprocity in optics," Rep. Prog. Phys. 67, 717-754 (2004). [CrossRef]
  28. M. Nieto-Vesperinas and E. Wolf, "Generalized Stokes reciprocity relations for scattering from dielectric objects of arbitrary shape," J. Opt. Soc. Am. A. 3, 2038 - 2046 (1986). [CrossRef]
  29. M. Born and E. Wolf, Principles of Optics 7th edition (Cambridge, Cambridge University Press, 1999), pp. 724-726.
  30. G. S. Agarwal and S. Dutta Gupta, "Reciprocity relations for reflected amplitudes," Opt. Lett. 27, 1205 - 1207 (2002). [CrossRef]
  31. S. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80, 908-910 (2002). [CrossRef]
  32. FullWAVE, Rsoft Inc. Research Software, http://www.rsoftinc.com.
  33. E. E. Narimanov and V. A. Podolskiy, "Dynamical localization in spiral microlasers with unidirectional emission," in Conference on Lasers and Electro-Optics 2004, (IEEE and Optical Society of America, 2004), paper IThI5.
  34. H. Chen, J. Y. Lee, A. W. Poon, and H. K. Tsang, "Non-evanescently pumped Raman silicon lasers using spiral-shaped microdisks," in Conference on Lasers and Electro-Optics 2007, (IEEE and Optical Society of America, 2007), paper JThD114. [CrossRef]

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