Abstract

We report on the design, fabrication, and demonstration of waveguide coupled channel drop filters at 1550 nm, on a silicon-on-insulator (SOI) substrate. These devices rely on resonant power transfer from a bus waveguide to side-walled Bragg resonators with quarter-wave shifts in the middle. By employing a second mirror resonator, and a tap-off waveguide, reflections along the bus waveguide can be reduced, leading to realization of circulator-free resonance filters. These devices were fabricated on SOI using e-beam lithography and inductively coupled plasma (ICP) etching. Fabricated devices with two coupled cavities are demonstrated to have rejection ratios greater than 20 dB and 3-dB bandwidths of 110 GHz, close to the values predicted by numerical modeling. We also demonstrate power tap-off at resonance of around 16 dB.

©2012 Optical Society of America

1. Introduction

Optical add-drop filters are essential components in wavelength division multiplexed (WDM) systems [1]. These can be implemented in a variety of travelling wave and standing wave formats that include ring resonators [2], fiber Bragg gratings (FBG) [3], dielectric thin films [4], arrayed waveguides (AWG) [5], and free standing micro-resonators which have been integrated with SOI waveguides [6]. Also, high bit-rate WDM systems require very narrow channel spacing in the order of tenths of nanometers, and transmission roll-offs typically in the order of 20 dB/decade around resonance for low BER operation [7].

The distributed feedback (DFB) proposed by Kogelnik and Shank [8] was initially realized using interferometric fabrication techniques [4], but now optical and e-beam lithographic techniques have evolved to be able to realize periods with sub-micron critical dimensions [7]. Narrow band distributed Bragg reflectors (DBR) were proposed for laser frequency selection [9], and for add-drop filtering [10]. Such uniform DFB structures have transmission peaks on either side of the stopband [11], and laser cavities utilizing such structures lase randomly at either of the two side peak frequencies [12]. The introduction of a quarter-wave shift in the middle of such a DFB device creates a Lorentzian shaped high-Q resonance in the centre of the stopband [13], and this narrow peak can be used as a filter. Waveguides, horizontally (in-plane structure) or vertically (multilayered structure) coupled with such a quarter-wave shifted Bragg resonator structure, exhibit resonance at the middle of the grating stop-band, while the power leaking from the resonator can be tapped off for signal re-routing in planar optoelectronic circuits [14].

In this paper, we propose an integrated Bragg resonator filter on the SOI platform, which consists of a waveguide horizontally coupled to vertical sidewalled Bragg grating resonators. Initially proposed [10, 13], but not demonstrated, using planar gratings for III-V material systems, we implement the concept on the SOI platform using vertical sidewalled gratings [15], and also demonstrate a proof-of-concept design. Vertical gratings have the added advantage of a single step fabrication of the waveguide as well as the grating feedback structure [16], whereas surface corrugations require an additional lithographic step [17]. Grating couplers are used to couple light in and out of the waveguides [18]. We present the design, simulation results, fabrication steps and experimental characterization of these devices.

2. Design and analysis

The schematic top view of the proposed device is shown in Fig. 1 . A bus waveguide carrying the broadband signal is evanescently coupled with a resonator called the output resonator connected to a tap waveguide. The output resonator consists of waveguide sidewalled Bragg gratings (width modulated) with a quarter wave defect in the middle. A tap-off waveguide is connected to the output resonator, which can extract power at the resonance frequency and re-route the signal in a planar circuit. The output resonator transmits back a portion of the signal at the resonance frequency back onto the bus waveguide through evanescent coupling. A second resonator called the mirror resonator, which is out of phase with the output resonator is added on the other side of the bus waveguide. This ensures that the reflections from the output and the mirror resonators coupled to the bus waveguide (indicated by the red dotted arrows in Fig. 1), add out of phase, and effectively leads to zero back reflection on the bus waveguide. The out of phase criterion between the output and mirror resonators is assured by precisely aligning their grating teeth with each another [13]. It was also shown that employing unbalanced resonators, where the quarter wave shift is off-center with uneven number of periods on either side, can control the power of the tapped off field [12,13].

 figure: Fig. 1

Fig. 1 Top schematic view of the waveguide coupled drop filter with side-etched gratings.

Download Full Size | PPT Slide | PDF

The electric field at the resonant wavelength in a Bragg grating with a quarter wave defect in the middle peaks at the center and decays exponentially towards the ends as shown in Fig. 2(a) . The field distribution for such an uncoupled resonator is shown in Fig. 2(a), and was obtained using the eigenmode expansion method (EEM) [19]. In a hypothetical infinitely long resonator with a quarter wave period in the middle, there is no power leakage from the ends of the resonator. However, in a practical resonator some resonant power can be tapped off through a leakage mechanism added at the end of the resonator [13]. In a coupled resonator system shown in Fig. 1, the electric field propagating in the waveguide couples through its evanescent tail into the resonator. The electric field at a cross-section of the superstructure is as shown in Fig. 2(b) indicating a long evanescent tail extending from the bus waveguide into the resonator region. The widths of the waveguide and the resonator are 600 nm, with 100 nm teeth width and 286 nm period in the resonator. At, and around resonance the resonator supports a mode, and the propagating lightwave excites this resonator mode. The quarter-wave defect induces a π-phase shift, and this leads to a transmission maximum at the middle of the resonator stopband. The position of the resonant wavelength can be tuned by varying the length of the defect.

 figure: Fig. 2

Fig. 2 (a) Electric field distribution in a Bragg resonator with a quarter-wave defect indicating an exponential decay towards either end. (b) The 2D refractive index profile and a cross-cut of the propagating electric field (Ey, at z = 5 μm) of the waveguide mode in the bus, indicating power transfer into the output resonator through its evanescent tail.

Download Full Size | PPT Slide | PDF

Figure 3(a) shows the top view of the refractive index profile of the device under consideration. The grating period Λ is given byΛ=λ/2N,where λ is the desired stopband center wavelength, and N is the effective index of the grating. The SOI substrate used in our work has a 260 nm silicon device layer and a 2 μm buried oxide (BOX) layer. The reflection spectrum and the stopband width are then determined by coupled mode theory [20] using

R=|κ|2sinh2(sL)s2cosh2(sL)+(Δβ/2)2sinh2(sL),
where s2=|κ2|+(Δβ/2)2, κ is the coupling coefficient, and Δβ is the frequency detuning. For the fundamental transverse electric (TE) mode, the coupling coefficient κ for the first-order vertical grating is obtained by a perturbation approach [21], and is given by [22]
κ=[ΓπλΔWSWeffnSi2N2Nq][N2nSi2N2nSiO22+1],
where Γ is the modal confinement factor with effective index N, WS is the stripe width of the waveguide, ΔWS is the sidewall etch depth, q=(N2/nSi2)+(N2/nSiO22)1,Weff=WS+(2/qγ), γ2=β2k2nSiO22,and N=β/k. The refractive indices of silica (nSiO2) and silicon (nSi) at 1550 nm wavelength are assumed to be 1.46 and 3.48 respectively. Once the resonator design parameters and the transmission response of an unperturbed resonator section are obtained using coupled mode theory, the effect of perturbation by the addition of the bus waveguide, and the tap-off section are computed using EEM [19]. This is further validated by 2D finite difference time domain (FDTD) simulations. All the simulations and results presented are for the TE polarization. The waveguide width WS = 600 nm, sidewall depth ΔWS = 100 nm, and period Λ = 286 nm in our designs. Devices with WS = 800 nm, ΔWS = 75 nm and Λ = 279 nm were also simulated. The air-gap distance between the bus waveguide and the resonators was 200 nm in all cases. The number of periods is adjusted such that the total length of the resonator is an integral multiple of the coupling length LC (LC=π/2κ) [23]. This assures that all the power at off-resonance wavelengths is coupled back into the bus waveguide. Figures 3(b) and 3(c) show the steady state electric field plot at off-resonance and on-resonance wavelengths for the above design with waveguide width of 600 nm. It is seen that at resonance there is considerable power tapped-off, with no power transmission through the bus waveguide, while there is ~100% transmission at off-resonance wavelengths. The tap-off power extraction efficiency is approximately 65% as indicated in Fig. 3(c).

 figure: Fig. 3

Fig. 3 (a) Top view of the FDTD model. (b) Electric field at an off-resonance wavelength indicating almost 100% transmission through the bus waveguide. (c) Electric field at resonance indicating power tap-off at the resonant wavelength. The electric field scale palette is also shown.

Download Full Size | PPT Slide | PDF

We then computed the variation of the drop channel response with the air-gap distance between the output resonator and the bus waveguide. Figure 4 shows the filter response, and the corresponding computed Q-factors for various airgap spacings. It is seen that the drop channel extinction ratio increases, while the 3-dB bandwidths reduce with reducing air-gaps. There is also a 1 nm shift in the resonance wavelength that can be attributed to the small change in the effective refractive index with increasing air-gaps, and consequently the phase matching condition. Considering the feature size limitations of our fabrication process, and necessity of extinction ratios greater than 20 dB for effective filtering, we chose an air-gap of 200 nm for our fabricated devices. Figure 5(a) compares the drop and tap channel response of a device with 200 nm air-gap using EEM and FDTD. The extinction ratios and the 3-dB bandwidths are equal in both methods, except for a small difference in the estimation of the resonant wavelength.

 figure: Fig. 4

Fig. 4 Variation of the drop channel response with the air-gap between the bus waveguide and resonator. The stripe width was 600 nm with 100 nm teeth, and a period of 286 nm. The computed Q-factors are also shown.

Download Full Size | PPT Slide | PDF

 figure: Fig. 5

Fig. 5 (a) Comparison of the dropped channel and tap-off efficiency using EEM (dashed lines) and FDTD method (solid lines). (b) Effect of coupling multiple cavities (Obtained using EEM).

Download Full Size | PPT Slide | PDF

Single cavities have a very narrow Lorentzian response, and can cause signal distortion at high bit rates [24]. For efficient filtering we ideally require a flat and wide wavelength response. To increase the passband width and to obtain a flat response, several cavities can be coupled in series, keeping the number of periods the same, so as to maintain a constant transmittance. Figure 6 shows the schematic of a waveguide coupled filter with two coupled cavities at the output resonator, each with a quarter wave period in the middle.

 figure: Fig. 6

Fig. 6 Top schematic view of the waveguide coupled drop filter with two coupled cavities in the output resonator.

Download Full Size | PPT Slide | PDF

Figure 5(b) shows the variation in the bandwidths obtained by coupling multiple cavities as obtained using EEM. It is seen that the 3-dB bandwidth has doubled to 0.8 nm (100 GHz) by coupling three cavities, and has a flat top response. Several devices with waveguide width of 600 nm and 800 nm, teeth etch depth of 100 nm and 75 nm respectively, and grating periods of 286 nm and 279 nm respectively were fabricated and tested.

3. Fabrication and experimental analysis

The waveguide-coupled drop filters shown in Fig. 1 were fabricated using a SOI substrate with a 260 nm silicon device layer and a 2 μm BOX layer. All the planar photonic circuits were first patterned on samples spin coated with ZEP520A electron-beam resist. After the e-beam exposure, the resist patterns were transferred to silicon by using an inductively coupled plasma (ICP) etch recipe with SF6/C4F8 chemistry. The etch is stopped when the buried oxide (BOX) is reached. Samples were then cleaned, PMMA electron-beam resist was spin coated, and the grating couplers were patterned. The last part was done by several successive alignment and exposure steps with a modified scanning electron microscope (SEM). Grating couplers with 120 nm etch depth were then obtained using the same ICP etching recipe described above. Figure 7 shows SEM images of the fabricated devices. Figure 7(a) shows the overall layout of the device indicative of the bus waveguide, and the S-bend in the tap-off waveguide. The zoomed in view of the region indicated as a dotted box is shown in Fig. 7(b). Figure 7(b) shows a section of the output resonator with the quarter wave defect in the middle, and is indicative of the aspect ratio of our fabricated devices.

 figure: Fig. 7

Fig. 7 (a) A top view SEM micrograph showing the S-bend and the bus waveguide. (b) A top perspective view SEM micrograph showing the output resonator with the λ/4 shift and the bus waveguide.

Download Full Size | PPT Slide | PDF

Because grating couplers were fabricated for coupling light into the devices, the fabricated devices were tested using a vertical coupling setup for routing light in and out of the chip. Cleaved SMF-28 fibers aligned at 6° to the vertical were precisely manipulated using nano-positioning stages at both the input and output ends. Custom fiber chucks were used to hold the fibers vertically. A C + L broadband source and an optical spectrum analyzer were used as the source and detector for approximate alignment. High spectral resolution results were then obtained by employing a tunable laser (with 20 pm resolution sweep) together with a detector. The schematic of the experimental setup is shown in Fig. 8 . The propagation loss in the devices is 0.1 dB/mm, and the average fiber-to-fiber insertion loss (including the grating coupler loss and device insertion loss) was 8 dB. The experimental results obtained for a single and coupled cavity device with 600 nm waveguide, 100 nm side etch depth, and 400 periods in the output and mirror resonator is as shown in Fig. 9(a) . It is to be noted that the relative transmission is shown as a function of the frequency detuning to compare the performance, since the Bragg wavelengths were different for these two devices, and was 1549 nm and 1540 nm respectively. The filters show extinction ratios of well over 20 dB and excellent agreement between simulation and experiments. It is also seen that filter with two coupled cavities exhibits a flat top response when compared to a single cavity, a 3-dB bandwidth of 110 GHz (0.88 nm), and a roll-off 50 dB/nm. Figure 9(b) shows the drop and tap response of a fabricated filter with 240 periods in the output and mirror resonator. It is shown that around 16 dB of the resonant power can be extracted by employing the tap-off waveguide. The tap spectrum (blue curve) is slightly broader than the drop spectrum (red curve) due to the presence of a S-bend in the tap waveguide, and some portion of the power at non-resonant frequencies couples from the bus waveguide to the tap waveguide. This can be mitigated by using sharper bends, at the expense of higher radiation losses.

 figure: Fig. 8

Fig. 8 Schematic of the experimental setup.

Download Full Size | PPT Slide | PDF

 figure: Fig. 9

Fig. 9 (a) Comparison of the experimental drop channel response for single and two coupled cavities. The 3-dB bandwidth of the coupled cavity filter is around 110 GHz, with a filter roll-off of 50 dB/nm, and a top-hat like profile. (b) Drop channel and the tap channel response of a fabricated device.

Download Full Size | PPT Slide | PDF

4. Conclusion

We have presented the design, working principle, and demonstration of waveguide coupled filters on SOI. We have demonstrated for the first time that the resonant filter scheme proposed by Haus and Lai [10] is indeed practical. These devices were fabricated using e-beam lithography and ICP etching. These devices rely on resonant power transfer from a bus waveguide to side-walled Bragg resonators, and generation of a narrow response due to the addition of a quarter-wave shift. We demonstrated numerically that by coupling multiple cavities, a wideband drop response with a steep roll-off can be obtained. We also demonstrated that the power at the resonant frequency can be tapped off effectively, without being reflected back into the bus waveguide. Further, tunable filters based on this working principle can be realized using thermal tuning, or by using two back-to-back gratings in a Vernier configuration. Since these filters operate as three or four port devices, it is not necessary to employ the circulators that are required in reflection type Bragg filters.

References and links

1. K. Vahala, Optical Microcavities (World Scientific, 2004).

2. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997). [CrossRef]  

3. C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J. Lightwave Technol. 15(8), 1391–1404 (1997). [CrossRef]  

4. D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24(4), 194–196 (1974). [CrossRef]  

5. P. Dumon, W. Bogaerts, D. Van Thourhout, D. Taillaert, R. Baets, J. Wouters, S. Beckx, and P. Jaenen, “Compact wavelength router based on a Silicon-on-insulator arrayed waveguide grating pigtailed to a fiber array,” Opt. Express 14(2), 664–669 (2006). [CrossRef]   [PubMed]  

6. Z. Tian, V. Veerasubramanian, P. Bianucci, S. Mukherjee, Z. Mi, A. G. Kirk, and D. V. Plant, “Single rolled-up InGaAs/GaAs quantum dot microtubes integrated with silicon-on-insulator waveguides,” Opt. Express 19(13), 12164–12171 (2011). [CrossRef]   [PubMed]  

7. V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, “Distributed Bragg grating integrated-optical filters: synthesis and fabrication,” J. Vac. Sci. Technol. B 13(6), 2859–2864 (1995). [CrossRef]  

8. H. Kogelnik and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett. 18(4), 152–154 (1971). [CrossRef]  

9. R. Kazarinov, C. Henry, and N. Olsson, “Narrow-band resonant optical reflectors and resonant optical transformers for laser stabilization and wavelength division multiplexing,” IEEE J. Quantum Electron. 23(9), 1419–1425 (1987). [CrossRef]  

10. H. A. Haus and Y. Lai, “Narrow-band optical channel-dropping filter,” J. Lightwave Technol. 10(1), 57–62 (1992). [CrossRef]  

11. D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997). [CrossRef]  

12. H. A. Haus and Y. Lai, “Narrow-band distributed feedback reflector design,” J. Lightwave Technol. 9(6), 754–760 (1991). [CrossRef]  

13. J. N. Damask, “Practical design of side-coupled quarter-wave shifted distributed-Bragg resonant filters,” J. Lightwave Technol. 14(5), 812–821 (1996). [CrossRef]  

14. V. Veerasubramanian, A. G. Kirk, G. Beaudin, A. Giguere, B. Le Drogoff, and V. Aimez, “Waveguide coupled drop filters on SOI using vertical sidewalled grating resonators, ” in Proceedings of 23rd Annual Meeting of the IEEE Photonics Society (IEEE, 2010), pp. 634–635.

15. P. Prabhathan, V. M. Murukeshan, Z. Jing, and P. V. Ramana, “Broadband tunable bandpass filters using phase shifted vertical side wall grating in a submicrometer silicon-on-insulator waveguide,” Appl. Opt. 48(29), 5598–5603 (2009). [CrossRef]   [PubMed]  

16. H.-C. Kim, J. Wiedmann, K. Matsui, S. Tamura, and S. Arai, “1.5 micron wavelength distributed feedback lasers with deeply etched first-order vertical grating,” Jpn. J. Appl. Phys. 40(Part 2, No. 10B), L1107– L1109 (2001). [CrossRef]  

17. H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, and S. Arai, “1.5 micron wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1146–1152 (2003). [CrossRef]  

18. D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004). [CrossRef]   [PubMed]  

19. P. Bienstman and R. Baets, “Advanced boundary conditions for eigenmode expansion models,” Opt. Quantum Electron. 34(5-6), 523–540 (2002). [CrossRef]  

20. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, 2007).

21. D. G. Hall, “Optical waveguide diffraction gratings: coupling between guided modes,” in Progress in Optics, E. Wolf, ed. (1991).

22. H.-C. Kim, K. Ikeda, and Y. Fainman, “Resonant waveguide device with vertical gratings,” Opt. Lett. 32(5), 539–541 (2007). [CrossRef]   [PubMed]  

23. H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989).

24. M. Menard and A. G. Kirk, “Integrated Fabry-Perot comb filters for optical space switching,” J. Lightwave Technol. 28(5), 768–775 (2010). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. K. Vahala, Optical Microcavities (World Scientific, 2004).
  2. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
    [Crossref]
  3. C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J. Lightwave Technol. 15(8), 1391–1404 (1997).
    [Crossref]
  4. D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24(4), 194–196 (1974).
    [Crossref]
  5. P. Dumon, W. Bogaerts, D. Van Thourhout, D. Taillaert, R. Baets, J. Wouters, S. Beckx, and P. Jaenen, “Compact wavelength router based on a Silicon-on-insulator arrayed waveguide grating pigtailed to a fiber array,” Opt. Express 14(2), 664–669 (2006).
    [Crossref] [PubMed]
  6. Z. Tian, V. Veerasubramanian, P. Bianucci, S. Mukherjee, Z. Mi, A. G. Kirk, and D. V. Plant, “Single rolled-up InGaAs/GaAs quantum dot microtubes integrated with silicon-on-insulator waveguides,” Opt. Express 19(13), 12164–12171 (2011).
    [Crossref] [PubMed]
  7. V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, “Distributed Bragg grating integrated-optical filters: synthesis and fabrication,” J. Vac. Sci. Technol. B 13(6), 2859–2864 (1995).
    [Crossref]
  8. H. Kogelnik and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett. 18(4), 152–154 (1971).
    [Crossref]
  9. R. Kazarinov, C. Henry, and N. Olsson, “Narrow-band resonant optical reflectors and resonant optical transformers for laser stabilization and wavelength division multiplexing,” IEEE J. Quantum Electron. 23(9), 1419–1425 (1987).
    [Crossref]
  10. H. A. Haus and Y. Lai, “Narrow-band optical channel-dropping filter,” J. Lightwave Technol. 10(1), 57–62 (1992).
    [Crossref]
  11. D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
    [Crossref]
  12. H. A. Haus and Y. Lai, “Narrow-band distributed feedback reflector design,” J. Lightwave Technol. 9(6), 754–760 (1991).
    [Crossref]
  13. J. N. Damask, “Practical design of side-coupled quarter-wave shifted distributed-Bragg resonant filters,” J. Lightwave Technol. 14(5), 812–821 (1996).
    [Crossref]
  14. V. Veerasubramanian, A. G. Kirk, G. Beaudin, A. Giguere, B. Le Drogoff, and V. Aimez, “Waveguide coupled drop filters on SOI using vertical sidewalled grating resonators, ” in Proceedings of 23rd Annual Meeting of the IEEE Photonics Society (IEEE, 2010), pp. 634–635.
  15. P. Prabhathan, V. M. Murukeshan, Z. Jing, and P. V. Ramana, “Broadband tunable bandpass filters using phase shifted vertical side wall grating in a submicrometer silicon-on-insulator waveguide,” Appl. Opt. 48(29), 5598–5603 (2009).
    [Crossref] [PubMed]
  16. H.-C. Kim, J. Wiedmann, K. Matsui, S. Tamura, and S. Arai, “1.5 micron wavelength distributed feedback lasers with deeply etched first-order vertical grating,” Jpn. J. Appl. Phys. 40(Part 2, No. 10B), L1107– L1109 (2001).
    [Crossref]
  17. H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, and S. Arai, “1.5 micron wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1146–1152 (2003).
    [Crossref]
  18. D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004).
    [Crossref] [PubMed]
  19. P. Bienstman and R. Baets, “Advanced boundary conditions for eigenmode expansion models,” Opt. Quantum Electron. 34(5-6), 523–540 (2002).
    [Crossref]
  20. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, 2007).
  21. D. G. Hall, “Optical waveguide diffraction gratings: coupling between guided modes,” in Progress in Optics, E. Wolf, ed. (1991).
  22. H.-C. Kim, K. Ikeda, and Y. Fainman, “Resonant waveguide device with vertical gratings,” Opt. Lett. 32(5), 539–541 (2007).
    [Crossref] [PubMed]
  23. H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989).
  24. M. Menard and A. G. Kirk, “Integrated Fabry-Perot comb filters for optical space switching,” J. Lightwave Technol. 28(5), 768–775 (2010).
    [Crossref]

2011 (1)

2010 (1)

2009 (1)

2007 (1)

2006 (1)

2004 (1)

2003 (1)

H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, and S. Arai, “1.5 micron wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1146–1152 (2003).
[Crossref]

2002 (1)

P. Bienstman and R. Baets, “Advanced boundary conditions for eigenmode expansion models,” Opt. Quantum Electron. 34(5-6), 523–540 (2002).
[Crossref]

2001 (1)

H.-C. Kim, J. Wiedmann, K. Matsui, S. Tamura, and S. Arai, “1.5 micron wavelength distributed feedback lasers with deeply etched first-order vertical grating,” Jpn. J. Appl. Phys. 40(Part 2, No. 10B), L1107– L1109 (2001).
[Crossref]

1997 (3)

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[Crossref]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J. Lightwave Technol. 15(8), 1391–1404 (1997).
[Crossref]

1996 (1)

J. N. Damask, “Practical design of side-coupled quarter-wave shifted distributed-Bragg resonant filters,” J. Lightwave Technol. 14(5), 812–821 (1996).
[Crossref]

1995 (1)

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, “Distributed Bragg grating integrated-optical filters: synthesis and fabrication,” J. Vac. Sci. Technol. B 13(6), 2859–2864 (1995).
[Crossref]

1992 (1)

H. A. Haus and Y. Lai, “Narrow-band optical channel-dropping filter,” J. Lightwave Technol. 10(1), 57–62 (1992).
[Crossref]

1991 (1)

H. A. Haus and Y. Lai, “Narrow-band distributed feedback reflector design,” J. Lightwave Technol. 9(6), 754–760 (1991).
[Crossref]

1987 (1)

R. Kazarinov, C. Henry, and N. Olsson, “Narrow-band resonant optical reflectors and resonant optical transformers for laser stabilization and wavelength division multiplexing,” IEEE J. Quantum Electron. 23(9), 1419–1425 (1987).
[Crossref]

1974 (1)

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24(4), 194–196 (1974).
[Crossref]

1971 (1)

H. Kogelnik and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett. 18(4), 152–154 (1971).
[Crossref]

Arai, S.

H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, and S. Arai, “1.5 micron wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1146–1152 (2003).
[Crossref]

H.-C. Kim, J. Wiedmann, K. Matsui, S. Tamura, and S. Arai, “1.5 micron wavelength distributed feedback lasers with deeply etched first-order vertical grating,” Jpn. J. Appl. Phys. 40(Part 2, No. 10B), L1107– L1109 (2001).
[Crossref]

Baets, R.

Beckx, S.

Bianucci, P.

Bienstman, P.

D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004).
[Crossref] [PubMed]

P. Bienstman and R. Baets, “Advanced boundary conditions for eigenmode expansion models,” Opt. Quantum Electron. 34(5-6), 523–540 (2002).
[Crossref]

Bogaerts, W.

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Damask, J. N.

J. N. Damask, “Practical design of side-coupled quarter-wave shifted distributed-Bragg resonant filters,” J. Lightwave Technol. 14(5), 812–821 (1996).
[Crossref]

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, “Distributed Bragg grating integrated-optical filters: synthesis and fabrication,” J. Vac. Sci. Technol. B 13(6), 2859–2864 (1995).
[Crossref]

Dumon, P.

Fainman, Y.

Ferrera, J.

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, “Distributed Bragg grating integrated-optical filters: synthesis and fabrication,” J. Vac. Sci. Technol. B 13(6), 2859–2864 (1995).
[Crossref]

Flanders, D. C.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24(4), 194–196 (1974).
[Crossref]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Friesem, A. A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[Crossref]

Giles, C. R.

C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J. Lightwave Technol. 15(8), 1391–1404 (1997).
[Crossref]

Hasegawa, T.

H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, and S. Arai, “1.5 micron wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1146–1152 (2003).
[Crossref]

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, “Distributed Bragg grating integrated-optical filters: synthesis and fabrication,” J. Vac. Sci. Technol. B 13(6), 2859–2864 (1995).
[Crossref]

H. A. Haus and Y. Lai, “Narrow-band optical channel-dropping filter,” J. Lightwave Technol. 10(1), 57–62 (1992).
[Crossref]

H. A. Haus and Y. Lai, “Narrow-band distributed feedback reflector design,” J. Lightwave Technol. 9(6), 754–760 (1991).
[Crossref]

Henry, C.

R. Kazarinov, C. Henry, and N. Olsson, “Narrow-band resonant optical reflectors and resonant optical transformers for laser stabilization and wavelength division multiplexing,” IEEE J. Quantum Electron. 23(9), 1419–1425 (1987).
[Crossref]

Ikeda, K.

Jaenen, P.

Jing, Z.

Kanjo, H.

H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, and S. Arai, “1.5 micron wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1146–1152 (2003).
[Crossref]

Kazarinov, R.

R. Kazarinov, C. Henry, and N. Olsson, “Narrow-band resonant optical reflectors and resonant optical transformers for laser stabilization and wavelength division multiplexing,” IEEE J. Quantum Electron. 23(9), 1419–1425 (1987).
[Crossref]

Kim, H. C.

H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, and S. Arai, “1.5 micron wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1146–1152 (2003).
[Crossref]

Kim, H.-C.

H.-C. Kim, K. Ikeda, and Y. Fainman, “Resonant waveguide device with vertical gratings,” Opt. Lett. 32(5), 539–541 (2007).
[Crossref] [PubMed]

H.-C. Kim, J. Wiedmann, K. Matsui, S. Tamura, and S. Arai, “1.5 micron wavelength distributed feedback lasers with deeply etched first-order vertical grating,” Jpn. J. Appl. Phys. 40(Part 2, No. 10B), L1107– L1109 (2001).
[Crossref]

Kirk, A. G.

Kogelnik, H.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24(4), 194–196 (1974).
[Crossref]

H. Kogelnik and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett. 18(4), 152–154 (1971).
[Crossref]

Lai, Y.

H. A. Haus and Y. Lai, “Narrow-band optical channel-dropping filter,” J. Lightwave Technol. 10(1), 57–62 (1992).
[Crossref]

H. A. Haus and Y. Lai, “Narrow-band distributed feedback reflector design,” J. Lightwave Technol. 9(6), 754–760 (1991).
[Crossref]

Laine, J. P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Matsui, K.

H.-C. Kim, J. Wiedmann, K. Matsui, S. Tamura, and S. Arai, “1.5 micron wavelength distributed feedback lasers with deeply etched first-order vertical grating,” Jpn. J. Appl. Phys. 40(Part 2, No. 10B), L1107– L1109 (2001).
[Crossref]

Menard, M.

Mi, Z.

Mukherjee, S.

Murphy, T. E.

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, “Distributed Bragg grating integrated-optical filters: synthesis and fabrication,” J. Vac. Sci. Technol. B 13(6), 2859–2864 (1995).
[Crossref]

Murukeshan, V. M.

Olsson, N.

R. Kazarinov, C. Henry, and N. Olsson, “Narrow-band resonant optical reflectors and resonant optical transformers for laser stabilization and wavelength division multiplexing,” IEEE J. Quantum Electron. 23(9), 1419–1425 (1987).
[Crossref]

Plant, D. V.

Prabhathan, P.

Ramana, P. V.

Rosenblatt, D.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[Crossref]

Schmidt, R. V.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24(4), 194–196 (1974).
[Crossref]

Shank, C. V.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24(4), 194–196 (1974).
[Crossref]

H. Kogelnik and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett. 18(4), 152–154 (1971).
[Crossref]

Sharon, A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[Crossref]

Smith, H. I.

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, “Distributed Bragg grating integrated-optical filters: synthesis and fabrication,” J. Vac. Sci. Technol. B 13(6), 2859–2864 (1995).
[Crossref]

Taillaert, D.

Tamura, S.

H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, and S. Arai, “1.5 micron wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1146–1152 (2003).
[Crossref]

H.-C. Kim, J. Wiedmann, K. Matsui, S. Tamura, and S. Arai, “1.5 micron wavelength distributed feedback lasers with deeply etched first-order vertical grating,” Jpn. J. Appl. Phys. 40(Part 2, No. 10B), L1107– L1109 (2001).
[Crossref]

Tian, Z.

Van Thourhout, D.

Veerasubramanian, V.

Wiedmann, J.

H.-C. Kim, J. Wiedmann, K. Matsui, S. Tamura, and S. Arai, “1.5 micron wavelength distributed feedback lasers with deeply etched first-order vertical grating,” Jpn. J. Appl. Phys. 40(Part 2, No. 10B), L1107– L1109 (2001).
[Crossref]

Wong, V. V.

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, “Distributed Bragg grating integrated-optical filters: synthesis and fabrication,” J. Vac. Sci. Technol. B 13(6), 2859–2864 (1995).
[Crossref]

Wouters, J.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24(4), 194–196 (1974).
[Crossref]

H. Kogelnik and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett. 18(4), 152–154 (1971).
[Crossref]

IEEE J. Quantum Electron. (2)

R. Kazarinov, C. Henry, and N. Olsson, “Narrow-band resonant optical reflectors and resonant optical transformers for laser stabilization and wavelength division multiplexing,” IEEE J. Quantum Electron. 23(9), 1419–1425 (1987).
[Crossref]

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

H. C. Kim, H. Kanjo, T. Hasegawa, S. Tamura, and S. Arai, “1.5 micron wavelength narrow stripe distributed reflector lasers for high-performance operation,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1146–1152 (2003).
[Crossref]

J. Lightwave Technol. (6)

H. A. Haus and Y. Lai, “Narrow-band distributed feedback reflector design,” J. Lightwave Technol. 9(6), 754–760 (1991).
[Crossref]

J. N. Damask, “Practical design of side-coupled quarter-wave shifted distributed-Bragg resonant filters,” J. Lightwave Technol. 14(5), 812–821 (1996).
[Crossref]

H. A. Haus and Y. Lai, “Narrow-band optical channel-dropping filter,” J. Lightwave Technol. 10(1), 57–62 (1992).
[Crossref]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J. Lightwave Technol. 15(8), 1391–1404 (1997).
[Crossref]

M. Menard and A. G. Kirk, “Integrated Fabry-Perot comb filters for optical space switching,” J. Lightwave Technol. 28(5), 768–775 (2010).
[Crossref]

J. Vac. Sci. Technol. B (1)

V. V. Wong, J. Ferrera, J. N. Damask, T. E. Murphy, H. I. Smith, and H. A. Haus, “Distributed Bragg grating integrated-optical filters: synthesis and fabrication,” J. Vac. Sci. Technol. B 13(6), 2859–2864 (1995).
[Crossref]

Jpn. J. Appl. Phys. (1)

H.-C. Kim, J. Wiedmann, K. Matsui, S. Tamura, and S. Arai, “1.5 micron wavelength distributed feedback lasers with deeply etched first-order vertical grating,” Jpn. J. Appl. Phys. 40(Part 2, No. 10B), L1107– L1109 (2001).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

P. Bienstman and R. Baets, “Advanced boundary conditions for eigenmode expansion models,” Opt. Quantum Electron. 34(5-6), 523–540 (2002).
[Crossref]

Other (5)

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, 2007).

D. G. Hall, “Optical waveguide diffraction gratings: coupling between guided modes,” in Progress in Optics, E. Wolf, ed. (1991).

V. Veerasubramanian, A. G. Kirk, G. Beaudin, A. Giguere, B. Le Drogoff, and V. Aimez, “Waveguide coupled drop filters on SOI using vertical sidewalled grating resonators, ” in Proceedings of 23rd Annual Meeting of the IEEE Photonics Society (IEEE, 2010), pp. 634–635.

K. Vahala, Optical Microcavities (World Scientific, 2004).

H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1 Top schematic view of the waveguide coupled drop filter with side-etched gratings.
Fig. 2
Fig. 2 (a) Electric field distribution in a Bragg resonator with a quarter-wave defect indicating an exponential decay towards either end. (b) The 2D refractive index profile and a cross-cut of the propagating electric field (Ey, at z = 5 μm) of the waveguide mode in the bus, indicating power transfer into the output resonator through its evanescent tail.
Fig. 3
Fig. 3 (a) Top view of the FDTD model. (b) Electric field at an off-resonance wavelength indicating almost 100% transmission through the bus waveguide. (c) Electric field at resonance indicating power tap-off at the resonant wavelength. The electric field scale palette is also shown.
Fig. 4
Fig. 4 Variation of the drop channel response with the air-gap between the bus waveguide and resonator. The stripe width was 600 nm with 100 nm teeth, and a period of 286 nm. The computed Q-factors are also shown.
Fig. 5
Fig. 5 (a) Comparison of the dropped channel and tap-off efficiency using EEM (dashed lines) and FDTD method (solid lines). (b) Effect of coupling multiple cavities (Obtained using EEM).
Fig. 6
Fig. 6 Top schematic view of the waveguide coupled drop filter with two coupled cavities in the output resonator.
Fig. 7
Fig. 7 (a) A top view SEM micrograph showing the S-bend and the bus waveguide. (b) A top perspective view SEM micrograph showing the output resonator with the λ/4 shift and the bus waveguide.
Fig. 8
Fig. 8 Schematic of the experimental setup.
Fig. 9
Fig. 9 (a) Comparison of the experimental drop channel response for single and two coupled cavities. The 3-dB bandwidth of the coupled cavity filter is around 110 GHz, with a filter roll-off of 50 dB/nm, and a top-hat like profile. (b) Drop channel and the tap channel response of a fabricated device.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

R= |κ | 2 sin h 2 (sL) s 2 cos h 2 (sL)+ (Δβ/2) 2 sin h 2 (sL) ,
κ=[ Γ π λ Δ W S W eff n Si 2 N 2 Nq ][ N 2 n Si 2 N 2 n Si O 2 2 +1 ],

Metrics