1. Introduction

Tunable-focus liquid crystal (LC) lenses and LC microlens arrays have been of interest and investigated widely for an increasing variety of optoelectronic applications including 3D displays, image processing, photonic devices, eye glasses and optical communications [1–6]. LC lenses have been fabricated using Fresnel zone plates [4,7], patterned electrodes [1,3,8], polymer dispersed LCs [9], polymer-stabilized LCs [10,11], and surface relief structures [2,5,12–15]. Refractive index modulation can be utilized for tuning many LC devices, and is dependent on the molecular orientation and the polarization direction of the incident light. Therefore, fabricating a LC lens which possesses the characteristic of polarization independence is crucial. In the future, the optoelectronic devices have to be upgraded and developed to allow faster electro-optic response time and to simplify the fabrication process. So the response time and the fabrication process of the LC microlens are also two of the factors that need to be considered.

In recent years, blue phase liquid crystals (BPLCs) have been widely investigated because of their unique characteristics of optical isotropy, selective Bragg reflection and fast response time (in the range of sub-millisecond), and they do not require the molecular alignment layer [7,8,16–21]. The blue phase can be found at temperature range between the cholesteric phase and the isotropic phase. In an external electric field, the BPLCs exhibit the insignificant local reorientation of LC directors, the reorientational transformation of crystals, and electrostriction, all of which lead to the Bragg reflection shift, phase shift and the Kerr effect [16–18]. Based on the above characteristics, the BPLCs have been developed to optoelectronic applications, such as tunable photonic crystals [7,17], photonic devices of phase modulation [7,8,19], and LC displays [20].

In this study, we propose a simple method of fabricating microlens arrays based on a surface relief structure with the BPLC material. The BPLC microlens has the polarization-independent feature, has fast tuned focal lengths, and can be fast switched between positive and negative lenses via controlling the strength of the electric fields.

2. Operating principle

Figure 1 shows a schematic diagram and the operating principles of the BPLC microlens array. The cell of the microlens array is fabricated using two ITO glasses. On the bottom substrate of the cell is the deposited concave polymer structure, as shown in Fig. 1. The two glass substrates are separated by two 3.5 μm-thick plastic spacers. The cavities of the microlens cell are filled with BPLCs. In a state in which an external field is not applied, the optical refractive-index ellipsoid of BPLCs is circular. Owing to the orientation of BPLCs in the cell being optically isotropic, its refractive index at zero applied voltage is given by n_iso = (n_e + 2n_o)/3, where n_e and n_o are the extraordinary and ordinary refractive indices of the LC host, respectively. When voltage is applied to the BPLC layer, the BPLCs will exhibit birefringence due to the extended Kerr effect [16,18]. Therefore, the refractive-index ellipsoid of BPLCs is transformed from a spherical to an ellipsoidal shape, where the optic axis of ellipsoidal refractive-index ellipsoid is parallel to the electric field [18,20]. When the normal incident light propagates along the optic axis of the BPLCs, the probe light will experience an effective refractive index n_o(V) which depends on the magnitude of the applied voltage (V). Based on the above electro-optical properties of the BPLCs, the refractive index of BPLCs can be modulated from a range of n_iso to n_o(V) by the applied voltage.

 

Fig. 1 Basic configuration and operating principles of the BPLC microlens array without electric state (left side) and with electric state (right side).

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3. Sample preparation and experimental setups

A concave polymer microlens array is deposited on the bottom ITO glass substrate. The first step is to spin-coat UV-curable polymer (Norland, NOA81) onto an ITO glass substrate at the rate of 3000 rpm for 25 sec. The second step is to produce a concave-shaped surface relief structure of the polymer by employing a uniform UV light through a photomask to expose onto the UV-curable polymer film, as shown in Fig. 2(a). The UV light (λ = 365 nm), with an intensity of 30 mW/cm², irradiates the deposited polymer for 19 min. The photomask is a circular array pattern of the metal coating with a diameter and pitch of 100 μm and 200 μm, respectively. The circular pattern of the photomask is designed to resist the UV light irradiating onto to UV-curable polymer film. Because the UV-curable polymer film is spatially-modulated exposed by using UV light with the photomask, it results in the monomeric density generating an uneven distribution. For the above reasons, there is a diffusion shift of the monomers from the unirradiated to the irradiated regions [2,22]. The monomers move to the illuminated regions and polymerize to form the concave-shaped surface structure on the bottom substrate. Figure 2(b) shows the profile image of a concave-shaped surface relief structure. The diameter and center depth of the concave structure are 140 μm and 7.3 μm, respectively.

 

Fig. 2 The SEM images of the concave-shaped surface relief structure.

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The BPLC mixture used in the experiment includes a nematic LC (Fusol material co., HTW114200-100; n_e = 1.77 and n_o = 1.51) and a left-handed chiral dopant (Merck, S811) at a ratio of 65:35 wt%. The BPLC microlens cell is heated up to above its clear point and then is cooled from the isotropic state down to the blue phase at a cooling rate of 0.01 °C/min by controlling the temperature. The temperature range of the blue phase is from 44 to 36 °C. In our experiment, the BP in the microlens array is 40 °C.

Figure 3 depicts the experimental setup for measuring the focusing properties and response times of the BPLC microlens array by using a CCD camera and a photo detector. A circularly polarized laser beam (from a He-Ne laser, wavelength: 633 nm) is magnified with a beam expander, which passes through a polarizer to change the polarization direction of the normal incident light and then illuminates the cell of the BPLC microlens array. Utilizing an imaging lens (L3) allows the transmitted light from the sample to be focused on the CCD camera. The CCD camera is placed near the position of the focal plane in order to analyze the intensity distribution of focused light of the microlens array. The sample is linearly moved along the optical path in order to determine the effective focal length.

 

Fig. 3 Experimental setup for measuring the focusing properties of the BPLC microlens array.

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4. Results and discussion

Figure 4(a) shows the polarizing microscopic image of the BPLC microlens array at zero applied voltage. The domain diameters of the platelet texture in the BPLC ranges from 100 to 200 μm at zero applied voltage. Because of the larger domain size, the scattering effect from the multi-domain is weak in the microlens array. Obviously, the microlens array can converge the incident light, as displayed in Fig. 4(a). Figures 4(b)–4(d) show focused images of the microlens array that are taken from the CCD camera at various applied voltages. At zero applied voltage, all focal points at the focal plane are uniform and consistent, and the convergent performance of the microlens can be clearly displayed, as shown in Fig. 4(b). When the voltage is increased to 70 V, the focal points gradually disappear and exhibit uniform intensity, as shown in Fig. 4(c). The BPLC effective refractive index n_o(V) matches the polymer refractive index n_p, resulting in the defocusing of the light. Figure 4(d) illustrates that when a voltage of 150 V is applied to the BPLC layer, the transmitted light from the microlens is diverged due to n_o(V) < n_p. Therefore, the focus of the microlens deteriorates significantly.

 

Fig. 4 (a) Polarizing microscopic image of the BPLC microlens array without applied voltage. The focused image of the BPLC microlens array at (b) V = 0, (c) V = 70 V, (d) V = 150 V, respectively.

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The tuning of the focal length can be achieved by utilizing the difference of the refractive indices between the BPLC and concave polymer structure. Owing to the concave shape of the polymer structure, the BPLC layer resembles a plano-convex lens. On the basis of Lensmaker’s formula, the focal length is determined by the curvature radius (r) of the surface relief structure, and the refractive index difference (Δn = n_o(V)−n_p) between the BPLC layer and the polymer, as f = r/(n_o(V)−n_p). In this experiment, the curvature radius of the surface relief structure r is about 138 μm, and the refractive index of the concave polymer structure n_p is 1.56. However, the measured focal length of the microlens is shown in Fig. 5. At V = 0, the refractive index of the BPLCs is larger than that of the polymer, and the focal length of the microlens is about 4.0 mm. When the difference of the refractive index between the BPLC layer and the polymer is the greatest, the focal length can be the shortest. After the applied voltage is higher than the threshold V_th ~20 V, the focal length increases via the increase in the applied voltage in the positive lens. Because the effective refractive index n_o(V) of the BPLCs equals the refractive index n_p of the polymer at the voltage range between 60 V and 70 V, there is no refracted light in the concave-shaped surface relief structure. Therefore, the focal length is infinite. In the negative lens, the BPLC refractive index is smaller than the polymer refractive index (n_o(V) < n_p), and the focal length gradually decreases from −12.0 mm to −3.7 mm by increasing applied voltage from 80 to 150 V. The tunability of the focal length is in the range of 2 mm in the positive lens and 8.3 mm in the negative lens. Therefore, by varying the voltage, the focal length can be continuously tuned between the positive lens and the negative lens. Under a high applied voltage, the BPLC effective index n_o(V) is gradually saturated and close to n_o. In the process of tuning the focal length, the matching of the refractive index difference between the BPLCs and polymer plays an important role. Therefore, the microlens may be formed via either a convex or a concave lens, depending on the difference values between n_p and n_o(V).

 

Fig. 5 Measured focal length of the BPLC microlens as a function of applied voltage.

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Figure 6(a) plots the intensity of the focused light at various polarization directions of the incident light. Under an applied voltage of 30 V, the photo detector is placed on the focal point of a BPLC microlens and measures the intensity of the focused light. As shown in Fig. 6(a), the BPLC microlens exhibits a focusing effect of polarization independence. As the polarization direction of the incident light changes, the intensity of the focal point remains constant. It is attributable to the optical isotropy of the BPLCs at zero applied voltage. Under a vertical electric field, the electrically tunable BPLC refractive index is insensitive to variation in polarization, because the propagation of a normal incident light is along the optic axis of the birefringence of the BPLC. This result implies that the microlens exhibits the polarization-independent feature.

 

Fig. 6 (a) Measurement of intensity of focused light for single BPLC microlens under applied voltage V = 30 V with various polarization directions of the incident light. (b) and (c) Measurement of response times for the BPLC microlenses (red lines) with the square-wave voltage (blue lines) switched between 0 and 80 V.

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The response time of the BPLCs depends on the strength of the electric field [21]. Therefore, the microlens is a thin cell gap, which can increase the electric field strength of the BPLC layer, and then it decreases the response time of the microlens. In this experiment, the thickness of the BPLC layer is less than 11 μm, so it can gain fast response times without using polymer network stabilized BPLCs. The response times are measured via switching the intensity of focused light of the microlens between convergence and divergence. The intensity of focused light of the microlens is measured at a focal length of −12 mm by switching an applied voltage which is 80 V with a square wave of 1 KHz. The measured response times of the BPLC microlens are at a rise time τ_rise of:0.86 msec and a decay time τ_decay of:0.74 msec, as shown in Fig. 6(b) and 6(c), respectively. The response times of the BPLC microlens are much shorter than those of the conventional nematic LC microlens, which are of the order of milliseconds [2,11,13,14].

5. Conclusion

In summary, this study successfully demonstrates a polarization-independent microlens array based on BPLCs. In this method of fabricating a microlens array, the BPLC material can be applied in the microlens array device without giving the molecular alignment layer. Therefore it simplifies the fabrication process, and it also promotes the properties of polarization independence and fast response. In addition to the advantage that the microlens can be tuned by the focal lengths, the microlens can also be switched between positive and negative lenses. The microlens array has potential in the future optoelectronic device applications.