1. Introduction

Photonic crystal fibers (PCFs) with air holes along the entire fiber length are one of the most successful photonic crystal applications. There are two guiding mechanisms in the PCF structures. One is the totally internal reflection (TIR) due to the refractive index of the solid core is larger than that of the air-hole cladding region [1, 2]. The other is the photonic band gap (PBG) effect resulting from the periodical air-hole array in the cladding [2, 3]. Many research efforts have been devoted to studying PCF structures for their amazing propagation characteristics, such as the endless single-mode operation [4], tailorable dispersion [5–7], high birefringence [8, 9], and large nonlinearity [10, 11]. All these useful properties are primarily determined by the size and arrangement of the air holes in the cladding region. Nevertheless, once a PCF is fabricated, it is hard to modulate its optical properties to function as a tunable optical device.

To introduce tunable optical properties into the PCF structures, one can infiltrate high-index liquids (or liquid crystals) into the air holes of the PCFs to form the liquid-filled PCFs [12–21]. The refractive index of the infused liquid can be varied by the operation temperature [13–15] or the external electric field [16, 17] to modulate the performance of the liquid-filled PCFs. These tunable PCF structures can be utilized in dispersion-related devices [13, 14], switches [15, 16], filters [17, 18], laser sources [19], and waveguide sensors [20, 21]. However, in most liquid-filled PCF applications the refractive index of the filling liquid is larger than that of the background material, which makes the liquid-filled PCF a pure PBG guiding structure and may destroy the single-mode operation. Besides, the propagation losses become much more serious in the liquid-filled PCFs for the finite liquid-hole layers and the lossy liquids infused in all the air holes of the cladding.

A. Bétourné et al. have utilized an extra air-hole ring on the outside of the cladding to reduce the bend loss in solid-core PBG fibers, and very good experimental results have been demonstrated [22]. Here, we will apply this double-cladding structure into the liquid-filled PCFs by selectively filling the high-index liquid into the PCFs to decrease the propagation losses and maintain the tunability properties. The effect of the number of air-hole layers will be theoretically investigated by using a full-vector finite-difference frequency-domain (FDFD) method [23]. Furthermore, we will also consider the complementary structures which contain liquid-hole layers on the outside of the air-hole cladding to find out their possible applications.

 

Fig. 1. (a). Internally liquid-filled PCFs with 1, 3, and 5 air-hole layers lying outside the inner liquid-hole layers. (b). Externally liquid-filled PCFs with 1, 3, and 5 liquid-hole layers lying outside the inner air-hole layers.

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2. Geometry and the numerical method

We consider two kinds of selectively liquid-filled PCFs with their cross-sections shown in Fig. 1. The original PCF contains six air-hole layers in the cladding region, and the lattice constant and air-hole diameter of the PCF are Λ and d, respectively. By selectively filling the high-index liquid into the inner air-hole layers of the PCFs, we can have internally liquid-filled PCFs with air-hole layers lying outside the inner liquid-hole layers as demonstrated in Fig. 1(a). On the contrary, if we selectively infuse the liquid into outer air-hole layers, we can obtain the complementary structures, externally liquid-filled PCFs, with the solid core surrounding by the inner air-hole layers as shown in Fig. 1(b).

To manufacture these selectively liquid-filled PCFs, one must first selectively block specified air holes and infuse the liquid into the unblocked holes. One possible way is to employ the fusion splicing technique with tailored electric arc energies and fusion times [24]. The cladding region of the PCF can then be selectively fused, and the air holes are collapsed from the outer layers to the inner layers [24]. Another way to selectively plug specified airhole layers in the PCFs is using microscopically position tips with glue [25]. Not only air-hole layers but a single air hole can be easily blocked by using this technique. In spite of the above methods, one can also selectively infiltrate the liquid into specified air-hole layers from a macroscopic fiber preform to a connected microstructured PCF by using an applied pressure as described in [13].

The numerical method we employed to find out the propagation properties of the selectively liquid-filled PCFs is the Yee-mesh-based full-vector FDFD method which is an efficient and accurate numerical mode solver for the analysis of optical waveguides and PCF structures [23, 26]. For the symmetric geometry as shown in Fig. 1, only one quarter of the selectively liquid-filled PCF is taken into account, and the perfectly matched layers (PMLs) are adopted as the absorbing boundary conditions. To improve the numerical accuracy, the index averaging scheme is utilized in our FDFD mode solver to deal with the dielectric discontinuities in the selectively liquid-filled PCF structures [23].

3. Numerical results

We first consider the internally liquid-filled PCFs shown in Fig. 1(a) with Λ = 2.3 μm, d = 1.0 μm, and the refractive index of the lossless liquid n_q being 1.6. Figure 2(a) shows the modal effective indices n^eff’s of the fundamental guided modes on variant internally liquid-filled PCFs by utilizing the FDFD mode solver. The dashed line is the core line and the solid lines represent the boundaries of PBGs as all the air holes are filled with the high-index liquid. Without any liquids filled in the air holes, the guiding mechanism of the PCF is the TIR effect, and we can find out the fundamental guided modes in all the wavelength range as shown in Fig. 2(a). As all the air holes are filtrated with the liquid, the liquid-filled PCF turns into a pure PBG guiding structure due to that the liquid possesses larger refractive index than that of the solid core. One can only observe guided modes when the wavelengths are within the PBGs. Applying the selective filling techniques we have mentioned, we can then increase the number of outer air-hole layers, and the solid core is still surrounded by the liquid-hole layers. It can be seen that the effective indices of the fundamental guided modes are almost the same as the original liquid-filled PCF due to the PBG effect induced by the inner liquid-hole layers as demonstrated in Fig. 2(a).

 

Fig. 2. (a). Effective indices and (b) losses versus the wavelength for variant internally liquid-filled PCFs.

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The corresponding confinement losses are shown in Fig. 2(b). Compared with the original liquid-filled PCF with liquid filtrated in all the air holes, one can see that as we increase the number of outer air-hole layers, the confinement losses are decreased. These outer air-hole layers in the internally liquid-filled PCFs function as a second cladding which can reduce the penetration of the light fields. At the same time, the inner liquid-hole layers can still induce the PBG effect to support the centrally located guided modes and remain the tunability property. Figures 3(a) and 3(b) show the contours of the field distributions for the fundamental guided modes on the original liquid-filled PCF and the internally liquid-filled PCF, respectively, with the wavelength being 1.5 μm. It can be seen that the internally liquid-filled PCF has almost the same field distribution as the liquid-filled PCF for the existence of the inner liquid-hole layers. Besides, very small amount of the light field can be observed in the outer cladding region of the internally liquid-filled PCF due to the outer air-hole layers. Thus, smaller confinement losses for the internally liquid-filled PCFs can be obtained. Figure 3(c) shows the field pattern of the liquid-filled PCF with only four liquid-hole layers. Compared with Fig. 3(a), one can see that a large amount of the light field penetrates into the outer cladding region for the insufficient liquid-hole layers in the cladding region. Again, our proposed internally liquid-filled PCF demonstrates the good ability to reduce the penetration of the light field with the aid of the outer air-hole layers as shown in Fig. 3(b).

In previous studies, the liquid-filled PCFs are employed in many optical devices with the liquid infiltrated into all the air holes to supply the PBG effect and tunability properties [12–21]. To have a good PBG guiding, the number of the liquid-hole layers should be large enough which might increase the propagation losses for the lossy liquid filled in all the air holes. In the internally liquid-filled PCFs, the outer air-hole layers with smaller effective indices can provide the TIR effect to reduce the penetration of the light field. Meanwhile, the center solid core is still surrounded by the inner liquid-hole layers to maintain the PBG and tunability effects. The propagation losses can then be efficiently reduced as we adopt the internally liquid-filled PCFs in the designs of tunable optical devices. However, if we further increase the number of the outer air-hole layers, the PBG effect becomes weaker and weaker, especially at the PBG boundaries. The guiding mechanism switches to be the TIR effect at the PBG boundaries with a higher field intensity obtained within the liquid holes. Thus, we can find out low-loss guided modes outside the PBGs as shown in Fig. 2. Besides, the tunability optical properties which are based on the PBG effect may fail to be introduced due to the insufficient liquid-hole layers in the internally liquid-filled PCFs.

 

Fig. 3. Contours of the field distributions for the fundamental guided modes on the (a) original liquid-filled PCF with six liquid-hole layers, (b) internally liquid-filled PCF with two outer airhole layers, and (c) liquid-filled PCF with only four liquid-hole layers, respectively, as λ = 1.5 μm.

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The complementary structure of the internally liquid-filled PCF is the externally liquid-filled PCF with the high-index liquid filled in the outer air-hole layers as demonstrated in Fig. 1(b). Applying the FDFD method, we can find out the effective indices and confinement losses of the fundamental guided modes on variant externally liquid-filled PCFs as shown in Figs. 4(a) and 4(b), respectively. For there always exist air-hole layers around the center solid core, the guiding mechanism remains the TIR effect, and we can see the index curves of these externally liquid-filled PCFs are almost the same as the original PCF as shown in Fig. 4(a). As we increase the outer liquid-hole layers, fewer inner air-hole layers are left to provide the TIR effect, which raises the confinement losses as shown in Fig. 4(b). Besides, we can also observe larger values of the confinement losses as the wavelengths are outside the PBGs, which results from the existence of the outer liquid-hole layers. Eventually, no guided modes outside the PBGs can be found as all the air holes are filled with the liquid.

Liquid-filled PCFs have been applied in long-period fiber gratings with all the air holes in the cladding region infiltrated with high-index liquids, and the periodic perturbations are induced mechanically or electrically [17]. This kind of devices suffers the high propagation losses and the destruction to the single-mode operation due to the lossy and high-index liquids filled in all the air holes. By using the externally liquid-filled PCFs, the high-index liquid is filtrated only into the outer air-hole layers to reduce the utilization of the lossy liquid, and the periodic perturbations can still be induced electrically or mechanically to form the long-period fiber gratings. The propagation losses of the fundamental core modes can then be highly reduced due to that the lossy liquids are only in the outer layers and the single-mode operation can be remained for the existence of the inner air-hole layers. Please note that insufficient liquid holes in externally liquid-filled PCFs may not induce the tunability optical properties which are based on the PBG effect. At least 2 liquid-hole layers are needed to support the PBG effect as shown in Fig. 4(b).

From these simulation results, it can be seen that the confinement losses of our proposed selectively liquid-filled PCFs can be efficiently reduced due to the existence of the outer or inner air-hole layers. Besides, by varying the refractive index of the liquid in both the internally liquid-filled PCFs and externally liquid-filled PCFs, we can easily modulate their optical properties. Thus, our proposed selectively liquid-filled PCFs possess the potential to be utilized in the further applications of tunable optical devices with low losses.

 

Fig. 4. (a). Effective indices and (b) losses versus the wavelength for variant externally liquid-filled PCFs.

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5. Conclusions

Applying the full-vector FDFD method, we have successfully obtained the propagation characteristics of two kinds of selectively liquid-filled PCFs, internally liquid-filled PCFs and externally liquid-filled PCFs. The outer air-hole layers in the internally liquid-filled PCFs are shown to function as the second cladding to reduce the penetration of the light field, and the inner liquid-hole layers can still induce the tunable PBG effects. As for the externally liquid-filled PCFs, the outer liquid-hole layers can decrease the use of the lossy liquid with the inner air-hole layers surrounding the solid core to maintain the single-mode operation by the TIR guiding. By mechanically or electrically inducing periodic perturbations on the outer liquid-hole layers, we can obtain tunable long-period fiber gratings based on the externally liquid-filled PCFs. Both the proposed selectively liquid-filled PCFs can efficiently reduce the confinement losses and still possess useful tunability properties for optical devices applications.