The Advantages of Dye-Doped Liquid Crystals in Constructing a Fresnel Zone Plate Lens

Transcription

1 The Advantages of Dye-Doped Liquid Crystals in Constructing a Fresnel Zone Plate Lens Joshua T. Wiersma (jwiersma@ .arizona.edu) College of Optical Sciences, University of Arizona, Tucson, Arizona 8571 Abstract: A Fresnel zone plate lens can be constructed using a dye-doped liquid crystal filled cell and photo-induced alignment techniques. Light passing through a Fresnel zone patterned photo-mask causes the dye-doped liquid crystal to align in such a way to produce odd and even zones on the lens 1. Diffraction of incident light through the odd and even zones of the lens allows the light to constructively interfere and come to a focus. The properties of the odd and even zones can be electronically controlled resulting in a tunable lens. The lens exhibits the properties of being scatter free, having a very low operating voltage (~5V rms ), producing separable zero and first focus orders, having adjustable diffraction efficiency, and having controllable polarization. The lens can be easily fabricated in comparison to other Fresnel zone plate lens designs 1. Introduction: Most lenses utilize the concept of refraction in order to focus light. Refraction occurs when light passes through an interface where the index of refraction changes. The larger the change in the index of refraction the more the light bends or changes its path. The index of refraction of a material depends on the wavelength of light it is transmitting. Some wavelengths outside of the visible spectrum cannot be focused using lenses that rely on refraction since materials with the necessary change in index of refraction do not exist 3. Therefore, lenses can also be constructed using the concept of diffraction in order to focus light. Diffraction occurs when light encounters an obstruction and appears to bend around the object. In fact, according to the Huygens-Fresnel principle, each unobstructed point of the wavefront appears as a secondary source of spherical waves when passing through or around an obstruction. In the case of Fresnel diffraction, either the incident or the received light deviates from being plane waves and has significant wavefront curvature 4. In this region, Fresnel or half-period zones exist where

2 the boundary of each annular region corresponds to the intersection of the wavefront with a series of spheres centered at P and of radii increasing by half-wavelengths as seen in figure(1). r 0+λ r 0+λ/ r 0 P Figure 1: Diagram showing Fresnel or half-wavelength zones Due to the separation of the zones by half a wavelength, adjacent zones will interfere destructively and thus nullify each other. Interference can be seen as the superposition of two or more waves producing a resulting wave that constitutes the sum of the contributions of the overlapping waves. Thus, if a peak and a trough of a wave meet, such being the case when separated by a half wavelength, they will cancel out. Therefore, constructive interference will occur and an image will form if only every other zone transmits light since the transmitted zones will be separated by an integer number of wavelengths. A lens, often referred to as a Fresnel zone plate lens, can therefore be constructed using diffraction principles by blocking or separating every other half-wavelength diffraction zone. Liquid crystal can be used to construct a Fresnel zone plate lens due to its high birefringence. Therefore, liquid crystal has two different indices of refraction depending on the orientation of the incident light. With the help of dye, the liquid crystal can be oriented so that it either rotates the polarization of the incoming light by 90 (odd zone) or allows the incoming light to pass unchanged (even zone) 1. The polarization of the light describes how the electric field of the light oscillates in space. With linearly polarized light the electric field oscillations are contained within a well defined plane which is perpendicular to the direction of propagation 4. Therefore, dye-doped liquid crystal will form a lens since the change in polarization between the odd and even zones essentially separates them from each other and allows them to constructively interfere. The electronic properties of the liquid crystal will allow for a tunable lens to be constructed 1.

3 Scientific Description: The construction of such a lens beings with the injection of a mixture of liquid crystal and azo dye between two glass slides. The ratio between the liquid crystal and the azo dye was 99:1 respectively. After being thoroughly mixed, the mixture was injected into a 10 µm gap between two indiumtin-oxide (ITO) coated glass slides. The bottom slide had been previously coated with a thin polyvinyl film (PVA) and was subsequently gently buffed. The strong anchoring energy of the rubbed surface of the bottom slide induced a homogeneous liquid crystal layer to form which became the even zones 1. In order to orient the liquid crystal molecules to the desired direction for the odd zones, the dye-doped liquid crystal must be illuminated with linearly polarized light of a wavelength close to the dye s absorption peak. The linearly polarized light induces a trans-cis isomerization of the dye, followed by molecular reorientation, diffusion, and absorption onto the surface of the untreated slide 1. A tans-cis isomerization occurs when the compound has a rearrangement of molecular groups around a double bond or some similar feature 5. This causes the long axes of the dye molecules to orient themselves along the untreated slide which in turn causes the liquid crystal to orient along the direction of the dye s long axis. However, due to the competition between the orienting force of the absorbed dyes and the anchoring force from the rubbed bottom slide, the sample must be illuminated for roughly 15 minutes at a relatively high intensity I=50 mw/cm ). Under these conditions, the dye can generate an anchoring force strong enough to over come that from the rubbed bottom slide 1. In order to generate the Fresnel zone patterns, the illuminating light passes through a photomask with the desired Fresnel pattern. The rings of the photomask must satisfy equation(1), r = nr (1) n 1 3

4 where n is the order number (n = 1,, 3, 4 ) and r 1 is the radius of the first ring. The radius of the first ring of the photo-mask used in the experiment was.5mm. Therefore, using equation(1), r = mm = mm, the radius of the 80 th ring on the photo-mask can be (.5 ) 4.47 Zone Radius as a function of Zone Number Zone Radius (mm) Zone Number Figure : A plot of Fresnel zone radii found to be 4.47mm. The increase in the radius of each concentric ring or zone extending outward decreases in order to maintain the same area in each zone as seen in figure() 1. After the aligning process, light passing through the odd zones of the sample cell the polarization of the light is rotated 90 while light passing through the even zones of the sample cell is unchanged. Thus, the light passing through the odd and even zones of the lens have different polarizations. The difference in the polarization of the light from each zone separates them from each other and keeps them from interfering. Therefore, the light from the odd zones can constructively interfere and form an image as can the light from the even zones. The arrangement of the liquid crystal in the lens after photo-alignment can be seen in figure(3) 1. 4

5 Fresnel Patterned Photo-Mask Incoming Light Liquid Crystal Glass Slide Figure 3: Liquid crystal arrangement after photo-induced alignment The process of fabricating a similar lens using quartz glass and liquid crystal along with micro-structuring techniques proves much more difficult since the rings must be created mechanically. Construction involves computer-aided design and multiple processing by photolithography and reactive ion etching techniques 6. Techniques creating 180 ferroelectric zones on lithium niobate wafers require extensive fabrication using advanced methods including lithography and precise exposing thresholds 7. Thus, the fabrication processes necessitated by the use of different materials prove much more involved than that required when using dye-doped liquid crystals 1. The focusing properties of the lens were studied using an expanded He-Ne laser beam which passed through a linear polarizer which was aligned with the rubbed axis of the liquid crystal cell. The light then passed through the lens, an analyzer, and finally onto a CCD camera connected to a computer. When light passed through the even zones of the sample cell, the polarization of the light was not changed since the even zones consisted of homogeneous liquid crystals. When light passed through the odd zones of the sample cell, the polarization of the light was rotated by 90 due to the orientation of the liquid crystal. Therefore, the zero focus order resulting from the even zones could be viewed by having the analyzer, in this case a linear polarizer, aligned with the polarizer filtering the laser light. The first focus order resulting from the odd zones could be viewed by having the analyzer rotated 90 from the polarizer filtering the laser light. This property demonstrates that the lens can produce separable zero and first focus orders. A letter L was observed with each of the focus orders with the CCD set 5cm behind the lens. The zero focus order produced a larger image, but both of the images were discernable 5

6 with some noise due to further diffraction effects. For the binary Fresnel lens constructed in the experiment the primary focal length is described by equation(), f r 1 = () λ where r 1 is the radius of the innermost Fresnel zone and λ is the wavelength of the light. In this experiment, the radius of the innermost Fresnel zone was.5mm and the wavelength of light was 633nm. Using equation(), f (.5 mm) = =.395m, the primary focal length of the lens was 633nm found to be.395mm. Such a focal length is practical as it is short enough for most applications 1. The diffraction efficiency of the lens can be varied by applying a voltage to the lens. The absolute phase difference ( δ) between the odd and even zones determines the first order diffraction efficiency of a Fresnel lens. The relative phase difference is given by equation(3), πd( neven nodd ) δ = (3) λ where d is the cell gap and n even and n odd are the respective effective indices of refraction of the liquid crystal in the even and odd zones. When the applied voltage exceeds roughly 1V rms the liquid crystal begins to be reoriented due to the electric field 1. In theory, a binary Fresnel lens will show maximum diffraction when the phase difference is an odd multiple of π and will have no diffraction when the phase difference is an even multiple of π 8. When the relative phase difference reaches about 1.5π, the diffraction efficiency reaches a maximum of roughly 31%. This occurs at about V rms, after this point the diffraction efficiency gradually declines since the index of refraction of both the even and the odd zones is reduced. The diffraction efficiency of the lens as a function of the applied voltage can be seen in figure(4) 1. 6

7 Diffraction Efficiency as a function of Applied Voltage Diffraction Efficiency (%) Applied Voltage (V rms ) Figure 4: A plot of diffraction efficiency The dye-doped liquid crystal technique has advantages over techniques using polymerstabilized liquid crystals. The polymer-stabilized liquid crystal lens has a lower peak diffraction efficiency (3%) at a higher operating voltage (~ 9V rms ). Also, a slight light scattering occurs when using polymer-stabilized liquid crystals in comparison with dye-doped liquid crystals 9. Techniques using polymer-dispersed liquid crystals have a higher peak diffraction efficiency (39%) at a much higher operating voltage (~180V rms ). Thus, it can easily be seen that techniques using dye-doped liquid crystals demonstrate a higher diffraction efficiency at a low operating voltage 8. Conclusion: A relatively simple fabrication process lead to the creation of a Fresnel zone plate lens using dye-doped liquid crystals. Illumination of the dye-doped liquid crystal through a Fresnel patterned photo-mask created even and odd zones resulting in orthogonal, separated by 90, polarization states. The even and odd zones were then able to constructively interfere and come to a focus due to their orthogonal polarizations. The zero and first focus orders of the lens were separated using an analyzer. The sample cell remains scatter free and operates at a relatively low voltage. The diffraction efficiency peak of the lens was roughly 31% and was achieved at an operating voltage of roughly V 1 rms. 7

8 Biographical Sketch: Dr. Shin-Tson Wu earned his Bachelor of Science degree in physics from National Taiwan University and his Doctor of Philosophy degree in quantum electronics from the University of Southern California. The photonics and displays research group at the University of Central Florida (UCF) is currently head by Dr. Wu who joined UCF in 001. Dr. Wu came to UCF after an 18 year stint working at Hughes Research Laboratories. In addition, Dr. Wu is a fellow of the Society for Information Display (SID), Institute of Electrical and Electronics Engineers (IEEE), and the Optical Society of America (OSA). Additionally, Dr. Wu is the founding Editor-in-Chief of the IEEE/OSA Journal of Display Technology. Furthermore, Dr. Wu has co-authored 4 books, 5 book chapters, over 350 papers, and can claim more than 55 issued and pending patents some of which are currently being implemented 10. Citations: 1) T. -H. Lin, Y. Huang, A. Y. G. Fuh, and S. -T. Wu, "Polarization controllable Fresnel lens using dye-doped liquid crystals," Opt. Express 14, (006) ) E. Hecht, Optics (Addison Wesley, San Fransisco, 00). 3) W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 000). 4) S. O. Kasap, Optoelectronics and Photonics (Prentice Hall, New Jersey, 001). 5) M. S. Silberberg, Chemistry (McGraw-Hill, New York, 003). 6) M. Ferstl and A. Frisch, "Static and dynamic Fresnel zone lenses for optical interconnections," J. Mod. Opt. 43, (1996). 7) R. Cudney, L. Ríos, and H. Escamilla, "Electrically controlled Fresnel zone plates made from ring-shaped 180 domains," Opt. Express 1, (004) 8) H. Ren, Y. H. Fan, and S. T. Wu, Tunable Fresnel lens using nanoscale polymerdispersed liquid crystals, Appl. Phys. Lett. 83, (003). 9) Y. -H. Fan, H. Ren, and S. -T. Wu, "Switchable Fresnel lens using polymer-stabilized liquid crystals," Opt. Express 11, (003) 10) Dr. Shin-Tson Wu, 8