Liquid-Crystal Devices and Waveplates for light controlling

Transcription

1 Armenian Journal of Physics, 2014, vol. 7, issue 2, pp Liquid-Crystal Devices and Waveplates for light controlling M.R. Hakobyan and R.S. Hakobyan Optics Department, Yerevan State University, 1 Alex Manoogian, 0025 Yerevan, Armenia * hamara404@gmail.com Received 17 December 2013 Abstract The main characteristics of liquid crystal devices (LCDs) are discussed with reference to various technologies. Principles of operation of some LCDs for light radiation parameters controlling are described. Two advanced waveplates are demonstrated: cycloidal diffractive waveplates (DWPs) and DWPs with axial symmetry. Achievements in the technology of producing highquality DWPs with practically 100% efficiency over a large area advance the prospects and the concepts of polarizer-free LCDs. These gratings could be used for beams combining and polarizing with high productivity. Observations prove the feasibility of new generation high-efficiency diffractive optical components, which are most promising for infrared and high-power applications owing to their enhanced transparency and reduced thermal effects in thin material layers. 1. Introduction. This paper reviews one specific type of electronic device the liquid-crystal device (LCD), and its emergent application as a spatial light modulator (SLM) for coherent optical processing. The LCD and its technology are discussed with reference to the wider world of electronic displays generally and to other devices whichcould be used in optical processing systems. LCDs have become the leading technology in the information display industry. They are used in smallsized displays such as calculators, cellular phones, digital cameras, and head mounted displays; in medium-sized displays such as laptop and desktop computers; and in large-sized displays such as direct-view TVs and projection TVs [1]. They have the advantages of high resolution and high brightness, and, being flat paneled, are lightweight, energy saving, and even flexible in some cases. LCs have also been used in photonic devices such as laser beam steering, optical limiting, variable optical attenuators, tunable-focus lenses, high efficiency polarizers, coherent incoherent mirrors, laser and optical ray combine and others. There is no doubt that LCs will continue to play an important role in the era of information technology. Along the long developmental paths, there have been numerous challengers such as thin film electroluminescence, vacuum fluorescence, electrochromics, plasma display panel and field emission displays. Spatial light modulators (SLM) also had very difficult paths from lightcrystal, electrophoretic, electrochemical, photochromic, electromechanical, cathodechromic, magneto-optic and deformagraphic. Each time, LCDs have been able to sustain the challenges and emerge victoriously. Now, it looks certain that thin-film-transistor LCDs will replace the ultimate king, cathode ray tubes, in the home s living room as the primary video display. The LCD technologies have amazing resources and versatility. For each new application, LCD engineers have been able to expand the LCD capabilities to meet the new demands in

2 LIQUID-CRYSTAL DEVICES AND WAVEPLATES Armenian Journal of Physics, 2014, vol. 7, issue 2 performance. Taking the latest TV application as an example, the LCD engineers have been able to solve issues such as wide viewing angle, fast response, and color shift versus gray levels and viewing angles. What will be the next major application beyond TV? We don t know yet. However, we are certain that LCD engineers will be able to rise above the challenges and bring the technology to the next level. Both light-emitting and light-modulating devices are used in optical processing systems. Light-modulating electronic displays are generally related to the class of devices now referred to as spatial light modulators, which are essential elements in real-time optical processing systems. They can be used as optical limiters, arrays of optical gates, variable diffractive elements, incoherent-to-coherent converters, wavelength shifters and light amplifiers. The LCD technologies will be the dominating flat panel display for many years to come. 2. Characterization of liquid crystals It was eventually established that a new state ofmatter, intermediate between the liquid and crystalline state, was involved and that transitions between the true liquid phase, the new liquid crystal or mesophase and the true solid or crystalline phase occurred sharply at well-defined temperatures [2]. Just as with the solid crystalline state, a number of distinct LC phases were discovered. These LCs are characterized by structural arrangements of individual molecules with a degree of ordering intermediate between the almost total lacks of order in true isotropic liquids, and the very high degree of order in true crystals, which of course are often anisotropic in their properties. LCs existing at temperatures between the isotropic liquid and true crystalline phasesare called thermotropic and these are the types which are mainly of current interest to optical device technologies.the anisotropy of the elastic, electric, magnetic, thermal, hydrodynamical and optical properties of LCs has led to their present usefulness. Thermotropic LCs are classified into nematics, cholesterics, smecticsand others. Nematic liquid crystals (NLCs) may be formed by compounds having elongated molecules. The characteristic order is a partial orientation of the molecules with their long axes parallel to a common direction (with unite vector ncalled as director). The extent of alignment along the director is characterized by an order parameter S. The distribution of the molecular centers of gravity, however, is without long-range order as in a normal isotropic liquid. So far only uniaxial order without polarization (n= n) has been observed. Cholesteric liquid crystals (CLCs) are formed by optically active compounds or optically active mixtures. Here a helical twist is imposed on the nematic ordering. In this structure the direction of the local optic axis is constant in planes that lie perpendicular to the twist axis and turns regularly along the axis. The distance for a 360 o turn is the pitch (P). Cholesteric structures may be formed, as well, by adding optically active compounds to nematics, in which case the pitch can be controlled by the amount of additive. Smectic LC that is characterized by ordering in layers and other types of LC will not discussed in this paper. Due to the preferred molecular orientation in LC phases, the properties are anisotropic. The most important properties from the device point of view are the refractive indices, the dielectric constants and the elastic constants. In thin layers the usual device configuration - the homeotropic alignment or texture appears dark between crossed polarizers. If the optical axis of the LC cellisslightly disturbed relative polarizersthere is a momentary flash of transmitted light, showing clearly that the medium is not isotropic. If the light is propagated along some other 60

3 Hakobyan et al. Armenian Journal of Physics, 2014, vol. 7, issue 2 direction, different vibrations are propagated at different speeds and fall progressively out of phase with each other. If white polarized light is passed through a LC at an arbitrary angle to the optical axis, the interference of different components gives rise to a colored output. Optical anisotropy means that the refractive index n = ε ε is dielectric permittivity in the limit of very high frequencies differs for light polarization along (n ) and perpendicular (n ) to the director. For similar reasons, the dielectric permittivity ε at low frequencies differs from directions parallel to (ε ) and perpendicular to (ε ) the long molecular axis. Whilst most LCs are positively birefringent, they can have both positive and negative dielectric anisotropy (ε a = ε ε ). A LC with positive ε a, will tend to align parallel to anapplied electric field while a negative LC will tend to align normal to the field. From a device point of view it is usually desirable to maximize ε a, since the larger the difference, the less the field strength required to cause alignment [3]. The dielectric constants undergo relaxations at different frequencies of applied field. Usually these relaxations are in the MHz region and therefore of no interest to current electro-optic device technology, but in some instances, relaxation of ε a, occurs in the khz region. This can actually cause a reversal of the sign of ε a, in some cases. This can be put to good use in two frequency devices as we shall see later. Liquid crystals are characterized by three elastic constants corresponding to splay (K 1 ), twist (K 2 ) and bend (K 3 ) distortions of a structure. The magnitudes of these constants are important in determining the time taken for the LC structure to revert to its initial state after some perturbation such as the application of an electric field. A theoretical analysis in [4] of the behavior of a homogeneously aligned positive nematic under an applied field E assuming only small displacements from equilibrium and for weak field strength, gave a time constant: ( ) 2 2 τon = γ K1 π / L εae 1, (1) where γ is a viscosity coefficient and L the cell thickness. The critical field is given by c ( π / )( / ε ) 1/2 E = L K. (2) So the critical voltage is independent of LC thickness. With zero fields the distortion decays exponentially with time constant: 2 1 τoff = γ K1 ( π / L). (3) 1 a 3. Basic elements of LCDs The basic element of an LCD system includes a thin layer of LC sandwiched between a pair of sheet polarizers. To control the optical transmission of the display element electronically, the LC layer is placed between transparent electrodes, e.g., indium tin oxide (ITO). In most highquality displays, thin optical films or birefringent materials are employed to improve the contrast ratios and colors at large viewing angles. The sheet polarizers, thin optical films, and the electrodes are cemented on the surfaces of the glass plates. The thickness of the glass plates can be from 0.5mm up to a few millimeters to maintain a uniform LC layer and the structural 61

4 LIQUID-CRYSTAL DEVICES AND WAVEPLATES Armenian Journal of Physics, 2014, vol. 7, issue 2 integrity of the panel. The thickness of the LC layer (also known as the cell gap) is kept uniform by using spacers made of glass fibers or transparent plastic microspheres. In somelcds, an array of micron-high posts is employed to maintain a uniform cellgap. Typical cell gaps are in the range of 5 μm. By applying a voltage acrossthe transparent electrodes, an electric field inside the LC can be obtained to control the orientation of the LC molecules and thus to change the optical property (e.g., phase retardation) of LC layer. This leads to a change of the transmission of light when the LC cellis sandwiched between a pair of polarizers. To achieve the display of information, we need a two-dimensional array of these electrodes. These electrodes can be driven electrically for data input by using two sets (x, y) of parallel arrays of electrodes. 4. Birefringent thin film a waveplate for polarization conversion Any light beam, generally, is a superposition of pair of orthogonal polarized beams. These pair can be two orthogonal linear polarized beams or right and left circular polarized beams. If phase difference between pair is constant, then in superposition we have polarized light. Otherwise, we have natural unpolarized light. Polarization is the attribute of light that provides means for easily and efficiently controlling its more discernible characteristics such as intensity and propagation direction. Its two orthogonal components can be separated using different kind of linear or circular polarizers. The state of light polarization can be controlled with a thin layer of an optically anisotropic material as well.the main characteristic of this kind of polarization convertor is phase retardation:γ= 2π n/λ where n= n n, λis the light wavelength. If Γ= π, then this half-waveplate (HWP) can rotate the polarization of incident linear polarized light at an angle β equal twice of the angle α between initial polarization and optical axis of retarder (β= 2α). When α= 45 one pair of linear orthogonal wave will convert to another. If incident wave is circular, then HWP will change the handedness of wave. Half-waveplate is known as condition since it takes place when the difference in optical paths for the orthogonal polarized beams is equal to the half of the light wavelength. Typically, n ~ 0.2, and a birefringent film of nearly 1 μm thickness is sufficient for transforming one orthogonal polarization into another. If Γ = π/2, then we have a quarter-waveplate (QWP) that convert linear polarized light into circular (and vice-versa) when α = A system of birefringent thin films The transmission of light through the single crystal placed between parallel polarizers and having optical axis with azimuthal angle 45 with respect to the polarizers is given by T = cos 2 (Γ/2). As we see from the phase retardation formula above, it is strongly dependent on the wavelength via the 1/λ factor. For most transparent crystals, the chromatic dispersion of n further increases the variation with the wavelength. In many optical applications, including LCDs, it is desirable to have waveplates (WPs) whose phase retardation is insensitive to the wavelength variation. Such WPs are known as achromatic. Two and more usual WPs provide new degrees of freedom to obtain the HWP condition practically independent on wavelength in a wide spectral range [5]. A symmetric combination of WPs is equivalent to single WP. The equivalent phase retardation Γ e of such a combination of WPs depends on the azimuth angles as well as phase retardation of individual plates. Under the appropriate conditions the equivalent phase retardation Γ e can be insensitive to the wavelength variation. Such kinds of WPs are called as Pancharatnam achromatic WPs. In the case of the combination of three WPs the transmission 62

5 Hakobyan et al. Armenian Journal of Physics, 2014, vol. 7, issue 2 of Pancharatnam achromatic WP is proportional to cos 4 (Γe/2). That is why for more of wavelength half-wave condition will be close to satisfied. By increasing the number of WP layers we can get much more power of cos(γ e /2) and wider range of achromaticity. A multitude of birefringent layers, each one having its optical axis orientation rotated with respect to its neighbor, produces a photonic bandgap. At the limit of continuous helical rotation of the optical axis orientation, that happens naturally in CLC, the bandgap acts as a circular polarizer reflecting light with wavelengths in the spectral range n P<λ<n P. Only the component polarized according to the helix is reflected while the orthogonal one propagates as through an isotropic material. 6. Electro-optic effect in twist nematic cell The most striking feature of cholesterics is their strong optical activity and the selective light reflection observable with the planar texture. The optical activity and the selective light reflection are due to the twisted structure and are directly related to the pitch. The pitch can be strongly temperature dependent. This causes light of different colors to reflect selectively in the Bragg sense from the parallel planes of which the helicoidal structure is composed. This effect is utilized in LC thermography. The optical rotary power of a cholesteric decreases more and more sharply with increasing temperature as the cholesteric to nematic transition is approached. In 10 μm layers, the decrease can be as much as 30 o of rotation per 6. The electro-optic effect most used in LCDs, particularly displays is that discovered by Schadt and Helfrich [7] and commonly known as the twisted nematic (TN) effect. Here an electric field perpendicular to the plates of the LC cell (easily applied by means of transparent electrodes on the plates) is used to realign a uniformly homogeneous positive nematic. In the TN cell, however, the original molecular alignment is such that the molecules (represented by the rods in Fig.1) near one plate are rotated in the plane of the cell by some angle, usually near 90, with respect to the molecules near the other plate. For the usual cell spacing of around 10μm, the molecules in the bulk of the LC gradually twist from one direction to the other as the thickness of the cell is traversed. Provided the cell thickness is considerably greater than the wavelength, this has the effect of guiding the polarization vector of incident polarized light through the same angle as the twist. In other words, the way the cell has been constructed has imparted optical activity to the layer of LC. 63

6 LIQUID-CRYSTAL DEVICES AND WAVEPLATES Armenian Journal of Physics, 2014, vol. 7, issue 2 When the field is applied, the molecules align along it and this optical activity diminishes and finally disappears. If the cell is placed between crossed polarizers it will transmit light when no field is applied and will not transmit light when activated. Figure 1summarizes the action of a TN cell. For the critical field and switch on and off times we have the same formulas as (1)-(3), but instead of K 1 supposed to be K 2. Usually neutral color polarizers are used to give a high contrast black and white display, but color-selective polarizers can also be used. 7. Addressing LCDs with few switchable elements can be addressed by running independent electrodes to each and every pixel. Commonly, high resolution LCDs have sets of parallel strip bus bars on each plate assembled so that the sets are orthogonal to each other. Pixels are defined at the crossing points of the electrodes. Data pulses are fed simultaneously down all column electrodes on one plate and the row electrodes on the other plate strobed synchronously to activate selected elements along one line at a time. Activation is achieved when row and columnpulses - usually bipolar square - are out of phase. In principle, the optically addressing radiation field could be the natural thermal emission from warm objects in a field-of-view focused onto the LC layer. This produces an image wise modulation of a LC optical property, e.g. color, which can be read directly simply by looking at it. This direct thermal imaging, however, lacks sensitivity. An improvement to the thermal imaging LCD is to read it by means of a scanned polarized laser beam and interrogate the reflected beam for its state of polarization using a Wollaston prism arrangement. If the writing light is visible, a separate light-sensitive layer may be incorporated so that electro-optic rather than thermo-optic LC effects may be exploited. Figure 2 shows the constructions of reflective (a) and transmissive (b) liquid crystal visible light valves (LCVLV). A photoconductive layer and a LC layer are separated by a dielectric mirror and a light blocking layer. The layers are enclosed between plates carrying transparent electrodes in the way usual in LCDs. A field just insufficient to activate the LC is applied. When light is incident on a region of the photoconductor itsthrough-film resistance is reduced and a greater proportion of the applied voltage drops across the LC layer there by activating it. In this way, an image wise modulation of intensity in the writing beam causes image wise modulation of the birefringence of the LC layer and the uniform reading beam 64

7 Hakobyan et al. Armenian Journal of Physics, 2014, vol. 7, issue 2 incident on the LC side of the cell is similarly modulated and reflected. Figure 2(b) shows a simpler structure which is used in the transmissive mode. 8. Spatial light modulators Optical processing systems using two-dimensional display-like components may be coherent or incoherent. Coherent systems are nearer practical utilization than systems performing digital or logical operations using optical gating. Particularly successful coherent optical processing systems use those based on the V an der Lugt architecture [8]. The component requirements are of course different and they are discussed in detail elsewhere [9]. Here we concentrate on the various LC devices that have been or could be used as real-time optical processing components. Liquid-crystal spatial light modulators may be placed in two distinct categories: (i) optically addressed, and (ii) electrically addressed. The latter arevery closely related to displays, so our remarks mainly refer to the optically addressed devices. Several such devices have been made by different groups of workers. They differ in mode of operation (transmission or reflection), in the light-sensitive elements and LC effects employed. The simplest device results from using a photoconductor with a high enough through-film resistivity to match the impedance of the LC layer. One such material is bismuth silicon oxide, Bi I2 SiO 20, which can be grown as a single crystal and thinned down to a thickness which absorbs most of the writing light but does not allow so much charge spreading that the device is degraded. Since its photoconductive response falls off with increasing wavelength, the device can read with red light in the transmissive mode [10]. With a photoconductor thickness of 500μm and careful choice of operating conditions, spatial resolution of 25 lines mm -1 at 50% modulation transfer function (MTF) can be achieved in a twisted nematic cell of 6μm LC thickness [11,12]. 9. Diffractive waveplates As we have mentioned above, the polarization rotation angle of linear polarized light at the output of HWP, β = 2α, depends on the orientation of the optical axis n in theplane of HWP. LC materials, both low molecular weight as well as polymeric, allow continuous rotation of n in the plane of the WP at high spatial frequencies, α = qx, where the spatial modulation period Λ= 2π/q can be comparable to the wavelength λ of visible light (Fig. 3). Polarization of light at the output of such a WP is consequently modulated in space, which is revealed under a polarizing microscope. The electric field in the rotating polarization pattern at the output of this WP is averaged out, <E > = 0, and there is no light transmitted in the direction of the incident beam. That pattern, however, corresponds to the overlap of two circularly polarized beams propagating at the angles ±λ/λ. Only one of the orders is present in the case of a circularly polarized input beam, the +1st or 1st, depending on whether the beam is 65

8 LIQUID-CRYSTAL DEVICES AND WAVEPLATES Armenian Journal of Physics, 2014, vol. 7, issue 2 right- or left-handed. Since a HWP reverses the sign of circular polarization, the emerging beam is polarized circularly orthogonal to the input beam. Thus, as opposed to CLCs, both polarization components are diffracted. The diffraction efficiency of a diffractive waveplate (DWP) is determined by the conversion factor of light into the orthogonal component of polarization at the output of the WP, sin 2 (Γ/2). This expression determines the total diffraction efficiency: that of the single diffraction order in the case of a circularly polarized incident beam, and that of both diffracted beams for an unpolarized or linearly polarized input. The validity of this description is indeed easily verified with the aid of elementary analysis of light propagation through the WP using a Jones matrix approach. The diffraction efficiency of DWPs is a smooth function of wavelength λ, and it exceeds a given value η in a bandwidth Δ λ~λ(1 η) 1/2. A spectral range Δ λ> 100 nm is thus achieved in the visible even for diffraction efficiency as high as 95 percent. These components were known in polarization holography as polarization gratings. Regarding them as DWPs allows for an easier understanding of all other features of these components that are not found in Bragg gratings. As WPs, their diffraction spectrum can be further broadened and practically made achromatic exceeding 200 nm for the visible and 300 nm for the visible/near-infrared spectral range. This is done by stacking WPs with certain angles between their optical axis orientations according to the method proposed by Pancharatnam. Combining DWPs into a full-wave WP would eliminate the diffraction altogether. Such a system of DWPs, one of them switchable between diffractive and non-diffractive states, allows switching the propagation of an incident light beam from the 0th to a 1st order without losses or distortions. Light propagates through the system as through a transparent optical window when both DWPs are in the state of a HWP, and the beam is fully deflected if one of the DWPs is switched off. This can be done electrically in the case of LCs and optically for both LCs and LC polymers [13]. Since the propagation direction of light depends on the sign of the circular polarization, it can be switched using an electrically controlled phase retarder without switching the DWP itself. 10. Diffractive waveplates with axial symmetry The cycloidal orientation pattern can be wrapped around the axis normal to the WP plane (z-axis). In this case the optical axis of the LC is rotating as a function of the azimuthal angle φ: α = q φ α 0, where q φ is the polar analog of the wave vector q and α 0 is the constant (see Fig. 4). This kind of DWP is called as axial waveplate or vector vortex waveplate (VVW). The polar wavevector q φ, often referred to as the vortex degree, singularity or topological charge, is an integer or a half-integer used to maintain continuity of the optical axis orientation. VVWs are DWPs with axially symmetric orientation of the optical axis, and their optical properties can well be understood by analogy with cycloidal DWPs. The VVWs between polarizers appear as a system of axially symmetric fringes, as opposed to the linear grating for cycloidal 66

9 Hakobyan et al. Armenian Journal of Physics, 2014, vol. 7, issue 2 DWPs. Number of these fringes is 4q φ. The diffraction orders of VVWs are extended into a ring that creates a doughnut beam the polar analog of the first-order diffraction by a cycloidal DWP [14]. The beam is widely used for optical tweezers, coronagraph and imaging applications. 11. Conclusion This paper has considered a unique technology which has had a profound impact on the venerable subject of electronic displays. Electronic displays play an ever increasing role in the modern world and constitute one of the fastest developing sectors of electronics. We have noted that despite their great diversity, electronic displays fall into two broad categories - light emitting and light modulating. The important attributes of displays are contrast, grey scale, color, speed, resolution, size and addressability. No one technology can offer, even in principle, a display which optimizes all of these characteristics simultaneously. Liquid crystals properties are complex and combine the anisotropy inherent in their crystallike nature with fluid properties. In particular, it is mainly their electro-optic properties which have given LCs their amazing versatility as display devices. The most important electro-optic effects technologically have been the twisted nematic, the phase-change effect and the use of guest dyes in liquid crystal hosts. More recently, variants of the twisted nematic - the π and 3π/2 cells, have proved useful. For the future, smectic liquid crystals, particularly ferroelectrics, offer the potential for high speed switching and highly complex displays. Liquid crystals can be optically addressed either through their thermo-optic effect or by using an adjacent photoconductive layer. Optically addressed LCDs have been less prominent up till recently than electrically addressed LCDs, but are now of increasing importance, not least in their new role as spatial light modulators. Spatial light modulators can be used in coherent optical processing systems, and therefore the LC is required to modulate only laser light rather than broad-band visible lightas in displays. Like displays, they may be addressed optically orelectronically, but in either case to be useful they must contain avery large number of addressable elements, have some greyscale and be fast. If they are optically addressed, they must have suitable spectral response and high sensitivity to the writing radiation. DWs could challenge Bragg gratings in many applications of critical importance, particularly those related to controlling and shaping high-power beams. They could be used for laser beams steering, polarization converting and combining as well. A system of axial DWs proves to be a most efficient tool for shaping laser beam profiles. DWs could be used for designing compact but highly efficient diffractive components not only in the UV and visible, but also in the infrared and even terahertz spectral regions, since the optical anisotropy of LC materials is high throughout the spectrum. Eventually, a new generation of multilayer coatings and photonics bandgaps may be developed, wherein the layers are made of anisotropic materials characterized not by a single parameter the refractive index but by a complex pattern of optical axis orientation. The multitude of highly efficient control parameters the local optical anisotropy, the optical axis modulation pattern, and the period in each layer could inject a whole range of new opportunities into the technology of dielectric coatings. Unfortunately, still are not solved some main problems in the area of WPs: 1) polarizers with near 100% efficiency to convert most of unpolarized light to polarized; 2) Wide range optical limitting to desine glasses that can limit light intensity in wide range of wavelength; 3) coherent 67

10 LIQUID-CRYSTAL DEVICES AND WAVEPLATES Armenian Journal of Physics, 2014, vol. 7, issue 2 incoherent mirrors to desine glasses that wholly reflect or absorbes coherent light and transmite incoherent light; 4) high efficiency laser and optical ray combine. This discussion has only dealt with some types of devices for optical processing and has not even mentioned the variety of experimental systems which have been realized using LCLVs and WPs. However, the characteristics of devices discussed here are important across the range of optical processing. Undoubtedly, the LCLV has served to greatly stimulate experimental work in real-time optical processing. Acknowledgments This work was supported by the grant no. 13-1C240 of the Ministry of Education and Science and the State Committee of Science of Armenia. References 1.S.T.Wu, D.Yang.Fundamentals of Liquid Crystal Devices.Wiley, P.G.de Gennes, J.Prost.The Physics of Liquid Crystals.Oxford: Clarendon press, L.M.Blinov.Structure and Properties of Liquid Crystals.Springer, D.J.Channin, A.Sussman.Liquid-crystal displays.display devices,ed. PankoveJ.I. Berlin: Springer, pp (1980). 5. P.Yen, C.Gu.Optics of Liquid Crystal Displays.Second edition, Wiley, Y.B.Andre, J.P.Chambaret, B.L.Lamouroux, B.S.Prade.Infrared Phys., 20, 341 (1980). 7. M.Schadt, W.Helfrich.Appl. Phys. Let., 18 (4), 127 (1971). 8. Van der Lugt.IEEE Trans. Information Theory, IT-10, 139 (1964). 9. A.R.Tanguay.Opt. Eng., 24, 2 (1985). 10. P.Aubourg, J.P.Huignard, M.Hareng, R.A.Mullen. Appl. Opt., 21, 3706 (1982). 11. S.S.Makh, A.D.Hart, P.M.Openshaw,W.L.Baillie.IEE Proc. Part J, 133(1), 60 (1986). 12. W.L.Baillie, P.M.Openshaw, A.D.Hart, S.S.Makh.IEE Proc. Part J, 133(1), 65 (1986). 13. S.R.Nersisyan, N.V.Tabiryan, D.M.Steeves, B.R.Kimball.Journal of Nonlinear Optical Physics & Materials, 18(1) 1 (2009). 14.R.S.Hakobyan, N.V.Tabiryan, E.Serabyn.Aerospace Conference, IEEE, p. 1 (2013). 68