Abstract

Ultra-compact 5th order ring resonator optical filters based on submicron silicon photonic wires are demonstrated. Out-of-band rejection ratio of 40dB, 1dB flat-top pass band of 310GHz with ripples smaller than 0.4dB, and insertion loss of only (1.8±0.5)dB at the center of the pass band are realized simultaneously, all within a footprint of 0.0007mm2 on a silicon chip.

© 2007 Optical Society of America

1. Introduction

Optical filters based on high order ring resonators attract a lot of attention due to their applications in optical signal processing and routing in various optical communication and interconnect systems [14]. One of the important applications of the optical filters is in wavelength division multiplexing (WDM) systems [5]. In such high order optical filters, light can resonantly tunnel through a series of coupled resonators if its frequency is in tune within the pass band of the system, and can be almost completely rejected if its frequency is tuned out of the pass band, leading to very large out-of-band rejection ratio [45]. On the other hand, the width of the pass band of such filters can be adjusted by tuning the inter-resonator coupling strengths. Most previous demonstrations in high order ring resonator based optical filters are realized in silicon oxynitride [5], silicon nitride [2], or polymer systems [4] in which low-loss and ultra-compact footprints are difficult to realize simultaneously due to the limited refractive index contrasts. Ultra-compact high order optical filters based on high refractive index contrast waveguide in GaAs/AlGaAs material system have been demonstrated previously [6]. However, very deep trench etch (~2µm) is necessary to prevent substrate leakage and losses reported are much higher than those of silicon waveguides. In this paper, we report such high order optical filters based on submicron silicon photonic wire waveguides. Due to extremely high index contrast between silicon and air (oxide) and tight confinement of the light, low loss micron scale waveguide bends can be realized [7]. Hence, ultra-compact and low-loss micro-scale ring resonators based on such waveguide bends can be realized [8]. Using 5 coupled silicon ring resonators with R=4µm radius, 1dB flat-top pass band of 310GHz with intensity ripples smaller than 0.4dB, out-of-band rejection ratio of 40dB, and transmission loss of only (1.8±0.5)dB at the center of the pass band are realized simultaneously, all within a footprint of 0.0007mm2. Additional CMOS (complementary metal-oxide-semiconductor) compatibility in material system and fabrication processes makes such filter an ideal candidate for applications in on-chip optical interconnects.

2. Design

Our design goals of high order optical filters for on-chip interconnect applications are: (i) wide (>300GHz) and flat (ripples <0.5dB) pass band that allows for accommodating large optical signal bandwidth and temperature variations in on-chip environment. (ii) the flat-top pass band should occupy approximately one seventh of the filter free spectral range (FSR) hence WDM devices with 5 to 7 channels can be constructed using such optical filters with detuned central wavelengths. (iii) high out-of-band rejection ratio (>30dB) and 1 to 20dB shape factor [5] approaching unity hence low crosstalk between different WDM channels can be achieved. (iv) small resonator perimeter hence the filter footprint can be small. On the other hand, small resonator perimeter leads to large FSR and pass band if the pass band occupies certain portion of the FSR.

Design of optical filters based on ring resonators consists of two steps: choosing proper inter-resonator coupling coefficients for given number of resonators and determining physical dimensions. Analysis method based on tight binding model [9] proposed by Yariv et al. predicts a flat pass band for coupled optical systems with infinite number of resonators. However, in this theory, the existence of Bloch mode in such infinitely long coupled system is presumed. In realistic coupled system with finite resonators, usually simple strip input/output waveguides are located on both sides of the coupled resonator system, and reflections at strip waveguide/coupled system interfaces lead to ripples in the pass band even when there are 100 coupled resonators between input and output strip waveguides [8]. In order to achieve flat-top pass band, the inter-resonator coupling coefficients should be tapered to minimize such reflections [3, 5, and 10]. Based on this concept of tapering inter-resonator coupling coefficients, simulations were performed using matrix approach reported previously [1112].

 

Fig. 1. Simulated responses of optical filters with 3 and 5 coupled ring resonators. The responses as functions of both FSR (for ring resonators with arbitrary size, in bottom x-axis) and absolute wavelength detuning (for ring resonators with properly designed physical dimensions in section 2, in top x-axis) are shown. Inset: schematic drawings of filters comprised of 3 and 5 ring resonators.

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The objective in the first design step is to achieve flat pass band and desirable pass band width simultaneously by adjusting inter-ring coupling strengths. In this step, a group index of 4.25 was assumed for such silicon photonic wires as reported in Refs. [1314]. No physical dimensions about the resonator were assumed in simulation and hence the frequency response is normalized to the free-spectral range (FSR) as shown in bottom x-axis of Fig. 1. No loss mechanisms were introduced in simulation either. Since losses in silicon resonator are extremely small (0.035dB per round trip) [7, 8], the design of filters is hardly affected by introduction of such losses. On the other hand, in order to fit 5 to 7 WDM channels using such optical filters within one free-spectral range (FSR) and at the same time maximizing the pass band of each filter, we designed the coupling strengths in such a way that flat-top 1dB pass band of the filter occupies about one-seventh of the FSR. For optical filter with 5 coupled rings, the inter-ring power coupling coefficient [4, 11], κ2 (κ itself defined as the field coupling coefficient), from left to right (including bus-ring coupling as shown in the inset of Fig. 1), are designed to be 0.45, 0.09, 0.05, 0.05, 0.09, and 0.45, respectively [15, 16]. For 3-ring optical filter, the inter-ring power coupling coefficients, κ2, from left to right, are 0.45, 0.09, 0.09, and 0.45, respectively. From the simulation results shown in Fig. 1, the ripples in the pass band of the 5-ring filter are smaller than ±0.15dB and the out-of-band rejection ratio is larger than 40dB. 5-resonator filter exhibits sharper rising and falling edges (1- to 20dB shape factor of around 0.7) in transmission spectra than that of 3-resonator filter (with 1- to 20dB shape factor of around 0.35), leading to lower crosstalk level between channels in WDM system.

 

Fig. 2. Simulated power beating length, LB, between two parallel photonic wires as a function of air gap distance between them. LB represents a length within which optical power transfers completely from one waveguide to another and is calculated through the index difference between the even (nE) and odd (nO) modes. The indices are calculated using a commercial FimmWave software package, version 4.3.4.

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After achieving design goals (ii) and (iii) in first design step using 5 coupled resonators with proper coupling strength, the second step is to achieve design goals (i) and (iv) by choosing proper resonator physical dimensions. In fact, given the fixed inter-resonator coupling coefficients in such optical filters, goals (i) and (iv) are correlated. Since the pass band of the optical filters with given inter-resonator coupling coefficients occupies certain fraction of the FSR and the FSR is inversely proportional to the perimeter of the resonator [13], LP, the pass band itself is inversely proportional LP. Hence, minimizing the perimeter of the resonator not only reduces the footprint of the optical filter, but also maximizes the pass band of the optical filters. The second step in this design process is then determining the physical dimension of the resonators so that required coupling coefficients, small footprint, and large pass band can be simultaneously achieved. In this step, there are three parameters to be determined: bending radius in the ring (r), straight coupling length in the ring (LC), and air gap widths between rings [13]. Bending radius of 4µm is chosen such that a balance between the footprint and loss is achieved [7]. Desirable straight coupling length LC can be inferred from Fig. 2 in which the calculated power beating length, LB, between two parallel photonic wires as a function of air gap distance between them is plotted. Physically, LB is the length within which optical power transfers completely from one waveguide to another. LB can be calculated using the following simple relation [17]:

LB=λ2(nEnO)

where λ is the wavelength of the light (here a wavelength of 1550nm is used), nE and nO are the effective indices of the fundamental (even) and first order (odd) modes of the two coupled parallel photonic wires at a wavelength of 1550nm. Here, nE and nO are calculated based on 3-D full vectorial mode matching method using commercial FimmWave software.

If the coupling in the bending region of the resonators is ignored due to the small waveguide bending radius (4µm), the power coupling coefficient, κ2, is [17]:

κ2=sin2(π2LCLB)

As can be inferred from Fig. 2 and Eq. (2), in order to achieve a power coupling coefficient of 0.45, the straight coupling length has to be as large as 12µm if an air gap spacing of about 100nm is adopted (LB is around 24.5µm in this case). In this case, the perimeter of each ring resonator, LP, is:

LP=2πr+2LC

The perimeter of each ring will be as large as 49µm, leading to a free spectral range of around 11nm. Then 1dB pass band is only about 1.5nm (187GHz), which is much smaller than our design goal (i). In future on-chip optical interconnects, it is desirable to have optical filters operational without active temperature control, hence a wide pass band is essential and rings with smaller perimeter are needed. One straightforward method to reduce the coupling length, LC, and hence the perimeter of the resonator is to choose smaller air gap spacing. For example, the coupling length LC can be reduced significantly to around 3µm if a gap width of 20nm is used. However, there are a few issues associated with this simple approach. First, this introduces certain difficulties in device fabrication. Second, from Eq. (2), the variation of the coupling coefficient as a function of beating length, LB, is:

Δ(κ2)=π2LCsin(πLCLB)1LB2ΔLB

Hence, the coupling is very sensitive to the beating length variation when beating length itself is small. On the other hand, the beating length, LB, almost varies linearly as a function of the air gap when the gap changes from 0 to 120nm as shown in Fig. 2. This almost linear dependence together with the high sensitive coupling variation at small beating length lead to large uncertainty in coupling coefficient even due to very small variation in this designed 20nm air gap. We resolve this issue by replacing the coupling region with a MMI (multimode interferometer) coupler. The width of the MMI coupler is designed to be around 100nm wider than the combination of two access waveguides as shown in lower left corner of Fig. 3. Three-dimensional beam propagation (BPM) method is used to determine the length of the MMI coupler. By choosing a coupling length of 3.5µm, the input power in one of the waveguide is split into two output waveguides at a ratio of 45:55. Such a MMI structure does introduce a few percent of mode conversion loss during this splitting process [13]. Such loss is not acceptable if optical delay lines will be constructed where a large number of resonators are involved. Fortunately, in our optical filters with only a few resonators, this mode conversion loss will not have significant impact on the overall filter performance.

Given a coupling length of 3.5µm, power coupling coefficients κ2 of 0.09 and 0.05 can be achieved using air gap widths of 90nm and 110nm, respectively, as can be inferred from Fig. 2 and Eq. (2). In this design, the perimeter of the individual ring is 32µm, leading to a free spectral range of 17.8um, which is significantly larger than the previous design with LC of 12µm. In this case, the designed 1-dB pass band of filter with 5 rings is 330GHz and the footprint of such a filter is 0.0007mm2. Both design goals (i) and (iv) are then fulfilled in this second design step.

In the entire design process, CIFS (coupling induced frequency shift) [1819] is not considered although in principle it will play a role in filter performance since air gap widths between different resonators are not identical. As will be shown in Section 4, final results indicate negligible CIFS effect since the experimental transmission spectra are flat and almost symmetric. This is probably due to extremely wide pass band in our filters (>310GHz). CIFS is relatively small when compared with this wide pass band and hence the effect introduced by CIFS is not significant.

3. Device fabrication

Fabrication processes of the optical filters are similar to those described in Refs. [7, 8, 1214]. Optical filters consisting of 3 and 5 resonators with parameters mentioned above were fabricated on silicon-on-insulator (SOI) Unibond 200mm wafers from SOITEC with 220nm lightly p-doped Si on a 2µm thick buried oxide (BOX) layer. The silicon photonic wire waveguide on top of 2µm thick BOX layer is about 500nm wide by 220nm thick. The measured linear propagation loss on the same wafer in such photonic wires is (3±0.5) dB/cm. Polymer waveguide couplers and silicon inverted tapers are used to enhance the coupling from a polarization maintaining lensed fiber to silicon photonic circuits. Scanning electron microscope images of the fabricated 5-ring optical filters in silicon photonic wires are shown in Fig. 3.

 

Fig. 3. Scanning electron micrograph (SEM) images of fabricated optical filters with 5 ring resonators.

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4. Measurements and results

TE (transverse electric) transmission spectra at drop ports of the optical filters with 3 and 5 coupled resonators were measured using the spectrum analyzer at a resolution of 60pm as reported previously [7, 12]. The measurements were performed around a wavelength of 1550nm and the responses are quite uniform in a wavelength range from 1500nm to 1600nm. The free spectral range is 18nm around 1550nm wavelength range, which is close to our designed value of 17.8nm. The x axis of the spectra is normalized to the central wavelength of the pass band, and the y axis of the spectra (drop port intensity) is normalized to the corresponding non-resonance through port intensity of each device far from the resonance. Both optical filters with 3 and 5 resonators show very good filter characteristics as can be seen in Fig. 4. The measured out-of-band rejection ratio in optical filters with 3 and 5 resonators are -35dB and -40dB, respectively. The out-of-band rejection ratio in filters with 5 resonators can be larger than 40dB in reality since the measured value (-40dB) is limited by the sensitivity of our setup. Transmission spectrum of 5-ring filter consisting of two adjacent FSRs is shown in Fig. 5.

 

Fig. 4. Experimental transmission responses of optical filters with 3 and 5 coupled ring resonators. The measured out-of-band rejection ratio (~40dB) for optical filters with 5 resonators is limited by the sensitivity of the experimental setup and can be larger.

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Fig. 5. Experimental transmission responses of optical filter with 5 coupled ring resonators containing two FSRs.

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Insertion losses at the center of pass band for optical filters with 3 and 5 resonators are (1±0.5) dB and (1.8±0.5) dB, respectively. The possible loss mechanisms include waveguide propagation loss, waveguide bending loss, reflection loss at the MMI input and output interfaces, and additional mode conversion loss resulting from small air gap between resonators. We are not able to accurately determine the contribution of each loss mechanism since the overall loss is relatively small. In coupled resonators with 3 to 5 rings which do not contain MMI couplers, we observe similar insertion loss. Hence, reflection loss at MMI input and output interfaces does not play a significant role. On the other hand, these measured 1dB and 1.8dB losses (in filters with 3 and 5 rings, respectively) only represent the losses introduced by coupled resonators. Additional coupling losses from optical fiber to silicon waveguides are similar to what reported in Ref. 7 since similar coupling scheme is used here. For optical filter applications in which only a few resonators (here at most 5) are involved, these loss mechanisms do not introduce large overall loss in contrast to all optical delay lines in which a very large number of cascaded resonators are involved and total loss can be very large [13].

In both filters, 1dB bandwidth is defined as bandwidth within which the transmission is smaller than the peak transmission by 1dB or less. Experimental 1dB bandwidth of 5-ring filter (310GHz) matches the simulation almost perfectly while experimental 1dB-bandwidth of the 3-ring device is about 25% larger than what obtained in simulation. We believe that this discrepancy is probably due to the slight deviation of the experimental coupling intensities from their original designed values in certain filters.

The amplitude of the transmission ripples within the 1dB pass band of 5-ring filter is smaller than 0.4dB which is determined by comparing the adjacent peaks and valleys of the ripples. In fact, such ripples can also be observed in the transmission spectra of simple strip silicon waveguide and the origin of these ripples is probably due to the reflections at the air/waveguide interfaces on both sides of the cleaved wafers. Hence, the origin of these ripples is intrinsically different from those observed in Ref. 8 in which reflection at the strip waveguide/coupled system plays a pivotal role. By optimization of coupling coefficients between resonators, reflections at the air/waveguide interfaces are minimized and similar FP ripples in the filter pass band are observed as in simple strip waveguides.

These filters are designed to favor TE mode operation only. In fact, the TM mode cutoff frequency is intentionally designed to be around 1550nm and TM light suffers high propagation and bending losses.

Thanks to the large free-spectral range and sharp rising and falling edges in filters with 5 resonators, a 6-channel WDM device can be constructed using 6 such filters with consecutively detuned central resonances by 3nm. Since a single filter occupies a footprint as small as 0.0007mm2, such a WDM device will have a footprint <0.004mm2.

5. Summary

In summary, we demonstrated extremely compact, high performance, silicon optical filters with flat-top 1dB pass band of 310GHz within a very compact footprint of 0.0007mm2. A coupling scheme containing a MMI coupling region is introduced to realize simultaneous optimization of fabrication, footprint, and free spectral range. Although similar filters were previously demonstrated in other material systems, our demonstration here in silicon have the advantages of large 1dB pass band, ultra-compact device footprint, and wide free spectral range (FSR). Besides, the CMOS compatibility leads to possible applications in integrated silicon photonic-electronic circuits for future on-chip optical interconnect systems.

Acknowledgment

Partial financial support from DARPA/ONR (J. Lowell, DSO), grant N00014-04-C-0455, is gratefully acknowledged. We thank W. Green and S. Assefa (IBM T. J. Watson Research Center) for helpful technical discussions.

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

2. T. Barwicz, M. A. Popović, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” J. Lightwave Technol . 24, 2207–2218 (2006). [CrossRef]  

3. F. Xia, M. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact silicon WDM optical filters with flat-top response for on-chip optical interconnects,” in Conference on Lasers and Electro-Optics 2007 Technical Digest (Optical Society of America, Washington, DC, 2007), paper CTuG3.

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

5. B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett . 16, 2263–2265 (2004). [CrossRef]  

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

7. Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12, 1622–1631 (2004). [CrossRef]   [PubMed]  

8. F. Xia, L. Sekaric, and Yu. A. Vlasov, “Ultra-compact optical buffers on a silicon chip,” Nature Photon . 1, 65–71 (2007). [CrossRef]  

9. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett . 24, 711–713 (1999). [CrossRef]  

10. Y. Ye, J. Ding, D. Y. Jeong, I. C. Khoo, and Q. M. Zhang, “Finite-size effect on one dimensional coupled resonator optical waveguides,” Phys. Rev . E 69, 056604 (2004).

11. J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103 (2004). [CrossRef]   [PubMed]  

12. F. Xia, L. Sekaric, M. O’Boyle, and Y. A. Vlasov, “Coupled resonator optical waveguides based on silicon-on-insulator photonic wires,” Appl. Phys. Lett . 89, 041122 (2006). [CrossRef]  

13. F. Xia, L. Sekaric, and Y. A. Vlasov, “Mode conversion losses in silicon-on-insulator photonic wire based racetrack resonators,” Opt. Express 14, 3872–3886 (2006). [CrossRef]   [PubMed]  

14. E. Dulkeith, F. Xia, L. Schares, W. M. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express 14, 3853–3863 (2006). [CrossRef]   [PubMed]  

15. C. Madsen and J. Zhao, Optical filter design and analysis: A signal processing approach (New York: Wiley-interscience, 1999), Chap. 5.

16. B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, “Filter synthesis for periodically coupled microring resonators,” Opt. Lett. 25, 344–346(2000). [CrossRef]  

17. S. L. Chuang, Physics of Optoelectronic Devices (New York: Wiley-interscience, 1995), Chap. 8.

18. M. Popovic, C. Manolatou, and M. Watts, “Coupling-induced resonance frequency shifts in coupled dielectric multi-cavity filters,” Opt. Express 14, 1208–1222 (2006). [CrossRef]   [PubMed]  

19. T. Barwicz, M. Popović, P. Rakich, M. Watts, H. Haus, E. Ippen, and H. Smith, “Microring-resonator-based add-drop filters in SiN: fabrication and analysis,” Opt. Express 12, 1437–1442 (2004). [CrossRef]   [PubMed]  

References

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  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," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
    [CrossRef]
  2. T. Barwicz, M. A. Popović, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, " Fabrication of add-drop filters based on frequency-matched microring resonators," J. Lightwave Technol. 24, 2207-2218 (2006).
    [CrossRef]
  3. F. Xia, M. Rooks, L. Sekaric, and Y. A. Vlasov, "Ultra-compact silicon WDM optical filters with flat-top response for on-chip optical interconnects," in Conference on Lasers and Electro-Optics 2007 Technical Digest (Optical Society of America, Washington, DC, 2007), paper CTuG3.
  4. J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, "Transmission and group delay of microring coupled-resonator optical waveguides," Opt. Lett. 31, 456-458 (2006).
    [CrossRef] [PubMed]
  5. B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
    [CrossRef]
  6. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. -T. Ho, "High order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
    [CrossRef]
  7. Y. A. Vlasov and S. J. McNab, "Losses in single-mode silicon-on-insulator strip waveguides and bends," Opt. Express 12, 1622-1631 (2004).
    [CrossRef] [PubMed]
  8. F. Xia, L. Sekaric, and Yu. A. Vlasov, "Ultra-compact optical buffers on a silicon chip," Nature Photon. 1, 65-71 (2007).
    [CrossRef]
  9. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999).
    [CrossRef]
  10. Y. Ye, J. Ding, D. Y. Jeong, I. C. Khoo and Q. M. Zhang, "Finite-size effect on one dimensional coupled resonator optical waveguides," Phys. Rev. E 69, 056604 (2004).
  11. J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Express 12, 90-103 (2004).
    [CrossRef] [PubMed]
  12. F. Xia, L. Sekaric, M. O’Boyle, and Y. A. Vlasov, "Coupled resonator optical waveguides based on silicon-on-insulator photonic wires," Appl. Phys. Lett. 89, 041122 (2006).
    [CrossRef]
  13. F. Xia, L. Sekaric, and Y. A. Vlasov, "Mode conversion losses in silicon-on-insulator photonic wire based racetrack resonators," Opt. Express 14, 3872-3886 (2006).
    [CrossRef] [PubMed]
  14. E. Dulkeith, F. Xia, L. Schares, W. M. Green, Y. A. Vlasov, "Group index and group velocity dispersion in silicon-on-insulator photonic wires," Opt. Express 14, 3853-3863 (2006).
    [CrossRef] [PubMed]
  15. C. Madsen and J. Zhao, Optical filter design and analysis: A signal processing approach (New York: Wiley-interscience, 1999), Chap. 5.
  16. B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, "Filter synthesis for periodically coupled microring resonators," Opt. Lett. 25, 344-346 (2000).
    [CrossRef]
  17. S. L. Chuang, Physics of Optoelectronic Devices (New York: Wiley-interscience, 1995), Chap. 8.
  18. M. Popovic, C. Manolatou, and M. Watts, "Coupling-induced resonance frequency shifts in coupled dielectric multi-cavity filters," Opt. Express 14, 1208-1222 (2006).
    [CrossRef] [PubMed]
  19. T. Barwicz, M. Popović, P. Rakich, M. Watts, H. Haus, E. Ippen, and H. Smith, "Microring-resonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437-1442 (2004).
    [CrossRef] [PubMed]

2007 (1)

F. Xia, L. Sekaric, and Yu. A. Vlasov, "Ultra-compact optical buffers on a silicon chip," Nature Photon. 1, 65-71 (2007).
[CrossRef]

2006 (6)

2004 (5)

T. Barwicz, M. Popović, P. Rakich, M. Watts, H. Haus, E. Ippen, and H. Smith, "Microring-resonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437-1442 (2004).
[CrossRef] [PubMed]

Y. Ye, J. Ding, D. Y. Jeong, I. C. Khoo and Q. M. Zhang, "Finite-size effect on one dimensional coupled resonator optical waveguides," Phys. Rev. E 69, 056604 (2004).

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Express 12, 90-103 (2004).
[CrossRef] [PubMed]

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Y. A. Vlasov and S. J. McNab, "Losses in single-mode silicon-on-insulator strip waveguides and bends," Opt. Express 12, 1622-1631 (2004).
[CrossRef] [PubMed]

2000 (2)

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. -T. Ho, "High order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, "Filter synthesis for periodically coupled microring resonators," Opt. Lett. 25, 344-346 (2000).
[CrossRef]

1999 (1)

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," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

F. Xia, L. Sekaric, M. O’Boyle, and Y. A. Vlasov, "Coupled resonator optical waveguides based on silicon-on-insulator photonic wires," Appl. Phys. Lett. 89, 041122 (2006).
[CrossRef]

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Phys. Rev. E (1)

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Other (3)

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S. L. Chuang, Physics of Optoelectronic Devices (New York: Wiley-interscience, 1995), Chap. 8.

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Figures (5)

Fig. 1.
Fig. 1.

Simulated responses of optical filters with 3 and 5 coupled ring resonators. The responses as functions of both FSR (for ring resonators with arbitrary size, in bottom x-axis) and absolute wavelength detuning (for ring resonators with properly designed physical dimensions in section 2, in top x-axis) are shown. Inset: schematic drawings of filters comprised of 3 and 5 ring resonators.

Fig. 2.
Fig. 2.

Simulated power beating length, LB, between two parallel photonic wires as a function of air gap distance between them. LB represents a length within which optical power transfers completely from one waveguide to another and is calculated through the index difference between the even (nE) and odd (nO) modes. The indices are calculated using a commercial FimmWave software package, version 4.3.4.

Fig. 3.
Fig. 3.

Scanning electron micrograph (SEM) images of fabricated optical filters with 5 ring resonators.

Fig. 4.
Fig. 4.

Experimental transmission responses of optical filters with 3 and 5 coupled ring resonators. The measured out-of-band rejection ratio (~40dB) for optical filters with 5 resonators is limited by the sensitivity of the experimental setup and can be larger.

Fig. 5.
Fig. 5.

Experimental transmission responses of optical filter with 5 coupled ring resonators containing two FSRs.

Equations (4)

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L B = λ 2 ( n E n O )
κ 2 = sin 2 ( π 2 L C L B )
L P = 2 π r + 2 L C
Δ ( κ 2 ) = π 2 L C sin ( π L C L B ) 1 L B 2 Δ L B

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