1. Introduction

Recently liquid crystals were recognized as fascinating materials for mirrorless dye micro-lasers with a distributed feedback, which can be constructed in the form of planar multi-pixel structures. Low-threshold, thin film lasers have been demonstrated based on dye-doped helical cholesteric liquid crystals (LC) with natural periodicity and photonic band-gap structure [1-6] and nematic LC [7-9] with the band-gap structures created artificially. Due to their labile structure, liquid crystals are extraordinary sensitive to external agents such as temperature, irradiation, chemical species (cholesteric LC lasers for sensors) or electric field (nematic LC for voltage tunable lasers and amplifiers [10, 11]). The most important parameter of any lasing medium is a gain coefficient that includes both the positive and negative absorption and scattering losses. This is also true for LC, which possess the absorption and refraction anisotropy and scatter light due to strong fluctuations of the local optical axis, i.e. director L(r). The light scattering is a generic effect in nematic LC. Depending on scattering geometry, its intensity can be several orders of magnitude larger for one polarization than for the other [12]. On the one hand, the scattering results in optical losses, which decrease the gain of the material. On the other hand, the same effect makes the light path l in the amplifying material longer, that increases the amplification and even promotes the random laser generation [13-14] and weak light localization [15]. Therefore, the measurements of polarized gain spectra for different nematic LC orientation is especially important. Here we report on the first measurements of the gain spectra in liquid crystals. Moreover, we show how the gain spectra can be controlled by an external electric field applied to the nematic cell. This possibility is based on the field-induced orientation of the LC molecules together with the luminescent dye molecules, the so-called guest-host effect.

2. Experimental

The gain g(λ) (in cm^-1) is a wavelength dependent positive coefficient in exponent e^g(λ)l providing the amplification of the light wave along the distance l. The spectra of g(λ) have been measured using the technique developed earlier [16] and based on the measurements of the amplified spontaneous emission (ASE) intensity spectra I(λ) for two different light paths, l and l/2, within the amplifying material. The ASE technique needs neither mirrors nor distributed feedback. Therefore, well-oriented dye-doped nematic LC layers placed in the planar capillaries were selected for our measurements, with the open capillary edges slightly misaligned from the perpendicular to the amplification path.

All the experiments have been carried out using two cells, each consisting of two 0.8 mm-thick glasses with a gap of 27 or 40µm in between. The inner surfaces of the thicker cell were covered with transparent indium-tin oxide (ITO) layers and, in both cells, polyimide alignment layers, unidirectionally rubbed with a velvet cloth, provided a uniform planar structure of the nematic phase. The cells were filled with a mixture E7 (from BDH) doped with dye 4-(Dicyanomethylene)-2-methyl-6-(4-dimethylamino-styryl)-4H-pyran (DCM, from Aldrich). The dye concentration was 0.5% and 0.16% in the thinner and thicker cells, respectively. The E7 mixture is well known in display technology for its wide temperature range, low viscosity and high dielectric anisotropy. The dye DCM is one of the most popular dyes in the laser technique.

The cells were pumped using the second harmonic of a Q-switched Nd³⁺:YAG laser (Surelite-II by Continuum). The linearly polarized pump beam was incident normally to the cell being focused by a cylindrical lens. The illuminated spot has a form of a narrow rectangular of size of 7×1.6mm² (area 0.112cm²) such that ASE is amplified along its longest side and leaves the cell from its edge. The pump energy was attenuated by a λ/4 plate combined with a Glan-Thomson prism and measured by a power/energy meter. The polarized ASE spectra were measured using a dichroic film analyzer A (e _y and e _z are the principal electric vectors of the ASE), neutral density filters and an AvaSpec-2048 CCD spectrometer equipped with an input fiber and a collimating microlens. The same spectrometer scale (in counts) was used in all figures (the detected pulse energy of 1nJ corresponds to 3.6×10⁴ counts·nm of the area under the ASE intensity spectra). The distance of s=120mm between the cell and the collimator satisfied the necessary condition for the gain measurements (s≫l) [16].

3. Results and discussion

Figure 1 shows the principal absorption coefficient spectra k _e and k _o of the 0.5% dye-doped mixture calculated from the experimental spectra of optical density D and cell thickness d=27µm according to formula: k_e,o(λ)=D_e,o(λ)/d log₁₀ e. The liquid crystal matrix absorbs at wavelength λ<350 nm, the band with a maximum at λ_m=480 nm belongs to DCM. The liquid crystal matrix orients the dye molecules due to an elongated shape of the latter. The corresponding dichroic ratio for the dye at λ_m is N=k _e/k _o=3.24. In the Inset to Fig. 1 the same spectra are blown in the range of the material ASE, which is observed between 600 and 625nm. As we shall see, the absorption in that range (especially k _e) significantly influences the gain polarization spectra.

 

Fig. 1. Spectra of absorption coefficients of the mixture E7/DCM(0.5%). The polarization of the spectrometer beam is either parallel (k _e) or perpendicular (k _o) to the director L. In the Inset, the long wavelength edges of the same spectra are magnified and the arrow shows the position of the ASE intensity maximum.

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The geometry and details of our measurements are shown in Fig. 2. The ASE spectrum I_l(λ) is measured for two different positions of the analyzer A (polarizations e _y and e _z). To measure the gain, the same procedure is repeated with the twice shorter pumped path (l/2=3.5mm). To this effect, the right part of the illuminated stripe (IS) was shadowed by a shutter and the two polarization spectra I_l/2(λ) were measured by a spectrometer. The gain spectra were calculated from the ratio of ASE intensity spectra I_l/I_l/2 using equation [16]

In Fig. 3 the ASE intensity and gain spectra of the mixture in the nematic phase are demonstrated for two different orientations of the director L within the plane of the cell. The results shown in Figs. 3(a), 3(b) correspond to the cell geometry of Fig. 2(a), with L and the pump beam polarization P along the x- and y-axis, respectively (L_x, P_y). In this case both the polarizations of the outgoing ASE beam e _y and e _z are perpendicular to the director.

 

Fig. 2. Geometries of the ASE intensity and gain measurements (top view on the planar nematic cell). Illuminated stripe IS has either full length l or a half of the full length ½.

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Fig. 3. The intensity and gain spectra in geometry of Fig. 2(a) (plots a and b) and geometry of Fig. 2(b) (plots c and d). a, c: The polarization spectra of ASE intensity with light electric vectors e _y and e _z; pump pulse energy W _p=5.9mJ/pulse. b, d: Gain spectra at different pump pulse energy (shown at the curves). Solid and dashed lines correspond to e _y and e _z electric vectors of ASE, respectively; nematic mixture E7/DCM(0.5%).

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Therefore, due to the uniaxial symmetry of the nematic phase, the ASE intensity from the dye electronic oscillators predominantly oriented around the x-axis would be the same for both polarizations if the excited molecules were also uniaxially distributed. Indeed, even at a high pump energy the ASE is weakly polarized. The polarization degree, defined for a uniaxial phase [17] as the ratio

is relatively small, I _y/I _z≈3.6, r≈0.47, see the intensity spectra in Fig. 3(a). For the same geometry, the gain spectra for different polarization e _y and e _z are very similar, see Fig. 3(b). This is indicative of the fast relaxation of the excited molecules rotating about their longitudinal axes and consistent with earlier dielectric measurements (rotation times τ_⊥≈0.1-1ns [18] less than the typical lifetime of the excited state τ_ex≈1-5ns [19]). The maximum gain reaches the value of g _max(L_x)≅6cm^-1 (at pump pulse energy of W _p=5.9mJ/pulse with absorbed part of ~50%) and g>0 is observed within the range of 590-630nm.

Plots (c and d) in Fig. 3 correspond to the cell geometry of Fig. 2(b) with both L and the pump beam polarization P along the y-axis (L_y, P_y). Unexpectedly, the ASE intensity in this geometry (plot c) is 12 times lower than in the previous case despite the absorbed part of the pump energy increased up to ~90%. The polarization state of ASE is also dramatically changed. Now the e _z component evidently dominates (I _y/I _z≈0.36, r≈-0.27). We also note a considerable difference between the z- and y-polarized gain spectra (plot d). The maximum gain for e _y and e _z polarizations is 2.7 and 5.0cm^-1, respectively. Moreover, now the positive gain (g>0) is only observed within the range of 605-640nm. This is a fingerprint of the essential role of the sample absorption, especially k _e for the (L_y, P_y) configuration.

Indeed, at λ=610nm, as seen in Inset to Fig. 1, the absorption coefficient k _e=11cm^-1, the absolute value considerably exceeding the maximum gain in all the cases. In fact, the y-polarized beam cannot be amplified at λ<605-610nm [solid curves in Fig. 3(d)]. For the z-polarized beam the absorption is much weaker (k _o=3cm^-1) and amplification is higher [dashed curves in Fig. 3(d)]. Therefore, despite the favorable asymmetry of the angular distribution function of the excited molecules and rather a slow relaxation of the LC (and dye) molecules about their short axes (τ_‖≈100ns [18]), the z-polarized ASE beam is stronger amplified due to the weaker positive absorption. We do not think that the effect of the gain spectral shift by about 15nm to the longer wavelengths (in plot (d) with respect to plot (b) in Fig. 3) may be attributed to the scattering by the director fluctuations, because the latter have characteristic times in the millisecond or even second range and can be considered “frozen” during the short pulse of ASE emission. As to the Rayleigh scattering, it should be very weak on the spatial scale of millimeters and its spectral selectivity (law I~λ^-4) is not enough to explain the spectral shift of the order of 10nm. By the way, the dramatic decrease in the emission intensity I in the range of 605-610nm especially for the y- component [compare Fig. 3(c) with Fig. 3(a)], it is just related to the considerable decrease of the gain in this spectral region according to exponential relation I~e^g(λ)l.

We have also carried out an additional experiment demonstrating the electric field control of the ASE intensity and gain spectra. To this effect, the same E7/DCM mixture was used. However, the dye concentration was smaller (0.16%) and the LC layer was thicker, d=40 µm (this provides more uniform pump beam absorption along the thickness). The cell was made of two glasses with ITO transparent electrodes, which allowed the application of the field along the z-axis. In the absence of the field the director was oriented along the y-axis as in Fig. 2(b). The a.c. voltage of U _rms=7V and frequency 1 kHz reorients the director into the z-direction (L_y→L_z) due to positive dielectric anisotropy of E7 (ε_a≈14). The pump beam was again polarized along the y-axis, therefore, the pump light absorption strongly decreased upon the director reorientation (from L_y to L_z).

The field-off and -on spectra of ASE intensity are shown in Fig. 4(a) for the y-polarized ASE beam. In the field-off initial state, the intensity is comparable to that shown in Fig. 4 due to the same geometry of Fig. 2(b) and similarity of parameters for the two cells. The voltage application reduces the intensity due to the reduced pump beam absorption, however, as seen in Fig. 4 (b), the gain markedly increases with voltage and, at U=7V, reaches the value as high as 7.1cm^-1. Moreover, the left edge of the field-assisted gain spectrum is considerably shifted to the shorter wavelengths. This is a consequence of low positive absorption in the range of 590-600nm. What is important here is the possibility to switch the gain from negative to positive in the range of λ<600nm. Imagine, for example, a laser oscillator operating at λ=600nm, e.g. based on a semiconductor or cholesteric LC. Its emission can be directed into the nematic waveguide and then either absorbed there or amplified depending on the electric field applied to the nematic LC. As shown by the arrow in Fig. 4(b), the voltage can switch the gain from 0 to 4.4cm^-1 (the latter corresponds to a very high beam amplification of 81 times per 1 cm path).

 

Fig. 4. The voltage dependence of ASE intensity (a) and gain spectra (b). The ASE polarization selected by analyzer is e _y. Upon application of the voltage, the director rotates from L_y direction (U=0V, solid lines) to L_z direction (U=7V, dashed lines). Nematic mixture E7/DCM(0.16%), pump pulse energy W _p=3.8mJ/pulse.

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3. Conclusions

In conclusion, we have measured the ASE intensity and gain spectra in polarized light for a dye doped nematic mixture often used in liquid crystal microlasers. The absolute values and the spectra of gain are considerably different in different experimental conditions including the director orientation, the pump intensity and polarization of the ASE beams. The maximum gain measured reaches the value of about 7 cm^-1. We have also shown a possibility to switch the gain of the nematic LC by an external electric field. Materials with field controlled gain can be used in both the waveguiding and planar micro-amplifiers.