Introduction

A symmetric 3×3 optical fiber coupler, where light is equally distributed at the three fiber outputs regardless of which fiber light is launched into, is a very useful device in applications such as fiber-optic gyroscopes [1], interferometers [2, 3], and fiber Bragg grating sensor interrogation [4]. The conventional method of making such a coupler is based on the fusion and tapering technique, where three identical single-mode fibers are fused together by using a suitable heat source (e.g., an electric arc) and at the same time tapered (by pulling) into a composite structure [5]. While this technique has been highly successful for the manufacturing of various kinds of 2 × 2 fiber couplers, it presents considerable difficulties in the production of 3 × 3 couplers (especially symmetric couplers), because of the much more stringent requirements in the handling of the fibers and the control of the fusion and tapering parameters. Nevertheless, fused tapered 3×3 fiber couplers are commercially available from a limited number of companies (see, for example, Ref. 6). In this paper, we propose a totally different approach of forming a symmetric 3×3 fiber coupler.

Our approach relies on evanescent-field coupling among three identical long-period fiber gratings (LPFGs). It is known that a LPFG formed in a single-mode fiber enables light coupling from the core to the cladding at specific resonance wavelengths and is intrinsically a band-rejection filter [7]. By placing two identical LPFGs in close parallel, the light spectrum rejected by one grating can be collected by the other grating, which results in complementary band-rejection and bandpass outputs from the two fibers, respectively [8, 9]. The principles of forming four-port [8, 9] and six-port [10] optical add/drop multiplexers (OADMs) with two and three parallel LPFGs, respectively, have been demonstrated. These devices are expected to find applications in coarse wavelength-division-multiplexed systems. In this paper, we show that a symmetric 3×3 coupler can be realized with three properly designed LPFGs placed side-by-side. Our technique requires only the assembly of three independently written LPFGs and is potentially a much more cost-effective technique for making symmetric 3×3 couplers.

1. Principle and experimental setup

 

Fig. 1. Realization of a 3 × 3 coupler with three parallel identical LPFGs.

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Figure 1 shows a schematic diagram of the 3 × 3 coupler, which consists of three parallel identical LPFGs of length L arranged in a symmetric triangular configuration. In practice, the three fiber sections that contain the gratings should be kept in close contact to each other. The refractive index of the surrounding medium can be changed by applying different index-matching liquids to the fibers. We consider the situation where light is launched into only one fiber, which is referred to as Fiber 1 (the input fiber). The other two fibers are referred to as Fiber 2 and Fiber 3 (the tapping fibers). The grating in the input fiber couples light from the guided mode to the cladding mode of the fiber. At the same time, the cladding modes of the other two fibers are excited through evanescent-field coupling between the three parallel fibers. They are coupled to the guided modes of the tapping fibers through their respective gratings. The efficiency of the process depends critically on the efficiency of the evanescent-field coupling between the cladding modes and hence the surrounding refractive index.

The resonance wavelength of a LPFG, λ ₀, is determined by the phase-matching condition [7]: λ ₀ = (N ₀₁ - N _0m)Λ, where N ₀₁ and N _0m are the effective indexes of the LP₀₁ guided mode and the LP_0m (m = 2, 3, 4, ⋯) cladding mode, respectively, and Λ is the pitch of the gratings. We denote the amplitudes of the LP₀₁ and LP_0m modes in the three fibers as A_i(z) and B_i(z) (i = 1, 2, 3), respectively. By extending the coupled-mode equations for two parallel LPFGs [8], we have

where δ= (2π/Λ)[λ ₀/λ-1] is a measure of the detuning of the operating free-space wavelength λ from λ ₀, κ_i are the coupling coefficients of the individual gratings [7, 11], and C is the coupling coefficient of two parallel fibers for the LP_0m modes [8, 9]. Assuming identical gratings, i.e., κ ₁= κ ₂ = κ ₃ ≡ κ, we solve Eq. (1) numerically with MATLAB and identify many conditions that can lead to equal power distribution at λ ₀ among the three fibers. The preferred conditions should also give a low power in the cladding modes at the outputs, because the power in the cladding modes is not collected by the fibers and therefore is considered to be a loss. A preferred condition for the gratings is κL = π and the corresponding CL value is 1.54. With these design values, the total power lost to the claddings is only 0.17 dB.

The 3×3 coupler considered here differs from the six-port OADM reported earlier [10] in two important aspects. First, the configuration of the OADM is asymmetric, where the grating in the input fiber is displaced from the other two gratings by an offset distance in the longitudinal direction. The offset distance is essential for the optimization of light coupling to the two channel-dropping fibers. On the other hand, the three gratings in the present coupler must be placed side-by-side and no offset distance between them is allowed, so that the performance of the coupler is independent of the input port (this is the requirement for a symmetric 3×3 coupler). Second, the OADM must provide an output with a deep notch at the operating wavelength. The gratings should be designed to give κL = π/2. On the other hand, without any offset distance, the interaction length available for evanescent-field coupling in the present coupler is limited by the grating length. A significantly larger coupling coefficient κ must be used to allow the light in the rejection band to couple to the cladding of the input fiber over a much shorter distance. This is the reason why the condition κL = π is chosen for the 3×3 coupler. It is known that the transmission of a LPFG at λ ₀ varies as cos²(κL) [7]. Therefore, a grating with κL = π/2 couples all the light at λ ₀ from the core to the cladding at the end of the grating, while a grating with κL = π couples all the light at λ ₀ to the cladding at the mid-way along the grating and then back to the core at the end of the grating, i.e., it functions as an over-coupled grating. In practice, it is more difficult to write high-quality gratings with larger values of κL.

2. Experimental results and discussion

Three LPFGs were fabricated in our laboratory, which were practically identical for our purpose. Each of them was written in a B-Ge co-doped photosensitive fiber by irradiating the fiber with a 248-nm ultra-violet (UV) excimer laser through an amplitude mask [7]. The index modulation in the fiber and hence the coupling coefficient κ was controlled by the UV dosage. By monitoring the transmission spectrum of the grating in real time during the UV-writing process, we were able to determine the value of κL [11]. The grating was 32-mm long and had a pitch of 320 μm. The coupled cladding mode was identified to be the LP₀₈ mode. The evolution of the transmission spectra of the grating measured at 200, 600, 1200, and 2100 UV pulses, respectively, is shown in Fig. 2(a). The initial resonance wavelength of the grating, λ ₀, appeared at ~1480 nm. When the number of UV pulses was increased, the resonance wavelength shifted to the longer wavelength and the contrast of the grating increased till it reached the maximum, in which case the value of κL was equal to ~π/2. When the number of UV pulses was increased further, the contrast at λ ₀ decreased. As it approached zero, we knew that the value of κL was close to π. It is seen from Fig. 2(a) that much more UV pulses were needed to bring κL to π. In general, the writing efficiency of a LPFG changes with the cladding mode order. According to our experiences, the writing efficiency of the LP₀₈ mode is among the highest for the photosensitive fiber we used. Therefore, the LP₀₈ mode was selected to minimize the number of UV pulses needed and hence the chance of damaging the fiber by excessive UV exposure. It should be noted, however, that gratings that couple to other cladding modes can also be used to construct the coupler. Fig. 2(b) shows the transmission spectra of the three gratings measured in air. The contrasts of the three gratings at λ ₀ were measured to be -0.23 dB, -0.50 dB, and -0.55 dB, respectively. The final resonance wavelength of the gratings was 1580.5 nm, which differed from the initial resonance wavelength by about 100 nm. The results suggest that the UV pulses had introduced a significant change in the average refractive index of the fiber core. It is seen from Fig. 2(b) that a side dip with a contrast of several dBs is present at a shorter wavelength (1551 –1554 nm), which is common for an over-coupled grating [11].

 

Fig. 2. (a). Evolution of the transmission spectra of the LPFG measured at 200 (green), 600 (blue), 1200 (red), and 2100 (black) UV pulses, respectively. (b) Transmission spectra of the three fabricated LPFGs measured in air, showing low contrasts at the resonance wavelength λ ₀.

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In our experiments, the three gratings were secured in two separated V-grooves on the two sides of the gratings. Suitable tension was applied along the fibers to keep them straight and in close contact with each other. Care was taken to ensure that the three gratings were placed side-by-side without introducing any offset between them. Light from a commercial (C+L)-band amplified spontaneous emission source was launched into one fiber (Fiber 1) and the output spectra of the three fibers were measured with an optical spectrum analyzer. The surrounding refractive index was varied by applying different index-matching liquids to the fiber sections that contained the gratings. The following refractive indices (provided by the supplier for the wavelength 589.3 nm) were used: 1.404, 1.420, 1.432, 1.440, 1.448, and 1.450. With the surrounding refractive index increased from 1.0 (air) to 1.450, the resonance wavelength of the gratings was found to shift towards the shorter wavelength by ~90 nm, which is similar to the result measured for a grating with κL = π/2 [12]. As the surrounding refractive index was increased, we observed that the power output from Fiber 1 (the input fiber) dropped and, at the same time, the power outputs from the other two fibers increased. The observed results can be understood by the fact that the strength of evanescent-field coupling between two parallel LPFGs increased with the surrounding refractive index [9]. As the surrounding index was increased, the evanescent field of the cladding mode spread more into the surrounding medium and, as a result, more light from the cladding of the input fiber coupled to the other two fibers and less remained in the input fiber.

The change in the ratio of the output power to the input power with the surrounding refractive index measured at the resonance wavelength for the three fibers is shown in Fig. 3. It is seen from Fig. 3 that the output power splitting ratio can be tuned over a wide range by controlling the surrounding refractive index. When the surrounding refractive index was equal to 1.448, the output power ratios of Fiber 1, Fiber 2, and Fiber 3 at the resonance wavelength (1505.5 nm) were measured to be -6.29 dB (23.5%), -6.16 dB (24.2%), and -6.22 dB (23.9%), respectively, which correspond to power splitting ratios of 32.8%, 33.8%, and 33.4%. We may say that the light was distributed almost equally among the three fibers (the non-uniformity was only 1%). The total power coupling efficiency of the coupler at the resonance wavelength was ~72% (i.e., the sum of the three power ratios), which corresponds to a loss of ~28% (~1.4 dB) of the input light or ~0.46 dB/port. The loss is believed to be mainly due to incomplete coupling among the fibers (i.e., there was still some light in the claddings at the fiber outputs). This excess loss is comparable to that of the commercial fused tapered 3×3 coupler, which has a typical excess loss of 0.2 – 0.4 dB/port [6]. The bandwidth of our coupler is also comparable to that of the commercial one. Simulation results calculated for the fiber, which has a core index of 1.4495, a core radius of 3.6 μm, a cladding index of 1.444, and a cladding radius of 62.4 μm, are also shown in Fig. 3 for two values of fiber separation. In the simulation, the coupling coefficient of two parallel fibers C was calculated from the fiber parameters given above [9] and the coupling coefficients κ_i were deduced from the contrasts of the gratings measured at λ ₀ with different surrounding refractive indices (note that the normalized contrast at λ ₀ is given by cos² κ_iL [7, 11]). The detailed measurement results used in the simulation are listed in Table 1. Using these values of C and κ_i, we solved Eq. (1) with δ= 0 (i.e., at λ ₀) and calculated the power ratio |A_i(L)|²/A ₁(0)|² (Fiber 1 as the input fiber). As shown in Fig. 3, the experimental results agree well with the simulation results.

 

Fig. 3. Dependence of the ratio of the output power to the input power with the surrounding refractive index measured at the resonance wavelength for the three fibers: (엯) Fiber 1 (input fiber), (◻) Fiber 2, and (▵) Fiber 3. Simulation results for two values of fiber separation d are shown for comparison.

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Table 1. Normalized contrasts of the three gratings measured at the resonance wavelength with different surrounding refractive indices.

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To demonstrate the symmetry property of the coupler, light was launched into the three fibers alternately and the transmission spectra of the fiber outputs were measured for each case with the surrounding refractive index fixed at 1.448. The results are shown in Fig. 4. It is seen from the figure that the output spectra for the three cases are almost the same. The coupler functioned as an equal power splitter at the resonance wavelength, regardless of which fiber was used as the input port. The small differences in the output spectra in the three cases were caused by the slight differences in the characteristics of the individual gratings.

 

Fig. 4. Normalized output spectra from the three fibers measured with a surrounding index of 1.448, when broadband light was launched into (a) Fiber 1, (b) Fiber 2, and (c) Fiber 3, respectively.

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For the development of a practical device, the gratings must be embedded in a stable low-index material (polymer or glass), instead of an index-matching liquid, whose strong temperature dependence in the refractive index affects the thermal stability of the coupler. We are currently working on a solution to the packaging problem based on placing the gratings in a properly designed groove that is subsequently filled with a low-index UV-curable epoxy. The temperature-compensation techniques developed for fiber grating packaging could be adapted for the packaging of the LPFG couplers. Polymer blending [13] could lead to a low-index material with an ultra-low thermo-optic coefficient suitable for packaging of LPFG couplers.

3. Conclusion

We demonstrated a symmetric 3 × 3 coupler as an equal power splitter with three parallel identical LPFGs. Using three 32-mm-long over-coupled gratings and a suitable surrounding refractive index, we achieved a total coupling efficiency of ~72%, which is equivalent to a total loss of ~1.4 dB or a loss of ~0.46 dB/port. The non-uniformity in the splitting ratios obtained was ~1%. The performance of the coupler is comparable to that of the commercial fused tapered coupler. There should be room to further improve its performance by improving the quality of the gratings. The coupler should find many potential applications in optical sensors and communications. Its wavelength selectivity and splitting-ratio tunability (by changing the surrounding index) may open up new applications. We believe that our technique of making symmetric 3 × 3 couplers is potentially much more cost-effective than the conventional fusion and tapering technique.