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The polarization filter characters of a gold-coated and liquid-filled photonic crystal fiber are studied using the finite element method. Results show that the resonance strength and wavelengths are different in two polarized directions. Filling liquid of refractive index (purified water) in holes in longitudinal direction can increase the loss of core mode polarized in the y-direction around the resonance peak. The resonance strength is much stronger in y-polarized direction than in x-polarized direction. The resonance strength can achieve 508dB/cm in y-polarized direction at the communication wavelength of 1311nm in one of our structures. Moreover, the full width half maximum is only 20nm. Such a small number makes such photonic crystal fibers promising candidate to filter devices. A liquid filled PCF of the small hole in the fiber core is designed and we find that filling liquid increases the resonance strength peak by thirty eight percent for the y-polarized resonance point.
©2013 Optical Society of America
1. Introduction
Since its first proposed in the early 90's, photonic crystal fibers (PCF) have driven lots of research activities all over the world [1]. Contrary to the conventional fibers, PCF offer people extra freedom in controlling the propagation of light inside them. The research on PCFs has promoted the development of the optical devices. Early research on PCFs focuses on the impact of different geometries on the characteristics of PCF, such as dispersion and nonlinearity [2]. Recently, other aspects of PCF have been explored, such as injecting gases [3], liquid crystals [4], filling or coating metal [5,6] in the air holes, and many interesting phenomenon have been observed. Such field is still going on and draws lots of research interests.
In recent years, surface plasmon resonance (SPR) has attracted much research attention all over the world. In the metal-filled or -coated PCF, the surface plasmon polariton (SPP) [7] can form on the surface of the metal, so the core guided light can be coupled with the SPP when the phase matching condition is met. Many researchers have drawn the metal-filled and -coated PCF by various methods. X. Zhang et al. [8] have selectively coated the silver on the inner walls of the fiber firstly, and used it to fabricate a in-fiber absorptive polarizer. H. K. Tyagi [9] reported the successful production of high-quality gold wires, with diameters down to 260 nm, by direct fiber drawing from a gold-filled fused-silica cane. W. Lee et al. [10] drawn the metal-filled PCF successfully and observed polarization-dependent coupling from the fiber core to the SPP resonances on the gold wire. B. H. Kim et al. [11] have demonstrated the large temperature sensitivity of the sagnac loop interferometer based on the birefringence of holey fiber filled with metal indium experimentally. De Matos, C.J. et al. [12] filled liquid into the core of a hollow-core PCF and a different liquid into its cladding. The SPP in PCFs have been used in many optical applications, most of which are sensors [13–16] and polarization splitters [17, 18].
The polarization splitter is one of the important parts of the optical integrated devices and has been designed by many researchers. Most of them designed the polarization splitter based on the coupling theory. The coupling length between the two orthogonal polarization directions can be decreased by increasing the birefringence, which could be achieved by either changing the sizes or the locations of the air holes [19] or using materials with high birefringence [20]. Akira Nagasaki et al. [21] have numerically investigated the polarization characteristics of PCF selectively filled with metal wires into cladding air holes, but the resonance strength is not strong enough and there are more than one resonance peak.
There are many polarization splitters based on metal-filled and -coated PCF. The metal-coated PCF not only saves the metal but also has a stronger resonance strength than that of the metal-filled PCF. In this paper, we investigated the polarization characteristics of gold-coated PCF filled with liquid of in the holes of the longitudinal (y-polarized direction) by the finite element method (FEM). The results show that the resonance peaks and wavelengths can be altered by adjusting the thickness and size of the metal, the birefringence of PCF. The resonance strength in y-polarized direction is much stronger than that in x-polarized direction around the resonance peak, which is extremely beneficial for the study of the polarization filter. Finally, a PCF which has a small hole in the fiber core is studied.
2. The structure and basic theory
The cross-section of the PCF suitable for the polarization filter is shown in Fig. 1. The PCF consists of five layers of air holes in the hexagonal structure. The diameter of the small air holes is d3 = 1.2μm. The diameter of the two big air holes in the horizontal direction is d1 = 2μm, which is beneficial for producing the birefringence. The pitch between two adjacent air holes is = 2μm. The black sections of the holes of d2 are coated with metal of Au, on whose surface SPP mode can form. To increase the loss in y-polarized direction, a liquid of is filled into the holes that are marked by the gray color.
The background material is pure silica. For the accurate calculation, its material dispersion is considered using the Sellmeier equation [22]. The water absorption loss is very small and is not considered in our calculation. The material dispersion of gold is characterized by a Drude-Lorentz model [23]. The modal loss can be defined as
where is the wavelength of light, is the imaginary part of the effective refractive index. The full width at half-minimum (FWHM) of the loss curve is a very important parameter because it corresponds to the bandwidth of the polarization filter. To decrease the energy loss, a perfectly matched layer and a scattering boundary condition are used in the calculation. The core guided light will couple to the SPP mode, when the phases of them match. So the loss of the fiber core will increase quickly at this wavelength.3. Simulation results and analysis
The dispersion relation of SPP modes for various-orders, together with the fiber core mode, and the losses of the core mode are shown in the Figs. 2(a) and 2(b), respectively. The refractive indexes of the fundamental and the first-order SPP modes are much higher than refractive indexes of the fiber core modes making them very difficult to couple these SPP modes to the fiber core modes. Higher order (2-nd or 3-rd) SPP modes can be coupled to the core guided modes when the phase matching condition is satisfied (resonance wavelength). Furthermore, the resonance wavelength corresponds to the point where the phases of the high order SPP mode match exactly. In Fig. 2(b), we can find out that the coupling between the second-order SPP mode and the core guided mode (absorption peak around 1.3 μm) is much stronger than that between the third-order SPP mode and the core guided mode (absorption peak around 0.9 μm).
Fig. 2 The dispersion relation of SPP modes for various-order and the fiber core mode in (a) and the loss spectra of core mode in (b).
From Fig. 3 we find that the resonance wavelength (1311nm) in the y-polarized direction lines in the communication wavelength. The loss reaches to 508.6dB/cm and the FWHM is only 20nm. These characteristics make such PCF a promising candidate for polarization filter devices. We plot the fundamental mode distributions at the wavelength of 1311nm in x- (a) and y-polarized (b) in Fig. 3. Indeed, one can clearly see that the coupling of the core guided mode to the SPP mode is much stronger in the y-polarized direction.
Fig. 3 Fundamental mode distribution in x-polarized (a) and y-polarized (b) directions at the wavelength of 1311nm.
The polarized filter characteristics can be altered by changing many parameters of the PCF. In this section, the impact of the birefringence of PCF, the thickness and the outside diameter (d2) of the metal layer will be discussed. Note that we only consider the second-order SPP mode here since we know from the previous section that the coupling between third-order SPP mode and the core guided mode is very weak.
In the previous section, we mentioned that the birefringence of PCF can lead to a situation where the resonance wavelength are different in two polarized directions and the resonance strength is much stronger in y-polarized direction, a feature that is beneficial for a polarizing filter. Therefore in this section, we studied the impact of the birefringence of the PCF by changing the diameter of two big air holes (d1).
Figure 4 shows the loss of the core guided mode as a function of the diameters of the big holes. The diameter of the big air holes is changed from 1.6μm to 2.2μm, while the diameter of other holes is 1.2μm. Generally the birefringence of the PCF increases with the diameter of the air hole (d1) in the structure shown in Fig. 1. Loss increase when the diameters of the big holes are increased from 1.6μm to 2.0μm. However, loss does not increase further as the birefringence of the PCF keeps increasing. Indeed, loss for a diameter at 2.2 μm is smaller than that at 2.0 μm, as can be seen from Fig. 4. This happens because the electric field energy of the core guided mode couples not only to the SPP mode of the gold, but also to the liquid in the four holes at the resonance point when the diameter is 2.0 μm. Another interesting point is that the phase matching point shifts to the longer wavelength direction as the diameters increases. It is worth noting that the loss is more than twenty times stronger in y-polarized direction than that in x-polarized in the resonance peaks, a feature that is beneficial for single polarized filter. So we can adjust the birefringence of the PCF to build selective polarized filter.
Fig. 4 Variation of the loss follows with the birefringence of PCF. The solid and dash lines are the loss of core guided modes in y-polarized and x-polarized direction respectively.
Surface plasmon waves are very sensitive to the thickness of the metal layer. Figure 5 shows the variation of the loss as the thickness of the gold is increased from 0.03μm to 0.06μm, while the other parameters of the PCF are fixed: the pitch between the adjacent air holes Λ = 2.0μm, the diameter of big air hole d1 = 2.0μm and the diameter of other hole is d2 = d3 = 1.2μm. From Fig. 5, we learn that the resonance wavelength moves to shorter wavelength as the metal thickness increase. However the resonance strength does not increase monotonically with the metal thickness, rather, it only increases within a certain range, which agrees with the finding in [24]. Therefore, one needs to carefully choose the appropriate thickness of the metal layer in order to achieve the desired polarization filtering effects.
Fig. 5 Variation of the loss as the thickness of the gold is increased from 0.03μm to 0.06μm. The solid and dash lines are the loss of core guided modes in y-polarized and x-polarized direction respectively.
As can be seen from Figs. 4 and 5, the resonance wavelengths are shorter and the resonance strengths are much greater for the y-polarized direction than the x-polarized direction. This feature can be used to filter light in one direction since loss in one polarized direction is so much stronger than the other.
Loss of the guided modes not only depends on the birefringence of the PCF and the thickness of the metal layer, but also depends on the outside diameter of gold. To investigate this dependence, we increase d2 from 1.0 to 1.4μm, and plot the variation of the loss in Fig. 6. Note that in all these simulations, we keep other parameters unchanged: the diameter of the big air holes is 2.0μm, the other diameter of holes is 1.2μm and the thickness of the gold layer is 0.04μm. As illustrated in Fig. 6, the loss of the PCF is greatly affected by the diameter of the holes coated metal. More specific, the loss coefficient for the y-polarized direction increase rapidly from 178 to 553 dB/cm as the diameter is increased from 1.0 to 1.4 μm. This increase in the loss coefficient is expected: as the diameter increases, metal (Au) becomes closer to the fiber core, leading to the enhancement of the coupling from the core guided mode to SPP modes.
Fig. 6 Variation of the loss as the outside diameter (d2) of gold is increased from1.0μm to 1.4μm. The solid and dash lines are the loss of core guided modes in y-polarized and x-polarized direction respectively.
The resonance wavelength can be tuned by a large amount by changing the diameters, as shown in Fig. 6. For example, a red shift of the wavelength of about 117nm can be realized by increasing the diameter from 1.0 to 1.2 μm. This important feature also tells us that the elective polarization filter built from such PCF can be realized by adjusting the diameter of these holes.
We consider the impact of filling liquid (n = 1.33) on the characteristics of PCF in this section. The parameters are chosen as follow: the diameter of the air holes is d2 = d3 = 1.2μm, d1 = 2μm, the pitch between two adjacent air holes is Λ = 2μm, the diameter of the small hole in the fiber core is 0.4μm. The liquid is filled in the center hole and the gray color hole (depicted in Fig. 1). The losses of liquid filled (red lines) and no liquid (black lines) PCF are shown in Fig. 7. As can be seen from Fig. 7, filling liquid affects the absorption peaks both for the x- and y-polarized directions. The y-polarized peak experiences a shift towards the shorter wavelength and increases, while the amplitude of x-polarized peak reduces by a large amount. Filling liquid into the holes can actually help improving the performance such PCF-based polarization filters. On one hand, liquid increases the absorption peak by about 38% from 343 to 474 dB/cm in y-polarized direction. On the other hand, liquid helps reducing the bandwidth of such filters: FWHM of the absorption peak is much smaller with the presence of liquid.
4. Conclusion
We have designed a PCF filled with liquid based on SPP, such a novel design PCF can be a promising candidate for polarization splitting devices. The resonance strength can reach 508 dB/cm in the y-polarized direction at 1311nm which is the communication wavelength, when the diameter of big air holes that lead to the birefringence is 2.0μm, the thickness of gold is 0.04μm and the diameter of other holes is 1.2μm. The resonance strength in y-polarized direction is far stronger than that in x-polarized direction around the resonance point. Numerical simulation results show that the filter characteristics are affected by the birefringence of PCF, the thickness of the gold, the size of the outer diameter of the gold layer. A liquid filled PCF of the small hole in the fiber core is designed. The resonance strength is much stronger in the liquid filled PCF at the y-polarized resonance point. Our design of PCF should be very useful in designing new types of polarization filters.
Acknowledgments
This study was supported by the National Natural Science Foundation of China (Grant Nos. 61178026 and 60978028), and the Natural Science Foundation of Hebei Province, China (Grant No. E2012203035).
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