Whispering gallery mode (WGM) microresonators are axially symmetric structures that trap light inside based on total internal reflection effect at the interface between the microresonator and the surrounding medium. A wide range of optical microresonators, such as microsphere , microbottles , micro-disks , micro-ring , and cylindrical microcavities , have attracted growing worldwide research interest. Due to their high optical quality, enhanced optical field, and small mode volume, optical microresonators have found various potential applications in optical filters , , low-threshold microlasers , as well as high sensitivity biological and chemical sensors , . It should be noted that WGM properties are generally determined by the relative index of refraction of the microresonator and its surrounding medium. With regard to practical applications, the spectral tunability of a silica microresonator is imperative for photonic devices. A good variety of tunable WGM devices have been developed by controlling the ambient temperature , refraction index , as well as geometry of the microresonator . There are also some reports on the investigation of microresonators based on water , glycerol , and magnetic fluids , , . However, the tuning of modes in these microresonators is not easy in the sense that their resonance mode frequencies cannot be changed easily or exhibit rather small shift. Recent studies on optical microcavities based on liquid crystals (LCs) ,  provide promising WGM tuning schemes by changing environmental temperature or applied electric field intensity to achieve large wavelength shifts. Due to the ease of deformation of PDMS coating under external force, the shape of the microresonator would change when strong electric field is applied, which may have a great impact on WGM characteristics. In a paper , we proposed that in a microresonator filled with nematic LC, the shape of the microresonator will not change at high applied electric field. All of these tuning methods were only able to achieve resonance wavelength shift toward a shorter wavelength or longer wavelength region.
In this paper, we propose and experimentally demonstrate an electrically tuned microstructured optical fiber (MOF) microresonator integrated with dual-frequency liquid crystals (DFLCs). A segment of grapefruit MOF serves as a cylindrical microresonator where the WGMs are excited by evanescent coupling of light propagating through a thin fiber taper placed perpendicularly and in direct contact with the MOF. Our work aims to propose an optical microresonator to achieve WGM resonance shift toward shorter and longer wavelength regions in the meantime based on electric field tuning approach.
2 Experimental setup
The experimental setup of testing the proposed MOF-based WGM microresonator infiltrated with DFLCs is shown in Figure 1. A continuous wave light from 1530 nm to 1560 nm with wavelength step of 0.5 pm is generated by a tunable laser (TL, KEYSIGHT, 8164B, USA). The polarization of light was adjusted by a polarization controller (PC, KEYSIGHT, N7786B, USA). The output spectra were measured with an optical power meter (OPM, KEYSIGHT, N7744A, USA). Meanwhile, the spectral information is transferred to a laptop for data processing.
The fiber used in our experiments is grapefruit MOF with six rings of air holes of 15 μm around its asymmetric solid core. LCs are infiltrated into the MOF air holes in the presence of capillary forces by dipping one end of the fiber into DFLCs. The whole experimental process is carried out at room-temperature and pressure conditions. Two DFLC samples are employed in this study: DFLC-1 (HEF951800-100, HCCH, China) with an optical birefringence Δn=0.218 at 25°C and phase transition temperature of 104.3°C and DFLC-2 (DP002-026, HCCH, China) with an optical birefringence Δn=0.263 at 25°C and phase transition temperature of 117°C. As WGMs are normally traveling close to the outer periphery of the circular optical microcavity in order to enhance the sensitivity of WGM properties to the refractive index variation of the LCs kept inside the air holes, the silica background of the grapefruit MOF is partially etched with hydrofluoric acid at a concentration of 40% by weight. The diameter of the HF-etched MOFs infiltrated with LCs is about 63.5 μm, and the gap between the holes and the outer surface is about 1.75 μm. In this case, the variation of cross-sectional refractive index distribution caused by the orientations of the LC molecules would cause the change of WGMs traveling along the outer periphery of the MOF microresonator. In general, the orientation of the LC molecules is determined by the surface anchoring energy of the LCs and the applied electric field intensity. Many optical ,  and nuclear magnetic resonance ,  studies reveal that the orientation of the LC molecules in cylindrical cavities with radius diameter between 0.5 and 200 μm would exhibit the escaped radial structure . In the escaped radial structure, LC molecules will be orientated with an angle of less than 90° with respect to the inner surface of the air holes and turns to be orientated parallel to the inclusion axis around the central area, as shown in Figure 1A. Figure 2 shows the images of the capillaries infiltrated with DFLCs captured by using a polarized microscope, which indicate that the LC molecules are in an escaped radial structure .
3 Theoretical analysis
In Figure 3, WGMs in optical microcavities are characterized by two types of polarization components, namely, TE mode and TM mode, where the electric field oscillates perpendicular and parallel to the cross-section of the microresonator, respectively. By adjusting the polarization state of the incident laser light, WGM resonances could be clearly acquired in the transmission spectrum in the absence of electric field, as the microresonator is coupled with the tapered fiber waveguide, as shown in Figure 3.
By adjusting the polarization state of the incident light, we have only acquired the WGM transmission spectra for TM modes, as shown in Figure 3. To theoretically analyze the WGM transmission characteristics, the resonant wavelength is satisfied with the asymptotic formula in cylindrical microresonators , :
where r is the inner radius of the mircroresonator; m>>1 is the angular mode order; l=1, 2, 3… is the radial mode number of WGMs; n2 is the index of pure silica; n1 is the effective index of the medium inside the microresonator; n=n1/n2; P=n1/n2=m for the TM mode while P=n2/n1=1/m for the TE mode; al is l – the zeroth order of Airy function.
According to the experimental spectral data in Figure 3, mode numbers of l, with m relating to specific polarization state, are fitted by using Eq. (1), showing that the experimentally observed WGM transmission spectrum results from a TM wave and the mode number (l, m) should be (1, 177–180) and (1, 175–178) for microresonators infiltrated with DFLC-1 and DFLC-2, respectively. As shown in Figure 3, resonance dips correspond to the fundamental WGMs and no higher radial order (l≥2) modes are excited due to the fact that the grapefruit MOF wall thickness is thin enough to suppress higher order WGMs. The free spectral ranges (FSR) between adjacent WGM peaks increase with the increment of WGM resonance wavelength. The experimental measured FSRs for microresonator filled with DFLC-1 between these four WGM resonance peaks are 8.1365 nm, 8.3525 nm, and 8.387 nm, respectively, which are in agreement with the calculated results of 8.1752 nm, 8.264 nm, and 8.3545 nm. And for the microresonator filled with DFLC-2, the experimental measured FSRs for these four WGM resonance peaks are 8.2945 nm, 8.2955 nm, and 8.483 nm, respectively, which agree well with the calculated results of 8.2701 nm, 8.361 nm, and 8.4535 nm.
To quantitatively characterize the resonance spectra, Lorentz fitting is performed on the WGM transmission spectra for the
Different from conventional LCs with single operation frequency, DFLCs show a unique feature in that their dielectric anisotropy (Δε) turns from positive value at low frequencies to negative value as the operation frequency passes by the crossover frequency (fc) , , as shown in Figure 5. The frequency-dependent reversible dielectric anisotropy makes it possible to align the DFLC molecules along or perpendicular to the electric field direction by adjusting the frequency of the driving electric signals. At low frequencies, f<fc (Δε>0), the rotation of the molecules around their short axis is unhindered and the molecules align parallel to the electric field. However, at higher frequencies, f>fc (Δε<0), only the transverse components of the molecular dipole moments are dominant, and consequently, the molecules would orient perpendicularly to the applied electric field. At crossover frequency, f=fc (Δε=0), dielectric anisotropy of DFLCs disappears. These intriguing features indicate that it is possible to achieve WGM resonance wavelength shift toward longer as well as shorter wavelength region in the meantime based on the frequency-dependent anisotropic transition mechanism.
To analyze the electric tuning characteristics of the proposed MOF-based microcavity infiltrated with DFLCs, the part of the fiber containing the DFLC is sandwiched between two electrodes with applied AC electric field. With no electric field applied, the distribution of LC molecules in microresonator is an escaped radial structure, and with the strengthening of the applied electric field at low frequencies, f<fc, the molecules located close to the interior surface of the microcavity tend to gradually align in the electric field direction. When the applied electric field operates at higher frequencies, f>fc, the molecules located close to the interior surface of the microcavity tend to gradually align perpendicularly to the electric field direction. The realignment of LCs molecules would change the effective refractive index of micoresonator, leading to the WGM resonance dips shifting to shorter or longer wavelength region.
4 Experimental results and discussion
For the grapefruit-MOF-based microresonator filled with DFLC-1, the WGM resonance dips move toward shorter wavelength region as the applied electric field frequency increases from 0.5 kHz to 10 kHz. At 30 kHz and 40 kHz, the resonance wavelength shifts toward longer wavelength region with the strengthening of the applied electric field; at 20 kHz, the WGM resonance wavelengths exhibit irregular fluctuations with the increment of the applied electric field intensity, as shown in Figure 6. At 0.5 kHz and 40 KHz, the WGM resonance dips shift by 2.628 nm and 0.64 nm, respectively. It could be found that below 20 kHz, WGM resonance dips shift toward shorter wavelength region as the applied electric field intensity gradually increases, while above this particular frequency, WGM resonance dips show wavelength shift in opposite direction. From Figure 6C, it could be seen that the crossover frequency of DFLC-1 is about 20 kHz.
We have also investigated the frequency-dependent resonance wavelength shift behavior for the grapefruit-MOF-based microresonator filled with DFLC-2, as shown in Figure 7. It is apparent that at 10 kHz and 20 kHz, the WGM resonance dips shift toward shorter wavelength region as the applied electric field intensity gradually increases, while at 30 kHz, 40 kHz, and 50 kHz, the resonance dips shift toward longer wavelength region. At 10 kHz and 50 kHz, the WGM resonance dips shift by 1.7615 nm and 0.8225 nm, respectively. From Figure 7, it could be seen that below 20 kHz, WGM resonance dips shift toward shorter wavelength region as the applied electric field intensity gradually increases, while above 30 kHz, WGM resonance dips show opposite wavelength shift behavior. Therefore, the crossover frequency of DFLC-2 should be located between 20 kHz and 30 kHz.
Crossover frequency is one of the most important indicators to evaluate the performances of DFLC. DFLC is an LC mixture whose ε|| (or εe) is highly dependent on the operation frequency normally ranging from kHz to MHz while ε⊥ (or ε0) is frequency independent within the above specific frequency range. Therefore, the dielectric anisotropy of DFLCs is positive at low frequencies while turns to be negative at high frequencies. The frequency where dielectric anisotropy changes its sign (Δε=0) is called crossover frequency (fc). The dielectric anisotropies of DFLC-1 and DFLC-2 at different frequencies are given in Table 1. The crossover frequency of DFLC-1 is between 10 kHz and 20 kHz at a temperature of 20°C, and the crossover frequency of DFLC-2 is about 20 kHz at a temperature of 20°C. The frequency of the applied electric field has great influence on the orientation of LC molecules. When f<fc, the molecular orientation aligns parallel to the electric field direction and the WGM resonance dips shift toward shorter wavelength region as the applied electric field intensity gradually increases. When f>fc, the molecular orientation tends to be perpendicular to the electric field direction and the WGM resonances dips move towards longer wavelength region with the strengthening of the applied electric field. From Figure 6C, it could be seen that for the MOF microresonator filled with DFLC-1, when the operation frequency is less than 20 kHz, WGM resonance dips shift toward shorter wavelength region, while when the frequency is larger than 20 kHz, WGM resonance move toward longer wavelength region; at 20 kHz, the WGM resonance dips almost do not exhibit any wavelength shift. Therefore, the crossover frequency of DFLC-1 is about 20 kHz, which is larger than the value in Table 1. From Figure 7C, it could be seen that for DFLC-2, when the frequency is less than 20 kHz, WGM resonance dips shift toward shorter wavelength region, while when the frequency is larger than 30 kHz, WGM resonance dips shift in the opposite direction. In this case, the crossover frequency of DFLC-2 should be located between 20 kHz and 30 kHz, which is also larger than the value in Table 1. The deviation of the experimentally acquired crossover frequencies of the DFLCs from the values in Table 1 could be attributed to the great impact of temperature on electrical and optical properties of DFLCs. The value of ∆ε decreases while fc increases with the increment of temperature, making the crossover frequency strongly temperature-dependent. As temperature increases, the crossover frequency would increase exponentially . As our experiment is conducted at 26°C, the experimentally acquired crossover frequencies turn to be larger than those in Table 1.
Values of dielectric anisotropy (∆ε) for DFLC-1 and DFLC-2 measured by HCCH, China.
|Frequency (f)||0.5 kHz||10 kHz||20 kHz||30 kHz||40 kHz||50 kHz|
Besides the frequency-dependent birefringence effect, Freedericksz transition  is also a fundamental phenomenon taking place in many LC-based devices, which is affected by the surface anchoring, elastic torque, electric field induced torque, as well as viscous torque of the LC devices and is known for the feature that LC molecules could be re-orientated in case the applied electric field intensity is beyond the Freedericksz transition threshold. As shown in Figures 6C and 7C, when the applied electric field intensity is not high enough, WGM resonance wavelengths exhibit irregular fluctuations. However, when the applied electric field intensity is beyond the Freedericksz transition threshold, WGM resonance wavelengths would exhibit regular shift with the increment of the applied electric field intensity. From Figures 6C and 7C, it could be found that the Freedericksz transition thresholds for DFLC-1 and DFLC-2 are about 1.8 V μm−1 and 1.0 V μm−1, respectively.
To investigate the frequency-dependent WGM tuning characteristics of the grapefruit-MOF-based microresonators infiltrated with different LCs, we have investigated WGM resonance wavelengths as functions of applied electric signal frequency for different electric field intensities, as shown in Figure 8A and B, respectively. It could be seen that with an increment of electric signal frequency, the WGM resonance dips shift toward longer wavelength region.
From Figure 8A, it is obvious that as electric signal frequency ranges from 2 kHz to 14 kHz, WGM resonance dips show more obvious regular shift at higher applied electric field strength. And the maximum WGM resonance wavelength shift reaches 1.1845 nm at 4.1 V μm−1. When electric signal frequency is larger than 14 kHz, WGM resonance dips show similar frequency-dependent wavelength shift behaviors at different applied electric field strengths. When electric signal frequency increases from 14 kHz to 30 kHz, the WGM resonance wavelength shift reaches 0.7545 nm, while as electric signal frequency ranges from 30 kHz to 40 kHz, the WGM resonance dips show no obvious wavelength shift with only irregular fluctuations.
From Figure 8B, it could be seen that WGMs in the microresonators filled with DFLC-2 are no longer supported at 1 V μm−1 when electric signal frequency is less than 10 kHz. As electric signal frequency ranges from 10 kHz to 50 kHz, WGM resonance dips show similar wavelength shift behaviors at different applied electric field strengths. When electric frequency ranges from 10 kHz to 32 kHz, WGM resonance dips shift regularly with the increment of electric signal frequency. The WGM dips move toward longer wavelength region by 2.396 nm at an applied electric field strength of 4 V μm−1. As applied electric signal frequency ranges from 32 kHz to 50 kHz, WGM resonance wavelengths exhibit no obvious shift with only irregular fluctuations.
We have proposed that for MOF-based microresonators, the crossover frequency and Freedericksz transition threshold properties of DFLCs should be investigated. The crossover frequency of DFLC-1 is about 20 kHz, and the crossover frequency of DFLC-2 is between 20 kHz and 30 kHz. The Freedericksz transition thresholds of DFLC-1 and DFLC-2 are 1.8 V μm−1 and 1.0 V μm−1, respectively. When the applied electric signal frequency is below the crossover frequency, WGM resonance dips show wavelength shift toward shorter wavelength region as the applied electric field is strengthened. However, when applied electric field frequency is larger than the crossover frequency, WGM resonance dips start to move toward longer wavelength with the increment of the applied electric field intensity. This property could be exploited for the design of bi-directional wavelength-tunable devices. In addition, the proposed electrically tunable micro-cavity integrated with DFLCs is anticipated to find potential applications in optical filtering, all-optical switching, as well as electrically controlled micro-optics devices.
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