Tunable liquid-crystal microshell-laser based on whispering-gallery modes and photonic band-gap mode lasing

Yuelan Lu; Yue Yang; Yan Wang; Lei Wang; Ji Ma; Lingli Zhang; Weimin Sun; Yongjun Liu

doi:10.1364/OE.26.003277

1. Introduction

Over the past 50 years, liquid crystals (LCs), high birefringence, and molecular reconfiguration ability have been introduced in optical devices, enabling realization of the liquid crystal display (LCD) [1]. LCs do not only comprise a display technology, but, due to their high optical quality and enhanced optical field, dye-doped cholesteric liquid crystals (DDCLCs) are of great research interest for developers of laser devices [2,3]. A laser device base on whispering-gallery modes (WGMs) microcavities that have a vast range of prospects, particularly in LC droplets [2,4,5]. Another efficient approach leverages the photonic band-gap (PBG) by doping a fluorescence dye in the cholesteric liquid crystals (CLCs) and the optically pumping in an appropriate way to produce a laser device with LCs which generate low-threshold lasing emission along the helical axis [6,7]. Optical microcavities confine light to small volumes by resonant recirculation, such as microdroplet, microdisk and microbubble, and $Q$ factors are up to approximately 10⁵ to 10¹⁰ [2]. In DDCLC lasers, the chiral pitch of the CLC material, the ability to tune the laser wavelength by temperature, the mechanical force, electric field or wedge structures are all marked differences from conventional lasers [8–12].

Recently, microfluidic technologies have been adopted to fabricate LC microdroplets and microshells [13–16], which are a common way, as reported in many papers, of solving the problem of critical polydispersity in LC emulsions. Due to the instability of the LC state, CLC microdroplets and microshells exhibit some potential problems and limitations in many possible applications of some fields [17].

Previous works used hollow or liquid cores. In this paper a novel DDCLC microshell laser is described. Here we proposed a DDCLC microshell laser with a silica-glass-microsphere at its center. Furthermore, the presence of silica-glass-microspheres plays a supporting role in LCs, which does not require other media to carry LCs. Here, the solid microsphere with a DDCLCs coating is attempted to improve the stability of fluidic LCs and non-tunability of solid-state microcavity. Therefore, DDCLC microshells are more flexibly than microdroplets or solid-state microcavity in application. We report the exciting of WGMs and PBG mode lasers of the DDCLC microshells, silica-glass-microsphere coated DDCLCs via a tapered optical fiber. The WGMs and PBG modes were separated to observe the temperature-tuning properties of the two modes by changing the chiral concentration and pump energy in the DDCLCs.

2. Experimental setup

We prepared three different CLC mixtures by using different chiral concentrations. The gain mediums of the three CLC mixtures were all prepared by doping 1.5-wt.% laser dye with 4-dicyanomethylene-2-methyl-(6-4-dimethylaminostryl)-4H-pyan. We used BHR32400-200, a high-birefringence ( $n_{e}$ = 1.765, $n_{o}$ = 1.566) nematic liquid crystal (NLCs) material which exhibits a phase transition of anisotropy to isotropic phase at 104°C. Sample Ι was prepared by adding 74-wt.% NLCs to 24.5-wt.% R811; sample ΙΙ was prepared with 78.5-wt.% NLCs and 20-wt.% R811; and sample ΙΙΙ was prepared with 66.5-wt.% NLC and 32-wt.% R811 (all materials were acquired from Bayispace, China). The DDCLC mixtures were mixed ultrasonically and heated in an oven at 110 °C so the mixtures were in the isotropic phase. To eliminate any remaining undissolved solid particles, the mixture was centrifuged after cooling to room temperature. For preparation of silica-glass-microspheres, the main process was as follows: 1) The cladding of one end of standard single-mode silica fiber was removed about 2–3 cm. 2) A CO₂ laser was configured so that the beam converged on the core of the stripped cladding and generated a sufficiently high temperature to melt the end of the core. A standard ball was formed under the action of the surface tension of the liquid. 3) The resulting silica-glass-microspheres, quartz glass microspheres with fiber handles, were naturally cooled in air. This fabrication technique is flexible, and it can produce silica-glass-microspheres in various sizes. The silica-glass-microspheres were coated in DDCLCs, and the thickness of the microshells was controlled by the number which silica-glass-microspheres were dipped, but each single dipping thickness was about 5 to 20 µm, which is not controlled accurately in a very fixed range. The size of silica-glass-microspheres has impact on the thickness ranges. Figure 1(a) shows an optical image of silica-glass-microspheres and Figs. 1(b) and 1(c) show optical images of DDCLC microshells. In the process of coating the DDCLCs with microspheres, it was noted that the silica-glass-microspheres cannot be coated completely, as shown in Fig. 1(b). We tried to coat the silica-glass-microspheres with UV glue, because the compatible LCs and UV curable adhesives are better than LCs and silica-glass-microspheres. As a result, we found it was difficult to coat a round object with a UV curable adhesive. Next, we used the method to treat the silica-glass-microspheres with a photo-alignment polyimide film before wrapping the LCs. This film was coated on the outside of the silica-glass-microspheres in a thickness of ~100 nm. Irradiated vertically with ultraviolet light for 5 min at an intensity of 20 mW/cm², the silica-glass-microsphere was rotated at regular intervals to ensure uniform irradiation. Figure 1 (c) shows the treated microspheres that were more easily coated with DDCLCs. As shown in Fig. 1(d), a frequency-doubled Nd:YAG pulsed laser (532-nm wavelength, 8-ns pulse width, and 10-Hz repetition rate) was used for excitation of the DDCLC microshells. The light emerging from the laser propagated through splitting prism. A portion of light went through power meter and another was coupled the microshells through the tapered tip (15 µm in diameter) of an optical fiber (SMF28, Corning). The microshell were operated and aligned via an x-y-z translation stage (resolution of 100 nm), and in a warm box for temperature sensing. The micro-manipulation process was observed through a 20 × microscope objective. CCD camera was used to take photomicrographs after 532 nm filter filtering light. The emission of the microshells was collected by a spectrometer with the resolution of 0.05 nm (PG2000, Ideaoptics Technology Ltd., China).

Fig. 1 Optical images of the (a) silica-glass-microsphere (b) incompletely coated DDCLC microshells, and (c) completely coated DDCLC microshells. (d) Experimental laser characterization setup.

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The finite-difference time-domain (FDTD) technique was used to analyze optical behaviors of the WGMs within the DDCLC microshells. The WGM lasing nature of the DDCLC microdroplets is further validated by numerical simulations and experiments. A tapered tip was established to transmit light and couple the microshells. The diameters of the microshells, and silica-glass-microspheres were set as 50 and 30 µm, respectively, in accord with the actual measured parameters in the experiments. Figures 2(a) and 2(b) show cross-sectional views of the electric field distributions inside the coupled system. Red and blue-shaded regions represent the highest and lowest field intensities, respectively. According to the simulation results, light from the fiber tip is efficiently confined via total internal reflection at the interface rather than leaked into the internal layer of the microshells. The normalized electric field intensity distribution in the radial direction of the y-z plane is plotted in Fig. 2(c). There are the optical behaviors of the WGMs and PBG modes within the DDCLC microdshells. As shown in Figs. 2(d) and 2(e), which present the radial helical structure and transverse magnetic (TM) modes of CLCs, respectively.

Fig. 2 Electric field distributions on the (a) y-z, (b) x-z planes of the tapered-fiber-coupled microdroplet system. (c) Normalized electric field intensity distribution in direction of the y-z plane. (d) The 3D schematic configuration of the helicoidal structures occuring redient in an equatorial region. (e) Schematic drawing of direction for TM modes.

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3. Results and discussion

Figure 3(a) presents a lasing spectrum from the ~51-µm-diameter (~30-µm silica-glass-microspheres) DDCLC microshells of sample ΙΙ. The lasing envelope and mode position (denoted by $•$ symbols) can be well explained by the WGM theory. The lasing modes number $l$ can be predicted from the following equation [18]:

\begin{array}{l} λ^{- 1} (D, n_{c a v}, n_{r}, q, l) = \frac{1}{π D n_{c a v}} [l + \frac{1}{2} + 2^{- 1 / 3} α (q) {(l + \frac{1}{2})}^{1 / 3} - \frac{L}{{(n_{r}^{2} - 1)}^{1 / 2}} + \frac{3}{10} 2^{- 2 / 3} α^{2} (q) {(l + \frac{1}{2})}^{- 1 / 3} \\ - 2^{- 1 / 3} L (n_{r}^{2} - \frac{2}{3} L^{2}) {(n_{r}^{2} - 1)}^{- 3 / 2} α (q) {(l + \frac{1}{2})}^{- 2 / 3}] \end{array}

where

D

is the diameter of the circular microcavity,

λ

is the resonant wavelength,

n_{c a v}

is the refractive index of the microcavity,

n_{r} = n_{c a v} / n_{e n v}

(

n_{e n v}

is the refractive index of the surrounding medium),

L = 1 / n_{r}

for transverse magnetic (TM) modes and

L = n_{r}

for transverse electric (TE) modes,

α (q)

is the roots of the Airy function where

q

is the radial mode number, and

l

is the mode number. If we insert

D

= 51 µm,

n_{c a v}

= 1.765 for the extraordinary refractive index of the CLC microshell, and 1 for the refractive index of the surrounding medium

n_{e n v}

, the lasing peaks can be well-fitted. As marked in Fig. 3(a), the corresponding mode numbers count from 451 to 453 belong to first order TM modes.

Q

factor can be calculated from the mode spectrum as

Q = λ / Δ λ

, where

λ

is the central wavelength of the resonance and

Δ λ

is the full-width at half-maximum (FWHM) of the resonance lineshape. The measured FWHM was about 0.12nm, resulting in a

Q

factor of ~5 × 10³ for the selected WGM. This

Q

value is ~10 times higher than that of the DDCLC microdroplets [13] and ~5 times higher than that of the DDCLC microshells [15]. However, it is of particular note is that these values are slightly above that of solid-state microspheres that was recently reported [19].

Fig. 3 (a) Lasing emission spectra from a ~51-µm-diameter DDCLC microshell. The inset shows microscopy image of the ~51-µm-diameter DDCLCs microshell; the equally spaced spectral peaks correspond to WGM lasing and the highest peak corresponds to PBG mode lasing. Normalized intensity of the peaks as a function of PPE of (b) PBG and (c) WGM mode lasing. The inset of (b) shows the lasing emission spectra of the PBG mode within a relatively low range of PPEs.

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The lasing spectra (denoted by $■$ symbols) is excited easily within a relatively low pump-pulse energy (PPE) and coincides well with the PBG [insets of Figs. 3(a) and 3(b)], as explained by the use of distributed feedback theory [7]. Figures 3(b) and 3(c) show the normalized intensity of the peaks as a function of PPE. An increase of emission with increasing PPE can be observed, which clearly indicates the lasing action. The lasing threshold of the PBG was approximately 6.9 µJ and that of the WGMs was higher, approximately 23.1 µJ. It is clear that the WGMs are more difficult to excite than the PBG modes. The excitation process of the WGM laser required more energy because of the higher losses. Meanwhile, we find the threshold of DDCLC microshell is higher than LC microdroplet in water [13]. The emission of the WGM lasing is related to the arrangement of the surface LC molecules. We speculate that the reason for higher threshold is that the arrangement of some surface LC molecules of microshell is not ordered enough. For PPEs below the threshold, weak and broad spontaneous emission was observed and no laser peaks appeared. For PPEs greater than or equal to threshold, the intensity of the peaks increased rapidly with the PPE. The threshold value of the PBG mode was measured less, because the two modes exist at the same time as the PPE increases, leading to difficulties in taking measurements.

To further make clear relation between the diameter and free spectral range (FSR) of the WGMs, we measured the emission spectra of the different diameters DDCLC microshells (~30-µm silica-glass-microsphere) using sample ΙΙΙ. For some experiments only WGM lasing, thereby eliminating any PBG mode lasing interference, is desirable. The relation between the lasing wavelength λ of the PBG mode and the helix pitch p is $λ = n_{e} p$ , where $n_{e}$ is the extraordinary refractive index. When the chiral agent concentration increases, both the helix pitch and emission wavelength decreases. The PBG mode laser is not in the spectrometer’s measurement range. $FSR = λ^{2} / (π n_{e f f} D)$ , where λ is the resonant wavelength and $n_{e f f}$ is effective refractive. The lasing wavelength of WGMs depends on size of the DDCLC microshell as shown in Figs. 4(a)-4(c). It can be seen that the FSRs are 1.05, 0.79, and 0.58 nm in microshells in which $D$ = 65, 85, and 125 µm, respectively. The FSR is inversely proportional to the diameter of a DDCLC microshell. In addition, the PBG mode lasing of DDCLC microshells (Sample Ι) with different diameters is shown as shown in Fig. 4(d). For the DDCLC microsshells with different diameters, $n_{e}$ is the same, while pitch automatically adjust size and number so that the thickness of the liquid crystal layer is an integer multiple of $p / 2$ [20]. In Fig. 4(d), diameter of silica-glass-microsphere is 80 µm and $D$ = 90, 95, and 100 µm. It is clear the PBG lasing mode evolve with diameter.

Fig. 4 WGM lasing emission spectra from DDCLC microshells with diameters of (a) 65, (b) 85, and (c) 125 µm, respectively. (d) PBG lasing emission spectra from DDCLC microshells with diameters of 90, 95, and 100 µm.

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Changing temperature is a form of tuning that changes the refractive index of a resonator. Since the refractive index of LCs is well known for its significant response to temperature [21–23], we attempted to verify the spectral tunability of DDCLC microshells by observe the changes in the PBG mode and WGM spectra. The PPE in the experiments was controlled under the threshold of the WGMs in order to excite only the PBG laser as shown in Fig. 5(a). When the temperature was increased, the redshift of the laser spectrum was observed. When the temperature measured by a temperature probe was 28.5 °C, the peak wavelength of the lasing modes appeared at 591.74 nm. As the temperature increased to 38.5 °C, the peak wavelength shifted to 601.56 nm. Obviously, the peak emission wavelengths exhibit an almost linear relationship with temperature (sensitivity of 0.982 nm °C⁻¹) with a tuning range of 9.82 nm within 10°C temperature intervals, as shown in the Fig. 5(c). The wavelength shifted by temperature is dependent on the pitch of the helix, with the equation $λ = n_{e} p$ . Several models have been attempted to address the wavelength and temperature dependencies of the LC refractive indices, we use the following temperature-dependent LCs refractive indices [22]:

\frac{d n_{e}}{d T} = - B - \frac{2 β {(Δ n)}_{o}}{3 T_{c} {(1 - \frac{T}{T_{c}})}^{1 - β}}

In Eq. (2),

- B

is a constant for a given material,

β

is an exponent,

T_{c}

is the clearing temperature of the LC material and

Δ n = n_{e} - n_{o}

, Both terms in the right-hand side are negative, so

n_{e}

decreases as the temperature increases throughout the entire nematic range of LCs. The chiral pitch [Fig. 2(d)] does not change monotonically with increasing temperature [24, 25]. The choice of LCs and chiral dopant can change the chiral pitch to either elongate or shorten with temperature [26]. The change in pitch also changes the position of the photonic band gap and therefore the lasing wavelength. The extraordinary refractive index is known to decrease with temperature. The peak wavelength of lasing is red-shifted, so the chiral pitch increases.

Fig. 5 (a) PBG mode lasing emission spectra and (c) peak of the PBG mode as a function of temperature from 28.5 to 38.5 °C, respectively. (b) WGM lasing emission spectra and (d) peak of the WGM as a function of temperature from 27 to 36 °C, respectively.

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One important aspect of WGM microshells is the ability to change their resonant frequencies in real time, as shown in Fig. 5(b). Changing the temperature is a common tuning technique that changes the refractive index of the LCs. Molecular system of LCs is complex involving short and long range molecular interactions [27]. LCs are birefringent and different polarizations sense different refractive indices. In the LCs droplets the optical axis points in the radial direction. Therefore, the TE modes sense the lower index ( $n_{o}$ ) and the TM modes sense the larger one ( $n_{e}$ ). The change of temperature affects the molecular structure of LCs, and $n_{o}$ and $n_{e}$ change with the change of molecular structure. The effective refractive index of the LCs is given by:

n_{e f f} = \sqrt{\frac{n_{e}^{2} n_{o}^{2}}{n_{o}^{2} \sin^{2} θ + n_{e}^{2} \cos^{2} θ}}

which

θ

is the angle between the propagation direction and the director (optic axis). In the experiments, the PPE was controlled to be approximately at the threshold of the WGMs in order to excite the WGM laser. Figure 5(d) plots the peak of the WGM as a function of temperature from 27 to 36 °C. It is clear that the lasing modes exhibit an integral blueshift with increasing temperature in the tuning range of 1.41 nm within 9-°C temperature intervals. The wavelength shifted by temperature is determined by the equation

λ = π n_{e f f} D / l

. In this experiment, only the TM mode, so the main factors of spectral move with temperature is

n_{e}

change. At zero field

θ

= 90°,

n_{e f f}

≈

n_{e}

. Taking the Eq. (2), we obtain the following equations:

\frac{d λ}{d T} = \frac{- B π D}{l} - \frac{2 π D β {(Δ n)}_{0}}{3 l T_{c} {(1 - \frac{T}{T_{c}})}^{1 - β}}

It is clearly that

λ

decreases as the temperature increases. We estimated the resolution of the CLC microdroplet-based temperature sensor to be 0.156 nm °C⁻¹.

4. Conclusions

In conclusion, the massive production of DDCLC microshells in which the microspheres are coated DDCLCs with diameters and shell thicknesses that were facilely controlled was achieved. To some extent, the production method is effective in solving the problem of instability of previous LC microdroplets and non-tunability of solid-state microcavity. However, our method also exhibits several shortcomings, including that the DDCLC microshell have a high threshold. By controlling optically pumping and the chiral agent concentration, we demonstrated that the control of the lasing modes, including WGMs and PBG modes. Moreover, due to the temperature dependence of the refractive index of the CLCs, the lasing wavelength was tunable by changing the temperature. A tuning range of 9.82 nm within a 10-°C temperature interval in PBG modes and one of 1.41 nm within a 9-°C temperature interval in WGMs were realized with sensitivities of 0.982 nm °C⁻¹ and 0.156 nm °C⁻¹, respectively, which makes DDCLC-droplet-based microlasers applicable for highly sensitive temperature sensing in flexible photo-thermic devices.

Funding

Joint Research Fund in Astronomy Under Cooperative Agreement Between the National Natural Science Foundation of China (NSFC); Chinese Academy of Sciences (CAS) (U1531102); National Natural Science Foundation of China (61107059, 61077047).

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Tunable liquid-crystal microshell-laser based on whispering-gallery modes and photonic band-gap mode lasing

Abstract

1. Introduction

2. Experimental setup

3. Results and discussion

4. Conclusions

Funding

References and links

Cited By

Figures (5)

Equations (4)

Optics Express