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In this paper, an in-line comb filter with flat-top spectral response is proposed and constructed based on a cascaded all-solid photonic bandgap fiber modal interferometer. It consists of two short pieces of all-solid photonic bandgap fiber and two standard single-mode fibers as lead fibers with core-offset splices between them. The theoretical and experimental results demonstrated that by employing a cut and resplice process on the central position of all-solid photonic bandgap fiber, the interference spectra are well tailored and flat-top spectral profiles could be realized by the controllable offset amount of the resplice. The channel position also could be tuned by applying longitudinal torsion with up to 4 nm tuning range. Such a flat-top fiber comb filter is easy-to-fabricate and with a designable passband width and flat-top profile.
©2013 Optical Society of America
1. Introduction
Multipassband optical comb filters attract considerable interest as wavelength-select elements for multichannel isolation filters and wavelength selective filters in the wavelength-division-multiplexed (WDM) optical fiber communication systems. A filter with periodic and flat-top passband bandwidth is much preferred for the signal stability, tolerance of signal wavelength drift and the reduction of adjacent channel crosstalk. Up to date, many methods have been proposed to implement flat-top comb filters, for example by using silicon nitride-based double-ring resonator [1], Michelson-Gires-Tournois etalons [2, 3], birefringence-based Sagnac loop [4, 5], cascaded Mach-Zehnder interferometers (MZIs) [6–8], planar lightwave circuit [9], and the fiber Bragg grating [10]. Among them, the cascaded interferometric comb filters have received much attention recently because they are easy-to-fabricate with various configurations and wavelength-switchable flexibly. However, optical fiber couplers with two or three ports or tunable optical couplers are required, which makes the system more complicated especially with multi-MZI cascaded.
In recent years, as a novel kind of photonic bandgap fibers, all-solid photonic bandgap fibers (AS-PBFs) have received great attentions. Different from hollow-core photonic bandgap fibers, AS-PBFs have a solid fiber core and a fiber cladding composed of high-index rods instead of air holes. Due to their designable pattern of transmission-inhibited bands and no suffering from surface modes, AS-PBFs can be applied to many devices such as sensing fibers, optical modulators, directional optical coupler and laser amplifiers. In previous works, we built a new cascaded MZI using electric arc discharge technique [11]. It is reported that by applying arc discharge to photonic crystal fiber which is spliced to lead-in and lead-out single-mode fibers with core offset, the in-line MZI could be simply cascaded. In this paper, instead of introducing of arc discharges, an alternative strategy is proposed to cascade an all-fiber inline MZI with all-solid photonic bandgap fiber (AS-PBF), and finally, the flat-top spectral feature on interference fringes is introduced and an all-fiber multipassband flat-top comb filter is fabricated.
2. Operation principle
The in-line flat-top comb filter in question is based on a cascaded AS-PBF-based MZI, and its schematic is shown as Fig. 1. It consists of two standard step-index single-mode fibers (SMFs) as lead fibers and two short segments of AS-PBF spliced between the SMFs. As Fig. 1 shows, both splice 1 and splice 2 are core-offset fused joints between SMFs and AS-PBF, and splice 3 is the joint respliced with two AS-PBF stubs, which has relatively small core-offset value compared to the form ones. With core-offset splice strategy, LP01 mode and LP11 mode are used as two optical arms here. At splice 1, a high-order mode of LP11 is excited with the lateral offset. As it travels to splice 3, it could be partly coupled to LP01 mode and at the same time, the LP11 mode is excited again. At splice 2, the LP01 mode and LP11 mode including new excited component and the ones not participated the interference at splice 3 are totally coupled to the lead-out SMF fiber and interferes with each other. Using such a strategy, an inline cascaded AS-PBF MZI is expected to be formed with three interference cavity lengths of l/2, l/2 and l.
As for two-mode interference, the modes excited at the offset splice 1 could interfere each other, and the electric field distribution produced by the interference at position 3 can be expressed by:
Where, βm is the longitudinal propagation constant of LP01 or LP11 mode, am is the coupling coefficient from the input field Es(r) to electric field of LP01 or LP11 mode, and can be expressed as:So after three interferences with physical lengths of l/2 and l, the output electric field can be expressed by:
Where, bm is the coupling coefficient from the field E3(r) to electric field of LP01 or LP11. After two times modal interference, the output intensity at the out port of AS-PBF can be figured out by . For simplicity, we can express it as follows:where I01 and I11 are the intensity of LP01 and LP11, φ = πΔneffl/λ + φ0 and φ′ = 2πΔneffl/λ + φ0 are the phase differences as a function of the AS-PBF physical length l, Δneff is the effective index difference between LP01 and LP11 mode, and φ0 is an initial phase. η is the normalized power ratio of the MZI with cavity l/2 in total interference spectrum, and it strongly depends on the offset amount of splice 3. If η = 0, it equalizes to the original single MZI enabled by splice 1 and splice 2, when 0 < η < 1, it cascades three MZIs with cavity lengths of l/2, l/2 and l, and η = 1 corresponds to the case that the LP11 mode is totally consumed at splice 3 and the interference with cavity l disappears, therefore it only includes two uniform MZIs with cavity of l/2. Since the core-offset directions of the three splice points are set to be staircase-like here, additional phase differences of 2π and 3π need to be added as shown in above Eq. (4) [12]. Figure 2 illustrates the theoretical transmission spectra with different values of η, and Δneff and fiber length l are taken to be 2 × 10−3 and 16 cm, respectively. It can be seen that the sinusoidal spectral can be well flatted when η approaches to be 0.7, and the flat-top passband of 1-dB bandwidth approaches 55% of the spectral spacing.
Fig. 2 Theoretical transmission spectra of a cascaded AS-PBF-based MZI with different offset amount of splice 3.
3. Device fabrication
The AS-PBF we used is fabricated by Yangtze Optical Fiber and Cable Company (YOFC co., China) with a plasma chemical vapor deposition (PCVD) process. As shown in Fig. 3(a), in this type of AS-PBF the Ge-doped high-index rod is surrounded by an index-depressed layer doped with fluorine, and both the transmission loss and bend loss can be effectively reduced [13]. The outer diameter of the fiber is 123 µm and the core diameter is around 11.8µm. The rod-to-rod spacing pitch A is 9.3 µm, and the relative diameters of high-index rods and depressed layers are dGe/A = 0.39 and dF/A = 0.7, respectively. The refractive index difference of the germanium-doped and fluorine-doped area are approximately ΔnG = 3.45 × 10−2 and ΔnF = −7.23 × 10−3, respectively. The first band gap formed by periodically arranged high-index rods is from 1140 nm to 1850 nm in which LP01 mode and LP11 mode could be guided with less transmission loss in a short AS-PBF.
Fig. 3 (a) cross section of AS-PBF and enlarged unit cell of high-index rod; (b), (c) and (d) are the x- and y-axis side views of splice 1, splice 3 and splice 2, respectively; (e) schematic of experimental setup with cascaded AS-PBF MZI.
The AS-PBF is unjacketed with polymer coating, and a commercial fusion splicer (Fujikura FSM-60s) is used to splice it with SMFs in a manual mode, its micro-positions are manually adjusted in the x- and y- axes at the butt position. From the early reports and our previous work [14], we know that the higher order core modes can be excited by laterally core-offset splicing between sensing fiber and lead fibers, so here, this strategy is also employed to excite more power of LP11 mode.
Firstly, an original single MZI is produced with permanent core-offset splice 1 and 2, and the side-views shown as Fig. 3(b) and Fig. 3(d). The amount of core offset is estimated to be 2 µm, and total insertion loss is reduced to be around 2 dB. Consequently, the AS-PBF is cut off from its central position, and the two fiber stubs are butt-coupled. Their offset micro-position along x- and y-axis and rotated angle along fiber-axis are adjusted meticulously, and when an optimal tailored interference spectral with flat-top response is observed, arc discharge is released to form splice 3(side view shown as Fig. 3(c)). The total insertion loss resulting from slightly misaligned splices is around 4 dB. Different from the splice between SMF and air-hole-cladding photonic crystal fiber, by applying high arc discharge intensity, a good physical strength splice joint could be obtained with no additional insertion loss between SMFs and such an all-solid photonic bandgap fiber. In experiment, it is tested that the fiber could be circled to be a loop with 3 cm diameter or a maximum longitudinal strain of 3000 µε could be applied before breaking. A staircase-like core-offset direction of the three splice points along a single x- or y-axis could benefit to the formation of flat-top profile and the improvement of the interference depth. A broad band source is employed as an incident light source and an optical spectrum analyzer (OSA, Agilent 86146B) is used to monitor the interference spectra in real time. The experimental setup is shown as Fig. 3(e).
4.Output spectra and discussions
We, firstly, checked the sinusoidal interference spectra of the original single MZIs enabled by splice 1 and splice 2. Its fringe space can be expressed by Λ = λ2/(Δneff⋅l) in theory. Various samples of MZIs with different lengths of AS-PBF are fabricated in experiment. With the knowledge of fringe spacing Λ and fiber length l in experiment, we can get the experimental effective refractive index difference of Δneff = 2.16 × 10−3 between LP01 mode and LP11 mode at 1546 nm, which agrees well with the theoretical value of 2.18 × 10−3. It is confirmed that LP11 mode is mainly excited by offset splice 1 in experiment.
Figure 4(a) shows the transmission spectra with different core-offset amount along x-axis at position 3 as the AS-PBF is cut off from its central position and butt-coupled. The AS-PBF length is l = 118 mm. The top panel shows the spectra with no offset at position 3 which corresponds to that of an original single MZI. The following second panel shows the spectra after introducing of one-step offset along x direction at position 3. It can be seen that the original interference spectrum is modulated periodically, and every other interference fringes are deepened and around those main dips locate minor fringes with reduced extinction ratio. With three-step offset, the spectrum is well tailored and a flat-top profile can be observed, and simultaneously the main dips are deepened to be 15 dB, as shown in the third panel of Fig. 4(a). However, with excessive offset amount, the sinusoidal spectrum appears again with fringe space enlarged two times as shown in the last panel.
Fig. 4 (a) Evolution of the interference spectra with different core offset amount in butt-coupled position 3; (b) FFT spatial spectra with different core-offset amount in butt-coupled position 3, and the inset is an enlarged view from 1538 to 1542 nm with different offset amount
Fast Fourier transformation is taken to get the corresponding spatial frequency spectra at each offset step, the results are shown as Fig. 4(b). For the original single MZ with cavity length of l, the interference spectrum is sinusoidal and only one dominant peak of 0.104 nm−1 in spatial spectrum is observed. As the core-offset amount increases at butt-couple position, another frequency of 0.052 nm−1 appears with gradually increased amplitude. With three offset steps, the amplitude ratio of 0.104 nm−1 to 0.052 nm−1 reaches 2.14, that is, the contribution of the MZ with l/2 cavity in the total interference spectrum is 0.68, which agrees well with the theoretical analysis. As the offset amount continues to be enlarged, the spatial frequency of 0.104 nm−1 gradually disappears, which means that the MZI with cavity of l doesn’t work anymore. The inset of Fig. 4(b) shows an enlarged view of the corresponding spectra from 1538 to 1542 nm with different offset amount, which also shows a well agreement between theoretical and experimental results.
After the optimized three-step core-offset amount is chosen, the arc discharge is released at position 3, and thus, an all-fiber comb filter with flat-top spectral profile is constructed permanently. Based on such a cascaded AS-PBF MZI, the flat-top response is controllable and comb filters with desirable optical characteristic could be designed. Figure 5(a) shows a typical spectrum of the flat-top comb filter with l = 158 mm. The expanded view of four channels in a wavelength range of 1525nm to 1585nm is shown as Fig. 5(b) and their corresponding optical specifications are listed in Table 1. The channel extinction ratios are measured to be ~15 dB, and the channel spacing is around 15 nm. The average 1-dB passband and 3-dB passband width in a large wavelength range from 1400 nm to 1600 nm are around 8.0 nm and 10 nm, respectively.
Fig. 5 (a) Output spectrum of the AS-PBF-MZI-based comb filter; (b) Expanded view of optical channels from 1525 nm to 1585 nm.
Table 1. optical properties of AS-PBF-MZI-based comb filter.
Since the elongation of AS-PBF induced by longitudinal torsion could result in the wavelength shift of intermodal interference pattern, the comb filter can be tunable by applying a longitudinal force on the AS-PBF. Figure 6(a) shows its spectral response for the comb filter with l = 158 mm. As the applied strain increases, the interference pattern shifts towards shorter wavelength with a speed of 1.96 pm/µε as shown in Fig. 6(b), and the corresponding maximum wavelength tuning range of channels approaches to be ~4 nm during which serious degenerations of the channel isolation and flatness of the filter are not observed. If the channel spacing is made to be narrow than 4nm, it is possible to fully tune a period of the interference spectrum by longitudinal torsion. Its temperature response is also checked, however, the sensitivity of 10.6 pm/°C with ambient temperature fluctuation could be alleviated by such a flat-top spectral profile.
Fig. 6 (a) Filter spectra with longitudinal strains of 0 and 1850 µε, respectively; (b) Temperature response and tunable channel characteristic of the comb filter with AS-PBF length of 158 mm.
The stability of the comb filter is essential for practical applications. It is observed that the maximum wavelength shift within 42 hours is ~0.05nm when the flat-top comb filter is placed at a long copper tube and kept at 25°C, and the measured data is shown as Fig. 7. As the comb filter is constructed by AS-PBF, the calculated average dispersion coefficients at the passband are around 11.2 ps/(km⋅nm) for LP01 mode and −37.5 ps/(km⋅nm) for LP11 mode. Therefore, the dispersion for our comb filter is very small and can be neglected.
5. Conclusion
In summary, an in-line flat-top comb filter is proposed and constructed with a cascaded AS-PBF MZI. It consists of two short pieces of AS-PBF and two standard single-mode fibers as lead fibers with core-offset splices between them. By employing a cut and resplice process on the central position of AS-PBF, the desired flat-top spectral profile can be tailored by the well controlled offset amount of the resplice. The channel isolation is 15 dB and total insertion loss is around 4 dB. The channel spacing is slightly large for realizing ITU-T grid, e.g., 1.6 nm or 0.8 nm. If the AS-PBF with a length large than 100 cm is employed, the channel spacing can be narrowed to 1.6 nm or 0.8 nm. However, a long straight AS-PBF filter is not convenient for practical application. When the AS-PBF filter is circled to a loop, the LP11 is certainly sensitive to bend and experiences large transmission loss, which makes the extinction ratio decreased. However, if a redesigned AS-PBF which has large intermodal effective refractive index difference and a relatively long fiber are employed for modal interferometer, a compact filter with the channel spacing down to 1.6 nm could be fabricated possibly.
Acknowledgments
This work is supported by Doctoral Fund of Ministry of Education of China (No. 20114408120002), the National Science Foundation of China (No. 61275125) and the Basic Research Program funds of Shenzhen. The authors are also grateful to YOFC co. for providing our PCFs.
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