Direct design of high channel-count fiber Bragg grating filters with low index modulation

doi:10.1364/OE.20.012095

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Direct design of high channel-count fiber Bragg grating filters with low index modulation

Hui Cao, Javid Atai, Xuewen Shu, and Guojie Chen »View Author Affiliations

Optics Express, Vol. 20, Issue 11, pp. 12095-12110 (2012)
http://dx.doi.org/10.1364/OE.20.012095

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– Abstract
1. Introduction
2. Theoretical analysis
3. Simulation and discussion
4. Conclusion
– References and links

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Abstract

a novel method for designing high channel-count fiber Bragg gratings (FBGs) is proposed. For the first time, tailored group delay is introduced into the target reflection spectra to obtain a more even distribution of the refractive index modulation. This approach results in the reduction of the maximum refractive index modulation to physically realizable levels. The maximum index modulation reduction factors are all greater than 5.5. This is a significant improvement compared with previously reported results. Numerical results show that the thus designed high channel-count FBG filters exhibit superior characteristics including 30 dB channel isolation, a flat-top and near 100% reflectivity in each channel.

1. Introduction

Ultra-narrow bandwidth high channel-count fiber Bragg gratings (FBGs) have recently attracted much attention due to their applications in dense wavelength-division-multiplexed (DWDM) systems, fiber-optic sensor systems, multi-wavelength fiber lasers and microwave photonic filters [1

Y. Dai and J. P. Yao, “Design of high channel-count multichannel fiber Bragg gratings based on a largely chirped structure,” IEEE J. Quantum Electron. 45(8), 964–971 (2009). [CrossRef]

–9

M. Li, T. Fujii, and H. Li, “Multiplication of a multichannel notch filter based on a phase-shifted phase-only sampled fiber Bragg grating,” IEEE Photon. Technol. Lett. 21(13), 926–928 (2009). [CrossRef]

]. In addition to their excellent optical spectral response, the FBGs are attractive due to their small size, low insertion loss, high reliability and the compatibility with other components [10

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]

]. In recent years, different types of multichannel FBGs have been proposed and experimentally demonstrated, such as the superimposed FBG, the sampled FBG (phase-only, amplitude-only, amplitude-phase sampling), the spectral Talbot-effect based FBG, the optimization algorithm based FBG and the layer-peeling (LP) algorithm based FBG [3

Y. Painchaud and M. Morin, “Iterative method for the design of arbitrary multi-channel fiber Bragg gratings,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, OSA Technical Digest (CD) (Optical Society of America, 2007), paper BTuB1.

,11

Q. Wu, P. L. Chu, and H. P. Chan, “General design approach to multichannel fiber Bragg grating,” J. Lightwave Technol. 24(3), 1571–1580 (2006). [CrossRef]

–18

H. Li, Y. Sheng, Y. Li, and J. E. Rothenberg, “Phased-only sampled fiber Bragg gratings for high channel-count chromatic dispersion compensation,” J. Lightwave Technol. 21(9), 2074–2083 (2003). [CrossRef]

]. Of these approaches, the most versatile are the sampling method and the LP algorithm. For instance, sampling method has been used to design a 405-channel FBG [19

M. Li, X. Chen, J. Hayashi, and H. Li, “Advanced design of the ultrahigh-channel-count fiber Bragg grating based on the double sampling method,” Opt. Express 17(10), 8382–8394 (2009). [CrossRef] [PubMed]

]. Phase-only sampling method has been utilized to design and fabricate an 81-channel FBG with a peak index modulation of

\approx 8 \times 10^{- 4}

[12

H. Li, M. Li, Y. Sheng, and J. E. Rothenberg, “Advances in the design and fabrication of high-channel-count fiber Bragg gratings,” J. Lightwave Technol. 25(9), 2739–2750 (2007). [CrossRef]

]. This approach has been improved to design FBGs with non-identical channels [2

M. Morin, M. Poulin, A. Mailloux, F. Trépanier, and Y. Painchaud, “Full C-band slope-matched dispersion compensation based on a phase sampled Bragg grating,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper WK1.

–4

Y. Painchaud, M. Poulin, M. Morin, and M. Guy, “Fiber Bragg grating based dispersion compensator slope-matched for LEAF fiber,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2006), paper OThE2.

]. One of the advantages of the LP method is that it can be used to design any kind of multichannel FBG (e.g. FBGs with non-identical channels and/or channel spacing). As a result, the LP algorithm based FBGs have received considerable attention due to the ideal flat-top profiles in their spectral response and the possibility of identical or non-identical channel-channel response [1

Y. Dai and J. P. Yao, “Design of high channel-count multichannel fiber Bragg gratings based on a largely chirped structure,” IEEE J. Quantum Electron. 45(8), 964–971 (2009). [CrossRef]

, 20

Y. Gong, X. Liu, L. Wang, X. Hu, A. Lin, and W. Zhao, “Optimal design of multichannel fiber Bragg grating filters with small dispersion and low index modulation,” J. Lightwave Technol. 27(15), 3235–3240 (2009). [CrossRef]

–24

A. Rosenthal and M. Horowitz, “Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings,” IEEE J. Quantum Electron. 39(8), 1018–1026 (2003). [CrossRef]

]. The LP algorithm based 16-channel FBG and 51channel FBG have been demonstrated in [20

] and in [1

Y. Dai and J. P. Yao, “Design of high channel-count multichannel fiber Bragg gratings based on a largely chirped structure,” IEEE J. Quantum Electron. 45(8), 964–971 (2009). [CrossRef]

], respectively.

However, with further increasing the number of channels (e.g., ~100) the maximum index modulation, which increases with the increasing of the channel count, may not be realizable. Hence, ensuring the maximum index modulation is physically realizable is a critical factor in designing high channel-count FBG. Although some methods have been reported to optimize the design of high channel-count FBGs with LP algorithm, the reduction of maximum index modulation is not significant. For example, Li et al. have demonstrated that the maximum index modulation of a nine-channel FBG can be reduced by a factor of three by optimally assigning an additional constant phase to each channel [21

H. Li and Y. Sheng, “Direct design of multi-channel fiber Bragg grating with discrete layer-peeling algorithm,” IEEE Photon. Technol. Lett. 15(9), 1252–1254 (2003). [CrossRef]

]. However, the reflectivity beyond the ninth channel becomes nonzero, which means that the extinction rate for the in-band signals to out-band noise becomes worse. Gong et al. developed an optimization method based on the nonlinear least squares method and the discrete layer peeling (DLP) algorithm. Applying this approach to a 16-channel FBG filter, it was shown that the maximum index modulation was reduced from 1.5 × 10⁻³ to 7.9 × 10⁻⁴ [20

]. In Ref [1

Y. Dai and J. P. Yao, “Design of high channel-count multichannel fiber Bragg gratings based on a largely chirped structure,” IEEE J. Quantum Electron. 45(8), 964–971 (2009). [CrossRef]

], Dai et al. designed a 51-channel FBG within 12-cm photosensitive optical fiber with a practically acceptable complex structure and index modulation. Their method is based on a chirped structure. Taking into account the characteristics of the linear chirp, a rational algebraic relationship was established between the chirp and the group delay. The linearly chirped structure was then converted into different group delays for different channels, thereby reducing the maximum index modulation. A drawback of this method is that it is not a direct design approach in that the chirped structure has to first be transformed into the group delay in the target reflection spectrum.

In this paper, we present a novel and direct method to reduce the maximum refractive index modulation of high channel-count FBG. In Section II, the origin of the increase of the maximum index modulation with the number of channels is analyzed and the method to reduce the maximum index modulation is discussed. The novelty of the method is the introduction of the tailored group delay in the target reflectivity spectrum. This leads to a more even distribution of the refractive index modulation, thereby reducing the maximum refractive index modulation to the physically realizable level. To illustrate the capabilities of the method, in Section III, the method is used to design an 80-channel FBG and a 101-channel FBG, respectively. In Section IV a summary of the results is presented.

2. Theoretical analysis

To analyze the origin of the increase of maximum index modulation with the increase of channel count, we consider a non-dispersive 8-channel 50GHz spaced FBG filter with flat group delay. The target reflectivity of the FBG can be described by

r (λ) = \sqrt{0.95} \times \sum_{j = 1}^{M} \exp (- {(\frac{2 π n_{e f f}}{a_{j}} (\frac{1}{λ} - \frac{1}{λ_{j}}))}^{b_{j}}) \begin{matrix} \exp (i 2 π n_{e f f} (\frac{1}{λ} - \frac{1}{λ_{0}}) L) & j = 1, 2, 3 \dots M \end{matrix}

(1)

where

n_{e f f}

is the effective refractive index,

λ_{j} = 1548 + j \times 0.4,

a_{j}

and

b_{j}

are the central wavelength and parameters of super-Gaussian functions for channel j, respectively. The central wavelength of the full spectra is

λ_{0} = 1550

nm, channel count M = 8, and the grating length L = 20 cm. Given Eq. (1), the LP algorithm can be used to directly reconstruct grating structure. The synthesized index modulation and its corresponding reflectivity spectra and group delay response are shown in Fig. 1 . Figure 1(b) shows that there is an excellent agreement between the synthesized reflectivity spectra and Eq. (1). Also, the fact that the group delay for each channel is very flat indicates that the designed filter is non-dispersive. In Fig. 1(c) we plot the group delay response for the 8-channel FBG filter, where the reflectivity spectra are added to indentify every channel. As is shown in Fig. 1(a), the maximum index modulation is 0.00132. Our goal is to come up with grating designs where maximum index modulation is below 0.001. Another noteworthy feature of Fig. 1(a) is that the refractive index modulation is concentrated in the middle of the grating.

Fig. 1 Designed 8-channel 50 GHz FBG filters with identical group delay. (a) Synthesized index modulation. (b) Comparison of the target reflectivity spectra (the solid line) and the reflectivity spectra of the synthesized grating (the dotted line). (c) Group delay response.

The evolution of the reflectivity spectra as a function of grating length is illustrated in Fig. 2 . The fact that all the channels are reflected at the same grating location indicates that 8 subgratings are overlapped in the same fiber section. It is this overlap that gives rise to high index modulation. This result can also be discerned from Eq. (1). Since the phase of each channel in Eq. (1) is given by

2 π n_{e f f} (1 / λ - 1 / λ_{0}) L

, the group delay for different channels will be the same. This means that different wavelengths will be reflected from the same location in the grating.

Fig. 2 Evolution of reflectivity spectra over the grating length for the target reflectivity

To avoid this overlap, one possible approach is to incorporate a tailored group delay profile to the target reflectivity spectra. For example, one may use a staircase group delay profile to assign different group delays to different channels. This gives rise to the following target reflectivity spectra:

r (λ) = \sqrt{0.95} \times \sum_{j = 1}^{M} \exp (- {(\frac{2 π n_{e f f}}{a_{j}} (\frac{1}{λ} - \frac{1}{λ_{j}}))}^{b_{j}}) \begin{matrix} \exp (i 2 π n_{e f f} (\frac{1}{λ} - \frac{1}{λ_{0}}) d_{k}) & j = 1, 2, 3 \dots M \end{matrix}

(2)

where the group delay parameter is given by

d_{k} = 0.05 + 0.04 \times (k - 1), k = 1, 2, 3 \dots M

and the other parameters are the same as those in Eq. (1).

The resynthesized grating and its corresponding spectral response are shown in Fig. 3 . As is shown in Fig. 3(a), 8 subgrating structures are evenly distributed along the grating, with little overlap. In this case, the maximum index modulation is 0.00018 which is almost 7.5 times smaller than that for Eq. (1). Figure 3(b) shows that the resynthesized grating generates desired reflectivity and staircase group delay. Figure 4 shows the evolution of reflectivity spectra for the resynthesized grating. It is clear that, due to the staircase group delay, the channels occur in different locations along the grating.

Fig. 3 The resynthesized index modulation and its corresponding spectral response. (a) Resynthesized index modulation. (b) Simulated group delay (the solid line) and simulated reflectivity spectra (the dotted line).

Fig. 4 Evolution of reflectivity spectra over the grating length for the case of staircases group delay

The group delay can be tailored to different profiles by employing different mappings between wavelength

λ_{j}

and group delay parameter

d_{k} .

For instance, the mapping

k = j

and

k = M - j,

will result in descending and ascending staircase group delays, respectively. Alternatively, if the mapping is

k = \frac{2 M + 1}{4} + \frac{2 M - 2 j + 1}{4} \times {(- 1)}^{j + 1},

the wedge shaped (‘>’ shape) group delay profile will be obtained. It will be demonstrated that this mapping is more effective than the staircase group delay in reducing the maximum index modulation.

An important question is how value of

d_{k}

should be chosen. To address this question, we consider the case of uniform distribution of sub-gratings. From Eq. (2) and Fig. 3(a), one can express the group delay parameter as

d_{k} = 2 \times [L_{L} + (k - 1) \times L_{s t e p}], \begin{matrix} k = 1, 2, \dots, M \end{matrix}

(3)

L_{s t e p} = \frac{L - (L_{R} + L_{L})}{M - 1},

(4)

where M is the channel count, L is the length of grating,

L_{s t e p}

is the separation between successive channels, and

L_{L}

and

L_{R}

are the locations of the first channel when counting from left side and right side, respectively. It should be pointed out that

L_{L}

and

L_{R}

should be carefully designed. On the one hand, for a given L and M, to reduce the overlap between subgratings,

(L_{L} + L_{R})

should be made as small as possible. On the other hand,

(L_{L} + L_{R})

should not be less than the length of the sub-grating, for the benefit of no damage to the spectra response of the far left and far right channel. All in all, to prevent degradation of the spectral response of the far left and far right channels,

(L_{L} + L_{R})

should not be smaller than the length of the subgrating. Therefore, before designing a high channel-count grating, the sub-grating (1-channel grating) should be designed to determine the values of

L_{L}

and

L_{R}

(in the case of asymmetrical subgrating

L_{L}

and

L_{R}

will not be equal). Figure 5 shows the grating structure of the subgrating with a −0.5-dB bandwidth of 0.2 nm and a −30-dB bandwidth of 0.3 nm. This subgrating will be used in the next section to design high channel-count gratings.

Fig. 5 Index modulation of the sub-grating (1-channel grating) with a 0.5-dB bandwidth of 0.2 nm, and a −30-dB bandwidth of 0.3 nm. The inset shows corresponding reflectivity spectra response.

3. Simulation and discussion

For comparison purposes, we first design an 80-channel FBG filter with the ITU channel separation of 50 GHz and flat group delay. The target reflectivity is given by the following expression:

r (λ) = \sqrt{0.95} \times \sum_{j = 1}^{80} \exp (- {(\frac{2 π n_{e f f}}{a_{j}} (\frac{1}{λ} - \frac{1}{λ_{j}}))}^{b_{j}}) \begin{matrix} \exp (i 2 π n_{e f f} (\frac{1}{λ} - \frac{1}{λ_{0}}) L) & j = 1, 2, 3 \dots 80 \end{matrix}

(5)

where the grating length is 10 cm,

λ_{0} = 1550

nm and

λ_{j}

is the central wavelength of channel j, which is monotonically increased from 1534.25 nm to 1565.90 nm as j varies from 1 to 80. The synthesized grating structure and its spectral response are shown in Fig. 6 . As one can see, the spectral response is acceptable. However, there are two major deficiencies in this design. Firstly, the maximum refractive index modulation is 0.00637 which is well above the required 0.001. Secondly, the local chirp is too complex.

Fig. 6 Designed 80-channel (50 GHz spacing) FBG filter with flat group delay. (a) Index modulation (the green line) and the local chirp (the blue line). (b) Reflectivity spectra (the green line) and group delay response (the blue line). (c) Group delay and reflectivity at three channels (central wavelengths: 1535.04 nm, 1535.43 nm and 1535.82 nm)

Next, we design an 80-channel 50 GHz spaced filter with staircase group delay with

L = 10 cm, L_{L} = 7.2 mm, L_{R} = 7.0 mm,

where

L_{L}

and

L_{R}

are shown in Fig. 5. Figure 7 depicts the synthesized grating and its spectral response. In this case, the maximum refractive index modulation is 0.00094 which is practically realizable. This clearly demonstrates that incorporating staircase group delay into the target reflectivity spectra is an effective method to decrease the maximum refractive index modulation. At the same time, the local chirp has been simplified compared with the counterpart in the case of flat group delay. Figure 8 further shows the spectral response for the wavelengths ranging from 1546 nm to 1554 nm. It is clearly seen that the group delay has staircase structure and the best channel isolation is as high as 30dB. The 3dB-bandwidth performance statistics for the filter is shown in Fig. 9 . As shown in Fig. 9(a), the variation of the 3-dB bandwidth with the channel number does not exceed 0.008 nm. At the same time, Fig. 9(b) shows that the variation of group delay ripple within the 3-dB bandwidth with the channel number is no more than 4 ps.

Fig. 7 Designed 80-channel (50GHz spacing) FBG filter with staircase group delay. (a) Index modulation (the green line) and the local chirp (the blue line). (b) Reflectivity spectra (the green line) and group delay response (the blue line).

Fig. 8 Zoom-in of the simulated result with limiting the wavelength between 1546nm and 1554nm. Simulated reflectivity spectra (the green line) and group delay response (the blue line).

Fig. 9 3-dB bandwidth performance statistics. (a) Variation of the 3-dB bandwidth of the reflectivity spectra with the channel number. (b) Variation of group delay ripples within the 3-dB bandwidth with channel number.

To further explore the capabilities of our method in reducing the maximum refractive index modulation, we design a 101-channel 50 GHz spaced FBG filter. We utilize the target reflectivity spectra given by Eq. (2) with

d_{k} = 2 \times (0.0072 + (k - 1) \times L_{s t e p}), j = 1, 2, 3 \dots 101.

λ_{j}

is the central wavelength of channel j with the ITU-T spacing of 50 GHz, ranging from 1529.94 nm to 1570.01 nm, and the grating length is 12 cm. Using the above values for

L_{L}

and

L_{R},

L_{s t e p}

will be equal to 1.06 mm.

The grating is designed for the staircase, the right wedge-shaped (‘>’) and the left wedge-shaped (‘<’) group delay profiles. In case of the staircase group delay,

k = j .

Fig. 10 shows the synthesized grating structures and the spectral response, respectively. As is shown in Fig. 10(a), the maximum refractive index modulation is 0.000922, which is practically realizable. It should be noted that synthesizing a 101-channel FBG filter with flat group delay profile gives rise to the maximum index modulation is 0.005257.

Fig. 10 Designed 101-channel (50 GHz spacing) FBG filters with staircases group delay. (a) Synthesized index modulation (the green line) and the local chirp (the blue line). (b) Reflectivity spectra (the green line) and group delay (the blue line). The inset shows the details of spectra at the central channel (central wavelength: 1550.12nm)

For the right wedge shaped (‘>) group delay profile, k is set to

\frac{2 M + 1}{4} + \frac{2 M - 2 j + 1}{4} \times {(- 1)}^{j + 1} .

The synthesized grating and its spectral response are shown in Fig. 11 . In this case, it is found that the maximum index modulation is 0.00085445 which is slightly better than that of the staircase profile. This may be attributed to the fact that different group delay profiles correspond to different permutations and combinations of subgratings. As a result, certain group delay profiles may lead to a more even distribution of index modulation.

Fig. 11 Designed 101-channel (50 GHz spacing) FBG filters with the right wedge-shaped (‘>’) group delay profile. (a) Synthesized index modulation (the green line) and the local chirp (the blue line). (b) Reflectivity spectra (the green line) and group delay response (the blue line). The inset shows the details of spectra at two channels (central wavelengths: 1569.59 nm and 1570.01 nm).

One advantage of our method is that for a given channel-count grating (say 101), one can improve the spectral response of designed grating by using nonuniform channel spacing. This is illustrated in Fig. 12 . In this case, the 101 channels are randomly chosen from 180 channels within ITU-T grid (50 GHz spacing). Here, the reflectivity spectra are very wide, ranging from 1517.94 nm to 1596.76 nm. Such FBGs may find applications in the design of DWDM multiplexer and demultiplexer covering L + C + S bands. Also, it should be noted that to design the grating shown in Fig. 12(c) we have utilized the left wedge-shaped (‘<’) group delay profile where

k = \frac{2 M + 1}{4} + \frac{2 j - 1}{4} \times {(- 1)}^{M - j} .

Fig. 12 Designed 101-channel nonuniformly spaced FBG filter with the left wedge shaped (‘<’) group delay. (a) Synthesized index modulation. (b) Reflectivity spectra. (c) The details of spectra at two channels (central wavelengths: 1538.98 nm and 1539.37 nm).

Table 1 summarizes these three cases with the maximum refractive index modulation and the corresponding reduction factor as well as other three cases based on reported results in [17

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39(1), 91–98 (2003). [CrossRef]

,20

,21

H. Li and Y. Sheng, “Direct design of multi-channel fiber Bragg grating with discrete layer-peeling algorithm,” IEEE Photon. Technol. Lett. 15(9), 1252–1254 (2003). [CrossRef]

]. Here, the maximum index modulation reduction factor is defined as the ratio of the maximum refractive index modulation (the original one divided by the minimized one). As is shown in Table 1, the method proposed in this paper is far superior than those of Refs [17

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39(1), 91–98 (2003). [CrossRef]

,20

,21

H. Li and Y. Sheng, “Direct design of multi-channel fiber Bragg grating with discrete layer-peeling algorithm,” IEEE Photon. Technol. Lett. 15(9), 1252–1254 (2003). [CrossRef]

]. in that it results in maximum index modulation reduction factors that are greater than 5.5.

Table 1 Maximum Index Modulation and Reduction Factor for 8-,80-,and 101-channel FBG Filter

Channel number	Maximum index modulation		Maximum index modulation Reduction factor	Optimization method	Data source
Channel number	the original one	the minimized one	Maximum index modulation Reduction factor	Optimization method	Data source
8	0.00132	0.00018	7.33	Staircase group delay	This paper
80	0.00637	0.00094	6.78
101	0.005257	0. 00092217	5.70
		0.00085445	6.15	Right wedge shaped (‘>’) group delay
		0.00090815	5.79	Left wedge shaped (‘<’) group delay
16	-	70% reduction	3.33	Dephasing technique	Reference [17 A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39(1), 91–98 (2003). [CrossRef] ]
16	0.0015	0.00079	1.90	Nonlinear least squares	Reference [20 Y. Gong, X. Liu, L. Wang, X. Hu, A. Lin, and W. Zhao, “Optimal design of multichannel fiber Bragg grating filters with small dispersion and low index modulation,” J. Lightwave Technol. 27(15), 3235–3240 (2009). [CrossRef] ]
9	0.0038	0.0018	2.11	Simulated annealing algorithm	Reference [21 H. Li and Y. Sheng, “Direct design of multi-channel fiber Bragg grating with discrete layer-peeling algorithm,” IEEE Photon. Technol. Lett. 15(9), 1252–1254 (2003). [CrossRef] ]

Note: Maximum index modulation reduction factor calculation example, for 8 channel case, 7.33 = 0.00132/0.00018.

It should be pointed out that increasing the number of channels does not necessarily require increasing the length of the grating. More specifically, we have shown that using our method a 12-cm-long 101-channel grating with practically acceptable structure and index modulation can be synthesized. This is a significant improvement compared with the results of Ref [1

Y. Dai and J. P. Yao, “Design of high channel-count multichannel fiber Bragg gratings based on a largely chirped structure,” IEEE J. Quantum Electron. 45(8), 964–971 (2009). [CrossRef]

]. where a 51-channel grating was synthesized within 12 cm of fiber.

Due to the complexity of the local chirp and the index modulation profiles in the above designs, it may be difficult to fabricate these FBGs by conventional fiber grating fabrication techniques. However, they can be fabricated plane-by-plane using the direct-writing technique [25

M. Ibsen, M. K. Durkin, M. J. Cole, M. N. Zervas, and R. I. Laming, “Recent advances in long dispersion compensating fibre Bragg gratings,” in IEE Colloquium on Optical Fibre Gratings (Institution of Electrical Engineers, London, 1999), pp. 6/1–6/7.

,26

X. Shu, E. Turitsyna, and I. Bennion, “Broadband fiber Bragg grating with channelized dispersion,” Opt. Express 15(17), 10733–10738 (2007). [CrossRef] [PubMed]

]. In this technique the interference of two focused UV beams produces a micron-sized nearly-circular spot. Grating structure is written by continually focusing the spot onto the photosensitive fiber/waveguide and translating the sample. For instance, in the case of the 12-cm-long 101-channel FBG, the FBG may be divided uniformly into 6000 segments. Each segment constitutes a 20-μm-long FBG which is sufficiently long compared with the grating period (

Λ = λ_{0} / (2 n) \approx 0.53 μ m

). As for the size of the UV beam, according to Ref [27

J. B. Hawthorn, A. Buryak, and K. Kolossovski, “Optimization algorithm for ultrabroadband multichannel aperiodic fiber Bragg grating filters,” J. Opt. Soc. Am. A 25(1), 153–158 (2008). [CrossRef]

], the smaller dimension of the elliptically shaped UV beam used for writing a grating with a bandwidth of

Δ λ

should be smaller than or equal to

Z_{\max} = λ_{0}^{2} / (2 n_{e f f} Δ λ),

where

λ_{0}

is the central wavelength. For our designed 101-channel FBG (50 GHz spacing),

Δ λ \approx 40 nm,

λ_{0} = 1549.78 nm,

and

n_{e f f} = 1.46.

This leads to

z_{\max} \approx 20 μ m

which is achievable in practice.

4. Conclusion

In this paper we present a new method for designing high-channel count FBG filters with low index modulation. To reduce the index modulation the target reflectivity spectra is tailored with staircase or wedge shaped group delay. The method is applied to the synthesis of 80-channel and 101-channel FBG filters. It is shown that both staircase and wedge shaped group delay profiles will result in reduction of the maximum index modulation to a practically realizable level. The maximum index modulation reduction factors are all greater than 5.5. This is a significant improvement compared with previously reported results. The thus designed high channel-count FBG filters are found to have superior characteristics such as 30-dB channel isolation, a flat-top and near 100% reflectivity in each channel. It is also shown that the proposed method can also be used to design wideband high channel-count grating covering L + C + S bands with nonuniform channel spacing.

Acknowledgments

This research was conducted during Dr Hui Cao’s visit to the School of Electrical and Information Engineering, The University of Sydney (April – September 2011). H.C. gratefully acknowledges the financial support received from Foshan Municipal Government. This research was supported by the National Natural Science Foundation of China (grant 61178030) and the Natural Science Foundation of Guangdong Province, China (grant S201101000122).

References and links

1.	Y. Dai and J. P. Yao, “Design of high channel-count multichannel fiber Bragg gratings based on a largely chirped structure,” IEEE J. Quantum Electron. 45(8), 964–971 (2009). [CrossRef]
2.	M. Morin, M. Poulin, A. Mailloux, F. Trépanier, and Y. Painchaud, “Full C-band slope-matched dispersion compensation based on a phase sampled Bragg grating,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper WK1.
3.	Y. Painchaud and M. Morin, “Iterative method for the design of arbitrary multi-channel fiber Bragg gratings,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, OSA Technical Digest (CD) (Optical Society of America, 2007), paper BTuB1.
4.	Y. Painchaud, M. Poulin, M. Morin, and M. Guy, “Fiber Bragg grating based dispersion compensator slope-matched for LEAF fiber,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2006), paper OThE2.
5.	X. Shu, B. A. L. Gwandu, Y. Liu, L. Zhang, and I. Bennion, “Sampled fiber Bragg grating for simultaneous refractive-index and temperature measurement,” Opt. Lett. 26(11), 774–776 (2001). [CrossRef] [PubMed]
6.	Q. Sun, D. Liu, L. Xia, J. Wang, H. Liu, and P. Shum, “Experimental demonstration of multipoint temperature warning sensor using a multichannel matched fiber Bragg grating,” IEEE Photon. Technol. Lett. 20(11), 933–935 (2008). [CrossRef]
7.	D. B. Hunter, M. A. Englund, and G. Edvell, “Multichannel fiber gratings with tailored dispersion profiles for RF filtering,” IEEE Photon. Technol. Lett. 17(10), 2173–2175 (2005). [CrossRef]
8.	K. H. Wen, L. S. Yan, W. Pan, B. Luo, X. H. Zou, J. Ye, and Y. N. Ma, “Analysis for reflection peaks of multiple-phase-shift based sampled fiber Bragg gratings and application in high channel-count filter design,” Appl. Opt. 48(29), 5438–5444 (2009). [CrossRef] [PubMed]
9.	M. Li, T. Fujii, and H. Li, “Multiplication of a multichannel notch filter based on a phase-shifted phase-only sampled fiber Bragg grating,” IEEE Photon. Technol. Lett. 21(13), 926–928 (2009). [CrossRef]
10.	T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]
11.	Q. Wu, P. L. Chu, and H. P. Chan, “General design approach to multichannel fiber Bragg grating,” J. Lightwave Technol. 24(3), 1571–1580 (2006). [CrossRef]
12.	H. Li, M. Li, Y. Sheng, and J. E. Rothenberg, “Advances in the design and fabrication of high-channel-count fiber Bragg gratings,” J. Lightwave Technol. 25(9), 2739–2750 (2007). [CrossRef]
13.	Y. Dai and J. P. Yao, “Multi-channel Bragg gratings based on nonuniform amplitude-only sampling,” Opt. Express 16(15), 11216–11223 (2008). [CrossRef] [PubMed]
14.	X. Chen, J. Hayashi, and H. Li, “Simultaneous dispersion and dispersion-slope compensator based on a doubly sampled ultrahigh-channel-count fiber Bragg grating,” Appl. Opt. 49(5), 823–828 (2010). [CrossRef] [PubMed]
15.	N. Q. Ngo, R. T. Zheng, J. H. Ng, S. C. Tjin, and L. N. Binh, “Optimization of fiber Bragg gratings using a hybrid optimization algorithm,” J. Lightwave Technol. 25(3), 799–802 (2007). [CrossRef]
16.	G. Tremblay, J.-N. Gillet, Y. Sheng, M. Bernier, and G. Paul-Hus, “Optimizing fiber Bragg gratings using a genetic algorithm with fabrication-constraint encoding,” J. Lightwave Technol. 23(12), 4382–4386 (2005). [CrossRef]
17.	A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39(1), 91–98 (2003). [CrossRef]
18.	H. Li, Y. Sheng, Y. Li, and J. E. Rothenberg, “Phased-only sampled fiber Bragg gratings for high channel-count chromatic dispersion compensation,” J. Lightwave Technol. 21(9), 2074–2083 (2003). [CrossRef]
19.	M. Li, X. Chen, J. Hayashi, and H. Li, “Advanced design of the ultrahigh-channel-count fiber Bragg grating based on the double sampling method,” Opt. Express 17(10), 8382–8394 (2009). [CrossRef] [PubMed]
20.	Y. Gong, X. Liu, L. Wang, X. Hu, A. Lin, and W. Zhao, “Optimal design of multichannel fiber Bragg grating filters with small dispersion and low index modulation,” J. Lightwave Technol. 27(15), 3235–3240 (2009). [CrossRef]
21.	H. Li and Y. Sheng, “Direct design of multi-channel fiber Bragg grating with discrete layer-peeling algorithm,” IEEE Photon. Technol. Lett. 15(9), 1252–1254 (2003). [CrossRef]
22.	Y. Ouyang, Y. Sheng, M. Bernier, and G. Paul-Hus, “Iterative layer-peeling algorithm for designing fiber Bragg gratings with fabrication constraints,” J. Lightwave Technol. 23(11), 3924–3930 (2005). [CrossRef]
23.	J. Skaar, “Synthesis and characterization of fiber Bragg gratings,” Ph.D. dissertation, Norwegian Univ. Sci. and Technol., Trondheim, Norway (2000).
24.	A. Rosenthal and M. Horowitz, “Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings,” IEEE J. Quantum Electron. 39(8), 1018–1026 (2003). [CrossRef]
25.	M. Ibsen, M. K. Durkin, M. J. Cole, M. N. Zervas, and R. I. Laming, “Recent advances in long dispersion compensating fibre Bragg gratings,” in IEE Colloquium on Optical Fibre Gratings (Institution of Electrical Engineers, London, 1999), pp. 6/1–6/7.
26.	X. Shu, E. Turitsyna, and I. Bennion, “Broadband fiber Bragg grating with channelized dispersion,” Opt. Express 15(17), 10733–10738 (2007). [CrossRef] [PubMed]
27.	J. B. Hawthorn, A. Buryak, and K. Kolossovski, “Optimization algorithm for ultrabroadband multichannel aperiodic fiber Bragg grating filters,” J. Opt. Soc. Am. A 25(1), 153–158 (2008). [CrossRef]

OCIS Codes
(060.4510) Fiber optics and optical communications : Optical communications
(060.3735) Fiber optics and optical communications : Fiber Bragg gratings
(130.7408) Integrated optics : Wavelength filtering devices

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: April 3, 2012
Revised Manuscript: April 29, 2012
Manuscript Accepted: April 30, 2012
Published: May 11, 2012

Citation
Hui Cao, Javid Atai, Xuewen Shu, and Guojie Chen, "Direct design of high channel-count fiber Bragg grating filters with low index modulation," Opt. Express 20, 12095-12110 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-11-12095

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References

Y. Dai and J. P. Yao, “Design of high channel-count multichannel fiber Bragg gratings based on a largely chirped structure,” IEEE J. Quantum Electron.45(8), 964–971 (2009). [CrossRef]
M. Morin, M. Poulin, A. Mailloux, F. Trépanier, and Y. Painchaud, “Full C-band slope-matched dispersion compensation based on a phase sampled Bragg grating,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper WK1.
Y. Painchaud and M. Morin, “Iterative method for the design of arbitrary multi-channel fiber Bragg gratings,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, OSA Technical Digest (CD) (Optical Society of America, 2007), paper BTuB1.
Y. Painchaud, M. Poulin, M. Morin, and M. Guy, “Fiber Bragg grating based dispersion compensator slope-matched for LEAF fiber,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2006), paper OThE2.
X. Shu, B. A. L. Gwandu, Y. Liu, L. Zhang, and I. Bennion, “Sampled fiber Bragg grating for simultaneous refractive-index and temperature measurement,” Opt. Lett.26(11), 774–776 (2001). [CrossRef] [PubMed]
Q. Sun, D. Liu, L. Xia, J. Wang, H. Liu, and P. Shum, “Experimental demonstration of multipoint temperature warning sensor using a multichannel matched fiber Bragg grating,” IEEE Photon. Technol. Lett.20(11), 933–935 (2008). [CrossRef]
D. B. Hunter, M. A. Englund, and G. Edvell, “Multichannel fiber gratings with tailored dispersion profiles for RF filtering,” IEEE Photon. Technol. Lett.17(10), 2173–2175 (2005). [CrossRef]
K. H. Wen, L. S. Yan, W. Pan, B. Luo, X. H. Zou, J. Ye, and Y. N. Ma, “Analysis for reflection peaks of multiple-phase-shift based sampled fiber Bragg gratings and application in high channel-count filter design,” Appl. Opt.48(29), 5438–5444 (2009). [CrossRef] [PubMed]
M. Li, T. Fujii, and H. Li, “Multiplication of a multichannel notch filter based on a phase-shifted phase-only sampled fiber Bragg grating,” IEEE Photon. Technol. Lett.21(13), 926–928 (2009). [CrossRef]
T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol.15(8), 1277–1294 (1997). [CrossRef]
Q. Wu, P. L. Chu, and H. P. Chan, “General design approach to multichannel fiber Bragg grating,” J. Lightwave Technol.24(3), 1571–1580 (2006). [CrossRef]
H. Li, M. Li, Y. Sheng, and J. E. Rothenberg, “Advances in the design and fabrication of high-channel-count fiber Bragg gratings,” J. Lightwave Technol.25(9), 2739–2750 (2007). [CrossRef]
Y. Dai and J. P. Yao, “Multi-channel Bragg gratings based on nonuniform amplitude-only sampling,” Opt. Express16(15), 11216–11223 (2008). [CrossRef] [PubMed]
X. Chen, J. Hayashi, and H. Li, “Simultaneous dispersion and dispersion-slope compensator based on a doubly sampled ultrahigh-channel-count fiber Bragg grating,” Appl. Opt.49(5), 823–828 (2010). [CrossRef] [PubMed]
N. Q. Ngo, R. T. Zheng, J. H. Ng, S. C. Tjin, and L. N. Binh, “Optimization of fiber Bragg gratings using a hybrid optimization algorithm,” J. Lightwave Technol.25(3), 799–802 (2007). [CrossRef]
G. Tremblay, J.-N. Gillet, Y. Sheng, M. Bernier, and G. Paul-Hus, “Optimizing fiber Bragg gratings using a genetic algorithm with fabrication-constraint encoding,” J. Lightwave Technol.23(12), 4382–4386 (2005). [CrossRef]
A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron.39(1), 91–98 (2003). [CrossRef]
H. Li, Y. Sheng, Y. Li, and J. E. Rothenberg, “Phased-only sampled fiber Bragg gratings for high channel-count chromatic dispersion compensation,” J. Lightwave Technol.21(9), 2074–2083 (2003). [CrossRef]
M. Li, X. Chen, J. Hayashi, and H. Li, “Advanced design of the ultrahigh-channel-count fiber Bragg grating based on the double sampling method,” Opt. Express17(10), 8382–8394 (2009). [CrossRef] [PubMed]
Y. Gong, X. Liu, L. Wang, X. Hu, A. Lin, and W. Zhao, “Optimal design of multichannel fiber Bragg grating filters with small dispersion and low index modulation,” J. Lightwave Technol.27(15), 3235–3240 (2009). [CrossRef]
H. Li and Y. Sheng, “Direct design of multi-channel fiber Bragg grating with discrete layer-peeling algorithm,” IEEE Photon. Technol. Lett.15(9), 1252–1254 (2003). [CrossRef]
Y. Ouyang, Y. Sheng, M. Bernier, and G. Paul-Hus, “Iterative layer-peeling algorithm for designing fiber Bragg gratings with fabrication constraints,” J. Lightwave Technol.23(11), 3924–3930 (2005). [CrossRef]
J. Skaar, “Synthesis and characterization of fiber Bragg gratings,” Ph.D. dissertation, Norwegian Univ. Sci. and Technol., Trondheim, Norway (2000).
A. Rosenthal and M. Horowitz, “Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings,” IEEE J. Quantum Electron.39(8), 1018–1026 (2003). [CrossRef]
M. Ibsen, M. K. Durkin, M. J. Cole, M. N. Zervas, and R. I. Laming, “Recent advances in long dispersion compensating fibre Bragg gratings,” in IEE Colloquium on Optical Fibre Gratings (Institution of Electrical Engineers, London, 1999), pp. 6/1–6/7.
X. Shu, E. Turitsyna, and I. Bennion, “Broadband fiber Bragg grating with channelized dispersion,” Opt. Express15(17), 10733–10738 (2007). [CrossRef] [PubMed]
J. B. Hawthorn, A. Buryak, and K. Kolossovski, “Optimization algorithm for ultrabroadband multichannel aperiodic fiber Bragg grating filters,” J. Opt. Soc. Am. A25(1), 153–158 (2008). [CrossRef]

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