1. Introduction

Band-rejection filters are important in the fields of high-speed communication, radar, microwave, sensing technologies and their applications. Following the rapid developments in these areas, broadband tuning ability is one of the most important characteristics to be considered. In previous reported works, band-rejection filters over fiber were mainly focused on straight fiber Bragg grating (FBG) [1,2] and long period grating (LPG) [3–6]. One of the key limitations of many reported band-rejection filters is that it is difficult to achieve a flexible spectral-trimming over a broadband spectrum (i.e. hundreds of nanometer). There are also some accessory spectral tuning methods reported which are mainly based on thermo-optical [7–9], electrical [10], magnetic [11] tuning techniques using FBGs or liquid-filled photonic crystal fibers, but the bandwidth tuning range is still limited (only cover C or L band) and the process is complex (liquid injection into micro-holes). The use of tilted fiber Bragg gratings (TFBG) as band-rejection filters was initially reported by Haggans et al. [12] and Kashyap et al. [13] (using TFBGs with tilt angles less than 8°). The advantages of TFBGs are that the tilted grating planes enhance the coupling of light from the core mode to a large number of backward propagating cladding-modes, resulting in a series of discrete resonances over a large wavelength range in transmission (from tens of nanometers to several hundred nanometers) [14,15]. Because each cladding mode has a narrow bandwidth (0.2 nm) and separated by about 0.7 nm from each other, the TFBG presents a perfect “comb”-like spectrum in transmission. In order to take advantages of such strong cladding modes over a large wavelength range, methods for suppression of discrete cladding mode resonances in TFBGs have been studied. One method is chemical etching the cladding of TFBG which leads to overlap of the resonances and a reduction of the amplitude of the modulation [16]. However, the suppressed transmission slope is still not smooth. The chemical etching processing should be carefully controlled and it also weakens the mechanical strength of TFBG. On the other hands, if the grating is chirped, the periods of the TFBG at different positions will have the effect of broadening each cladding mode resonance to such an extent that they end up overlapping considerably. The result is that in transmission, instead of the multiple cladding resonances with clear sub-peaks at discrete wavelengths, a continuous spectral profile with an improved slope-efficiency over a broadened band appears. Therefore, a chirped and tilted FBG (CTFBG) provides good potential for broadband-rejection filters. However, in all CTFBG based band-rejection filters reported so far, the effective bandwidth tuning range is limited to several tens of nanometer [17–20]. Designing band-rejection filters with better quality (broadband tuning and spectral trimming ability to hundreds of nanometers) and lower cost (based on well-established grating fabrication techniques) encourages further research in this field.

In this paper, wideband-adjustable band-rejection filters (with bandwidths from 10 nm to 150 nm) based on flexible chirped and widely tilted CTFBGs are proposed. We experimentally demonstrate the feasibility of achieving in-fiber broadband filtering functions (with tailored bandwidth, slope profile, wavelength and amplitude) by adjusting the tilt angle, chirp rate and UV irradiation time using only one or two phase masks. The filters further show a low insertion loss (less than 1dB), a negligible back-reflection (lower than −20 dB) and insensitive to polarization, temperature, axial strain and surrounding refractive index (SRI). The sloped profiles of the proposed band-rejection filters can be further smoothened by coating the CTFBG with a suitable polymer (whose refractive index (RI) is close to that of the cladding glass). The improvements in the spectral tailoring and smoothing of CTFBGs demonstrated here over large wavelength ranges will help further encourage the use of such devices for high-quality band rejection filtering, edge filters and gain equalizers.

2. Theory of CTFBG

As shown in Fig. 1, the CTFBG is formed by continually changing grating period (${\Lambda }_g$(z)) with grating planes that are slanted or blazed with respect to the fiber axis (tilt angle of $\theta$). In detail, the period along fiber axial direction ${\Lambda }_g(z)$ is changing linearly with position z with a chirp rate F, and can be expressed as [21]:

 

Fig. 1 The schematic diagram of CTFBG.

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Based on the above analysis, the wavelength of the core mode ${\lambda }_{core}$ and ith cladding mode ${\lambda }_{clad,i}$ at position z can be expressed as:

Therefore, the broadened coupling bandwidths of the core mode $\Delta {\lambda }_{core}$ and ith cladding mode $\Delta {\lambda }_{clad,i}$ can be expressed as:

3. Realization of a CTFBG band-rejection filter

The key idea of the realization of a broadband and tuning band-rejection filter lies in the combination of the two effects (grating chirping and grating tilt) over one fiber grating, i.e. a CTFBG. Figure 2 presents the schematic diagrams and spectral characteristics of three kinds of gratings, namely, CFBG, TFBG and CTFBG, and reveals the inter-relationship of how a broadband, non-reflective CTFBG spectrum can be achieved by the combination of CFBG and TFBG.

 

Fig. 2 How to get a broadband CTFBG spectrum by the combination of CFBG and TFBG: (a) chirped FBG without tilt (chirp rate of 20 nm/cm); (b) tilted FBG without chirping (tilt angle of 15°); (c) chirped and tilted FBG (chirp rate of 20 nm/cm and tilt angle of 15°) before and after polymer coating. All spectra are measured experimentally.

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First, if we only consider the effect of grating chirp, as the configuration and spectra of a chirped FBG shows in Fig. 2(a), the non-uniformity of the grating periods located at different positions will reflect a number of sub-peaks at slightly different wavelengths. Since the shift of each sub-peak is comparatively smaller than its spectrum bandwidth and therefore most part of the sub-peaks overlap with each other, resulting in a broadband resonance spectrum. On the other hand, if we only consider the effect of grating tilt, the tilted grating planes enhance the coupling of light from the core mode to a large number of backward propagating cladding-modes (hundreds of cladding modes), resulting in a “comb” like discrete resonances over a large range of spectrum in transmission as shown in Fig. 2(b). However, if we combine the aforementioned two effects together, i.e. a grating with chirped periods and tilted planes, then we can get a continuous spectral profile with an improved slope-efficiency over a broadened bandwidth, as the chirped and tilted FBG transmission (green line) shown in Fig. 2(c). This comes from the effect that grating chirping broadens the original narrow and discrete resonances of the tilted FBG to such extent that they finally overlap totally. Therefore, the chirped and tilted FBG provides the following obvious advantages for band-rejection filtering: a continuous broadband and slope-efficiency improved spectral profile, i.e. a CTFBG provides a 150 nm bandwidth compared to 80 nm for the tilted FBG (with the same tilt angle but no chirping) and to 52 nm for the chirped FBG (with the same grating chirping but no tilt) and presents a suppressed back-reflection (lower than −20 dB). Meanwhile, compared to the TFBG with no chirping (Fig. 2(b)) the amplitudes of core mode and ghost mode of CTFBG have been significantly suppressed (Fig. 2(c)) while the depth of the cladding mode envelope remains similar. This is because the Bragg resonance involves only one mode and the ghost one only a few; then the effect of chirping reduces the modulation amplitude per unit wavelength mode and reduce the resonances to negligible values. For the higher order resonances, they are so closely and densely spaced that their overlap upon chirping compensates for the reduced grating strength per wavelength. Furthermore, by coating the CTFBG with a suitable polymer (whose thickness is of the order of 125 um and refractive index near 1.46 is slightly higher than that of the cladding glass), can be used to eliminate the remaining weak cladding mode discrete resonances (absorbing the cladding modes into leaky modes) and to leave a smoothly varying attenuation spectrum, as the red line shown in Fig. 2(c). The effects demonstrated in Fig. 2 are obtained through conventional photosensitivity of the core of the fiber. In the conditions used, no index modulation or core-cladding interface damage is produced in the cladding and the smoothing is entirely due to chirp-induced spectral broadening.

The gratings are manufactured using the techniques reviewed in [13], i.e. in a commercial single-mode fiber (Corning SMF-28) with a chirped and tilted FBG inscribed in the fiber core. The experimental setup is shown in Fig. 3.The gratings are inscribed by the well-established phase-mask technique using 193 nm UV light with 3 mJ per pulse at a frequency of 200 Hz. Two linearly chirped phase masks with a period of 1064 nm are used, with chirp rates of 20 nm/cm and 10 nm/cm respectively, as shown in Fig. 4.The chirped phase mask and the hydrogen-loaded fiber are parallel to each other, fixed with a very small gap between them, and both are mounted on a rotation stage for the tilting operation. The tilt angle in the fiber is related to the rotation angle by Snell’s law. Finally, all the gratings (CFBG, TFBG and CTFBG) discussed here have a length of 15 mm, with grating inscription time no more than 3 minutes. The tilt of the grating is an important parameter that can be used to choose which set of modes (core or cladding modes) is going to be excited, as shown in Fig. 3. As a result, it makes it possible to adjust the operating range of the filters (both in bandwidth and wavelength) by using only one or two phase masks, which will be discussed in detail in the following section.

 

Fig. 3 Experimental setup of CTFBG inscription system.

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Fig. 4 Spectral trimming of CTFBG with different tilt angles: (a) moderate band-rejection of CTFBGs inscribed by a 10 nm/cm phase mask; (b) broad band-rejection of CTFBG inscribed by a 20 nm/cm phase mask.

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4. Spectral trimming of CTFBG band-rejection filters

We now proceed to show that the slope and bandwidth of this kind of broadband filter can be tailored by using different tilt angles and chirp rates (from the phase masks). In order to meet different filtering ranges, two linearly-chirped phase masks are used with chirp rates of 10 nm/cm and 20 nm/cm respectively. The transmission and reflection spectra for the two cases are shown in Fig. 4. For the moderate band-rejection filtering (bandwidth range from 10 nm to 50 nm (Fig. 4(a)), the chirp rate is fixed at 10 nm/cm and tilt angles are selected over the range of 0° to 10°. For the broad band-rejection filters (bandwidth range from 50 nm to 150 nm as shown in Fig. 4(b)), the chirp rate is fixed at 20 nm/cm and tilt angles are chosen over the range of 10° to 30°. Meanwhile, the transmission and reflection of a straight chirped FBG with the same grating length (15 mm) and chirp rate (20 nm/cm and 10 nm/cm, respectively) are provided for comparison. Clearly, compared with a quasi-square transmission profile (consisting of broadened core mode reflection) provided by a CFBG, CTFBGs provide much broadened Gaussian profiles in transmission because these profiles essentially consist of hundreds of cladding modes which can be flexibly controlled by the tilt angle. Meanwhile, the reflections of CTFBGs have been significantly suppressed, especially when the tilt angle is higher than 10 degrees (the amplitude of CTFBG reflection is suppressed down to −40 dB or even lower, as shown in Fig. 4(b)). The central wavelength of the loss profile is determined by the original Bragg wavelength (itself a function of the average of the grating period) but shifted toward shorter wavelengths (hundreds of cladding modes with chirping). Meanwhile, the chirp rate of the grating also has a crucial impact on the bandwidth, which is that a larger chirp rate corresponds to more broadened profiles. Therefore, a variety of filtering functions with tailored bandwidth (from 10 nm to 150 nm) over more than two hundred nm of spectral range (from 1320 nm to 1562 nm) have been achieved flexibly by selecting a proper tilt angle over two phase masks. The slope efficiency can also be adjusted by controlling the writing time during fabrication but it is eventually dependent on the maximum obtainable grating strength. Therefore, the parameters that determine the slope profile are the chirp rate (original filter bandwidth), tilt angle (filter bandwidth trimming), and grating writing time (filter amplitude). This summarizes the technique for designing and fabricating controllable tunable band rejection filters based on CTFBGs.

5. Characteristics of CTFBG band-rejection filters

It should be noted that because the broadband spectral profile of CTFBG is essentially composed of cladding modes, it potentially exhibits a certain polarization dependence. However, unlike the “comb” like spectrum of discrete resonances of a TFBG, this effect has been much suppressed. As shown in Fig. 5, with orthogonally polarized launch conditions (P and S linear polarizations, relative to the tilt plane orientation [13]), the transmissions show a maximum 0.3 dB and 0.5 dB polarization-dependent-loss for moderate and broad band-rejection filters.

 

Fig. 5 Polarization dependence of CTFBG transmission spectra: (a) a 8° CTFBG inscribed by 10 nm/cm chirp rate; (b) a 15° CTFBG inscribed by 20 nm/cm chirp rate.

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The responses of CTFBG to temperature, axial strain and SRI have also been characterized, as shown in Fig. 6(a), 6(b) and 6(c), respectively. In detail, a linear temperature response with sensitivity of 6.7 × 10⁻³ nm/°C over the range from 30 °C to 90 °C and a linear axial strain response with sensitivity of 1.0 × 10⁻³ nm/με over the range of 0 με to 1450 με have been demonstrated for a 15° CTFBG inscribed by 20 nm/cm chirp rate, which are similar to that of a straight FBG and much lower than a long period grating (LPG). Compared to the broadband filtering profile with bandwidth of 100 nm, the total wavelength shift is in the range of 1.5 nm and the shape of spectral profile is unchanged, as shown in Fig. 6(a) and 6(b). Meanwhile, for SRI changes from 1.0 to 1.45 as shown in Fig. 6(c), the spectral profile of CTFBG presents a negligible wavelength shift (less than 0.6 nm). With the SRI increase, the broadband profile with small ripples (arising from residual discrete cladding mode coupling) gradually becomes a smoothly continuous spectral profile to provide a better edge filter quality. Actually, the latter result points to use a matched index polymer coating as both a protective layer on the filter and as a spectral smoothing help. Therefore, as a broadband-trimming band-rejection filter, CTFBG is insensitive to polarization of launch condition, temperature, axial strain and SRI, identifying its significant advantages over other grating based filters, especially LPGs and interferometric type devices.

 

Fig. 6 Spectral characteristics of CTFBG to (a) temperature, (b) axial strain, and (c) SRI.

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6. Conclusion

Broadband trimming band-rejection filters based on CTFBGs have been demonstrated. The inter-relationship between the broadband spectrum of CTFBG and the combined effects of CFBG and TFBG have been discussed in details and experimentally verified. Varieties of in-fiber band-rejection filters with broadened width (from 10 nm to 150 nm) and smooth slope profiles can be achieved by selecting a grating with proper chirp-rate and tilt-angle based on well-established grating fabrication techniques. The flexible bandwidth trimming ability, together with a low insertion loss (less than 1dB), a negligible back-reflection (lower than −20 dB) and insensitivity to input polarization, temperature, axial strain and SRI, make the proposed CTFBG a good candidate for high quality in-fiber band-rejection filter, edge filters and gain equalizers.