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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 25 — Dec. 5, 2011
  • pp: 24980–24985
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Characterizing and modeling backscattering in silicon microring resonators

G. C. Ballesteros, J. Matres, J. Martí, and C. J. Oton  »View Author Affiliations


Optics Express, Vol. 19, Issue 25, pp. 24980-24985 (2011)
http://dx.doi.org/10.1364/OE.19.024980


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Abstract

We present an experimental technique to characterize backscattering in silicon microring resonators, together with a simple analytical model that reproduces the experimental results. The model can extract all the key parameters of an add-drop-type resonator, which are the loss, both coupling coefficients and backscattering. We show that the backscattering effect strongly affects the resonance shape, and that consecutive resonances of the same ring can have very different backscattering parameters.

© 2011 OSA

1. Introduction

Silicon photonics has recently emerged as a viable technology for integrated photonic devices. Microring resonators are elements which are simple to fabricate and are used for devices such as optical filters, [1

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 SiO Microring Resonator,” IEEE Photon. Technol. Lett.10, 549–551 (1998). [CrossRef]

] sensors, [2

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, 7610–5 (2007). [CrossRef] [PubMed]

] modulators, [3

3. R. R. P. Vilson, R. Almeida, Carlos A. Barrios, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004). [CrossRef]

] etc. The quality factor is usually the parameter that determines the performance of the device; however, in this technology the limiting factor is in most cases not the propagation loss, which can reach values below 2.4 dB/cm [4

4. P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-Loss SOI Photonic Wires and Ring Resonators Fabricated With Deep UV Lithography,” IEEE Photon. Technol. Lett. 16, 1328–1330 (2004). [CrossRef]

], but the backscattering effect due to sidewall roughness [5

5. F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96, 081112 (2010). [CrossRef]

]. Backscattering in a resonator cannot be accounted for as a loss mechanism because in a cavity it grows coherently in each loop. Backscattering is a well known cause of resonance splitting [6

6. B. E. Little, J. P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22, 4–6 (1997). [CrossRef] [PubMed]

, 7

7. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669–71 (2002). [CrossRef]

]; but even before splitting occurs, it can dramatically modify the depth of the resonance; this can sometimes be useful to improve the extinction ratio of the peak [8

8. Z. Zhang, M. Dainese, L. Wosinski, and M. Qiu, “Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling,” Opt. Express 16, 4621 (2008). [CrossRef] [PubMed]

]. If this effect is not taken into account and one extracts the parameters of the ring from a fit, it can produce a good curve agreement but with wrong results. In this paper, we propose a characterization technique and a fully analytical fitting procedure that allows a complete characterization of all the parameters of the ring including backscattering, without the need of a coherent backscattering measuring system as in [5

5. F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96, 081112 (2010). [CrossRef]

, 9

9. F. Morichetti, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett. 104, 1–4 (2010). [CrossRef]

].

2. Experiment

Silicon waveguides were fabricated through the ePIXfab service at CEA-LETI, France, using silicon-on-insulator wafers with 220nm Si thickness and 2 μm buried oxide thickness. Waveguides are fully-etched 220×450nm channels which are covered with a 2 μm SiO2 layer, and shallow-etched grating couplers were used for coupling the light vertically from standard single-mode fibers at 10° angle. Waveguides and gratings were both patterned with deep-UV lithography. Transverse-electric (TE) polarization was used in all the experiments. Transmission spectra were collected with a tunable laser with 1 pm resolution and 2 dBm input power in fiber. The rings had a 20 μm radius and two coupling points, providing a through and a drop port. However, in this experiment we also collected the signal from the counter-propagating drop port, which we will call counter-drop port (as shown in Fig. 1). Measuring this port is crucial to fully characterize the ring, as it directly provides the information about the backscattering inside the cavity. The gap of the through and drop couplers was 275nm and 300nm respectively.

Fig. 1 (Color online) Schematic view of the layout of add-drop rings with drop (D), counter-drop (C) and through (T) ports. The back reflected port represents the backreflected signal that returns to the input port

Fig. 2 (Color online)Top panel: Transmission spectrum of each port of the microring: the through (red, solid), the drop (blue, dashed), and the counter-drop (green, dash-dot). Bottom panels: Detail of 3 resonances corresponding to the peaks at 1549, 1553 and 1558 nm, where transmission has been normalized. Solid curves are the experimental data and dashed lines are the analytical curves using the parameters extracted from the fitting procedure and shown on top of each subplot.

3. Theory

One way to extract the ring parameters from the experiment would be to find the parameters that produce the best fit to the experimental curves; however fitting three curves simultaneously is not straightforward. For this reason, we have calculated all the Q-factors of the ring as a function of specific values which are easily extracted from the experimental curves, which are the central values of the three ports (T0, D0 and C0, all measured at ω0), and the parameter Δω′, defined as the normalized frequency width between the points where C = C0/2. When the peak has not yet split, this corresponds to the full-width at half maximum (FWHM) of the counter-drop resonance peak. However, if the peak is split in two, the maximum is not located at C0, thus Δω′ would not be the FWHM anymore, although the expressions are still valid using its mathematical definition. After some algebraic manipulation, the equations that allow extracting all the parameters from the experimental curves are the following:
Q=1Δω(CoDo1+2(CoDo)2+1)1/2
(4a)
Qr=1QDoCo
(4b)
Qe,1=2Q(Q2+Qr2)(1±To)
(4c)
Qe,2=2(1±To)QDo(Q2+Qr2)
(4d)

Once all the Q-factors are calculated, one can relate them to the loss, coupling coefficients and backreflection by using Eqs. (1) and (2). The sign ambiguity in Eqs. (4c) and (4d) is a byproduct of the existence of two degenerate operation regimes in the ring with different parameters but the same resonance shape. This ambiguity is well known in cases without any backreflection effect, and it is due to the fact that in some cases one cannot distiguish between the intrinsic and the extrinsic loss. Some possible solutions to overcome this problem are proposed in [14

14. W. R. McKinnon, D. X. Xu, C. Storey, E. Post, A. Densmore, A. Delâge, P. Waldron, J. H. Schmid, and S. Janz, “Extracting coupling and loss coefficients from a ring resonator,” Opt. Express 17, 18971–82 (2009). [CrossRef]

], and consist in looking at the dependence on wavelength or measuring rings with different geometrical parameters. In our case, the ambiguity only occurs for the peak with lowest reflection coefficient, as in the other two cases it would give rise to a negative loss coefficient, which is unphysical, because it requires gain from the medium. As the sign has to be the same in all the peaks of the same ring, this provides an additional way to decide the correct sign in the expressions by analyzing more than one peak and looking for non-physical solutions.

Looking at Eqs. (3), one can identify 3 main regimes of operations in which the ring can work. They are distinguished by how strong the backreflection is in relation to the total Q-factor, that is, how large Qr is in comparison with Q. In the case where QrQ, the coupling can be considered to be negligible and the parameters can be extracted with already existing methods like in [14

14. W. R. McKinnon, D. X. Xu, C. Storey, E. Post, A. Densmore, A. Delâge, P. Waldron, J. H. Schmid, and S. Janz, “Extracting coupling and loss coefficients from a ring resonator,” Opt. Express 17, 18971–82 (2009). [CrossRef]

], or by making 1/Qr = 0 in Eq. (3a) and solving for Qe,1 and Q as a function of the extinction ratio and the full-width at half depth (FWHD). In this situation all resonances tend to have approximately the same shape and they do not split up. When the intention is to achieve high quality factors, then Q can start to approach to Qr and the expressions described in this paper should be used. Nevertheless, it may not be obvious from a measurement of a single resonance of the through port that the latter is the actual mode of operation since resonances do not always split; under these circumstances one should look at different peaks and see if they vary in an apparently random fashion, and where possible, measure the counter-drop port response. In the case where the coupling is so strong that QrQ, which may happen if the rings are intentionally designed for this purpose, then simplified expressions can be found as well, which are more practial than Eqs. (4). If this is the case then splitting is very evident showing two clearly defined peaks around each resonance frequency. Table 1 summarizes the three operation regimes and the expressions to use in each case.

Table 1. Summary of expressions for calculating Q-factors of ring-resonators working under different backscattering regimes

table-icon
View This Table

4. Results

From the experimental data shown in Fig. 2, we have chosen three consecutive resonances which show quite different behavior in terms of extinction ratio and degree of splitting. The results obtained from the method described in section 3 for each resonance are also shown in Fig. 2, and the corresponding theoretical curves are shown in the insets, where a good agreement is observed. It is worth noting that the coupling constants and the loss show small variations among resonances, being R the one showing much higher variability (reaching one order of magnitude). This is expected from the nature of backscattering, and is a demonstration of the validity of our model. The asymmetry of the shape of peaks 1 and 3, which is not reproduced in the theory, can be explained by sudden variations in the reflection coefficient along the width of the resonance, which was not considered in the model.

The maximum reflection coefficient measured is 0.18%, which corresponds to Qr ∼ 25 000. This means that for this waveguide section and quasi-TE polarization, resonances with Q-factors higher than 104 will be affected by backscattering. If one requires pure resonances with higher Q-factors, waveguides with weaker backscattering are needed, which can be achieved by using quasi-TM polarization or by widening the channel.[9

9. F. Morichetti, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett. 104, 1–4 (2010). [CrossRef]

]

5. Conclusion

We have described an analytical model and a fitting procedure that allows extraction of all the key parameters of a silicon microring resonator with two coupling points. These parameters are the two coupling constants, propagation loss and the backscattering coefficient. With this method, we demonstrate that variations of the backscattering parameter are the cause of the strong variations in the shape of different resonances of the same microring. All these parameters can be extracted from simple measurements using a standard transmission characterization setup, and the experimental results from a ring resonator are succesfully fitted to the analytical model.

Acknowledgments

The authors acknowledge financial support from the Spanish Ministry of Science and Innovation through contract SINADEC ( TEC2008-06333). Joaquin Matres is supported by the Formación de Personal Investigador grant program of the Universidad Politécnica de Valencia.

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 SiO Microring Resonator,” IEEE Photon. Technol. Lett.10, 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, 7610–5 (2007). [CrossRef] [PubMed]

3.

R. R. P. Vilson, R. Almeida, Carlos A. Barrios, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004). [CrossRef]

4.

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-Loss SOI Photonic Wires and Ring Resonators Fabricated With Deep UV Lithography,” IEEE Photon. Technol. Lett. 16, 1328–1330 (2004). [CrossRef]

5.

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96, 081112 (2010). [CrossRef]

6.

B. E. Little, J. P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22, 4–6 (1997). [CrossRef] [PubMed]

7.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27, 1669–71 (2002). [CrossRef]

8.

Z. Zhang, M. Dainese, L. Wosinski, and M. Qiu, “Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling,” Opt. Express 16, 4621 (2008). [CrossRef] [PubMed]

9.

F. Morichetti, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett. 104, 1–4 (2010). [CrossRef]

10.

H. A. Haus, Waves and field in optoelectronics (Prentice-Hall, 1984).

11.

T. A. I. J. Heebner and R. Grover, Optical Microresonators: Theory, Fabrication and Applications (Springer-Verlag, 2008).

12.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997). [CrossRef]

13.

F. Morichetti, A. Canciamilla, and A. Melloni, “Statistics of backscattering in optical waveguides,” Opt. Lett. 35, 1777–9 (2010). [CrossRef] [PubMed]

14.

W. R. McKinnon, D. X. Xu, C. Storey, E. Post, A. Densmore, A. Delâge, P. Waldron, J. H. Schmid, and S. Janz, “Extracting coupling and loss coefficients from a ring resonator,” Opt. Express 17, 18971–82 (2009). [CrossRef]

OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(230.3990) Optical devices : Micro-optical devices
(230.5750) Optical devices : Resonators
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Integrated Optics

Citation
G. C. Ballesteros, J. Matres, J. Martí, and C. J. Oton, "Characterizing and modeling backscattering in silicon microring resonators," Opt. Express 19, 24980-24985 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-24980


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References

  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 SiO Microring Resonator,” IEEE Photon. Technol. Lett.10, 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. Express15, 7610–5 (2007). [CrossRef] [PubMed]
  3. R. R. P. Vilson, R. Almeida, Carlos A. Barrios, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431, 1081–1084 (2004). [CrossRef]
  4. P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-Loss SOI Photonic Wires and Ring Resonators Fabricated With Deep UV Lithography,” IEEE Photon. Technol. Lett.16, 1328–1330 (2004). [CrossRef]
  5. F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett.96, 081112 (2010). [CrossRef]
  6. B. E. Little, J. P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett.22, 4–6 (1997). [CrossRef] [PubMed]
  7. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett.27, 1669–71 (2002). [CrossRef]
  8. Z. Zhang, M. Dainese, L. Wosinski, and M. Qiu, “Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling,” Opt. Express16, 4621 (2008). [CrossRef] [PubMed]
  9. F. Morichetti, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett.104, 1–4 (2010). [CrossRef]
  10. H. A. Haus, Waves and field in optoelectronics (Prentice-Hall, 1984).
  11. T. A. I. J. Heebner and R. Grover, Optical Microresonators: Theory, Fabrication and Applications (Springer-Verlag, 2008).
  12. B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol.15, 998–1005 (1997). [CrossRef]
  13. F. Morichetti, A. Canciamilla, and A. Melloni, “Statistics of backscattering in optical waveguides,” Opt. Lett.35, 1777–9 (2010). [CrossRef] [PubMed]
  14. W. R. McKinnon, D. X. Xu, C. Storey, E. Post, A. Densmore, A. Delâge, P. Waldron, J. H. Schmid, and S. Janz, “Extracting coupling and loss coefficients from a ring resonator,” Opt. Express17, 18971–82 (2009). [CrossRef]

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