A tunable fiber polarizing filter based on selectively filling a single hole of a solid-core polarization maintaining photonic crystal fiber with high index liquid are proposed and demonstrated. Two groups of polarization-dependent resonance dips in the transmission spectrum of the single-hole-infiltrated photonic crystal fiber are observed. Theoretical and experimental investigations reveal that these resonant dips result from the couplings between the silica core fundamental mode at x or y polarization and high order modes (TM01, TE01 and HE11) in the liquid core. Especially, a distinctive characteristic near the strongest resonant point (SRP) is demonstrated and revealed. The transmission loss and spectral shape at the SRP wavelength are extremely sensitive to the filling length and temperature (or Refractive Index, RI), which permits a fiber bandpass or bandstop polarizing filter with a good performance on tunability and controllability. Furthermore, the narrowband dips on both sides of the SRP wavelength have wavelength-dependent tuning velocities, providing a method to achieve flexible and controllable filters as well as two- or multi-parameter sensors with a compact structure.
© 2014 Optical Society of America
Optical fiber polarizing devices play significant roles in both optical communication systems and fiber sensing systems. Two common methods to construct fiber polarizing devices are used frequently. One method is writing grating on fiber and achieves fiber-grating-based polarizing devices, such as high-performance optical fiber polarizers based on long-period gratings in birefringent optical fibers or photonic crystal fibers (PCFs) [1, 2], and utilizing the strong polarization dependent loss of 45°-tilted fiber Bragg grating . The fiber-grating-based polarizing devices have some advantages such as low insertion loss, compact structure and narrowband spectrum. Another method is filling liquids into PCFs to realizing polarization-dependent devices, which are more easily tunable, controllable and can be flexibly designed than the one based on fiber gratings for the various properties of the functional materials. At 2011, Zheng et al. proposed a tunable single-polarization single-mode photonic crystal fiber based on selectively infiltrating liquid into air holes of a polarization maintaining photonic crystal fiber (PM-PCF) , and achieved a tunable sensitivity of about 1.975 nm/°C, which is three orders of magnitude higher than the polarizer based on a long-period fiber grating . In the same year, a fiber polarizer was demonstrated by partially liquid-filled some air holes of a hollow-core photonic crystal fiber , which is weak dependence on temperature. Also some anisotropic liquids are used to design fiber polarizing devices. Unlike the other fiber polarizing devices tuning by temperature, an electrically tunable and rotatable polarizer was designed by infiltrating liquid crystal into a PCF .
Although the fiber polarizing devices based on liquid infiltration proposed in the literatures have good performance on tunability and controllability, most of them are working on wideband and cannot be used as narrowband polarizing filter. Moreover, large insertion loss is also a major challenge affecting the practical application. In recent years, resonant dips as similar as fiber gratings, introduced by mode coupling between the silica core mode and liquid rod modes in selectively fluid-filled PCFs, provide a new way to design fiber narrowband devices. Wu et al. first proposed an ultrasensitive refractive index (RI) sensor by selectively infiltrating of a single hole with fluid along a PCF , and the LP01 core mode was coupled to LP11 liquid mode in an adjacent fluid-filled waveguide to generate resonant dips. Another higher sensitivity sensor was designed based on selectively filling a single air hole of a PCF, resulting in the resonance coupling from the LP01 silica core mode to the LP01 liquid rod mode . By filling two different liquids into two air holes of a PCF, Liang et al. simultaneously realized the mode coupling from LP01 silica core mode to LP01 liquid rod mode at 1310 nm and to LP11 liquid rod mode at 1550 nm . More recently, Luo et al. realized twin resonance couplings by filling only one air hole of a PCF and demonstrated ultrahigh sensitivity temperature (RI)/force sensors . However, the resonance couplings reported in the above-mentioned literatures are all based on symmetrical PCFs without or with weak polarization properties. Also no one pays attention to that how the filling fiber length, dispersion characteristics of the PCF and external parameters influence the spectral shape in resonant region.
In this paper, we present a fiber polarizing filter by selectively filling a single hole located at the cladding of a solid-core polarization maintaining photonic crystal fiber (PM-PCF) with a liquid prossessing refractive index of 1.51 at 589 nm. Two groups of polarization-dependent resonance dips are observed in the transmission spectrum. The polarization extinction ratio of the deepest dip is about 20 dB. Theoretical and experimental investigations reveal that these resonant dips result from the couplings between the silica core fundamental mode at x or y polarization and the high order mode (TM01, TE01 and HE11) in the liquid core while the filling length is far longer than coupling length, which is different from previous works of only paying attention to the single peak characteristics in the resonant region [7~10]. Especially, a distinctive characteristic near the strongest resonant point (SRP), where the refractive index difference between silica core fundamental mode and the high order modes (TM01, TE01, HE11) in the liquid core achieves the minimum, is demonstrated and revealed. The transmission loss and spectral shape at the SRP wavelength are extremely sensitive to the filling length and temperature (or RI) and permit a fiber polarizing filter with a good performance on tunability and controllability. The temperature tuning velocity of our polarizing filter is about 5 nm/°C and a hundred times than the one based on long-period fiber gratings . Furthermore, the narrowband dips on both sides of the SRP wavelength have wavelength-dependent tuning velocities, providing a method to achieve flexible and controllable filters as well as two- or multi-parameter sensors with a compact structure.
2. Experimental setup and operation principle
The experimental setup, as shown in Fig. 1(a), includes a supercontinuum light source, a polarizer, a polarization controller (PC), a filled PM-PCF in the temperature chamber and an optical spectrum analyzer (OSA). The spectrum range of the light source is from 600 nm to 1700 nm, and the OSA has a highest resolution of 0.02 nm.
The cross section of PM-PCF used here is shown in Fig. 1(b), which is fabricated by Yangtze Optical Fiber and Cable Company Ltd. of China. In the cross section of the fiber, there are five rings of air holes arranged in a regular hexagonal pattern with two larger holes beside fiber core along x axis. Hence, the PCF possesses birefringence property and has a high birefringence of about 6.25 × 10−4 at 1550 nm. The diameters of large holes and small holes are about 5.6 μm and 2.1 μm, respectively. The distance between adjacent small air holes is 4.9 μm. The single-hole-infiltration PCF as shown in Fig. 1(c) was realized by selectively infiltrating one air hole at the second layer of the PCF with a liquid which is produced by Cargille Laboratories Inc and possesses a refractive index of 1.51 at 589.3 nm for 25°C and a thermal-optic coefficient of −0.000404/°C. The filled hole could be considered as a liquid core waveguide.
Firstly, we theoretically investigated the characteristics of the single-hole-filled PM-PCF. All the theoretical calculations were based on the full-vector finite element method (FEM). As shown in Fig. 1(b), the hole-to-hole distance and the hole diameters of the PCF are not identical. While calculating this model by FEM tool, we found that changing the hole-to-hole distance or the diameters of the holes would mainly impact on the location of the resonant region, which would not impact on our qualitative discussion. Thus we used a perfect fiber model in our simulation calculation. Figure 2 shows the modal effective indices of the y-polarization HE11 silica core mode ny (red line), the liquid core TM01 mode nly (black line) and the liquid core HE21 mode n2y (olive line). And the dash line represents the resonant region, where the three modes coupled to each other. As the changing process of mode fields shown in Fig. 2(b), the silica core mode and the liquid core modes will not couple at shorter wavelength, and then experience a complex coupling process in the resonant region. While at longer wavelength, the mode fields of the three modes are exchanged and keep independent transmission. As seen from Fig. 2, in the center of the resonant region, the dispersion curves are close and their phase matching conditions are easy to meet, which means the mode couplings are strongest. While deviating from the center of the resonant region, the phase mismatch will be increased and the resonance will become weaker. The resonance situation of x polarization is nearly the same as that of the y polarization, except for a red-shift about 45 nm because of the high birefringence in the core. Although the resonant region described in Fig. 2 is more than 100 nm width, the strong coupling area is only existed at tens of nanometers wavelength range because of the phase mismatch when the wavelength deviates from the center of the resonant region. It means that in the strong resonant region, energy transfer from fiber core to liquid core occurs only for one polarized component, whereas optical energy for another polarized mode is only weak coupling to liquid core and can be approximately regarded as remaining inside the fiber core.
To simply analyze the particular coupling processes, we consider the solid core and the liquid core as parallel symmetric waveguide. When light coupling from the fiber silica core to the liquid core, the coupling length can be expressed as:
According to Eq. (2), we can calculate the transmission spectrum of the filled fiber, which will include some resonant peaks or dips if L>Lc. The wavelengths of the resonant dips satisfy:
In order to discuss the temperature response of the resonant dips, after taking the derivative of both sides of the Eq. (4) with respect to temperature, we deduce the temperature tuning velocity S of the dip wavelength as follows:
Where is the group refractive indices difference between two coupling modes, and dL/L is the coefficient of thermal expansion of the filled liquid, which is 0.0008 /°C here.
Paying more attention to the temperature response properties, the temperature tuning velocities in resonant region at two different temperatures were calculated and shown in Fig. 3. In our calculation, we chose the liquid core mode which has stronger coupling with the silica core mode and ignored the weaker coupling one. The black curves are the temperature tuning velocity at room temperature 25 °C while the red curves are that at 30 °C. For the black lines, they can be divided into two regions by the vertical line at about 1315 nm. The vertical lines stand for the zero denominators of Eq. (5) which results in theoretically infinite temperature tuning velocity at this temperature. In the region at the left of the vertical line, all the values of tuning velocities are negative, which means that a resonant dip locating at this region will experience a blue shift with temperature raising. The curves of the tuning velocities access gradually the vertical line. When the resonant dip is very close to 1315 nm, the absolute value of tuning velocity will increase rapidly. At the wavelength longer than 1315 nm, the tuning velocities abrupt change to positive values. In this region, the S is positive at shorter wavelengths while it is negative at longer wavelengths. It means that the dips locating at this region would experience either red shift or blue shift. In the blue-shift region, the absolute value of tuning velocities will increase with wavelength increasing. When we change the temperature of the PM-PCF, at 30 °C as shown in Fig. 3 (red curves), the curves of its temperature tuning velocities will undergo blue shift and maintain the properties above mentioned.
What we discussed above reveals that resonant dips at different wavelengths have distinct temperature tuning velocities. And according to the Eq. (4), the resonant dips’ locations are decided by the filling length L and the refractive index n of the filling liquid. The simulated normalized transmission spectra at different temperatures calculated by Eq. (2) are shown in Fig. 4. While we do the calculation, we prefer to ignore the influence of coupling strength in order to simplify the calculation, which would not impact our analyzing. The filling length L is set to 9.8 cm. Several dips are observed in the transmission spectra. Specially, a peculiar region appears at the middle of the transmission spectra which according to the wavelength position in the vicinity of the vertical line of Fig. 3. At the wavelength of the vertical line, where the refractive index difference between the silica core fundamental mode and the high order modes in the liquid core achieves the minimum and we call the wavelength as strongest resonant point (SRP). The SRP will be blue-shift with a shifting velocity about 6 nm/°C while temperature increasing. Furthermore, the spectrum at peculiar region will also vary its shape from peak to dip or even generate conjoint two dips.
Then we analyze how the filling length L influences the location of the resonant dip. Figure 5 shows the transmission spectra at 25 °C with three different filling lengths L of 10.1 cm (blue curves), 21.5 cm (red curves) and 42.5 cm (black curves), respectively. We can see that at the SRP of nearly 1315 nm, the shape of spectrum in the peculiar center region can be changed with different L/LC. In fact, the variation of the center shape is regular. With the filling length increasing, the center shape will firstly be changed from flat to concave. Then the concave would be split into two small incomplete dips. At last, the interval of the two small dips will increase and the two dips become complete. If the spacing increases longer, the center shape will come back flat and be like the original one. Based on the above investigation, the center shape can be determined by controlling either the filling length or the index of liquid (temperature). Another effect based on changing filling length is that the density of the dips will be changed. To see the variations of the dips clearly, we just draw the two dips closest to center at some filling lengths. When the filling length getting long, the spacing of the two dips beside SRP will reduce and their temperature tuning velocity will be changed. As shown in Fig. 5, while filling length is changed from 21.5 cm to 42.5 cm (the two dips in the black curves that closer to the center are not whole and only one status of the center shapes), the spacing is reduced from 12.4 nm to 11.7 nm. Above all, we can regulate the shape of the center, the density and the temperature tuning velocities of the dips. For these properties, we can control the location of polarization dependent resonant dips and the polarization extinction ratio of the center region. Therefore, a flexible polarizing bandpass or bandstop filter could be designed.
3. Experimental results and discussion
In experiment, one hole at the second layer of the PM-PCF as shown in Fig. 1(c) was selective filled by the direct manual gluing method  with liquid above mentioned. The length of the filled liquid is about 10 cm. When we spliced the fiber with standard singe mode fiber (corning SMF-28), the air holes of two ends of the PCF were left without fluid for reducing the splice loss. During all the measurements, the PM-PCF was located in the temperature chamber for changing the refractive index of the liquid.
Figure 6 shows the transmission spectra of two polarized lights at the resonant region at temperature of 16 °C. The black curve is the transmission spectrum of y-polarized and the red curve is that of x-polarized light. The insertion loss is less than 7 dB, which is mainly due to mode field mismatch of splicing between PCF and SMF. As same as the theoretical prediction, two groups of dips corresponding to two polarization states are observed in the transmission spectra and for every polarized light, the several dips change periodically with wavelength. Moreover, the resonant dips for the two polarized lights appear at different wavelengths, i.e. at specific wavelengths only one polarized light can transfer light from fiber silica core to liquid core while another polarized light is maintained at fiber silica core. The wavelength separation of the two groups of dips is about 33 nm. The largest polarization extinction ratio occurs at about 1356 nm (B1 point), which is about 20 dB. The variant depth of these dips mainly dues to the different phase mismatch as well as different coupling strength at different wavelength, which isn’t considered in the simulated spectra.
Then, we investigate the temperature tuning characteristics of this liquid filled fiber. Figure 7(a) shows the transmission spectrum at 23 °C, 30 °C, and 37 °C. With temperature raising, all the dips in the resonant region experience blue shift, and the changes of the spectra are the same as that of the simulation analysis in Fig. 4. The experiment results agree well with theoretical simulation. It’s worth to further discuss about the specific temperature tuning velocities of these dips. As shown in Fig. 7(b), the relationship between the resonant wavelengths and the temperature keeps a good linearity. Furthermore, we pay more attention to all these marked dips. The temperature tuning velocities of A1 ~ A4 and B1 ~ B3 are −5.75 nm/°C, −5.65 nm/°C, −5.61 nm/°C, −5.59 nm/°C, and −5.29 nm/°C, −5.37 nm/°C, −5.41 nm/°C, respectively, which is a hundred times higher than that of long period fiber grating-based devices . The variation trend of their temperature tuning velocities agree also with our theoretical calculation, and the difference of the tuning velocities between experimental and theoretical results mainly come from the slight deviation of the fiber parameters used in theoretical model and actual fiber.
Then, we study the force dependence of resonant dips further by axially loading force along the PM-PCF at a constant temperature. Figure 8 shows the transmission spectra of the resonant dips under different forces. With the force increasing, photo-elastic effect slightly reduces the refractive index of the silica core, while the refractive index of the liquid core doesn't change. So the red curve in Fig. 2(a) will be lower and the resonant region will experience red shift as the Fig. 8 shown. The inset of Fig. 8 shows that dips A1 and B1 are linearly change with force increasing and have different shift velocities. The tuning velocity of dip A1 is 3.58 nm/N and that of B1 is 2.89 nm/N. According to the relationship between the axial strain (ε) and force (F): ε = F/AE, where A is the total glass cross-section area of the section fiber, and E is the elastic modulus of fiber which is about 7.2*104 MPa. Thus, the strain tuning velocities of A1 and B1 are about 3.07 pm/με and 2.48 pm/με, respectively, which is the same order of magnitude as ordinary long period fiber gratings . Based on the above results, this fluid-filled PCF has also a potential to be a two-parameter sensor.
We have realized a single-hole-infiltration PM-PCF and have investigated numerically and experimentally its mode coupling and tunable characteristics. We find that for the high birefringence of PM-PCF, two polarized silica core fundamental modes are coupled with the high order modes (TM01, TE01 and HE11) in the liquid core at different wavelengths. In addition, several dips are observed in the spectra due to the periodical coupling process and SRP which has a special characteristic has been demonstrated and revealed. We can control the wavelengths of the resonant dips by flexibly changing the filling fiber length and temperature (or RI), and a new kind of tunable fiber polarizing filter can be designed. The resonant dips also have high tuning velocities of temperature higher than −5 nm/°C and tuning velocities of strain about 3 pm/με. It also has a potential application in simultaneous measurement of temperature and force based on different tuning velocities of the dips. Hence this filled PM-PCF can be used as flexible and controllable filters as well as two- or multi-parameter sensors with a compact structure.
This work was supported by the National Key Basic Research and Development Program of China (Grant No. 2010CB327605 and 2011CB301701), the National Natural Science Foundation of China (Grant Nos. 61322510, 11174154 and 11174155), and the Tianjin Natural Science Foundation (Grant No. 12JCZDJC20600). The authors thank Yangtze Optical Fiber and Cable Co. Ltd. (Wuhan, China) for providing the MOF.
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