Abstract

We demonstrate spiral integrated Bragg gratings (IBGs) in 60-nm-thick strip waveguides on the silicon-on-insulator (SOI) platform. The length of the spiral IBG is 2 mm, occupying an area of 147 × 141 μm2 with a minimum bending radius of 20 μm. Experiments show that the spiral IBGs exhibit a single narrow transparent peak with a Q-factor of 1 × 105 in a broad stopband, induced by the phase shift of the S-junction at the spiral center. This phenomenon is analogous to the electromagnetically induced transparency (EIT) effect. The transparent peak can periodically shift in the stopband upon heating of the S-junction using a TiN-based heater on top. The peak transmittance and Q-factor are dependent on the reflectivity of the spiral IBG. The transparent peak can be completely eliminated under a certain tuning power, and the spiral IBG hence behaves as a bandstop optical filter. The bandwidth is 0.94 nm and the extinction ratio is as high as 43 dB. The stopband can also be shifted by heating the Bragg gratings using a separate TiN heater. The experimental results agree well with the modeling results based on the transfer matrix method.

© 2016 Optical Society of America

1. Introduction

Bragg gratings have been widely used as key functional components in optical communications, sensing and microwave photonic signal processing. Many researchers have been exploring the integrated Bragg gratings (IBGs) on the silicon-on-insulator (SOI) platform for its small footprint and low-cost fabrication. Uniform [1–3], phase-shifted [4–6], superimposed [7], sampled [3] and phase-engineered [8,9] IBGs have already been demonstrated. Most of them are short Bragg gratings (a few hundreds of microns in length) with large coupling coefficients. For applications that need narrow bandwidths (<1nm) or well-controlled spectral profiles, it is required to fabricate longer IBGs with weaker coupling coefficients. However, implementation of these kinds of IBGs are quite challenging for two main reasons. Firstly, the sidewall corrugations on the strip waveguide are limited to a few nanometers due to the strong overlap of the optical mode with the sidewall [3]. Such small corrugations are very difficult to fabricate, given the limited resolution in photolithography. Several approaches have been demonstrated to solve this issue. One is to use rib waveguides with larger corrugations on the rib or the slab sidewalls, but it requires two etching steps [1, 10–12]. Another one is to use weakly coupled pillars outside the core waveguide [13]. The pillars are of small size, still difficult to fabricate using photolithography. Secondly, long IBGs are quite sensitive to the accumulated phase noise caused by the variation in waveguide width and height [14–16]. The uniformity of waveguide width cannot be guaranteed after photolithography and dry etch; the waveguide height also changes due to the variation of silicon layer thickness in SOI wafers. The width-induced phase noise can be reduced by using wider waveguides [17,18]. However, a wide waveguide may support high-order modes, and the cross coupling among multiple modes could degrade the device performances significantly, especially in grating-assisted couplers and FSR-free Bragg grating filters [19–21]. The spiral configuration has been shown to be an effective way to reduce the phase noise caused by the variation in waveguide dimensions [22–25].

In our previous work, we have demonstrated Bragg gratings based on the 60-nm-thick silicon strip waveguides [26]. Compared to the typical 500 nm × 220 nm strip waveguide, the ultra-thin waveguide processes a fundamental mode with much lower optical confinement in the waveguide core. A small coupling coefficient thus can be achieved using relatively large corrugations on the strip waveguide sidewalls. Meanwhile, as the mode of the ultra-thin waveguide interacts weakly with the sidewalls, the waveguide is less sensitive to the sidewall roughness, resulting in low phase noise. As the ultra-thin waveguides are still sensitive to the waveguide height, we design spiral-shape IBGs to reduce the height variation. The main challenges in making spiral IBGs lie in the effective index variation when the bending radius changes. The bending radius becomes smaller in the center and the bending curvature discontinues at the S-junction. Recently, spiral IBGs based on wide strip waveguides have been theoretically analyzed and experimental demonstrated [24]. It reveals that the spiral IBGs without phase correction show a strong Bragg wavelength perturbation at the center of the stopband. Correction of grating period was proposed to compensate for the bending-induced phase noise. However, the grating period should be well controlled within the range of a few nanometers, imposing a great challenge in device fabrication. Though one can increase the bending radius to reduce the waveguide effective index variation [27], this however inevitably increases the device size.

In this paper, we report spiral IBGs based on the 60-nm-thick strip waveguides on the SOI platform. The typical transmission spectrum of the spiral IBG exhibits a single narrow transparent peak in the stopband of the Bragg grating. Similar characteristic has been observed in a 220-nm-thick passive spiral IBG [24]. Here, our experiment reveals that the transparency peak can periodically shift in the stopband upon heating of the center S-junction. In particular, the transparent peak is absent under a certain tuning power. We also demonstrate that the transmittance and Q-factor of the transparent peak in the stopband are dependent on the reflectivity of the spiral IBG. The paper is organized as follows. Firstly, we present the design and fabrication of spiral IBGs. Then we show the measured transmission spectra of three spiral IBGs with different bending radii. A distributed feedback (DFB) grating model based on the transfer matrix method is used to fit the experimental results. Lastly, we present the experimental results to show the effect of grating coupling efficiency on the device performance.

2. Device design and fabrication

Figure 1(a) shows the schematic structure of the spiral IBG. The bending radius in each half circle remains constant. This structure is similar to that reported in [25]. In the center of the spiral, the two semi-circular waveguides form an S-shaped waveguide with sharp discontinuity in the bending curvature. The discontinuity results in a certain phase shift when light propagates through the center S-junction. The grating corrugation is located at the sidewalls of the spiral waveguide as shown in Fig. 1(b). Two TiN-based heaters are positioned on top of the spiral waveguide and the center S-bend to separately tune the Bragg reflection (tuning power P2) and the phase shift (tuning power P1), respectively. The response time of these heaters is in the order of μs [28]. Figure 1(c) shows the 3D structure of the active device. The critical dimensions of the device are labeled in the cross-sectional waveguide structure shown in Fig. 1(d). The gap size between the TiN strips is 2 μm. The resistivity of TiN is around 25 μΩ·cm. In order to reduce thermal crosstalk between the two heaters and increase the thermal tuning efficiency, trenches are etched down into the silicon substrate to isolate the heaters. The transverse magnetic (TM) mode has a large modal profile and interacts severely with the TiN heater and the silicon substrate, leading to a much higher propagation loss than the transverse electric (TE) mode. Therefore, we designed the spiral grating based on the TE mode. Figure 1(e) shows the microscopic image of a fabricated active spiral IBG.

 

Fig. 1 (a) Schematic of the spiral IBG. R0 is the minimum bending radius. (b) Zoom-in view showing the grating details. Λ: grating period, Wcorr: corrugation width, g: waveguide spacing. (c) 3D perspective view of the active spiral IBG with TiN heaters on top for thermal tuning. (d) Cross section of the active spiral waveguide. (e) Microscopic image of a fabricated active spiral IBG.

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The key design parameters of the spiral waveguides include the waveguide spacing (g), the minimum bending radius (R0), and the number of half circles (NR). The spacing g is chosen to be 5.5 μm to ensure low crosstalk. Note that this value is quite conservative and could be reduced to make the spiral more compact. The variation of waveguide bending radius results in the change of waveguide effective index and the mode mismatch between two consecutive half circles of waveguides. Using the Lumerical MODE Solutions, we calculate the effective index variation δneff relative to a straight waveguide as a function of bending radius as shown in Fig. 2(a). As expected, δneff decreases as the radius increases. The variation in waveguide effective refractive index generates unwarranted chirp in the spiral grating, making the stopband become broader. For R0 = 20 μm, δneff is relatively small (~6 × 10−4). According to our calculation based on the transfer matrix method (TMM) [29], such a small value of δneff causes slight stopband broadening of 0.08 nm, approximately 6% of the original bandwidth. Hence, in our design, we choose R0 ≥ 20 μm. The mode mismatch between two sections of curved waveguides with different bending radii will cause junction loss. As the bending curvature changes its sign at the S-junction, the induced loss is the dominate junction loss. The black line in Fig. 2(b) shows the simulated S-junction loss as a function of R0. It can be seen that the S-junction loss decreases as the bending radius increases. Note that the mode mismatch also results in certain phase shift for light propagating through it. Thereby, the spiral grating works like a phase-shifted Bragg grating where a resonance is generated inside the stopband. A high intrinsic resonance quality-factor (Q-factor) can be obtained with a small S-junction loss. The packing efficiency of the spiral, α, is defined as L/A, where L is the grating length and A is the area of the entire spiral [23]. The packing efficiency is an important parameter to measure the device compactness. The height variation and thus the induced phase noise are small for a spiral with a high packing efficiency. The calculated α as a function of R0 is shown by the blue line in Fig. 2(b). It can be seen that a high packing efficiency can be obtained at the expense of an increased loss. The R0 is chosen to be between 20 μm to 35 μm in our design, which brings a good compromise between device compactness and loss.

 

Fig. 2 (a) Effective refractive index change as a function of waveguide bending radius. (b) S-junction loss and packing efficiency (α) of the spiral grating as a function of the minimum bending radius R0.

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The spiral IBGs are realized by introducing periodic corrugations on both sidewalls of the spiral waveguide in our design. The grating coupling coefficient is determined by the corrugation width Wcorr and the minimum waveguide width Wmin. It should be noted that the difference in coupling coefficient for curved and straight waveguides is negligibly small when R0 ≥ 20μm, and hence we used the straight grating waveguide to calculate the coupling efficiency in our design. The grating period is chosen to set the Bragg wavelength close to 1550 nm.

The device fabrication was started using an SOI wafer with a top layer thickness of 220 nm and a buried oxide (BOX) layer thickness of 3 μm. Firstly, the SOI wafer was thinned down to 60 nm using thermal oxidation. Compared to plasma dry etch, oxidation can result in smoother surface and more precisely controlled silicon layer thickness. The device patterns were defined by 248-nm deep ultra-violet (DUV) photolithography, followed by anisotropic dry etch of silicon. Then, a 2-μm-thick silicon dioxide layer was deposited using plasma-enhanced chemical vapor deposition (PECVD). After that, heaters were made by deposition and dry etching of a 120-nm-thickness TiN layer. Another oxide layer of 0.42 μm in thickness was deposited above the TiN layer by PECVD. Subsequently, contact holes were etched and aluminum was deposited to form metal connection. Finally, trenches were etched deep down into the silicon substrate (100-μm deep) using inductively coupled plasma (ICP) etch to isolate the micro-heaters. The fabrication was done using the IME 180-nm fabrication process.

3. Experimental characterization

We used Yenista Optics’s tunable laser (Tunics-T100S-HP) and component tester (CT400) to characterize the device transmission performance. A polarization controller was placed in front of the device to set the TE polarization. On-chip grating couplers were used for input and output coupling with optical fibers. The coupling loss per facet is about 6.5 dB. We implemented four spiral IBGs with the design parameters listed in Table 1. The grating length of all four devices is around 2 mm. The devices I, II, and III have different R0 in order to explore the effect of bending radius on the device performance. Device IV uses the same set of design parameters as device III except the minimum waveguide width Wmin. The device I has the most compact size, occupying an area of 147 × 141 μm2 with a packing efficiency of 14.1.

Tables Icon

Table 1. Design Parameters for Four Spiral IBGs

3.1 Optical spectrum measurement

Figure 3 shows the measured transmission spectra for devices I to III. It can be seen that all these spectra exhibit a narrow transparent peak in the grating stopband. It is analogous to the electromagnetically-induced transparency (EIT) effect in the atomic systems due to the coherent interference [30]. This unique feature of the EIT-effect has many applications in narrow-band filtering [31], optical sensing [32], optical modulation [4–6], and optical signal processing [33, 34]. A DFB grating model based on the transfer matrix method is used to fit the experimental results. The phase shift Δφ and loss at the S-junction are taken into account in our model. The grating coupling coefficient κ is extracted from the measured spectra usingκ=πngΔλ/λ02, where ng is the group index of the waveguide, Δλ is the measured stopband width, and λ0 is the Bragg wavelength [35]. The effective index difference (Δneff) between the two sections in one grating period used in the transfer matrix is obtained byΔneff=κλ0/2 [36]. Upon fitting, the phase shift induced by the S-junction is extracted to be Δφ = 1.18π, 1.16π, 1.15π for the three devices shown in Figs. 3(a)-3(c), respectively. The theoretical model has good agreement with the experimental results. The measurement indicates that the phase shift induced by the S-junction is difficult to eliminate even when the bending radius increases to 35 μm. The insets in Fig. 3 show the magnified resonance peaks. The losses (excluding the coupling loss) of the resonance peaks are 6.7dB, 6.9dB, and 7.0 dB for the three devices and the Q-factors are 1.17 × 105, 1.25 × 105, and 1.7 × 105, respectively. As the spiral grating works like a phase-shifted Bragg grating, the overall Q-factor (Q) is expressed as:

1Q=1QC+1QI
where QC represents the external Q-factor given by the transmittance of the half gratings on both sides of the S-junction, and QI represents the intrinsic Q-factor given by the cavity loss including the spiral waveguide loss and the S-junction loss. If there were no intrinsic cavity loss, Q would be equal to QC. Hence, we can obtain QC by measuring the Q-factor of the resonance peak from the spectrum given by the theoretical model by assuming no intrinsic loss. The derived QC values are 2.88 × 105, 3.0 × 105, 3.25 × 105 for the three devices, respectively. QI is thus calculated to be 2.0 × 105, 2.1 × 105, 3.6 × 105 using Eq. (1). Then the cavity loss per half round-trip is deduced to be 0.07 dB, 0.06 dB and 0.04 dB [36], respectively. It indicates that the cavity loss decreases with an increased bending radius, thus leading to a higher QI. Note that QC is determined by the reflectivity of the Bragg grating. One can increase QC by using a high reflectivity Bragg grating.

 

Fig. 3 Transmission spectra of three devices with (a) R0 = 20 μm, (b) R0 = 25 μm, and (c) R0 = 35 μm. The solid black lines represent the experimental spectra and the dashed red lines represent the modeled spectra. The insets show the magnified transparent peaks in the stopbands. The 3-dB bandwidths are labeled.

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3.2 Thermal active tuning

When the S-shaped waveguide is heated locally, the effective refractive index of the grating in this region increases due to the thermo-optic effect, resulting in an increased phase shift. Thereby, the original transparency peak caused by the S-junction will be gradually red-shifted. Figure 4(a) shows the evolution of the transparent peak with tuning power P1 for device I. Simulation results with Δφ as the fitting parameter are shown in Fig. 4(b). Similar phenomena were observed for devices II and III. It can be seen that the transparent peak periodically shifts in the stopband. The transparent peak is completely absent when P1 is around 173 mW. In this case, the spiral IBG behaves as a bandstop filter. The full width at half maximum (FWHM) of the stopband is 0.94 nm and the extinction ratio is as high as 43 dB. The single-notch stopband can also be shifted by tuning two heaters simultaneously as shown in Fig. 4(c). Figure 4(d) depicts the extracted peak wavelength shift in one period as a function of tuning power P1. The thermal tuning efficiency is around 4.3 pm/mW. The single-notch stopband shift as a function of total power consumption is shown in Fig. 4(e). The thermal tuning efficiency is around 1 pm/mW. The tuning efficiency of the two heaters can be improved by reducing the waveguide separation to make the device more compact or by removing the silicon substrate which is the main source for heat leakage.

 

Fig. 4 (a) Evolution of the transparent peak upon thermal tuning of the S-junction. The spectra are shifted vertically in purpose for better clarity. (b) Simulation results showing the similar evolution trend. (c) Shift of the stopband upon tuning of both the spiral waveguide and the center S-junction. (d) Extracted transparency peak wavelength as a function of the tuning power P1. (e) Extracted central wavelength of the stopband as a function of the total tuning power P1 + P2.

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3.3 Effect of the grating coupling efficiency

In most applications, a high transmittance of the resonance peak is needed. One can increase the transmittance of the resonance peak by reducing the reflectivity of the spiral IBG [37]. Figure 5(a) shows the evolution of the transmission spectrum in response to the tuning power on the S-junction for device IV. Compared to device III, Wmin of this device is increased while Wcorr is unchanged and thereby the grating coupling coefficient decreases, leading to reduced reflectivity of the Bragg grating. It can be seen that the extinction ratio of the stopband is reduced, while the peak transmittance in the stopband always approaches unit. Figure 5(b) shows the resonance Q-factor as a function of peak wavelength offset with respect to the stopband center wavelength. It can be seen that the Q-factor reduces when the peak moves away from the center of the stopband, due to the reduced reflectivity close to the edges of the stopband. The maximum Q-factor, as shown in the inset of Fig. 5(b), is 7.8 × 104 obtained at the center of the stopband. However, this maximum Q-factor of device IV is still lower than that of device III. It implies that a higher transmittance of the resonance peak is obtained at the expense of a reduced Q-factor.

 

Fig. 5 (a) Transmission spectra of device IV in response to the tuning power P1. (b) Q-factor as a function of the resonance offset from the stopband center wavelength. The inset shows magnified resonance peak when Q reaches the maximum.

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4. Conclusions

We have demonstrated spiral IBGs in 60-nm-thick strip waveguides on the SOI platform. Our experimental results show that the spiral IBGs exhibit a single transparent peak in a narrow stopband, analogous to the EIT effect. The transparent peak with a Q-factor up to ~105 can periodically shift in the stopband upon heating using a TiN-based heater on top of the S-junction. The sharp peak can be exploited for narrow-band filtering, optical sensing, and optical signal processing. Under a certain tuning power, the transparent peak is completely eliminated, which makes the spiral IBG behave as a band-stop filter. The stopband is 0.94 nm wide and the extinction ratio is 43 dB. The stopband can be shifted by using another separate TiN heater. We experimentally explored the effect of bending radius on the device performances, especially on the Q-factor of the transparency peak. The phase shift induced by the S-junction is inevitable due to the asymmetric mode distribution in the S-junction. However, the loss induced by this asymmetric mode distribution can be reduced by increasing the bending radius and as a result the Q-factor of the transmission peak can be improved. We also investigated the dependence of the peak transmittance and Q-factor on the reflectivity of the spiral IBG. The peak transmittance increases and the Q-factor decreases as the reflectivity decreases. A theoretical model has been used to fit the experimental results with good agreement.

Acknowledgment

This work was supported in part by the National Natural Science Foundation of China (NSFC) (61422508, 61535006, 61505105), the Shanghai Rising-Star Program (14QA1402600). We also acknowledge IME Singapore for device fabrication.

References and links

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References

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  1. X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,” Opt. Express 20(14), 15547–15558 (2012).
    [Crossref] [PubMed]
  2. Y. Painchaud, M. Poulin, C. Latrasse, N. Ayotte, M.-J. Picard, and M. Morin, “Bragg grating notch filters in silicon-on-insulator waveguides,” in Bragg Gratings Photosensitivity, Poling Glass Waveguides, BW2E.3, Optical Society of America (2012).
  3. X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photonics Technol. Lett. 23(5), 290 (2011).
  4. K. Bédard, A. D. Simard, B. Filion, Y. Painchaud, L. A. Rusch, and S. LaRochelle, “Dual phase-shift Bragg grating silicon photonic modulator operating up to 60 Gb/s,” Opt. Express 24(3), 2413–2419 (2016).
    [Crossref] [PubMed]
  5. W. Zhang, N. Ehteshami, W. Liu, and J. Yao, “Silicon-based on-chip electrically tunable sidewall Bragg grating Fabry-Perot filter,” Opt. Lett. 40(13), 3153–3156 (2015).
    [Crossref] [PubMed]
  6. M. Caverley, X. Wang, K. Murray, N. A. F. Jaeger, and L. Chrostowski, “Silicon-on-insulator modulators using a quarter-wave phase-shifted Bragg grating,” IEEE Photonics Technol. Lett. 27(22), 2331–2334 (2015).
    [Crossref]
  7. M. J. Strain, S. Thoms, D. S. MacIntyre, and M. Sorel, “Multi-wavelength filters in silicon using superposition sidewall Bragg grating devices,” Opt. Lett. 39(2), 413–416 (2014).
    [Crossref] [PubMed]
  8. D. T. H. Tan, K. Ikeda, R. E. Saperstein, B. Slutsky, and Y. Fainman, “Chip-scale dispersion engineering using chirped vertical gratings,” Opt. Lett. 33(24), 3013–3015 (2008).
    [Crossref] [PubMed]
  9. G. F. R. Chen, T. Wang, C. Donnelly, and D. T. H. Tan, “Second and third order dispersion generation using nonlinearly chirped silicon waveguide gratings,” Opt. Express 21(24), 29223–29230 (2013).
    [Crossref] [PubMed]
  10. W. Zhang and J. Yao, “Photonic generation of linearly chirped microwave waveforms using a silicon-based on-chip spectral shaper incorporating two linearly chirped waveguide Bragg gratings,” J. Lightwave Technol. 33(24), 5047–5054 (2015).
    [Crossref]
  11. G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).
  12. S. Khan, M. A. Baghban, and S. Fathpour, “Electronically tunable silicon photonic delay lines,” Opt. Express 19(12), 11780–11785 (2011).
    [Crossref] [PubMed]
  13. D. T. H. Tan, K. Ikeda, and Y. Fainman, “Cladding-modulated Bragg gratings in silicon waveguides,” Opt. Lett. 34(9), 1357–1359 (2009).
    [Crossref] [PubMed]
  14. A. D. Simard, N. Ayotte, Y. Painchaud, S. Bedard, and S. LaRochelle, “Impact of sidewall roughness on integrated Bragg gratings,” J. Lightwave Technol. 29(24), 3693–3704 (2011).
    [Crossref]
  15. A. D. Simard, G. Beaudin, V. Aimez, Y. Painchaud, and S. Larochelle, “Characterization and reduction of spectral distortions in silicon-on-insulator integrated Bragg gratings,” Opt. Express 21(20), 23145–23159 (2013).
    [Crossref] [PubMed]
  16. L. Chrostowski, X. Wang, J. Flueckiger, Y. Wu, Y. Wang, and S. Talebi Fard, “Impact of fabrication nonuniformity on chip-scale silicon photonic integrated circuits,”in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper Th2A.37.
  17. A. D. Simard, M. J. Strain, L. Meriggi, M. Sorel, and S. LaRochelle, “Bandpass integrated Bragg gratings in silicon-on-insulator with well-controlled amplitude and phase responses,” Opt. Lett. 40(5), 736–739 (2015).
    [Crossref] [PubMed]
  18. A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photonics Technol. Lett. 24(12), 1033–1035 (2012).
    [Crossref]
  19. W. Shi, V. Veerasubramanian, D. Patel, and D. V. Plant, “Tunable nanophotonic delay lines using linearly chirped contradirectional couplers with uniform Bragg gratings,” Opt. Lett. 39(3), 701–703 (2014).
    [Crossref] [PubMed]
  20. H. Qiu, G. Jiang, T. Hu, H. Shao, P. Yu, J. Yang, and X. Jiang, “FSR-free add-drop filter based on silicon grating-assisted contradirectional couplers,” Opt. Lett. 38(1), 1–3 (2013).
    [Crossref] [PubMed]
  21. W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. Jaeger, and L. Chrostowski, “Silicon photonic grating-assisted, contra-directional couplers,” Opt. Express 21(3), 3633–3650 (2013).
    [Crossref] [PubMed]
  22. Z. Chen, J. Flueckiger, X. Wang, F. Zhang, H. Yun, Z. Lu, M. Caverley, Y. Wang, N. A. F. Jaeger, and L. Chrostowski, “Spiral Bragg grating waveguides for TM mode silicon photonics,” Opt. Express 23(19), 25295–25307 (2015).
    [Crossref] [PubMed]
  23. S. Zamek, D. T. H. Tan, M. Khajavikhan, M. Ayache, M. P. Nezhad, and Y. Fainman, “Compact chip-scale filter based on curved waveguide Bragg gratings,” Opt. Lett. 35(20), 3477–3479 (2010).
    [Crossref] [PubMed]
  24. A. D. Simard, Y. Painchaud, and S. LaRochelle, “Integrated Bragg gratings in spiral waveguides,” Opt. Express 21(7), 8953–8963 (2013).
    [Crossref] [PubMed]
  25. X. Wang, H. Yun, and L. Chrostowski, “Integrated Bragg gratings in spiral waveguides,” in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2013), paper CTh4F.8.
    [Crossref]
  26. Z. Zou, L. Zhou, X. Li, and J. Chen, “60-nm-thick basic photonic components and Bragg gratings on the silicon-on-insulator platform,” Opt. Express 23(16), 20784–20795 (2015).
    [Crossref] [PubMed]
  27. A. D. Simard, Y. Painchaud, and S. LaRochelle, “Integrated Bragg gratings in curved waveguides,” in the 23rd Annual Meeting of the Photonics Society Denver, USA, paper ThU3 (2010).
    [Crossref]
  28. A. H. Atabaki, E. Shah Hosseini, A. A. Eftekhar, S. Yegnanarayanan, and A. Adibi, “Optimization of metallic microheaters for high-speed reconfigurable silicon photonics,” Opt. Express 18(17), 18312–18323 (2010).
    [Crossref] [PubMed]
  29. J. Hong, W. Huang, and T. Makino, “On the transfer matrix method for distributed-feedback waveguide devices,” J. Lightwave Technol. 10(12), 1860–1868 (1992).
    [Crossref]
  30. S. Harris, “Laser without inversion: Interference of lifetime-broadened,” Phys. Today 50(7), 36–42 (1997).
    [Crossref]
  31. W. Li, M. Li, and J. Yao, “A narrow-passband and frequency-tunable microwave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 60(5), 1287–1296 (2012).
    [Crossref]
  32. S. A. Schmidt, J. Flueckiger, W. Wu, S. M. Grist, S. Talebi Fard, V. Donzella, P. Khumwan, E. R. Thompson, Q. Wang, P. Kulik, J. T. Kirk, K. C. Cheung, L. Chrostowski, and D. M. Ratner, “Improving the performance of silicon photonic rings, disks, and Bragg gratings for use in label-free biosensing,” SPIE Optics + Photonics, 9166 (2014).
  33. M. Burla, M. Li, L. R. Cortés, X. Wang, M. R. Fernández-Ruiz, L. Chrostowski, and J. Azaña, “Terahertz-bandwidth photonic fractional Hilbert transformer based on a phase-shifted waveguide Bragg grating on silicon,” Opt. Lett. 39(21), 6241–6244 (2014).
    [Crossref] [PubMed]
  34. W. Zhang, W. Li, and J. Yao, “Optical differentiator based on an integrated sidewall phase-shifted Bragg grating,” IEEE Photonics Technol. Lett. 26(23), 2383–2386 (2014).
    [Crossref]
  35. R. Kashyap, Fiber Bragg Gratings (Academic, 1999).
  36. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University, 2007).
  37. P. Prabhathan, V. M. Murukeshan, Z. Jing, and P. V. Ramana, “Compact SOI nanowire refractive index sensor using phase shifted Bragg grating,” Opt. Express 17(17), 15330–15341 (2009).
    [Crossref] [PubMed]

2016 (1)

2015 (6)

2014 (4)

2013 (5)

2012 (3)

W. Li, M. Li, and J. Yao, “A narrow-passband and frequency-tunable microwave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 60(5), 1287–1296 (2012).
[Crossref]

X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,” Opt. Express 20(14), 15547–15558 (2012).
[Crossref] [PubMed]

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photonics Technol. Lett. 24(12), 1033–1035 (2012).
[Crossref]

2011 (4)

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photonics Technol. Lett. 23(5), 290 (2011).

A. D. Simard, N. Ayotte, Y. Painchaud, S. Bedard, and S. LaRochelle, “Impact of sidewall roughness on integrated Bragg gratings,” J. Lightwave Technol. 29(24), 3693–3704 (2011).
[Crossref]

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

S. Khan, M. A. Baghban, and S. Fathpour, “Electronically tunable silicon photonic delay lines,” Opt. Express 19(12), 11780–11785 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (2)

2008 (1)

1997 (1)

S. Harris, “Laser without inversion: Interference of lifetime-broadened,” Phys. Today 50(7), 36–42 (1997).
[Crossref]

1992 (1)

J. Hong, W. Huang, and T. Makino, “On the transfer matrix method for distributed-feedback waveguide devices,” J. Lightwave Technol. 10(12), 1860–1868 (1992).
[Crossref]

Adibi, A.

Aimez, V.

Atabaki, A. H.

Ayache, M.

Ayotte, N.

Azaña, J.

Baehr-Jones, T.

Baghban, M. A.

Beaudin, G.

Bedard, S.

Bédard, K.

Belhadj, N.

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photonics Technol. Lett. 24(12), 1033–1035 (2012).
[Crossref]

Burla, M.

Caverley, M.

Z. Chen, J. Flueckiger, X. Wang, F. Zhang, H. Yun, Z. Lu, M. Caverley, Y. Wang, N. A. F. Jaeger, and L. Chrostowski, “Spiral Bragg grating waveguides for TM mode silicon photonics,” Opt. Express 23(19), 25295–25307 (2015).
[Crossref] [PubMed]

M. Caverley, X. Wang, K. Murray, N. A. F. Jaeger, and L. Chrostowski, “Silicon-on-insulator modulators using a quarter-wave phase-shifted Bragg grating,” IEEE Photonics Technol. Lett. 27(22), 2331–2334 (2015).
[Crossref]

Chen, G. F. R.

Chen, J.

Chen, R.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

Chen, Z.

Chrostowski, L.

Cortés, L. R.

Donnelly, C.

Eftekhar, A. A.

Ehteshami, N.

Fainman, Y.

Fathpour, S.

Fernández-Ruiz, M. R.

Filion, B.

Flueckiger, J.

Grist, S.

Harris, S.

S. Harris, “Laser without inversion: Interference of lifetime-broadened,” Phys. Today 50(7), 36–42 (1997).
[Crossref]

Hochberg, M.

Hong, J.

J. Hong, W. Huang, and T. Makino, “On the transfer matrix method for distributed-feedback waveguide devices,” J. Lightwave Technol. 10(12), 1860–1868 (1992).
[Crossref]

Hu, T.

Huang, W.

J. Hong, W. Huang, and T. Makino, “On the transfer matrix method for distributed-feedback waveguide devices,” J. Lightwave Technol. 10(12), 1860–1868 (1992).
[Crossref]

Ikeda, K.

Jaeger, N. A.

Jaeger, N. A. F.

Z. Chen, J. Flueckiger, X. Wang, F. Zhang, H. Yun, Z. Lu, M. Caverley, Y. Wang, N. A. F. Jaeger, and L. Chrostowski, “Spiral Bragg grating waveguides for TM mode silicon photonics,” Opt. Express 23(19), 25295–25307 (2015).
[Crossref] [PubMed]

M. Caverley, X. Wang, K. Murray, N. A. F. Jaeger, and L. Chrostowski, “Silicon-on-insulator modulators using a quarter-wave phase-shifted Bragg grating,” IEEE Photonics Technol. Lett. 27(22), 2331–2334 (2015).
[Crossref]

X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,” Opt. Express 20(14), 15547–15558 (2012).
[Crossref] [PubMed]

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photonics Technol. Lett. 23(5), 290 (2011).

Jiang, G.

H. Qiu, G. Jiang, T. Hu, H. Shao, P. Yu, J. Yang, and X. Jiang, “FSR-free add-drop filter based on silicon grating-assisted contradirectional couplers,” Opt. Lett. 38(1), 1–3 (2013).
[Crossref] [PubMed]

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

Jiang, X.

H. Qiu, G. Jiang, T. Hu, H. Shao, P. Yu, J. Yang, and X. Jiang, “FSR-free add-drop filter based on silicon grating-assisted contradirectional couplers,” Opt. Lett. 38(1), 1–3 (2013).
[Crossref] [PubMed]

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

Jing, Z.

Khajavikhan, M.

Khan, S.

LaRochelle, S.

Li, M.

M. Burla, M. Li, L. R. Cortés, X. Wang, M. R. Fernández-Ruiz, L. Chrostowski, and J. Azaña, “Terahertz-bandwidth photonic fractional Hilbert transformer based on a phase-shifted waveguide Bragg grating on silicon,” Opt. Lett. 39(21), 6241–6244 (2014).
[Crossref] [PubMed]

W. Li, M. Li, and J. Yao, “A narrow-passband and frequency-tunable microwave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 60(5), 1287–1296 (2012).
[Crossref]

Li, W.

W. Zhang, W. Li, and J. Yao, “Optical differentiator based on an integrated sidewall phase-shifted Bragg grating,” IEEE Photonics Technol. Lett. 26(23), 2383–2386 (2014).
[Crossref]

W. Li, M. Li, and J. Yao, “A narrow-passband and frequency-tunable microwave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 60(5), 1287–1296 (2012).
[Crossref]

Li, X.

Lin, C.

Liu, W.

Liu, Y.

Lu, Z.

MacIntyre, D. S.

Makino, T.

J. Hong, W. Huang, and T. Makino, “On the transfer matrix method for distributed-feedback waveguide devices,” J. Lightwave Technol. 10(12), 1860–1868 (1992).
[Crossref]

Meriggi, L.

Murray, K.

M. Caverley, X. Wang, K. Murray, N. A. F. Jaeger, and L. Chrostowski, “Silicon-on-insulator modulators using a quarter-wave phase-shifted Bragg grating,” IEEE Photonics Technol. Lett. 27(22), 2331–2334 (2015).
[Crossref]

Murukeshan, V. M.

Nezhad, M. P.

Painchaud, Y.

Patel, D.

Plant, D. V.

Prabhathan, P.

Qiu, H.

Ramana, P. V.

Rusch, L. A.

Saperstein, R. E.

Shah Hosseini, E.

Shao, H.

Shi, W.

Simard, A. D.

Slutsky, B.

Sorel, M.

Strain, M. J.

Tan, D. T. H.

Thoms, S.

Vafaei, R.

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photonics Technol. Lett. 23(5), 290 (2011).

Veerasubramanian, V.

Wang, M.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

Wang, T.

Wang, X.

Wang, Y.

Yang, J.

H. Qiu, G. Jiang, T. Hu, H. Shao, P. Yu, J. Yang, and X. Jiang, “FSR-free add-drop filter based on silicon grating-assisted contradirectional couplers,” Opt. Lett. 38(1), 1–3 (2013).
[Crossref] [PubMed]

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

Yao, J.

W. Zhang and J. Yao, “Photonic generation of linearly chirped microwave waveforms using a silicon-based on-chip spectral shaper incorporating two linearly chirped waveguide Bragg gratings,” J. Lightwave Technol. 33(24), 5047–5054 (2015).
[Crossref]

W. Zhang, N. Ehteshami, W. Liu, and J. Yao, “Silicon-based on-chip electrically tunable sidewall Bragg grating Fabry-Perot filter,” Opt. Lett. 40(13), 3153–3156 (2015).
[Crossref] [PubMed]

W. Zhang, W. Li, and J. Yao, “Optical differentiator based on an integrated sidewall phase-shifted Bragg grating,” IEEE Photonics Technol. Lett. 26(23), 2383–2386 (2014).
[Crossref]

W. Li, M. Li, and J. Yao, “A narrow-passband and frequency-tunable microwave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 60(5), 1287–1296 (2012).
[Crossref]

Yegnanarayanan, S.

Yu, P.

Yun, H.

Zamek, S.

Zhang, F.

Zhang, W.

Zhou, L.

Zhou, Q.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

Zou, Z.

IEEE Photonics Technol. Lett. (5)

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photonics Technol. Lett. 23(5), 290 (2011).

M. Caverley, X. Wang, K. Murray, N. A. F. Jaeger, and L. Chrostowski, “Silicon-on-insulator modulators using a quarter-wave phase-shifted Bragg grating,” IEEE Photonics Technol. Lett. 27(22), 2331–2334 (2015).
[Crossref]

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photonics Technol. Lett. 24(12), 1033–1035 (2012).
[Crossref]

W. Zhang, W. Li, and J. Yao, “Optical differentiator based on an integrated sidewall phase-shifted Bragg grating,” IEEE Photonics Technol. Lett. 26(23), 2383–2386 (2014).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

W. Li, M. Li, and J. Yao, “A narrow-passband and frequency-tunable microwave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 60(5), 1287–1296 (2012).
[Crossref]

J. Lightwave Technol. (3)

Opt. Express (11)

G. F. R. Chen, T. Wang, C. Donnelly, and D. T. H. Tan, “Second and third order dispersion generation using nonlinearly chirped silicon waveguide gratings,” Opt. Express 21(24), 29223–29230 (2013).
[Crossref] [PubMed]

K. Bédard, A. D. Simard, B. Filion, Y. Painchaud, L. A. Rusch, and S. LaRochelle, “Dual phase-shift Bragg grating silicon photonic modulator operating up to 60 Gb/s,” Opt. Express 24(3), 2413–2419 (2016).
[Crossref] [PubMed]

X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,” Opt. Express 20(14), 15547–15558 (2012).
[Crossref] [PubMed]

A. D. Simard, G. Beaudin, V. Aimez, Y. Painchaud, and S. Larochelle, “Characterization and reduction of spectral distortions in silicon-on-insulator integrated Bragg gratings,” Opt. Express 21(20), 23145–23159 (2013).
[Crossref] [PubMed]

S. Khan, M. A. Baghban, and S. Fathpour, “Electronically tunable silicon photonic delay lines,” Opt. Express 19(12), 11780–11785 (2011).
[Crossref] [PubMed]

W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. Jaeger, and L. Chrostowski, “Silicon photonic grating-assisted, contra-directional couplers,” Opt. Express 21(3), 3633–3650 (2013).
[Crossref] [PubMed]

Z. Chen, J. Flueckiger, X. Wang, F. Zhang, H. Yun, Z. Lu, M. Caverley, Y. Wang, N. A. F. Jaeger, and L. Chrostowski, “Spiral Bragg grating waveguides for TM mode silicon photonics,” Opt. Express 23(19), 25295–25307 (2015).
[Crossref] [PubMed]

A. H. Atabaki, E. Shah Hosseini, A. A. Eftekhar, S. Yegnanarayanan, and A. Adibi, “Optimization of metallic microheaters for high-speed reconfigurable silicon photonics,” Opt. Express 18(17), 18312–18323 (2010).
[Crossref] [PubMed]

A. D. Simard, Y. Painchaud, and S. LaRochelle, “Integrated Bragg gratings in spiral waveguides,” Opt. Express 21(7), 8953–8963 (2013).
[Crossref] [PubMed]

Z. Zou, L. Zhou, X. Li, and J. Chen, “60-nm-thick basic photonic components and Bragg gratings on the silicon-on-insulator platform,” Opt. Express 23(16), 20784–20795 (2015).
[Crossref] [PubMed]

P. Prabhathan, V. M. Murukeshan, Z. Jing, and P. V. Ramana, “Compact SOI nanowire refractive index sensor using phase shifted Bragg grating,” Opt. Express 17(17), 15330–15341 (2009).
[Crossref] [PubMed]

Opt. Lett. (9)

M. Burla, M. Li, L. R. Cortés, X. Wang, M. R. Fernández-Ruiz, L. Chrostowski, and J. Azaña, “Terahertz-bandwidth photonic fractional Hilbert transformer based on a phase-shifted waveguide Bragg grating on silicon,” Opt. Lett. 39(21), 6241–6244 (2014).
[Crossref] [PubMed]

A. D. Simard, M. J. Strain, L. Meriggi, M. Sorel, and S. LaRochelle, “Bandpass integrated Bragg gratings in silicon-on-insulator with well-controlled amplitude and phase responses,” Opt. Lett. 40(5), 736–739 (2015).
[Crossref] [PubMed]

S. Zamek, D. T. H. Tan, M. Khajavikhan, M. Ayache, M. P. Nezhad, and Y. Fainman, “Compact chip-scale filter based on curved waveguide Bragg gratings,” Opt. Lett. 35(20), 3477–3479 (2010).
[Crossref] [PubMed]

W. Shi, V. Veerasubramanian, D. Patel, and D. V. Plant, “Tunable nanophotonic delay lines using linearly chirped contradirectional couplers with uniform Bragg gratings,” Opt. Lett. 39(3), 701–703 (2014).
[Crossref] [PubMed]

H. Qiu, G. Jiang, T. Hu, H. Shao, P. Yu, J. Yang, and X. Jiang, “FSR-free add-drop filter based on silicon grating-assisted contradirectional couplers,” Opt. Lett. 38(1), 1–3 (2013).
[Crossref] [PubMed]

D. T. H. Tan, K. Ikeda, and Y. Fainman, “Cladding-modulated Bragg gratings in silicon waveguides,” Opt. Lett. 34(9), 1357–1359 (2009).
[Crossref] [PubMed]

W. Zhang, N. Ehteshami, W. Liu, and J. Yao, “Silicon-based on-chip electrically tunable sidewall Bragg grating Fabry-Perot filter,” Opt. Lett. 40(13), 3153–3156 (2015).
[Crossref] [PubMed]

M. J. Strain, S. Thoms, D. S. MacIntyre, and M. Sorel, “Multi-wavelength filters in silicon using superposition sidewall Bragg grating devices,” Opt. Lett. 39(2), 413–416 (2014).
[Crossref] [PubMed]

D. T. H. Tan, K. Ikeda, R. E. Saperstein, B. Slutsky, and Y. Fainman, “Chip-scale dispersion engineering using chirped vertical gratings,” Opt. Lett. 33(24), 3013–3015 (2008).
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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of the spiral IBG. R0 is the minimum bending radius. (b) Zoom-in view showing the grating details. Λ: grating period, Wcorr: corrugation width, g: waveguide spacing. (c) 3D perspective view of the active spiral IBG with TiN heaters on top for thermal tuning. (d) Cross section of the active spiral waveguide. (e) Microscopic image of a fabricated active spiral IBG.
Fig. 2
Fig. 2 (a) Effective refractive index change as a function of waveguide bending radius. (b) S-junction loss and packing efficiency (α) of the spiral grating as a function of the minimum bending radius R0.
Fig. 3
Fig. 3 Transmission spectra of three devices with (a) R0 = 20 μm, (b) R0 = 25 μm, and (c) R0 = 35 μm. The solid black lines represent the experimental spectra and the dashed red lines represent the modeled spectra. The insets show the magnified transparent peaks in the stopbands. The 3-dB bandwidths are labeled.
Fig. 4
Fig. 4 (a) Evolution of the transparent peak upon thermal tuning of the S-junction. The spectra are shifted vertically in purpose for better clarity. (b) Simulation results showing the similar evolution trend. (c) Shift of the stopband upon tuning of both the spiral waveguide and the center S-junction. (d) Extracted transparency peak wavelength as a function of the tuning power P1. (e) Extracted central wavelength of the stopband as a function of the total tuning power P1 + P2.
Fig. 5
Fig. 5 (a) Transmission spectra of device IV in response to the tuning power P1. (b) Q-factor as a function of the resonance offset from the stopband center wavelength. The inset shows magnified resonance peak when Q reaches the maximum.

Tables (1)

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Table 1 Design Parameters for Four Spiral IBGs

Equations (1)

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1 Q = 1 Q C + 1 Q I

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