Abstract

We analyze the resonance spectrum in silicon microring resonators taking into account the end-facet reflection from a coupled waveguide, which can provide a dense set of Fabry-Perot resonances. Based on the simple configuration of a microring coupled with a waveguide, the resulting asymmetric Fano-like non-Lorentzian resonance is obtained by scattering theory and experiment. Enhanced sensing performance with steeper slope to the resonance is theoretically predicted and experimentally demonstrated for a 10-μm racetrack silicon microring resonator. A high sensitivity of ~10−8 RIU in terms of the detection limit is obtained in a 30-dB signal-to-noise ratio (SNR) system.

©2010 Optical Society of America

1. Introduction

Silicon (Si) microrings (MRs) offer high quality factor Q and compact size making such structures attractive for telecommunications and sensing applications [1,2]. There are two commonly employed sensing schemes exploiting MR’s: one is by monitoring the resonance wavelength shift and the other is by measuring the output intensity change at fixed wavelength [3]. The wavelength-shift sensing scheme has large dynamic range, but renders the sensor slow due to the necessity of a time-consuming spectrum measurement. The intensity sensor has a small dynamic range, which can be increased by enhancing the extinction ratio with critical coupling, but also enables a rapid intensity measurement. The higher sensitivity of intensity sensors has been reported in theory and practice [4,5]. Even with stringent requirements on the light source and detector, high sensitivity sensors have been realized with Qas high as 20,000 and a detection limit of one in 10−7 [5]. Consequently, intensity sensors may be most suitable for microscale sensing with highly sensitivity.

High-transmission waveguides with tight bends can be realized due to the large refractive-index difference between Si and SiO2 [6]. The large index contrast, however, introduces a strong reflection by the end facet of the coupling waveguide as shown in Fig. 1 [7]. A Fabry-Perot (FP) resonance is formed by the end-facet reflections with a small free spectral range (FSR) and low extinction ratio. The strong FP resonances show up as noise in some applications, which can obscure the MR resonance and degrade device performance [8]; however, the theoretical concept of the FP-resonance coupled microring resonator has been reported as a Fano resonator in Ref [9]. Some other components have been used to form the FP resonances coupled with a microring, such as an offset waveguide or fiber Bragg grating [1012]. These concepts are all in the limit of a narrow microring resonance compared with the FP resonance, which requires comparable cavity length between the FP resonator and the MR. In our case, the FP FSR is far less than that of the MR because the coupled waveguide is much longer than the MR circumference.

 figure: Fig. 1

Fig. 1 MR resonator with end facet reflection

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In this paper, we implement—both theoretically and experimentally—Si MR resonators as sensors taking into account coupling to the dense FP resonances. The slope of the coupled resonance is studied as one of the most important factors in sensing [3]; it is thus shown that the sensitivity can be enhanced by steepening the slope by means other than boosting Q. Since the asymmetric resonance with high sensitivity has been demonstrated elsewhere in practice as an intensity sensor [10], we concentrate here on the experimental demonstration of the forming of the asymmetric resonance itself. Thus, our work points the way to inexpensive and easily fabricated high-sensitivity devices for chemical detection. Scattering theory is used to obtain the MR resonance spectral shape coupled with the FP resonance [9]. Finally, the result is compared with experiment in which a Si MR resonator is fabricated.

2. Theory

Let us review the basic optical properties of MR resonators first in the absence of the FP resonance associated with the waveguide termination: we call this the pure resonance. The transfer matrix of the resonator can be obtained from scattering theory as [9]

Tr=[1iWωω0iWωω0iWωω01+iWωω0],
where Wis the half width at half maximum of the resonance and ω0is the resonance frequency.

Next, taking into account the FP resonance due to coupling to the terminated waveguide, the resulting resonance is called a coupled resonance whose transfer matrix is represented as

T=TFP[eiφ00eiφ]Tr[eiφ00eiφ]TFP,
where φis the phase between MR and end facet,φ=ωL/(2c), Lis the optical length between MR and end facet. TFPis the transfer matrix of the partially reflecting end facet, and can be expressed as
TFP=1i1r2[1rr1],
where r is the amplitude reflectivity of the waveguide termination. According to the Fresnel formula at normal incidence between air and Si,
r=neff1neff+1,
where neffis the effective index of the Si waveguide; ris about 0.4 for the Si waveguide. The sensitivity of an intensity sensor in terms of the detection limit δnis [4]
δn=δIS,
where δIis the intensity detection limit originating in the detection ability of equipments; Sis the sensitive of the intensity sensor andS=dI/dn. The intensity change dI originates in the shift of shape of the resonance due to the effective index changednat fixed wavelength. Thus, the steeper the slope, the higher the sensitivitySresulting from the enhancement in dI [3].

3. Simulation and experiment

We take the waveguide length Lto be 10 mm and the effective index to be 2.46. The phase difference between resonances of the MR and FP is defined asα. The combined resonances with various αare showed in Fig. 2 . The pure resonances are affected significantly by the FP resonance. The reason is that the FP resonance has a wavelength-dependent coupling to the MR resonance; the coupling varies strongly withα. Only whenα=π, the coupled resonance results in a single dip with steep slope. Otherwise, the spectrum possesses numerous dips, which may in practice render the device useless. For typical sensing applications, a spectrum with an isolated dip produces the steepest slope, and is thus desired.

 figure: Fig. 2

Fig. 2 (a) SEM image of racetrack microring. (b) Simulation results showing the coupled MR-waveguide resonance for W = 0.032 nm for α=0.13πandα=0.5π, W = 0.02 nm for α=π. (c) Experimental results showing the coupled resonance for racetrack MRs, upper two curves with 10 μm and lower curve with 6 μm coupling length, and the length of the bus waveguide is about 10 mm.

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We now present experimental results verifying our theoretical analysis. Coupled waveguide-MR devices were fabricated using a Si-on-insulator (SOI) wafer shown in 
Fig. 2(a), which has a 1 μm buffered oxide layer topped with 230 nm of Si. Structures are defined by electron-beam lithography using a JEOL JBX-9300FS system, and the e-beam resist is ZEP520A. Then the pattern is etched with a STS Standard Oxide Etcher. In Fig. 2(b), the phase difference between the microring and FP resonances leads to a modified coupled resonance shape. The dashed line indicates the pure FP resonance involved in the resonances coupling. With the smaller phase differenceα=0.13πin the top curves, the shape of the coupled resonance contains two comparable dips originating in FP resonances between which a peak locates at the microring resonance. With increasing phase differenceα=0.5πin the middle curves, the peak approaches the FP resonance as the left dip looses and right dip gains strength. In the case of α=πin the bottom curves, the shape of the coupled resonance merges into one dip with steeper slope. The experimental spectrum in Fig. 2(c) is obtained with different size microrings, but coupled waveguides of the same length. Using a vertical logarithmic scale makes it easier to observe the resonance dips; the dashed line represents the FP resonance involved. The dips change according to the phase difference α, which is consistent with the theoretical curves of Fig. 2(b).

By changing the end-facet reflection, the extinction ratio of the FP resonance is adjusted to α=π. Consequently, the coupled resonances are showed in Fig. 3 . Forr = 0, there is no FP resonance. In this case, the MR resonance is a pure resonance and appears as a Lorentzian. When r is varied, the Lorentzian shape is modified, and the coupled resonance is asymmetric with a steeper slope that increases with increasingr. Meanwhile, the flat region away from the MR resonance becomes dominated by the numerous dips associated with the FP resonances. The resulting multiple FP resonances due to the end reflections can obscure the detailed shape of the relevant MR resonance in some applications. Antireflective coatings or subwavelength gratings on the facets may be introduced to suppress the FP resonances. In our sensing application, however, reduced end-facet reflection will in fact lower the sensitivity as the spectral slope becoming less steep. However, the Fresnel reflectivity, with the normal cleaved waveguide, is typically of the order of 30% [13], which can also be calculated by 
Eq. (4). This is enough to enhance the slope significantly with strong FP resonance as in 
Fig. 3. Furthermore, an enhanced reflectivity may be obtained by an end-facet coating, or by enhancing the effective mode index with tapered waveguide termination, through which the reflection can be enhanced based on Eq. (4).

 figure: Fig. 3

Fig. 3 The coupled resonance with different end-facet reflection coefficientsr, W = 0.032 nm.

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For Fig. 4(a) , the Si waveguide has the end facet reflection r about 0.4; the parameters are same as in Fig. 2. In Fig. 4(a), the experimental resonance is represented in circle line. The solid line represents the simulated coupled resonance. Both sides of the resonance dip in the measured data are modified with respect to the Lorentzian and the lineshape is well fit by the solid theoretical curve. The coupled resonance is therefore demonstrated in theory and experiment. The quality factor is measured as Q = 3.8×104. The slope is much steeper in the non-Lorentzian lineshape resulting from coupling to the FP resonances. With the steeper slope of the asymmetric resonance, a detection limit of ~10−8 RIU in a 30-dB signal-to-noise ratio (SNR) system is obtained. Though Q is not extremely high, a significantly steeper slope of the resonance is obtained here and demonstrates our theory in practice. Taking into account the same end-facet reflection in reported ultra-high Q microring resonators (Q~106) [14], the combined resonance is shown in Fig. 4(b). The coupled resonance can still have a steeper slope within its asymmetric non-Lorentzian lineshape. As a result, such a sensor can provide more sensitivity by exploiting the Si waveguide end-facet reflections.

 figure: Fig. 4

Fig. 4 (a) Resonances in a Si MR resonator. The dashed line represents the pure resonance, the solid line represents the combined resonance, and the circles represent the experimentally measured spectrum. (b) The end-facet reflection in ultra high Q microring resonator.

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4. Conclusion

The spectra of Si MR resonators coupled with waveguides possessing an end-facet reflections are discussed theoretically and experimentally. The end-facet reflection in a Si waveguide forms a FP resonator that couples to the MR resonance, thus changing the Lorentzian MR-resonance lineshape to a strongly asymmetric shape. The physics underlying this change in lineshape is closely related to the Fano lineshape [15], which results from a discrete resonance coupled to a continuum—here the quasicontinuum of densely spaced FP resonances of the waveguide. The spectral slope is demonstrated to become steeper when the resonances of FP and MR have a π phase difference. This requirement is easy to meet because the long cavity of FP resonance leads to dense collection of resonances with small FSR. For applications that have much shorterL, an asymmetric resonance can also be obtained but by judicious choice of the parameter φ [912]. Therefore, our device can provide asymmetric resonance with easier design. Because a steeper slope is obtained in asymmetric resonance shape, Si MR resonators can provide enhanced sensitivity in chemical-detection application. Thus, this feature can reduce the stringent requirement of a high quality factor in MR resonators as in our demonstration experiment. With regard to device fabrication, this means there can be greater tolerance to imperfections in the MR and in the waveguide end facets. This is an effective method to produce inexpensive and easily fabricated chemical sensors.

Acknowledgments

HY and ZZ were partially supported by the National Natural Science Foundation of China by grant 60578048. DSC was supported in part by the National Science Foundation by grant ECCS 0523923 and acknowledges the support of the CNRS and the Region of Lorraine. The authors are grateful Prof. Ali Adibi and graduate student Qing Li for the assistance in optical characterization of devices.

References and links

1. 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,” Photon. Technol. Lett. 10(4), 549–551 (1998). [CrossRef]  

2. K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007). [CrossRef]   [PubMed]  

3. C.-Y. Chao and L. J. Guo, “Design and optimization of microring resonators in biochemical sensing applications,” J. Lightwave Technol. 24(3), 1395–1402 (2006). [CrossRef]  

4. Z. Xia, Y. Chen, and Z. Zhou, “Dual waveguide coupled microring resonator sensor based on intensity detection,” IEEE J. Quantum Electron. 44(1), 100–107 (2008). [CrossRef]  

5. C.-Y. Chao, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 134–142 (2006). [CrossRef]  

6. Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-microm radius,” Opt. Express 16(6), 4309–4315 (2008). [CrossRef]   [PubMed]  

7. M. Hammer and E. van Groesen, “Total multimode reflection at facets of planar high-contrast optical waveguides,” J. Lightwave Technol. 20(8), 1549–1555 (2002). [CrossRef]  

8. A. Nitkowski, L. Chen, and M. Lipson, “Cavity-enhanced on-chip absorption spectroscopy using microring resonators,” Opt. Express 16(16), 11930–11936 (2008). [CrossRef]   [PubMed]  

9. S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002). [CrossRef]  

10. C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microring with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003). [CrossRef]  

11. V. M. N. Passaro and F. De Leonardis, “Modeling and design of a novel high-sensitivity electric field silicon-on-insulator sensor based on a whispering-gallery-mode resonator,” IEEE J. Sel. Top. Quantum Electron. 12(1), 124–133 (2006). [CrossRef]  

12. W. Liang, L. Yang, J. K. S. Poon, Y. Huang, K. J. Vahala, and A. Yariv, “Transmission characteristics of a Fabry-Perot etalon-microtoroid resonator coupled system,” Opt. Lett. 31(4), 510–512 (2006). [CrossRef]   [PubMed]  

13. J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, and D. X. Xu, “Gradient-index antireflective subwavelength structures for planar waveguide facets,” Opt. Lett. 32(13), 1794–1796 (2007). [CrossRef]   [PubMed]  

14. C. P. Michael, M. Borselli, T. J. Johnson, C. Chrystal, and O. Painter, “An optical fiber-taper probe for wafer-scale microphotonic device characterization,” Opt. Express 15(8), 4745–4752 (2007). [CrossRef]   [PubMed]  

15. U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961). [CrossRef]  

References

  • View by:

  1. 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,” Photon. Technol. Lett. 10(4), 549–551 (1998).
    [Crossref]
  2. K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007).
    [Crossref] [PubMed]
  3. C.-Y. Chao and L. J. Guo, “Design and optimization of microring resonators in biochemical sensing applications,” J. Lightwave Technol. 24(3), 1395–1402 (2006).
    [Crossref]
  4. Z. Xia, Y. Chen, and Z. Zhou, “Dual waveguide coupled microring resonator sensor based on intensity detection,” IEEE J. Quantum Electron. 44(1), 100–107 (2008).
    [Crossref]
  5. C.-Y. Chao, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 134–142 (2006).
    [Crossref]
  6. Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-microm radius,” Opt. Express 16(6), 4309–4315 (2008).
    [Crossref] [PubMed]
  7. M. Hammer and E. van Groesen, “Total multimode reflection at facets of planar high-contrast optical waveguides,” J. Lightwave Technol. 20(8), 1549–1555 (2002).
    [Crossref]
  8. A. Nitkowski, L. Chen, and M. Lipson, “Cavity-enhanced on-chip absorption spectroscopy using microring resonators,” Opt. Express 16(16), 11930–11936 (2008).
    [Crossref] [PubMed]
  9. S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002).
    [Crossref]
  10. C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microring with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003).
    [Crossref]
  11. V. M. N. Passaro and F. De Leonardis, “Modeling and design of a novel high-sensitivity electric field silicon-on-insulator sensor based on a whispering-gallery-mode resonator,” IEEE J. Sel. Top. Quantum Electron. 12(1), 124–133 (2006).
    [Crossref]
  12. W. Liang, L. Yang, J. K. S. Poon, Y. Huang, K. J. Vahala, and A. Yariv, “Transmission characteristics of a Fabry-Perot etalon-microtoroid resonator coupled system,” Opt. Lett. 31(4), 510–512 (2006).
    [Crossref] [PubMed]
  13. J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, and D. X. Xu, “Gradient-index antireflective subwavelength structures for planar waveguide facets,” Opt. Lett. 32(13), 1794–1796 (2007).
    [Crossref] [PubMed]
  14. C. P. Michael, M. Borselli, T. J. Johnson, C. Chrystal, and O. Painter, “An optical fiber-taper probe for wafer-scale microphotonic device characterization,” Opt. Express 15(8), 4745–4752 (2007).
    [Crossref] [PubMed]
  15. U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
    [Crossref]

2008 (3)

2007 (3)

2006 (4)

V. M. N. Passaro and F. De Leonardis, “Modeling and design of a novel high-sensitivity electric field silicon-on-insulator sensor based on a whispering-gallery-mode resonator,” IEEE J. Sel. Top. Quantum Electron. 12(1), 124–133 (2006).
[Crossref]

W. Liang, L. Yang, J. K. S. Poon, Y. Huang, K. J. Vahala, and A. Yariv, “Transmission characteristics of a Fabry-Perot etalon-microtoroid resonator coupled system,” Opt. Lett. 31(4), 510–512 (2006).
[Crossref] [PubMed]

C.-Y. Chao and L. J. Guo, “Design and optimization of microring resonators in biochemical sensing applications,” J. Lightwave Technol. 24(3), 1395–1402 (2006).
[Crossref]

C.-Y. Chao, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 134–142 (2006).
[Crossref]

2003 (1)

C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microring with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003).
[Crossref]

2002 (2)

S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002).
[Crossref]

M. Hammer and E. van Groesen, “Total multimode reflection at facets of planar high-contrast optical waveguides,” J. Lightwave Technol. 20(8), 1549–1555 (2002).
[Crossref]

1998 (1)

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,” Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

1961 (1)

U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[Crossref]

Baets, R.

Bartolozzi, I.

Beausoleil, R. G.

Bienstman, P.

Borselli, M.

Chao, C.-Y.

C.-Y. Chao and L. J. Guo, “Design and optimization of microring resonators in biochemical sensing applications,” J. Lightwave Technol. 24(3), 1395–1402 (2006).
[Crossref]

C.-Y. Chao, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 134–142 (2006).
[Crossref]

C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microring with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003).
[Crossref]

Cheben, P.

Chen, L.

Chen, Y.

Z. Xia, Y. Chen, and Z. Zhou, “Dual waveguide coupled microring resonator sensor based on intensity detection,” IEEE J. Quantum Electron. 44(1), 100–107 (2008).
[Crossref]

Chrystal, C.

Chu, S. T.

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,” Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

De Leonardis, F.

V. M. N. Passaro and F. De Leonardis, “Modeling and design of a novel high-sensitivity electric field silicon-on-insulator sensor based on a whispering-gallery-mode resonator,” IEEE J. Sel. Top. Quantum Electron. 12(1), 124–133 (2006).
[Crossref]

De Vos, K.

Fan, S.

S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002).
[Crossref]

Fano, U.

U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[Crossref]

Fattal, D.

Foresi, J. S.

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,” Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Fung, W.

C.-Y. Chao, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 134–142 (2006).
[Crossref]

Greene, W.

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,” Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Guo, L. J.

C.-Y. Chao and L. J. Guo, “Design and optimization of microring resonators in biochemical sensing applications,” J. Lightwave Technol. 24(3), 1395–1402 (2006).
[Crossref]

C.-Y. Chao, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 134–142 (2006).
[Crossref]

C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microring with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003).
[Crossref]

Hammer, M.

Haus, H. A.

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,” Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Huang, Y.

Ippen, E. P.

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,” Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Janz, S.

Johnson, T. J.

Kimerling, L. C.

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,” Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Lapointe, J.

Liang, W.

Lipson, M.

Little, B. E.

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,” Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Michael, C. P.

Nitkowski, A.

Painter, O.

Passaro, V. M. N.

V. M. N. Passaro and F. De Leonardis, “Modeling and design of a novel high-sensitivity electric field silicon-on-insulator sensor based on a whispering-gallery-mode resonator,” IEEE J. Sel. Top. Quantum Electron. 12(1), 124–133 (2006).
[Crossref]

Poon, J. K. S.

Post, E.

Schacht, E.

Schmid, J. H.

Steinmeyer, G.

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,” Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Thoen, E. R.

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,” Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Vahala, K. J.

van Groesen, E.

Xia, Z.

Z. Xia, Y. Chen, and Z. Zhou, “Dual waveguide coupled microring resonator sensor based on intensity detection,” IEEE J. Quantum Electron. 44(1), 100–107 (2008).
[Crossref]

Xu, D. X.

Xu, Q.

Yang, L.

Yariv, A.

Zhou, Z.

Z. Xia, Y. Chen, and Z. Zhou, “Dual waveguide coupled microring resonator sensor based on intensity detection,” IEEE J. Quantum Electron. 44(1), 100–107 (2008).
[Crossref]

Appl. Phys. Lett. (2)

S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002).
[Crossref]

C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microring with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003).
[Crossref]

IEEE J. Quantum Electron. (1)

Z. Xia, Y. Chen, and Z. Zhou, “Dual waveguide coupled microring resonator sensor based on intensity detection,” IEEE J. Quantum Electron. 44(1), 100–107 (2008).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

C.-Y. Chao, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 134–142 (2006).
[Crossref]

V. M. N. Passaro and F. De Leonardis, “Modeling and design of a novel high-sensitivity electric field silicon-on-insulator sensor based on a whispering-gallery-mode resonator,” IEEE J. Sel. Top. Quantum Electron. 12(1), 124–133 (2006).
[Crossref]

J. Lightwave Technol. (2)

Opt. Express (4)

Opt. Lett. (2)

Photon. Technol. Lett. (1)

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,” Photon. Technol. Lett. 10(4), 549–551 (1998).
[Crossref]

Phys. Rev. (1)

U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 MR resonator with end facet reflection
Fig. 2
Fig. 2 (a) SEM image of racetrack microring. (b) Simulation results showing the coupled MR-waveguide resonance for W = 0.032 nm for α = 0.13 π and α = 0.5 π , W = 0.02 nm for α = π . (c) Experimental results showing the coupled resonance for racetrack MRs, upper two curves with 10 μm and lower curve with 6 μm coupling length, and the length of the bus waveguide is about 10 mm.
Fig. 3
Fig. 3 The coupled resonance with different end-facet reflection coefficientsr, W = 0.032 nm.
Fig. 4
Fig. 4 (a) Resonances in a Si MR resonator. The dashed line represents the pure resonance, the solid line represents the combined resonance, and the circles represent the experimentally measured spectrum. (b) The end-facet reflection in ultra high Q microring resonator.

Equations (5)

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T r = [ 1 i W ω ω 0 i W ω ω 0 i W ω ω 0 1 + i W ω ω 0 ] ,
T = T F P [ e i φ 0 0 e i φ ] T r [ e i φ 0 0 e i φ ] T F P ,
T F P = 1 i 1 r 2 [ 1 r r 1 ] ,
r = n e f f 1 n e f f + 1 ,
δ n = δ I S ,

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