1. Introduction

Liquid crystals (LCs) are switchable anistropic liquids and thus are used in various opto-electronic devices [1]. One of the emerging applications of LCs is in the field of microlasers: because they are liquid, they can carry organic dyes and thus function as gain media. Also, because of the anisotropy and fluidity of LCs, LC microlasers are generally polarization sensitive and tunable, making them useful for such applications where a particular polarization or wavelength is required. Since the observation of the first laser emission from cholesteric LCs in 1980 [2], LC lasers using various LC phases and/or device structures have been proposed. Chiral LC phases such as the cholesteric phase, smectic C* or the blue phase possessing helical-periodic order have been employed as self-organizing distributed feedback (DFB) cavities capable of emitting circularly polarized light [3–6]. Tuning of the emission wavelength has been performed in chiral LC lasers both in surface-emitting and waveguiding configurations, utilizing the sensitivity of the helix pitch to external perturbations such as heat or electric fields [7–9]. Random lasing from nematic LCs have also been actively investigated, utilizing multiple scattering and light localization occurring in both static and dynamic regimes [10–12]. In contrast to the self-organizing LC lasers mentioned above, LCs have been incorporated in photonic cavities to allow simple tuning of beam polarization and wavelength. Wavelength-tunable linearly polarized lasing has been performed in LCs placed between two distributed Bragg reflectors (DBRs) [13], and electro-tuning of the output polarization has been demonstrated by combining a DFB cavity with LCs [14].

However, in spite of the various LC lasers proposed to date, there are no reports of obtaining output beams with spatially variant polarization. Light beams with their states of polarization arranged in particular patterns, for example with axial symmetry, are known to possess propagation and focusing properties not observed in beams with spatially homogeneous states of polarization [15]. The ability to generate such complex beams will add to the functionality of these electro-optic microlasers. Here, we present a cell structure that allows direct projection of the LC alignment on the polarization of the output laser beam and demonstrate the generation of laser light with patterned polarization. As an example, we use a concentrically aligned LC layer and demonstrate lasing with azimuthal polarization.

2. Structure and working principles

The proposed cell structure is schematically illustrated in Fig. 1 . The cell is composed of a pair of silicon dioxide (SiO₂)/ titanium dioxide (TiO₂) multilayers with a dye-doped nematic LC with positive dielectric anisotropy placed between the multilayers as the gain material and the polarizing element. The multilayers are fabricated on transparent electrode (ITO)-coated substrates to apply a voltage across the LC layer. The nematic LC is initially homogeneously aligned in the cell-depth direction, but appropriate surface treatment is performed on the surface of the multilayers to align the LCs in a particular pattern in the cell-plane direction. In this configuration, the two-dimensional alignment pattern of the LC layer is projected onto the polarization of the output laser beam.

 

Fig. 1 Schematic illustration of the proposed cavity structure.

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The principle of alignment-to-polarization projection is explained as follows [13,16]. Since the proposed cell structure is a Fabry-Peròt cavity, lasing occurs from the resonant modes which appear at spectral positions determined by the Eq. (1), where λ_peak,m, m, n_def, L_def, n_BR, L_BR, k_B are the mode number, wavelength of the m^th mode, refractive index and length of the defect layer, average refractive index and length of the Bragg reflector and wavenumber at the Bragg condition, respectively:

However, because nematic LCs are uniaxially anisotropic, two refractive indices, the extraordinary refractive index (n_e) and ordinary refractive index (n_o) exist at two orthogonal directions, in directions parallel and perpendicular to the LC director, respectively. This breaks the degeneracy of the system and causes two kinds of resonant eigenmodes to appear in the system: one attributed to n_e and polarized along the director, and the other attributed to n_o and polarized in the direction perpendicular to the director. Consequently, two kind of lasing modes exist: one attributed to n_e, polarized in the direction parallel to the LC director, and n_o-experiencing modes which are linearly polarized in the direction perpendicular to the LC director (that is, orthogonally to the n_e-experiencing modes). By introducing a laser dye that aligns itself with the LC molecules so that the transition moment is greater either along or across the LC director, one of the two orthogonally polarized modes can be selected as the more favourable lasing mode. As a result, either the alignment pattern itself, or the pattern orthogonal to the alignment of the LC, is projected on the output beam as its spatially variant polarization. Also, upon application of an electric field, the nematic LC reorients its director parallel to the electric field, that is, out-of-plane direction from the substrate. This causes a decrease in the effective n_e of the LC according to the Eq. (2), where θ is the angle of LC director from the substrate. Electro-tuning of the lasing wavelength is thus possible for n_e modes without changing the output polarization pattern.

3. Experimental Details

We used a cyanobiphenyl and terphenyl-based nematic LC mixture (E47, Merck) with positive optical and electrical anisotropy and doped it with a laser dye, 4-dicyanomethylene-2- methyl-6-p-dimethyl aminostyryl-4H-pyran (DCM, Exciton, concentration 0.5 wt%) which aligns its transition moment parallel to the LC director. The dye-doped nematic LC was placed in a cavity formed between two multilayers using PET spacers with approximate thickness of 4 μm. The thicknesses of the materials composing the dielectric multilayer were 111 nm for SiO₂ (n = 1.46) and 69 nm for TiO₂ (n = 2.35), and the number of the SiO2 / TiO2 pairs was five to obtain a well-defined stop-band around λ = 650 nm. The multilayers were coated with polyimide (JSR, AL1254) to ensure planar alignment of the LC molecules at the LC / multilayer interface. One of the dielectric multilayers was treated for concentric alignment by pressing a rubbing cloth against the substrate while spinning the substrate on a spinner at 3000 rpm.

The optical texture of the fabricated sample was observed on a polarizing optical microscope (POM, Nikon, Optiphot2-POL). As shown in Fig. 2(a) , a centrosymmetric texture with four dark brushes stretching out from the center was observed, and as the analyzer of the microscope was rotated, the dark brushes rotated in the same direction. This indicated that the dark brushes corresponded to regions in which the LC molecules were either aligned horizontally (vertical brushes) or vertically (horizontal brushes) in the field of view, confirming that a concentrically-aligned LC was obtained. A schematic representation of the concentric alignment is shown in Fig. 2(b).

 

Fig. 2 (a) Optical texture of the sample and (b) schematic illustration of the molecular orientation. Four dark brushes are observed as a result of the LC molecules overlapping with the absorption direction of the polarizer or the analyzer.

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The transmittance spectrum of the sample was measured prior to pumping the laser dye to investigate its polarization characteristics. The sample was placed on the POM and the transmittance was measured at a location several tens of μm below the center of the concentric texture in Fig. 2(a). The incident light was depolarized by removing the polarizer and inserting a depolarizer instead, and the polarization of the output light was measured by an output analyzer, with the 0° position defined as the initial analyzer position in Fig. 2(a). The applied voltage dependence of the transmittance spectrum was also investigated as a rectangular voltage with a frequency of1 kHz was applied across the LC layer.

The lasing characteristics of the sample was investigated by focusing a second harmonic from a Neodymium-doped YAG laser (Spectron Lasers: SL-802, pulse width ~20 ns, repetition rate 10 Hz) after passing through a depolarizer. In order to investigate the threshold characteristics of lasing, the pump beam was focused on the sample to a spot with diameter ~10 μm at a position several 10 μms from the center of the concentric texture. The fluorescence spectrum was measured by collecting the emission in the cell-normal direction (in which the cavity exists) through a × 20 objective lens with N.A. 0.4. A CCD multichannel spectrophotometer (Hamamatsu Photonics: PMA-11 Model C7473-36) with a spectral resolution of 2 nm was used. The polarization profile of the emitted laser beam was investigated by focusing the pump beam to a spot with diameter ~40 μm at the center of the concentric texture and observing the output beam through the same objective lens. The applied voltage dependence of the lasing characteristics was investigated by applying a rectangular voltage with a frequency of 1 kHz across the LC layer.

4. Results and Discussion

The transmittance spectra of the sample at various analyzer angles are shown in Fig. 3(a) . Within the optical stop-band of the multilayer, multiple transmitting modes were observed as a result of the relatively thick, 4 μm LC layer introduced. The transmittance spectrum was seen to change at different analyzer angles: the spectra were distinctively different at analyzer positions of 0 and 90°: and at 45°, the transmitting modes were observed at wavelengths which existed at either 0° or 90°, but had a smaller transmittance. This clearly indicates that the defect modes were split in polarization and spectral position because of the anisotropy of the nematic LC. Considering the relationship between the LC alignment and the analyzer angle, the defect modes observed at an analyzer angle of 90°were determined to be the n_e modes. Because of rotational symmetry around the center of the pattern, the transmittance spectrum remained constant as the sample was rotated about the center of the texture.

 

Fig. 3 (a) Transmittance spectra of the sample measured at a position few 10 μms from the center of the texture in Fig. 2(a). Dotted lines are drawn as a guide to emphasize the change in the transmitting mode wavelength depending on the polarization. (b) Applied voltage dependence of the transmittance peak wavelengths appearing in the optical stop-band.

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Figure 3(b) shows the applied voltage dependence of the resonance wavelength of the two kinds of transmitting modes. Of the two modes, only one of the modes, the n_e modes were seen to shift, attributed to field-induced reorientation of the nematic LC (Frederiks transition). The Frederiks transition occurred only above a certain threshold voltage because of the strong surface anchoring induced by the rubbing process.

Figure 4(a) and 4(b) show the fluorescence spectra of the sample at low and high pump energies and the pump energy dependence of the fluorescence intensity (with the pump beam focused to a spot of approximately 10 μm in diameter). Fluorescence from the DCM dye modulated by the cavity modes were observed, and upon pumping above threshold, sharp emission peaks were observed. With no applied voltage, lasing occurred at two wavelengths, 614 and 642 nm, which were found to be n_e-modes after measuring the polarization direction and comparing its wavelength with the resonance mode wavelength in Fig. 3. Lasing from the n_e-modes can be explained from the fact that the DCM dye doped in the LC aligns their transition dipole moment along the director, causing more light to be emitted along the direction of the director [17]. The threshold for lasing was approximately 7 mJ/cm²/pulse for both wavelengths, but the slope efficiency was higher for light at 642 nm, because of stronger light confinement near the center of the optical stop-band. Figure 4(c) shows the applied voltage dependence of the normalized lasing spectrum for the mode which initially lased at 642 nm. Above the threshold voltage of Frederiks transition, blue-shift of the emission wavelength occurred, corresponding to the shift in the resonance wavelength of the n_e modes. Also, for constant pump power, the emission intensity decreased with increasing voltage, possibly as a result of the transition moment of the DCM being reoriented out-of-plane to the pump beam polarization.

 

Fig. 4 (a) Fluorescence spectra at low and high pump energies and (b) pump energy dependence of the laser emission with no applied voltage, and (c) voltage dependence of the lasing spectrum (intensity normalized to 1 at the lasing wavelength).

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The far-field patterns of the laser emission with and without an applied voltage of 1.5 V are shown in Fig. 5 . In both situations, the obtained patterns were similar, although the contrast of the image is smaller when the voltage was applied, because of the lower emission intensity. When the intensity pattern was observed without an output polarizer, a donut-shaped profile was observed, and a centrosymmetric intensity pattern was observed as the output polarizer was inserted and rotated. These observations are clear indications of azimuthally polarized light: thus we have shown that wavelength-tuning of the lasing wavelength is possible without losing the polarization pattern projected by the LC alignment.

 

Fig. 5 Far-field patterns of the output laser beam at (a) 0 V and (b) 1.5V. The direction of the white arrow indicates the transmission axis of the output polarizer. The left-most image was acquired with the polarizer removed.

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5. Conclusions

We presented a LC microlaser structure which, by selecting the appropriate combination of the laser dye and the host nematic LC, projects a pattern parallel or perpendicular to the LC director distribution on the output laser beam. The simple structure also allows the lasing wavelength to be tuned electrically, without losing the polarization properties. As an example, we utilized a concentrically aligned nematic LC layer and demonstrated azimuthally polarized lasing, which could be tuned over 20 nm at a driving voltage of 1.6 V. Although we employed the rubbing technique to obtain concentric alignment, employing newer LC alignment techniques such as photoalignment [18] or microfabrication [19,20] allow more complex patterns to be obtained. The proposed device is therefore extremely versatile.