Abstract

We propose a novel silicon-based comb filter with tunable channel spacing using a Michelson interferometer consisting of a pair of apodized linearly chirped Bragg gratings (ALC-BGs). The channel spacing of the proposed comb filter can be continuously tuned with a large tuning range by changing the effective refractive index of one of the ALC-BGs through the thermo-optic effect. Our numerical calculation shows that the channel spacing can be continuously tuned form 8.21 nm to 0.19 nm with an out-of-band rejection ratio of greater than 30 dB.

© 2014 Optical Society of America

1. Introduction

Optical comb filters have attracted much attention as key functional components in optical signal processing and multi-wavelength laser sources. In optical networks, optical comb filters can be used to implement format conversion between the return-to-zero (RZ) and the non-return-to-zero (NRZ) signals [13], suppress inter-channel optical noise and direct a large group of optical data channels to selected destinations [4]. In the generation of multi-wavelength laser sources, many experiments have been accomplished by using optical comb filters as external filters in conjunction with broadband gain media or semiconductor optical amplifiers [57]. In order to increase the operation flexibility and functionality, tunability of the channel spacing is highly desired. So far, several methods have been proposed to construct channel-spacing tunable all-fiber comb filters, such as using polarization diversity loops [5, 8], Lyot configurations [9, 10], fiber Bragg gratings [6,11], Sagnac birefringence loops [12], cascaded variable differential group delay elements [13], and modified Mach-Zehnder interferometers (MZIs) [7,14,15].

The silicon-on-insulator (SOI) material system is attractive for realizing photonic integrated circuits, benefiting from its high refractive index contrast and noteworthy advances in nanoscale fabrication. The compatibility of SOI material system with microelectronics allows for mass production of very-large-scale photonic integration. There have been multiple implementations of silicon comb filters based on ring resonators [16], Archimedean spiral cavities [17], sampled gratings [18, 19], MZIs [3], and Fabry-Perot resonators formed by Sagnac loop mirrors [20]. Although the working wavelengths of such comb filters can be tuned through free-carrier plasma dispersion effect or thermo-optic effect, the channel spacing is fixed, which cannot meet the requirement in certain applications as mentioned above.

In this paper, we propose a novel tunable comb filter using a Michelson interferometer (MI) comprising two identical apodized linearly chirped Bragg gratings (ALC-BGs). The channel spacing can be continuously tuned by changing the effective refractive index of one ALC-BG through the thermo-optic effect. The proposed comb filter can offer a large tuning range of channel spacing due to the slow light effect of Bragg gratings. It can also be easily integrated with other SOI-based devices to be potentially used in large-scale silicon photonic integrated circuits (PICs).

2. Operation principle

Figure 1(a) shows the schematic of the proposed comb filter. The two ALC-BGs are connected by a 2 × 2 3-dB multimode interference (MMI) coupler to form the MI. The input light is equally split by the 3-dB MMI coupler, and the split light beams are reflected back when they encounter the ALC-BGs if the wavelength is within the reflection band of the ALC-BGs. It should be noted that linear chirp of the grating generates a linear group delay where shorter wavelengths are reflected at the front end while longer wavelengths are reflected at the back end. Apodizing the grating is to suppress spectral ripples otherwise incurred on the linear group delay [21]. The reflected light beams interfere at the MMI coupler and generate the transmission spectrum. If the two ALC-BGs are identical, the two light beams will always constructively interfere to give unit transmission. The spectral width of the unit transmission is determined by the reflection bandwidth of the ALC-BGs as depicted in Fig. 1(b). When the refractive index of one ALC-BG is varied, the group delay curve of that ALC-BG shifts, resulting in fixed group delay difference experienced by the two light beams. The consequent interference results in cosine modulation of the transmission spectrum as depicted in Fig. 1(c). If the refractive index of the ALC-BG is continuously tuned, the group delay difference and hence the resultant modulation period can be varied continuously. The larger the index variation is, the denser the comb channels become, as shown in Fig. 1(d). In this way, the channel spacing of the comb filter is variable by tuning one of the ALC-BGs.

 figure: Fig. 1

Fig. 1 (a) Schematic of the proposed silicon comb filter with tunable channel-spacing. Inset shows the cross-sectional schematic of the p-i-p junction-based resistive micro-heater. (b)-(d) illustrate the working principle of the comb filter. The solid purple lines are the comb filter output transmission spectra. The solid black and red lines are the reflection spectra of the two ALC-BGs, and the dashed black and red lines are their corresponding delay spectra. From (b) to (d), the group delay difference increases.

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The group delay of the ALC-BG in the reflection bandwidth must be linear or otherwise the group delay difference is not constant upon tuning, leading to nonuniform channel spacing. There are two ways to introduce linear chirp into the Bragg gratings. The first one is to linearly vary the effective refractive index by tapering the waveguide width [2123], and the other is to linearly vary the grating period [24]. In our scheme, we choose the second approach because the variation of grating period has an effect three orders of magnitude stronger than the variation of waveguide width in terms of the chirp strength [25].

3. Theoretical modeling

We model the proposed comb filter using the transfer-matrix method. To simplify the analysis we assume that the loss of the coupler is negligible. The steady-state relationship between the input and output electric-fields can be expressed as:

[E3E4]=[1KjKjK1K][Rg1(λ)eiφ1(λ)00Rg2(λ)eiφ2(λ)][1KjKjK1K][E1E2]
where E1(E3) and E2(E4) are the input (output) electric-fields, K is the power coupling coefficient of the MMI coupler, Rgi(λ) (i = 1, 2 for the two gratings) is the power reflectivity of the grating, and φi(λ) is the associated phase change. For a 3-dB coupler, we have K = 0.5. Assuming input is only from one end (E2 = 0), we can derive the normalize field transmission as
t=E4E1=12jeiφ1(λ)[Rg1(λ)+Rg2(λ)ei(φ2(λ)φ1(λ))]
Hence, the power transmission is
T=|E4E1|2=14[Rg1(λ)+Rg2(λ)+2Rg1(λ)Rg2(λ)cos(Δφ)]
where ∆φ = φ2(λ)-φ1(λ) is the phase difference upon reflection from the gratings. It can be seen that the output transmission is modulated by ∆φ.

The two ALC-BGs are identical before tuning and therefore we have Rg1 = Rg2 and ∆φ = 0. The transmission is thus simplified as

T=Rg1(λ)=Rg2(λ)
which suggests the transmission is determined by the reflection of the ALC-BG. When one grating is varied by ∆ne in its effective refractive index, the central Bragg wavelength shifts by ∆λ = λ0∆ne /ng, where λ0 is the original central Bragg wavelength, ng is the average group refractive index of the grating. We assume the length of the ALC-BGs is Lg and the reflection bandwidth is ∆λchirp. Light entering into the ALC-BG (period increasing along the grating) experiences a time delay τ(λ) on reflection [26]:
τ(λ)(λλ0)Δλchirp2Lgνg
where νg denotes the average group velocity of light in the ALC-BGs.

Therefore, the group delay difference ∆τ after reflection from the two ALC-BGs is

Δτ(λλ0)Δλchirp2Lgνg(λλ0Δneλ0/ng)Δλchirp2Lgνg=2LgΔneλ0cΔλchirp
where c is the speed of light in vacuum. It can be seen that Δτ is linearly proportional to Δne and independent of wavelength. The output comb frequency spacing or the free spectral range (FSR) is given by
FSRv=1Δτ=cΔλchirp2LgΔneλ0
It indicates the comb passbands in the output spectrum have an equal frequency-spacing. The FSR in the wavelength domain is expressed as
FSRλ=λ2cΔτλ0Δλchirp2LgΔne
Therefore, the number of the comb passbands in the comb transmission band is

Ncomb=Δλchirp-ΔλFSRλ=2LgΔneλ0-2LgΔne2ngΔλchirp

4. Simulation results and discussions

We use the transfer matrix method to calculate the reflectivity Rgi(λ) and the phase response φi(λ) of the gratings. The validity and accuracy have been proved by numerous researchers [27, 28]. Once Rgi(λ) and φi(λ) are obtained, the transmission characteristics of the comb filter can be calculated from (3).

4.1 Comb filter using LC-BGs without apodization

We first study the comb filter composed of linearly chirped Bragg gratings (LC-BGs) without apodization. Figure 2 shows the reflectivity and group delay of the two LC-BGs and the resulted transmission spectra of the comb filter in response to various refractive index changes in one LC-BG (grating 2). The LC-BGs used in the calculation have a length of Lg = 5760 µm, a linear chirp period (50% duty cycle) from 285.5 nm at the beginning to 290.5 nm at the end, a mask width of 760 nm, and a space width of 740 nm. The waveguide propagation loss is assumed to be 1.5 dB/cm [25]. The rib and slab heights of the silicon waveguide are 220 nm and 60 nm, respectively. The device is clad with silicon dioxide. The effective refractive index of each section of the grating is calculated using the finite element simulation by CMOSOL. The reflection bandwidth is calculated to be ∆λchirp = 20 nm. It can be seen that across the reflection band, the group delay of the LC-BG linearly increases with the wavelength. The small ripple in the delay spectrum results from the interference between the reflections from the edge of the grating and from inside the grating [26]. Without tuning, the filter output transmission spectrum is exactly the same as the grating reflection spectrum. With effective refractive index changes of Δne = 8 × 10−4, 1.6 × 10−3, 3.2 × 10−3 introduced to Grating 2 (using the thermo-optic effect, for instance), the average group delay differences between the two gratings are 2.5 ps, 5 ps, and 10 ps, respectively. The filter output spectrum exhibits multiple uniform comb passbands. Note that we only consider the comb passbands within the overlapped 1-dB reflection band of LC-BGs, for the comb passbands at the reflection edges are severely affected by the incomplete interference. There are 5, 11, and 23 combs with the channel spacing of 3.29, 1.63, and 0.81 nm for the three tuning cases, respectively, which is in agreement with the calculation from (8) and (9).

 figure: Fig. 2

Fig. 2 Intensity (left plots) and group delay (right plots) spectra of the comb filter and LC-BGs in response to various refractive index changes in Grating 2. The refractive index changes are 0, 8 × 10−4, 1.6 × 10−3, and 3.2 × 10−3 from top to bottom, respectively. The insets in the right plots show the magnified group delay spectra.

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It can be seen that the filter transmission spectrum exhibits small ripples, more apparent at the short wavelength side. These ripples are resulted from the group delay fluctuation (~15 ps peak to peak magnitude) of the LC-BGs. It is necessary to eliminate the fluctuation in order to obtain a clear comb filter spectrum.

4.2 Comb filter using LC-BGs with apodization

The group delay fluctuation is resulted from the reflection at the grating front end. To eliminate such reflection, the LC-BGs need to be apodized by adiabatically varying the grating coupling strength at the ends so that the undesired reflection is suppressed [29]. The coupling strength can be varied either by changing the duty cycle or the effective refractive index difference between the grating masks and spaces. In our device, the sidewall corrugation is varied to obtain the desired apodization. The apodization profile needs to be carefully chosen, or otherwise it could make the group delay increase nonlinearly with wavelength [30]. Moreover, the apodization also affects the shape of the reflection band. Generally, the shape of the reflection spectrum closely follows the apodization profile [31]. Hence, the criterion for apodization is to reduce the group delay fluctuation and meanwhile maintain the linear group delay and sharp reflection band edge. An apodization function with a flat region in the grating center and a constant decaying slope towards the grating ends can be used [30, 31]. In our design, we use the positive hyperbolic-tangent apodization profile (tanh) for the refractive index modulation:

δneff(z)={δneff0tanh[2azLg],0zLg2δneff0tanh[2a(Lgz)Lg],Lg2zLg
where δneff0 is the maximum index modulation and a is a variable that determines the slope of the profile (a = 5 in our device). In order to compare with the grating without apodization, δneff0 is set equal to 0.008 as used in the LC-BGs. The other parameters are the same as those in Section 4.1. Figure 3(a) shows the magnitude of the refractive index modulation along the grating. Meanwhile, the average refractive index along the grating is kept constant (i.e., zero dc index change) by tapering the spaces and masks using complementary tanh profiles, the corresponding grating mask and space widths are shown in Fig. 3(b). No additional chirp is introduced to the LC-BGs upon apodization.

 figure: Fig. 3

Fig. 3 (a) Refractive index modulation in the gratings. (b) Width of the grating masks (red line) and spaces (black line).

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Figure 4 shows the reflection and delay spectra of the LC-BGs after apodization, together with the comb filter output spectrum. The grating reflection intensity bandwidth is narrowed by 2.6 nm, due to the suppression of reflection at both ends of the grating. The group delay remains linear with wavelength while the ripples are highly suppressed. The reflection band has sharp edges and the comb channel spacing is almost the same with that without apodization. Owing to the narrowed reflection band, the number of combs is reduced to 21 in Fig. 4(g), while it remains the same for the other two cases.

 figure: Fig. 4

Fig. 4 Intensity and group delay spectra of the comb filter and ALC-BGs in response to various refractive index changes in Grating 2. The tuning parameters are the same with those in Fig. 2.

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4.3 Active tuning

The refractive index of grating can be actively tuned through the free-carrier plasma dispersion (FCD) effect or the thermo-optic (TO) effect. The FCD introduces additional loss due to the free carrier absorption, leading to unbalanced interference between the two arms and consequently reducing the filter out-of-band rejection ratio. For example, if the refractive index of the grating is tuned by Δne = 1.1 × 10−3 through the FCD effect, the additional loss is around 21 dB/cm and consequently the rejection ratio is lowered down to 5 dB. In contrast, the TO effect does not induce any additional loss and is more suitable for filter tuning. In our previous work [32], we have demonstrated a resistive micro-heater based on a p-i-p structure embedded in the waveguide. When current flows through the p-i-p micro-heater, heat will be generated therein, leading to a refractive index change of the waveguide due to the TO effect. Compared to the conventional metallic heater positioned on top of the silicon waveguide, it has faster response and lower power consumption. Hence we suggest the tuning of the grating is enabled by the p-i-p micro-heater.

The cross-sectional schematic of the p-i-p micro-heater is shown in the inset of Fig. 1(a). The waveguide width is 740 nm and the height is 220 nm with a 60 nm slab. The highly p-type doped regions have a doping concentration of 1020 cm−3, separated from waveguide edge by 0.6 μm. The waveguide is lightly p-type doped with a concentration of 1015 cm−3. All these parameters are the same as those in our previous paper [32] except for the waveguide width. The resistance of the p-i-p micro-heater is around 600 kΩ·µm. We employ the ALTAS from SILVACO to obtain the current density J and the electrical field E under a certain applied voltage. The generated heat power P is given by P = J·E. We then employ the COMSOL to simulate the effective refractive index change in response to waveguide heating. The details of the analytic method can be referred to [32].

Figure 5(a) shows the simulated waveguide effective refractive index and free-carrier absorption induced excess loss changing with the tuning power. The waveguide effective refractive index increases linearly with the tuning power. The waveguide loss increases slightly with tuning power, resulted from the small increase in free carrier concentration. It is less than 0.3 dB/cm even at a high tuning power of 2.47 W (corresponding to a waveguide effective refractive index change of 0.013). Figure 5(b) shows the channel spacing and the number of comb passbands changing with the tuning power. As the tuning power gradually increase from 54 mW to 2.47 W, the channel spacing gradually decreases from 8.21 nm to 0.19 nm with the number of comb passbands increasing from 1 to 65. It should be noted that the power consumption is proportional to the length of ALC-BGs. In our design, long ALC-BGs are used in order to show that the device can provide large reflection bandwidth and consequently a large number of comb passbands. In fact, the power consumption can be reduced by designing short ALC-BGs if only a small number of comb passbands are needed. It should also be noted that the input pulse duration must be longer than the group delay difference between the two arms in order for the comb filter to work properly, or otherwise there will be no overlap between the reflected pulses and the output will exhibit two successive pulses.

 figure: Fig. 5

Fig. 5 (a) Waveguide effective refractive index and propagation loss change with tuning power. (b) Channel spacing and number of the comb passbands change with tuning power.

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Figure 6(a) shows the transmission spectrum of the comb filter with tuning power of 0.82 W. It can be seen that the out-of-band rejection ratio is not uniform, first increasing and then decreasing. Two facts influence the rejection ratio. Firstly, with the increasing tuning power the group delay at a fixed wavelength decreases in the tuning arm, making the accumulated propagation loss lower than in the other arm. Secondly, the free carrier absorption loss in the tuning arm increases with tuning power [see Fig. 5(a)], and the increment is more significant for longer wavelengths (due to the longer propagation distance). Hence, at a certain wavelength these two factors are canceled out, leading to balanced loss between the two arms where the rejection ratio reaches the maximum. The loss becomes unbalanced towards either end, leading to reduced rejection ratio. Figure 6(b) shows the lowest rejection ratio changing with the tuning power. It can be seen that although the rejection ratio decreases with the increasing tuning power, it is still greater than 30 dB even when the tuning power reaches 2.47 W.

 figure: Fig. 6

Fig. 6 (a) Transmission spectrum of the comb filter with tuning power of 0.82 W. (b) Lowest out-of-band rejection ratio in the full reflection band changes with the tuning power.

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5. Conclusions

We proposed a novel silicon comb filter with the channel spacing continuously tunable by changing the refractive index of one ALC-BG. Active tuning of the comb filter is enabled using a p-i-p resistive micro-heater. Theoretical modeling and numerical simulation based on the transfer matrix method were carried out. In particular, the influence of apodization of the Bragg gratings on the device performance was explored. The proposed comb filter exhibits a large tuning range in channel spacing. Our numerical example shows that the channel spacing can be continuously tuned form 8.21 nm to 0.19 nm (number of comb passbands increasing from 1 to 65) while maintaining an out-of-band rejection ratio of greater than 30 dB. Such design has the potential for integration of comb-filter-defined functions into large-scale integrated photonics circuits for a wide range of applications such as reconfigurable WDM optical systems and optical signal processing.

Acknowledgment

This work was supported in part by the 973 program (ID2011CB301700), the 863 program (2013AA014402), the National Natural Science Foundation of China (NSFC) (61127016, 61107041), SRFDP of MOE (Grant No. 20130073130005). We also acknowledge IME Singapore for device fabrication.

References and links

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2. Y. Ding, C. Peucheret, M. Pu, B. Zsigri, J. Seoane, L. Liu, J. Xu, H. Ou, X. Zhang, and D. Huang, “Multi-channel WDM RZ-to-NRZ format conversion at 50 Gbit/s based on single silicon microring resonator,” Opt. Express 18(20), 21121–21130 (2010). [CrossRef]   [PubMed]  

3. L. Xiang, D. Gao, Y. Yu, M. Ye, B. Zou, and X. Zhang, “Silicon-Based Integrated Comb Filter and Demultiplexer for Simultaneous WDM Signal Processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200208 (2014). [CrossRef]  

4. B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photon. Technol. Lett. 20(10), 767–769 (2008). [CrossRef]  

5. S. Roh, S. Chung, Y. W. Lee, I. Yoon, and B. Lee, “Channel-Spacing- and Wavelength-Tunable Multiwavelength Fiber Ring Laser Using Semiconductor Optical Amplifier,” IEEE Photon. Technol. Lett. 18(21), 2302–2304 (2006). [CrossRef]  

6. Y. G. Han, F. Fresi, L. Poti, J. H. Lee, and X. Dong, “Continuously spacing-tunable multiwavelength semiconductor-optical-amplifier-based fiber ring laser incorporating a superimposed chirped fiber Bragg grating,” Opt. Lett. 32(9), 1032–1034 (2007). [CrossRef]   [PubMed]  

7. D. Chen, S. Qin, and S. He, “Channel-spacing-tunable multi-wavelength fiber ring laser with hybrid Raman and Erbium-doped fiber gains,” Opt. Express 15(3), 930–935 (2007). [CrossRef]   [PubMed]  

8. Y. W. Lee, H.-T. Kim, and Y. W. Lee, “Second-order all-fiber comb filter based on polarization-diversity loop configuration,” Opt. Express 16(6), 3871–3876 (2008). [CrossRef]   [PubMed]  

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References

  • View by:

  1. Y. Zhang, E. Xu, D. Huang, and X. Zhang, “All-optical format conversion from RZ to NRZ utilizing microfiber resonator,” IEEE Photon. Technol. Lett. 21(17), 1202–1204 (2009).
    [Crossref]
  2. Y. Ding, C. Peucheret, M. Pu, B. Zsigri, J. Seoane, L. Liu, J. Xu, H. Ou, X. Zhang, and D. Huang, “Multi-channel WDM RZ-to-NRZ format conversion at 50 Gbit/s based on single silicon microring resonator,” Opt. Express 18(20), 21121–21130 (2010).
    [Crossref] [PubMed]
  3. L. Xiang, D. Gao, Y. Yu, M. Ye, B. Zou, and X. Zhang, “Silicon-Based Integrated Comb Filter and Demultiplexer for Simultaneous WDM Signal Processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200208 (2014).
    [Crossref]
  4. B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photon. Technol. Lett. 20(10), 767–769 (2008).
    [Crossref]
  5. S. Roh, S. Chung, Y. W. Lee, I. Yoon, and B. Lee, “Channel-Spacing- and Wavelength-Tunable Multiwavelength Fiber Ring Laser Using Semiconductor Optical Amplifier,” IEEE Photon. Technol. Lett. 18(21), 2302–2304 (2006).
    [Crossref]
  6. Y. G. Han, F. Fresi, L. Poti, J. H. Lee, and X. Dong, “Continuously spacing-tunable multiwavelength semiconductor-optical-amplifier-based fiber ring laser incorporating a superimposed chirped fiber Bragg grating,” Opt. Lett. 32(9), 1032–1034 (2007).
    [Crossref] [PubMed]
  7. D. Chen, S. Qin, and S. He, “Channel-spacing-tunable multi-wavelength fiber ring laser with hybrid Raman and Erbium-doped fiber gains,” Opt. Express 15(3), 930–935 (2007).
    [Crossref] [PubMed]
  8. Y. W. Lee, H.-T. Kim, and Y. W. Lee, “Second-order all-fiber comb filter based on polarization-diversity loop configuration,” Opt. Express 16(6), 3871–3876 (2008).
    [Crossref] [PubMed]
  9. M. P. Fok, C. Shu, and W. W. Tang, “A Cascadable Approach to Produce Widely Selectable Spectral Spacing in Birefringent Comb Filters,” IEEE Photon. Technol. Lett. 18(18), 1937–1939 (2006).
    [Crossref]
  10. L. S. Yan, J. Ye, H. Y. Jiang, W. Pan, B. Luo, A. L. Yi, Y. H. Guo, and X. S. Yao, “A Photonic Comb Filter With Independently and Digitally Tunable Bandwidth and Frequency Spacing,” IEEE Photon. Technol. Lett. 23(13), 857–859 (2011).
    [Crossref]
  11. Y. Zhao, T. Song, and Z. Huo, “Tunable Optical Fiber Filter Based on a Fiber Bragg Grating Loop Mirror,” J. Lightwave Technol. 29(24), 3672–3675 (2011).
    [Crossref]
  12. W. Jin, C. Wang, H. Xuan, and W. Jin, “Tunable comb filters and refractive index sensors based on fiber loop mirror with inline high birefringence microfiber,” Opt. Lett. 38(21), 4277–4280 (2013).
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  13. H. Y. Jiang, L. S. Yan, J. Ye, W. Pan, B. Luo, and X. S. Yao, “Comb filter with independently tunable wavelength spacing and bandwidth using cascaded variable differential group delay elements,” Opt. Lett. 36(12), 2305–2307 (2011).
    [Crossref] [PubMed]
  14. Z. Luo, W. Cao, A. Luo, and W. Xu, “Polarization-Independent, Multifunctional All-Fiber Comb Filter Using Variable Ratio Coupler-Based-Zehnder Interferometer,” J. Lightwave Technol. 30(12), 1857–1862 (2012).
    [Crossref]
  15. Z. Zhao, M. Tang, H. Liao, G. Ren, S. Fu, F. Yang, P. P. Shum, and D. Liu, “Programmable multi-wavelength filter with Mach-Zehnder interferometer embedded in ethanol filled photonic crystal fiber,” Opt. Lett. 39(7), 2194–2197 (2014).
    [Crossref] [PubMed]
  16. P. Dong, S. F. Preble, and M. Lipson, “All-optical compact silicon comb switch,” Opt. Express 15(15), 9600–9605 (2007).
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  17. D. X. Xu, A. Delâge, R. McKinnon, M. Vachon, R. Ma, J. Lapointe, A. Densmore, P. Cheben, S. Janz, and J. H. Schmid, “Archimedean spiral cavity ring resonators in silicon as ultra-compact optical comb filters,” Opt. Express 18(3), 1937–1945 (2010).
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  18. I. Giuntoni, P. Balladares, R. Steingrüber, J. Bruns, and K. Petermann, “WDM Multi-Channel Filter Based On Sampled Gratings In Silicon-on-Insulator,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThV3.
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  19. V. Veerasubramanian, G. Beaudin, A. Giguere, B. Le Drogoff, V. Aimez, and A. G. Kirk, “Design and Demonstration of Apodized Comb Filters on SOI,” IEEE Photon. J. 4(4), 1133–1139 (2012).
    [Crossref]
  20. X. Sun, L. Zhou, J. Xie, Z. Zou, L. Lu, H. Zhu, X. Li, and J. Chen, “Tunable silicon Fabry-Perot comb filters formed by Sagnac loop mirrors,” Opt. Lett. 38(4), 567–569 (2013).
    [Crossref] [PubMed]
  21. I. Giuntoni, D. Stolarek, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Integrated Dispersion Compensator Based on Apodized SOI Bragg Gratings,” IEEE Photon. Technol. Lett. 25(14), 1313–1316 (2013).
    [Crossref]
  22. I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012).
    [Crossref] [PubMed]
  23. S. Khan and S. Fathpour, “Complementary apodized grating waveguides for tunable optical delay lines,” Opt. Express 20(18), 19859–19867 (2012).
    [Crossref] [PubMed]
  24. D. T. H. Tan, K. Ikeda, and Y. Fainman, “Coupled chirped vertical gratings for on chip group velocity dispersion engineering,” Appl. Phys. Lett. 95(14), 141109 (2009).
    [Crossref]
  25. I. Giuntoni, D. Stolarek, A. Gajda, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Integrated Dispersion Compensator Based on SOI Tapered Gratings,” in 37th European Conference and Exposition on Optical Communications (Ecoc), p.Th.12.LeSaleve.4 (2011).
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  26. R. Kashyap, Fiber Bragg Gratings (Academic Press, New York, 2009).
  27. S. Khan and S. Fathpour, “Demonstration of complementary apodized cascaded grating waveguides for tunable optical delay lines,” Opt. Lett. 38(19), 3914–3917 (2013).
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  28. S. Khan and S. Fathpour, “Demonstration of tunable optical delay lines based on apodized grating waveguides,” Opt. Express 21(17), 19538–19543 (2013).
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  29. L. Poladian, “Graphical and WKB analysis of nonuniform Bragg gratings,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 48(6), 4758–4767 (1993).
    [Crossref] [PubMed]
  30. D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14(11), 2581–2588 (1996).
    [Crossref]
  31. K. Ennser, M. N. Zervas, and R. L. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34(5), 770–778 (1998).
    [Crossref]
  32. L. Zhou, X. Zhang, L. Lu, and J. Chen, “Tunable vernier microring optical filters with p-i-p type microheaters,” IEEE Photon. J. 5(4), 6601211 (2013).
    [Crossref]

2014 (2)

L. Xiang, D. Gao, Y. Yu, M. Ye, B. Zou, and X. Zhang, “Silicon-Based Integrated Comb Filter and Demultiplexer for Simultaneous WDM Signal Processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200208 (2014).
[Crossref]

Z. Zhao, M. Tang, H. Liao, G. Ren, S. Fu, F. Yang, P. P. Shum, and D. Liu, “Programmable multi-wavelength filter with Mach-Zehnder interferometer embedded in ethanol filled photonic crystal fiber,” Opt. Lett. 39(7), 2194–2197 (2014).
[Crossref] [PubMed]

2013 (6)

2012 (4)

2011 (3)

2010 (2)

2009 (2)

Y. Zhang, E. Xu, D. Huang, and X. Zhang, “All-optical format conversion from RZ to NRZ utilizing microfiber resonator,” IEEE Photon. Technol. Lett. 21(17), 1202–1204 (2009).
[Crossref]

D. T. H. Tan, K. Ikeda, and Y. Fainman, “Coupled chirped vertical gratings for on chip group velocity dispersion engineering,” Appl. Phys. Lett. 95(14), 141109 (2009).
[Crossref]

2008 (2)

B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photon. Technol. Lett. 20(10), 767–769 (2008).
[Crossref]

Y. W. Lee, H.-T. Kim, and Y. W. Lee, “Second-order all-fiber comb filter based on polarization-diversity loop configuration,” Opt. Express 16(6), 3871–3876 (2008).
[Crossref] [PubMed]

2007 (3)

2006 (2)

M. P. Fok, C. Shu, and W. W. Tang, “A Cascadable Approach to Produce Widely Selectable Spectral Spacing in Birefringent Comb Filters,” IEEE Photon. Technol. Lett. 18(18), 1937–1939 (2006).
[Crossref]

S. Roh, S. Chung, Y. W. Lee, I. Yoon, and B. Lee, “Channel-Spacing- and Wavelength-Tunable Multiwavelength Fiber Ring Laser Using Semiconductor Optical Amplifier,” IEEE Photon. Technol. Lett. 18(21), 2302–2304 (2006).
[Crossref]

1998 (1)

K. Ennser, M. N. Zervas, and R. L. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34(5), 770–778 (1998).
[Crossref]

1996 (1)

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14(11), 2581–2588 (1996).
[Crossref]

1993 (1)

L. Poladian, “Graphical and WKB analysis of nonuniform Bragg gratings,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 48(6), 4758–4767 (1993).
[Crossref] [PubMed]

Aimez, V.

V. Veerasubramanian, G. Beaudin, A. Giguere, B. Le Drogoff, V. Aimez, and A. G. Kirk, “Design and Demonstration of Apodized Comb Filters on SOI,” IEEE Photon. J. 4(4), 1133–1139 (2012).
[Crossref]

Beaudin, G.

V. Veerasubramanian, G. Beaudin, A. Giguere, B. Le Drogoff, V. Aimez, and A. G. Kirk, “Design and Demonstration of Apodized Comb Filters on SOI,” IEEE Photon. J. 4(4), 1133–1139 (2012).
[Crossref]

Bergman, K.

B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photon. Technol. Lett. 20(10), 767–769 (2008).
[Crossref]

Biberman, A.

B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photon. Technol. Lett. 20(10), 767–769 (2008).
[Crossref]

Bruns, J.

I. Giuntoni, D. Stolarek, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Integrated Dispersion Compensator Based on Apodized SOI Bragg Gratings,” IEEE Photon. Technol. Lett. 25(14), 1313–1316 (2013).
[Crossref]

I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012).
[Crossref] [PubMed]

Cao, W.

Capmany, J.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14(11), 2581–2588 (1996).
[Crossref]

Cheben, P.

Chen, D.

Chen, J.

X. Sun, L. Zhou, J. Xie, Z. Zou, L. Lu, H. Zhu, X. Li, and J. Chen, “Tunable silicon Fabry-Perot comb filters formed by Sagnac loop mirrors,” Opt. Lett. 38(4), 567–569 (2013).
[Crossref] [PubMed]

L. Zhou, X. Zhang, L. Lu, and J. Chen, “Tunable vernier microring optical filters with p-i-p type microheaters,” IEEE Photon. J. 5(4), 6601211 (2013).
[Crossref]

Chung, S.

S. Roh, S. Chung, Y. W. Lee, I. Yoon, and B. Lee, “Channel-Spacing- and Wavelength-Tunable Multiwavelength Fiber Ring Laser Using Semiconductor Optical Amplifier,” IEEE Photon. Technol. Lett. 18(21), 2302–2304 (2006).
[Crossref]

Delâge, A.

Densmore, A.

Ding, Y.

Dong, P.

B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photon. Technol. Lett. 20(10), 767–769 (2008).
[Crossref]

P. Dong, S. F. Preble, and M. Lipson, “All-optical compact silicon comb switch,” Opt. Express 15(15), 9600–9605 (2007).
[Crossref] [PubMed]

Dong, X.

Ennser, K.

K. Ennser, M. N. Zervas, and R. L. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34(5), 770–778 (1998).
[Crossref]

Fainman, Y.

D. T. H. Tan, K. Ikeda, and Y. Fainman, “Coupled chirped vertical gratings for on chip group velocity dispersion engineering,” Appl. Phys. Lett. 95(14), 141109 (2009).
[Crossref]

Fathpour, S.

Fok, M. P.

M. P. Fok, C. Shu, and W. W. Tang, “A Cascadable Approach to Produce Widely Selectable Spectral Spacing in Birefringent Comb Filters,” IEEE Photon. Technol. Lett. 18(18), 1937–1939 (2006).
[Crossref]

Fresi, F.

Fu, S.

Gao, D.

L. Xiang, D. Gao, Y. Yu, M. Ye, B. Zou, and X. Zhang, “Silicon-Based Integrated Comb Filter and Demultiplexer for Simultaneous WDM Signal Processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200208 (2014).
[Crossref]

Giguere, A.

V. Veerasubramanian, G. Beaudin, A. Giguere, B. Le Drogoff, V. Aimez, and A. G. Kirk, “Design and Demonstration of Apodized Comb Filters on SOI,” IEEE Photon. J. 4(4), 1133–1139 (2012).
[Crossref]

Giuntoni, I.

I. Giuntoni, D. Stolarek, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Integrated Dispersion Compensator Based on Apodized SOI Bragg Gratings,” IEEE Photon. Technol. Lett. 25(14), 1313–1316 (2013).
[Crossref]

I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012).
[Crossref] [PubMed]

Guo, Y. H.

L. S. Yan, J. Ye, H. Y. Jiang, W. Pan, B. Luo, A. L. Yi, Y. H. Guo, and X. S. Yao, “A Photonic Comb Filter With Independently and Digitally Tunable Bandwidth and Frequency Spacing,” IEEE Photon. Technol. Lett. 23(13), 857–859 (2011).
[Crossref]

Han, Y. G.

He, S.

Huang, D.

Huo, Z.

Ikeda, K.

D. T. H. Tan, K. Ikeda, and Y. Fainman, “Coupled chirped vertical gratings for on chip group velocity dispersion engineering,” Appl. Phys. Lett. 95(14), 141109 (2009).
[Crossref]

Janz, S.

Jiang, H. Y.

H. Y. Jiang, L. S. Yan, J. Ye, W. Pan, B. Luo, and X. S. Yao, “Comb filter with independently tunable wavelength spacing and bandwidth using cascaded variable differential group delay elements,” Opt. Lett. 36(12), 2305–2307 (2011).
[Crossref] [PubMed]

L. S. Yan, J. Ye, H. Y. Jiang, W. Pan, B. Luo, A. L. Yi, Y. H. Guo, and X. S. Yao, “A Photonic Comb Filter With Independently and Digitally Tunable Bandwidth and Frequency Spacing,” IEEE Photon. Technol. Lett. 23(13), 857–859 (2011).
[Crossref]

Jin, W.

Khan, S.

Kim, H.-T.

Kirk, A. G.

V. Veerasubramanian, G. Beaudin, A. Giguere, B. Le Drogoff, V. Aimez, and A. G. Kirk, “Design and Demonstration of Apodized Comb Filters on SOI,” IEEE Photon. J. 4(4), 1133–1139 (2012).
[Crossref]

Kroushkov, D. I.

Laming, R. L.

K. Ennser, M. N. Zervas, and R. L. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34(5), 770–778 (1998).
[Crossref]

Lapointe, J.

Le Drogoff, B.

V. Veerasubramanian, G. Beaudin, A. Giguere, B. Le Drogoff, V. Aimez, and A. G. Kirk, “Design and Demonstration of Apodized Comb Filters on SOI,” IEEE Photon. J. 4(4), 1133–1139 (2012).
[Crossref]

Lee, B.

S. Roh, S. Chung, Y. W. Lee, I. Yoon, and B. Lee, “Channel-Spacing- and Wavelength-Tunable Multiwavelength Fiber Ring Laser Using Semiconductor Optical Amplifier,” IEEE Photon. Technol. Lett. 18(21), 2302–2304 (2006).
[Crossref]

Lee, B. G.

B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photon. Technol. Lett. 20(10), 767–769 (2008).
[Crossref]

Lee, J. H.

Lee, Y. W.

Li, X.

Liao, H.

Lipson, M.

B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photon. Technol. Lett. 20(10), 767–769 (2008).
[Crossref]

P. Dong, S. F. Preble, and M. Lipson, “All-optical compact silicon comb switch,” Opt. Express 15(15), 9600–9605 (2007).
[Crossref] [PubMed]

Liu, D.

Liu, L.

Lu, L.

X. Sun, L. Zhou, J. Xie, Z. Zou, L. Lu, H. Zhu, X. Li, and J. Chen, “Tunable silicon Fabry-Perot comb filters formed by Sagnac loop mirrors,” Opt. Lett. 38(4), 567–569 (2013).
[Crossref] [PubMed]

L. Zhou, X. Zhang, L. Lu, and J. Chen, “Tunable vernier microring optical filters with p-i-p type microheaters,” IEEE Photon. J. 5(4), 6601211 (2013).
[Crossref]

Luo, A.

Luo, B.

H. Y. Jiang, L. S. Yan, J. Ye, W. Pan, B. Luo, and X. S. Yao, “Comb filter with independently tunable wavelength spacing and bandwidth using cascaded variable differential group delay elements,” Opt. Lett. 36(12), 2305–2307 (2011).
[Crossref] [PubMed]

L. S. Yan, J. Ye, H. Y. Jiang, W. Pan, B. Luo, A. L. Yi, Y. H. Guo, and X. S. Yao, “A Photonic Comb Filter With Independently and Digitally Tunable Bandwidth and Frequency Spacing,” IEEE Photon. Technol. Lett. 23(13), 857–859 (2011).
[Crossref]

Luo, Z.

Ma, R.

Marti, J.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14(11), 2581–2588 (1996).
[Crossref]

McKinnon, R.

Ortega, D.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14(11), 2581–2588 (1996).
[Crossref]

Ou, H.

Pan, W.

L. S. Yan, J. Ye, H. Y. Jiang, W. Pan, B. Luo, A. L. Yi, Y. H. Guo, and X. S. Yao, “A Photonic Comb Filter With Independently and Digitally Tunable Bandwidth and Frequency Spacing,” IEEE Photon. Technol. Lett. 23(13), 857–859 (2011).
[Crossref]

H. Y. Jiang, L. S. Yan, J. Ye, W. Pan, B. Luo, and X. S. Yao, “Comb filter with independently tunable wavelength spacing and bandwidth using cascaded variable differential group delay elements,” Opt. Lett. 36(12), 2305–2307 (2011).
[Crossref] [PubMed]

Pastor, D.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14(11), 2581–2588 (1996).
[Crossref]

Petermann, K.

I. Giuntoni, D. Stolarek, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Integrated Dispersion Compensator Based on Apodized SOI Bragg Gratings,” IEEE Photon. Technol. Lett. 25(14), 1313–1316 (2013).
[Crossref]

I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012).
[Crossref] [PubMed]

Peucheret, C.

Poladian, L.

L. Poladian, “Graphical and WKB analysis of nonuniform Bragg gratings,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 48(6), 4758–4767 (1993).
[Crossref] [PubMed]

Poti, L.

Preble, S. F.

Pu, M.

Qin, S.

Ren, G.

Roh, S.

S. Roh, S. Chung, Y. W. Lee, I. Yoon, and B. Lee, “Channel-Spacing- and Wavelength-Tunable Multiwavelength Fiber Ring Laser Using Semiconductor Optical Amplifier,” IEEE Photon. Technol. Lett. 18(21), 2302–2304 (2006).
[Crossref]

Schmid, J. H.

Seoane, J.

Shu, C.

M. P. Fok, C. Shu, and W. W. Tang, “A Cascadable Approach to Produce Widely Selectable Spectral Spacing in Birefringent Comb Filters,” IEEE Photon. Technol. Lett. 18(18), 1937–1939 (2006).
[Crossref]

Shum, P. P.

Song, T.

Stolarek, D.

I. Giuntoni, D. Stolarek, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Integrated Dispersion Compensator Based on Apodized SOI Bragg Gratings,” IEEE Photon. Technol. Lett. 25(14), 1313–1316 (2013).
[Crossref]

I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012).
[Crossref] [PubMed]

Sun, X.

Tan, D. T. H.

D. T. H. Tan, K. Ikeda, and Y. Fainman, “Coupled chirped vertical gratings for on chip group velocity dispersion engineering,” Appl. Phys. Lett. 95(14), 141109 (2009).
[Crossref]

Tang, M.

Tang, W. W.

M. P. Fok, C. Shu, and W. W. Tang, “A Cascadable Approach to Produce Widely Selectable Spectral Spacing in Birefringent Comb Filters,” IEEE Photon. Technol. Lett. 18(18), 1937–1939 (2006).
[Crossref]

Tatay, V.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14(11), 2581–2588 (1996).
[Crossref]

Tillack, B.

I. Giuntoni, D. Stolarek, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Integrated Dispersion Compensator Based on Apodized SOI Bragg Gratings,” IEEE Photon. Technol. Lett. 25(14), 1313–1316 (2013).
[Crossref]

I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012).
[Crossref] [PubMed]

Vachon, M.

Veerasubramanian, V.

V. Veerasubramanian, G. Beaudin, A. Giguere, B. Le Drogoff, V. Aimez, and A. G. Kirk, “Design and Demonstration of Apodized Comb Filters on SOI,” IEEE Photon. J. 4(4), 1133–1139 (2012).
[Crossref]

Wang, C.

Xiang, L.

L. Xiang, D. Gao, Y. Yu, M. Ye, B. Zou, and X. Zhang, “Silicon-Based Integrated Comb Filter and Demultiplexer for Simultaneous WDM Signal Processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200208 (2014).
[Crossref]

Xie, J.

Xu, D. X.

Xu, E.

Y. Zhang, E. Xu, D. Huang, and X. Zhang, “All-optical format conversion from RZ to NRZ utilizing microfiber resonator,” IEEE Photon. Technol. Lett. 21(17), 1202–1204 (2009).
[Crossref]

Xu, J.

Xu, W.

Xuan, H.

Yan, L. S.

H. Y. Jiang, L. S. Yan, J. Ye, W. Pan, B. Luo, and X. S. Yao, “Comb filter with independently tunable wavelength spacing and bandwidth using cascaded variable differential group delay elements,” Opt. Lett. 36(12), 2305–2307 (2011).
[Crossref] [PubMed]

L. S. Yan, J. Ye, H. Y. Jiang, W. Pan, B. Luo, A. L. Yi, Y. H. Guo, and X. S. Yao, “A Photonic Comb Filter With Independently and Digitally Tunable Bandwidth and Frequency Spacing,” IEEE Photon. Technol. Lett. 23(13), 857–859 (2011).
[Crossref]

Yang, F.

Yao, X. S.

L. S. Yan, J. Ye, H. Y. Jiang, W. Pan, B. Luo, A. L. Yi, Y. H. Guo, and X. S. Yao, “A Photonic Comb Filter With Independently and Digitally Tunable Bandwidth and Frequency Spacing,” IEEE Photon. Technol. Lett. 23(13), 857–859 (2011).
[Crossref]

H. Y. Jiang, L. S. Yan, J. Ye, W. Pan, B. Luo, and X. S. Yao, “Comb filter with independently tunable wavelength spacing and bandwidth using cascaded variable differential group delay elements,” Opt. Lett. 36(12), 2305–2307 (2011).
[Crossref] [PubMed]

Ye, J.

H. Y. Jiang, L. S. Yan, J. Ye, W. Pan, B. Luo, and X. S. Yao, “Comb filter with independently tunable wavelength spacing and bandwidth using cascaded variable differential group delay elements,” Opt. Lett. 36(12), 2305–2307 (2011).
[Crossref] [PubMed]

L. S. Yan, J. Ye, H. Y. Jiang, W. Pan, B. Luo, A. L. Yi, Y. H. Guo, and X. S. Yao, “A Photonic Comb Filter With Independently and Digitally Tunable Bandwidth and Frequency Spacing,” IEEE Photon. Technol. Lett. 23(13), 857–859 (2011).
[Crossref]

Ye, M.

L. Xiang, D. Gao, Y. Yu, M. Ye, B. Zou, and X. Zhang, “Silicon-Based Integrated Comb Filter and Demultiplexer for Simultaneous WDM Signal Processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200208 (2014).
[Crossref]

Yi, A. L.

L. S. Yan, J. Ye, H. Y. Jiang, W. Pan, B. Luo, A. L. Yi, Y. H. Guo, and X. S. Yao, “A Photonic Comb Filter With Independently and Digitally Tunable Bandwidth and Frequency Spacing,” IEEE Photon. Technol. Lett. 23(13), 857–859 (2011).
[Crossref]

Yoon, I.

S. Roh, S. Chung, Y. W. Lee, I. Yoon, and B. Lee, “Channel-Spacing- and Wavelength-Tunable Multiwavelength Fiber Ring Laser Using Semiconductor Optical Amplifier,” IEEE Photon. Technol. Lett. 18(21), 2302–2304 (2006).
[Crossref]

Yu, Y.

L. Xiang, D. Gao, Y. Yu, M. Ye, B. Zou, and X. Zhang, “Silicon-Based Integrated Comb Filter and Demultiplexer for Simultaneous WDM Signal Processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200208 (2014).
[Crossref]

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[Crossref]

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L. Xiang, D. Gao, Y. Yu, M. Ye, B. Zou, and X. Zhang, “Silicon-Based Integrated Comb Filter and Demultiplexer for Simultaneous WDM Signal Processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200208 (2014).
[Crossref]

L. Zhou, X. Zhang, L. Lu, and J. Chen, “Tunable vernier microring optical filters with p-i-p type microheaters,” IEEE Photon. J. 5(4), 6601211 (2013).
[Crossref]

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[Crossref] [PubMed]

Y. Zhang, E. Xu, D. Huang, and X. Zhang, “All-optical format conversion from RZ to NRZ utilizing microfiber resonator,” IEEE Photon. Technol. Lett. 21(17), 1202–1204 (2009).
[Crossref]

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Y. Zhang, E. Xu, D. Huang, and X. Zhang, “All-optical format conversion from RZ to NRZ utilizing microfiber resonator,” IEEE Photon. Technol. Lett. 21(17), 1202–1204 (2009).
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Zhao, Y.

Zhao, Z.

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L. Zhou, X. Zhang, L. Lu, and J. Chen, “Tunable vernier microring optical filters with p-i-p type microheaters,” IEEE Photon. J. 5(4), 6601211 (2013).
[Crossref]

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[Crossref]

I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012).
[Crossref] [PubMed]

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L. Xiang, D. Gao, Y. Yu, M. Ye, B. Zou, and X. Zhang, “Silicon-Based Integrated Comb Filter and Demultiplexer for Simultaneous WDM Signal Processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200208 (2014).
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Appl. Phys. Lett. (1)

D. T. H. Tan, K. Ikeda, and Y. Fainman, “Coupled chirped vertical gratings for on chip group velocity dispersion engineering,” Appl. Phys. Lett. 95(14), 141109 (2009).
[Crossref]

IEEE J. Quantum Electron. (1)

K. Ennser, M. N. Zervas, and R. L. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34(5), 770–778 (1998).
[Crossref]

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

L. Xiang, D. Gao, Y. Yu, M. Ye, B. Zou, and X. Zhang, “Silicon-Based Integrated Comb Filter and Demultiplexer for Simultaneous WDM Signal Processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200208 (2014).
[Crossref]

IEEE Photon. J. (2)

L. Zhou, X. Zhang, L. Lu, and J. Chen, “Tunable vernier microring optical filters with p-i-p type microheaters,” IEEE Photon. J. 5(4), 6601211 (2013).
[Crossref]

V. Veerasubramanian, G. Beaudin, A. Giguere, B. Le Drogoff, V. Aimez, and A. G. Kirk, “Design and Demonstration of Apodized Comb Filters on SOI,” IEEE Photon. J. 4(4), 1133–1139 (2012).
[Crossref]

IEEE Photon. Technol. Lett. (6)

I. Giuntoni, D. Stolarek, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Integrated Dispersion Compensator Based on Apodized SOI Bragg Gratings,” IEEE Photon. Technol. Lett. 25(14), 1313–1316 (2013).
[Crossref]

B. G. Lee, A. Biberman, P. Dong, M. Lipson, and K. Bergman, “All-optical comb switch for multiwavelength message routing in silicon photonic networks,” IEEE Photon. Technol. Lett. 20(10), 767–769 (2008).
[Crossref]

S. Roh, S. Chung, Y. W. Lee, I. Yoon, and B. Lee, “Channel-Spacing- and Wavelength-Tunable Multiwavelength Fiber Ring Laser Using Semiconductor Optical Amplifier,” IEEE Photon. Technol. Lett. 18(21), 2302–2304 (2006).
[Crossref]

Y. Zhang, E. Xu, D. Huang, and X. Zhang, “All-optical format conversion from RZ to NRZ utilizing microfiber resonator,” IEEE Photon. Technol. Lett. 21(17), 1202–1204 (2009).
[Crossref]

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[Crossref]

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[Crossref]

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I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012).
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Y. Ding, C. Peucheret, M. Pu, B. Zsigri, J. Seoane, L. Liu, J. Xu, H. Ou, X. Zhang, and D. Huang, “Multi-channel WDM RZ-to-NRZ format conversion at 50 Gbit/s based on single silicon microring resonator,” Opt. Express 18(20), 21121–21130 (2010).
[Crossref] [PubMed]

D. Chen, S. Qin, and S. He, “Channel-spacing-tunable multi-wavelength fiber ring laser with hybrid Raman and Erbium-doped fiber gains,” Opt. Express 15(3), 930–935 (2007).
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Other (3)

I. Giuntoni, D. Stolarek, A. Gajda, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Integrated Dispersion Compensator Based on SOI Tapered Gratings,” in 37th European Conference and Exposition on Optical Communications (Ecoc), p.Th.12.LeSaleve.4 (2011).
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[Crossref]

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic of the proposed silicon comb filter with tunable channel-spacing. Inset shows the cross-sectional schematic of the p-i-p junction-based resistive micro-heater. (b)-(d) illustrate the working principle of the comb filter. The solid purple lines are the comb filter output transmission spectra. The solid black and red lines are the reflection spectra of the two ALC-BGs, and the dashed black and red lines are their corresponding delay spectra. From (b) to (d), the group delay difference increases.
Fig. 2
Fig. 2 Intensity (left plots) and group delay (right plots) spectra of the comb filter and LC-BGs in response to various refractive index changes in Grating 2. The refractive index changes are 0, 8 × 10−4, 1.6 × 10−3, and 3.2 × 10−3 from top to bottom, respectively. The insets in the right plots show the magnified group delay spectra.
Fig. 3
Fig. 3 (a) Refractive index modulation in the gratings. (b) Width of the grating masks (red line) and spaces (black line).
Fig. 4
Fig. 4 Intensity and group delay spectra of the comb filter and ALC-BGs in response to various refractive index changes in Grating 2. The tuning parameters are the same with those in Fig. 2.
Fig. 5
Fig. 5 (a) Waveguide effective refractive index and propagation loss change with tuning power. (b) Channel spacing and number of the comb passbands change with tuning power.
Fig. 6
Fig. 6 (a) Transmission spectrum of the comb filter with tuning power of 0.82 W. (b) Lowest out-of-band rejection ratio in the full reflection band changes with the tuning power.

Equations (10)

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[ E 3 E 4 ]=[ 1K j K j K 1K ][ R g1 (λ) e i φ 1 (λ) 0 0 R g2 (λ) e i φ 2 (λ) ][ 1K j K j K 1K ][ E 1 E 2 ]
t= E 4 E 1 = 1 2 j e i φ 1 (λ) [ R g1 (λ) + R g2 (λ) e i( φ 2 (λ) φ 1 (λ)) ]
T= | E 4 E 1 | 2 = 1 4 [ R g1 (λ)+ R g2 (λ)+2 R g1 (λ) R g2 (λ) cos(Δφ) ]
T= R g1 (λ)= R g2 (λ)
τ(λ) (λ λ 0 ) Δ λ chirp 2 L g ν g
Δτ (λ λ 0 ) Δ λ chirp 2 L g ν g (λ λ 0 Δ n e λ 0 / n g ) Δ λ chirp 2 L g ν g = 2 L g Δ n e λ 0 cΔ λ chirp
FS R v = 1 Δτ = cΔ λ chirp 2 L g Δ n e λ 0
FS R λ = λ 2 cΔτ λ 0 Δ λ chirp 2 L g Δ n e
N comb = Δ λ chirp -Δλ FS R λ = 2 L g Δ n e λ 0 - 2 L g Δ n e 2 n g Δ λ chirp
δ n eff (z)={ δ n eff0 tanh[ 2az L g ],0z L g 2 δ n eff0 tanh[ 2a( L g z) L g ], L g 2 z L g

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