Efficiency improvements in a dichroic dye-doped liquid crystal Fresnel lens

: A dichroic dye-doped liquid crystal Fresnel lens was fabricated and investigated to observe the combination of phase and amplitude modulation based focusing. An anthraquinone dichroic dye was doped into a liquid crystal host, which when in the Fresnel lens conﬁguration, generates a Fresnel zone plate with alternating “transparent” and “opaque” zones. The zones were induced by using photo-alignment of a light-sensitive alignment layer to generate the alternating pattern. The voltage dependency of eﬃciency for the dye-doped and pure liquid crystal Fresnel devices were investigated. Incorporation of dyes into the device yielded a signiﬁcant 4% improvement in relative eﬃciency in the lens, giving a maximum of 37% achieved in the device, much closer to the theoretical 41% limit when compared with the non-dye-doped device. The input polarization dependence of eﬃciency was also investigated, showing very small ﬂuctuations ( ± 1.5%), allowing further insight into the eﬀect of fabrication method on these liquid crystal Fresnel devices.

The LC Fresnel lens reported here was fabricated using direct substrate photo-alignment [34]. Alternating zones of orthogonal director alignment were created on one surface, which generated the Fresnel pattern, with the other surface treated for homeotropic alignment, Fig. 1(a). This device geometry creates an alternating hybrid aligned nematic (HAN) director field inside the device. Previous dye-doped LC Fresnel lens devices have focused on the use of doped dyes either to generate alternating alignment directions [25][26][27] or to photo-induce zone specific phase transitions [20,21], and have not investigated their potential impact on efficiency. Use of the dichroic dyes in the LC will generate alternating "opaque" and "transparent" zones which is in effect a Fresnel zone plate. Fresnel zone plates focus light via amplitude modulation (similar to a standard diffraction grating). However, when considering a dye doped LC Fresnel lens the amplitude modulation focusing will combine with the phase focusing effects of the birefringent material. This report investigates the direct effect of an anthraquinone dichroic dye [35] amplitude modulation based focusing on the efficiency of a switchable dye-doped guest-host LC Fresnel lens. Anthraquinone dichroic dyes have a transition moment approximately parallel to the molecular long axis, which results in a polarization angle dependent absorption. When doped into a LC (host) the dichroic dye (guest) will be oriented by the bulk LC director [36], with the dye long-axis parallel to the director. Therefore, when a LC Fresnel device configuration is considered, a Fresnel zone plate with alternating strongly absorbing and weakly absorbing zones is generated. Fresnel zone plates have a maximum theoretical relative efficiency (ratio of the focused spot intensity to the total transmitted intensity, used commonly in LC Fresnel characterization [4, 10, 16, 19, 20, 23, 25, 30 & 33]) of ∼21% (∼10.5% absolute efficiency). The light transmitted through this LC Fresnel device will therefore undergo amplitude modulation based focusing due to the alternating absorption caused by the dichroic dye guest-host effect, determined by components of the parallel and perpendicular absorption coefficients, a | | and a ⊥ . Under application of a sufficiently large E-field (the threshold voltage of the device must be exceeded) the director will re-orient and approach the homeotropic (HT) alignment state. This will remove the contrast between zones and the dye absorption will become constant across the device, removing the amplitude-focusing effect. The LC Fresnel device will also focus light due to the inherent birefringence of the LC that causes a phase-shift between alternate zones, Φ=2π∆nd/λ, where ∆n is the birefringence, d is the cell gap, and λ the wavelength. The peak in efficiency due to the phase effect occurs when Φ=π (maximum theoretical efficiency ∼41%). The refractive index difference between zones can also be controlled via E-field application, and eventually reduced to zero when the device approaches the HT state.
In this report we investigate the coupling of the phase and amplitude modulation focusing effects on the efficiency of this switchable dye-doped LC Fresnel lens.

Materials and methods
The LC Fresnel lens described here was fabricated using a masked photo-alignment technique.
The photomask was designed with rings of radii; R n = nλ f + nλ 4 , where λ=532 nm, n is the ring number (156 total rings, R max =5 mm), and f the focal point is 0.3 m. A polyamic acidcontaining azobenzene in the backbone structure (Azo-PAA, obtained from JNC Petrochemical Co.) [34] was spin coated onto indium tin oxide (ITO) glass before being treated with a 3-step patterning technique, depicted in Fig. 1(b). Initial irradiation of the substrate with linearly polarised light (150 Jcm −2 ) gives homogenous planar alignment perpendicular to the irradiation polarization. The substrate is then irradiated with unpolarised UV light at 45°incidence angle (220 Jcm −2 ), inducing a pre-tilt angle of ∼2°. The pre-tilt is induced due to the affinity for the Azo-PAA to orient perpendicular to the UV irradiation polarization. In this case it is unpolarised and therefore results in a preferred orientation into the irradiation direction, more information on this alignment technique can be found in [34]. This step is introduced into the fabrication process to remove defect lines generated by reverse-splay HAN domains which would occur for 0°pre-tilt and cause scattering in the final implementation of the device. Finally, a chrome photomask is placed in contact with the substrate and then irradiated with linear polarised light at 90°to the first irradiation (720 Jcm −2 ). This generates orthogonal alignment in the photomask transparent zones with a 0°pre-tilt angle. The substrate is then baked at 250°C for 2 hours to fix the alignment. To create the bottom HT aligned substrate, a side-chain-containing AZO-PAA [37] was spin coated onto ITO glass and then baked. The device was then assembled using 50 µm spacer film, chosen to give optimal contrast between orthogonal dye doped zones, calculated from 15NB3 guest-host absorption coefficients and the Beer-Lambert law (a // =0.11% −1 µm −1 and a ⊥ =0.0087% −1 µm −1 ).
The LC host chosen for this study was MLC-7023 (∆n = 0.0609 and ∆ǫ=7.9) obtained from Merck Chemicals Ltd.. This LC was doped, close to the solubility limit, with 0.50%(w/w) 15NB3 anthraquinone dye (λ max =540 nm) synthesized at the University of York [38]. Both pure and dye doped devices were fabricated for direct comparison.

Results and discussion
The effective birefringence (∆n eff ) for each sample was measured in the HAN device (λ=589 nm) configuration with varying voltage from 0 to 20 V rms ( Fig. 2(a)). For MLC-7023, ∆n eff varies from 0.034→0.001, whilst 15NB3-doped MLC-7023 has a slightly lower birefringence, varying from 0.031→0.001, due to the difference in composition. The measurements of birefringence allow the phase shift in the device to be calculated, allowing a direct comparison of efficiency measurements between samples. The absorption of green laser light (λ=543.5 nm) polarised parallel and perpendicular to the bulk director (A // and A ⊥ ) was characterized as a function of voltage through use of a photodiode, Fig. 2(b). At 0 V rms A // =(0.95 ± 0.02) OD, much larger compared to A ⊥ =(0.372 ± 0.005) OD. Upon increasing voltage, the contrast in absorption, ∆A = A // -A ⊥ , decreases as each zone approaches the HT state, going from ∆A=(0.57 ± 0.02) OD to ∆A=(0.029 ± 0.001) OD. Thus, a continuous reduction in amplitude modulation focusing is generated in the dye doped LC Fresnel lens device.
Polarizing optical microscopy (POM) was used to image the LC Fresnel lens, as shown in Figs. 2(c) and 2(d). Excellent alignment in each device is observed. Figure 2(c) is the MLC-7023 sample viewed between crossed polarisers, with a λ-plate allowing the orthogonal alignment to be observed. Figure 2(d) shows the dye doped sample viewed with a single input polariser, clearly demonstrating the alternating zone absorption effects that are under investigation here. The colour intensity alternates between zones due to orthogonal director alignment.
The focusing efficiency of the device was measured as a function of voltage (0 -20 V rms , frequency = 10 kHz) using an expanded green laser (λ=543.5 nm, f lens =0.29 m). The relative The absolute efficiency measured in the device will also be demonstrated. The device will exhibit losses with respect to the initial intensity due to dye absorption, and therefore lower absolute efficiency maxima as observed in other amplitude based focusing systems.
To account for the difference in the birefringence of the mixtures (Fig. 2(a)), as well as the small cell gap differences between the devices (50.3 and 50.5 µm), the applied voltage was converted to the equivalent phase shift, Φ/π=2∆nd/λ, to allow a clear comparison between measurements. The maximum phase focusing efficiency component will theoretically occur when Φ=π (Φ/π=1), with Φ continuously decreasing with increasing voltage. It is noted that the small (∼3%) wavelength dispersion and temperature dependence of the LC birefringence will impact the calculated phase shift, and therefore the peak in efficiency vary slightly from Φ/π=1; nonetheless this calculation gives a facile comparison of devices. The amplitude-focusing efficiency component will theoretically start at a maximum at 0 V rms , corresponding to maximum dye contrast, and will then decrease continuously with increasing voltage. Figure 3(a) shows how the relative efficiency varies with Φ/π for the MLC-7023 and 15NB3 doped MLC-7023 devices (this parameter varies as the applied voltage increases). The dye doped sample provides a 4% increase in efficiency in the phase-focusing states, which correspond to the peaks in efficiency. Away from the phase-focusing states, Φ nπ, a 3.5% improvement is also observed. The improvements to efficiency are a result of the addition of the amplitude-focusing effects, which are independent of the phase shift. Table 1 demonstrates how these values for efficiency compare with previous literature. Whilst the pure LC Fresnel lens demonstrated here is slightly lower than similar devices (likely due to device imperfections e.g. scattering from zone boundaries), the dye doped device shows a clear improvement, moving the device towards the top end of currently achieved efficiencies. When comparing devices this close to the maximum theoretical efficiency an improvement of ∼4% can provide quite an advantage over other devices. The measured efficiency is lower at low voltages due to the scattering at the zone boundaries where the director field is less ordered at these lower voltages. Figure 3(b) demonstrates the difference between the absolute and relative efficiencies of the dye doped Fresnel device. The absorption caused by the dichroic dye in the system results in a lower overall transmission through the device and therefore a lower absolute efficiency.  The polarization angle dependency of this device was thoroughly investigated via efficiency measurements at 0 V rms (Φ π) and 3.7 V rms (Φ=π) (Fig. 3(c)). Note that 0°polarisation angle corresponds to the alignment of the polarisation of light with the pre-tilted director. Typically, a Fresnel device with orthogonal alignment zones would have polarization independence, however here a small variation in the efficiency of each device with respect to input polarization angle is measured (maximum ± 1.5%). This is a direct result of the alignment layer pre-tilt angle (∼2°) that occurs only in the even zones. The polarization dependence of each device is 90°out of phase with respect to the other, the result of the different types of focal effects (phase or amplitude modulation), each of which is considered here in turn.
In the case of the pure MLC-7023 device at 0 V rms the device is not in the Φ=nπ condition, and increases in voltage (decrease in phase-shift/birefringence) increases the efficiency towards the maximum. When the input polarization is at 0°the birefringence between zones is ∆n = n e,Θ -n o , where n e,Θ is the pre-tilted extraordinary refractive index and n o is the ordinary refractive index. At 90°the birefringence between zones is simply ∆n = n e -n o , where n e is the extraordinary refractive index. This means that on rotating the input polarisation from 0 to 90°, a small increase in birefringence is observed, moving the device further away from the phase-focusing peak, effectively reducing the efficiency. This can be observed in Fig. 3(c) where the MLC-7023 device efficiency without an applied voltage starts with a maximum value at 0°and decreases slightly to a minimum at 90°. The same effect, although smaller due to the decrease in zone difference under applied voltage, is observed when 3.7 V rms is applied; the shift in birefringence again moves away from the peak in efficiency.
In the case of the 15NB3 doped MLC-7023 device at 0 V rms we have a large difference between A // and A ⊥ . At 0°input polarization angle there is an effective contrast between zones ∆A = A Θ -A ⊥ , where A Θ is the absorption parallel to the long axis of the pre-tilted director. When the input polarization is at 90°there is an effective contrast between zones of ∆A = A // -A ⊥ , which is greater than the contrast at 0°. Therefore, on rotation from 0 to 90°we get an increase in absorption contrast and therefore an increase in the amplitude-focusing effect. This can be observed in Fig. 3(c) where the 15NB3 doped MLC-7023 efficiency starts at a minimum at 0°a nd increases towards a maximum at 90°. The same effect is observed at 3.7 V rms , although with a smaller amplitude, again due to the decrease in zone difference under an applied voltage.

Conclusion
Development of a dye doped guest-host LC Fresnel lens has been undertaken to investigate the effect of amplitude modulation focusing on the relative efficiency of the Fresnel device. Inclusion of an anthraquinone dichroic dye into the LC host generates a clear improvement in the maximum efficiency of the device from 33 to 37%. Application of a voltage across the device allows the efficiency to be controlled, approaching 0% at voltages ∼20 V rms , offering a clear variation from focusing to non-focusing. The polarization dependence of the device was investigated and shown to vary due to device pre-tilt, by up to ± 1.5% depending on the input polarization angle. This can be attributed to the difference in the pre-tilt alignment of the different zones, and it is noted that the dependency can be removed if device fabrication ensures identical pre-tilt angle between zones.