Electrically controlled diffraction employing electrophoresis, supercapacitance, and total internal reflection Jason C. Radel and Lorne A. Whitehead* University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia V6T 1Z1, Canada *Corresponding author: [email protected] Received 26 July 2013; revised 1 October 2013; accepted 1 October 2013; posted 2 October 2013 (Doc. ID 194301); published 21 October 2013

The reflectance of a surface can be altered by controlling the concentration of dye ions in a region adjacent to an optically transparent and electrically conductive thin film. We present a method for nonmechanical light deflection achieved by altering the reflectance of a diffraction grating, an approach that creates new diffraction peaks that lie between those associated with the original grating spacing. We have demonstrated this effect by applying an electrical potential difference between interdigitated indium-tin oxide (ITO) electrodes and measuring the intensity of one of the new diffraction peaks. The measured diffraction peak intensities were found to reversibly deflect approximately 7% of the reflected light to previously nonexistent peaks. The diffraction grating was formed by patterning a thin film of planar, untreated ITO on a glass substrate using standard photolithography techniques. The size scale for this method of electrically controlled diffraction is limited only by the lithographic process; thus there is potential for the grating to deflect light to angles greater than those achievable using other methods. This approach could be used in applications such as telecommunications, where large deflection angles are required, or other applications where alternate beam-steering methods are cost prohibitive. © 2013 Optical Society of America OCIS codes: (050.1950) Diffraction gratings; (240.0240) Optics at surfaces; (260.6970) Total internal reflection; (190.2055) Dynamic gratings; (240.6645) Surface differential reflectance. http://dx.doi.org/10.1364/AO.52.007469

1. Introduction

The use of fiber-optics in telecommunications has risen dramatically over the past 20 years due in part to its capability to efficiently transmit information at a high rate over long distances. A limitation of communicating via light or infrared radiation is the difficulty in the angular redirection that is required in fiber-optic networks in order to switch optical signals from one fiber to another and for wavelength-division multiplexing and demultiplexing [1]. Light beam steering is also used in free space communications where the directions of the transmitter and receivers are not fixed [2], industrial laser drilling or cutting, 1559-128X/13/317469-10$15.00/0 © 2013 Optical Society of America

and in holographic data storage [3]. Applications that require the light to be redirected by angles of more than a few degrees typically require moving parts such as micromirror arrays [4], but such devices are cumbersome and expensive. Light deflection that does not require moving parts could avoid these problems, but a method has yet to be devised to costeffectively deflect light to angles exceeding 10°. One potentially practical way to redirect light is by means of controlled diffraction. Current methods for controlled diffraction that do not require moving parts make use of acoustic waves [5] or liquid crystals [6]. The acoustic wave approach works by generating waves in either the bulk of a material or on its surface, wherein the wavelength determines the diffraction grating spacing. Acoustic waves have the advantage of giving continuous control of the diffracted angle 1 November 2013 / Vol. 52, No. 31 / APPLIED OPTICS

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of a light beam; however, deflecting light to angles of more than a few degrees requires operation at relatively high power and high frequencies. Liquid crystal-based diffraction gratings typically consist of a liquid crystal material placed between two substrates coated with transparent and electrically conductive films. A diffraction grating is created by orienting the molecules in a liquid crystal in a spatially periodic array. The orientation of the molecules in the liquid crystal can be controlled by applying an external electric field between the two substrates, and the optical path length of light through the liquid crystal will depend on the orientation of these molecules. If a spatially periodic electric field is applied between these substrates, the light passing through the liquid crystal will diffract, resulting in a diffraction pattern that depends on the periodicity of the applied field. A layer of liquid crystal must be at least a few micrometers thick in order to effectively rotate the polarization of the transmitted light. Since the pitch of the diffraction grating is limited by electric field fringing effects, this means that the minimum possible pitch is limited to a few micrometers. This restricts these types of devices to diffract light to angles of typically no more than 5° [7,8]. A third method for controlling diffraction uses controlled reflection from transparent interdigitated electrodes in contact with a solution containing lightabsorbing, electrically charged particles [9]. The diffraction grating is formed by the interdigitated electrodes. The reflectance from these electrodes is controlled by altering the local concentration of the light-absorbing particles next to these electrodes using electrophoresis. A new diffraction pattern resulting from two or more times the spacing between the interdigitated electrodes can be created by increasing the local concentration of light-absorbing particles next to one of the two interdigitated electrodes. The diffraction periods achievable by this method are restricted only by the lithographic process used to create the interdigitated electrodes. This method is therefore superior in that it is capable of diffracting light to a wider range of angles. The number of light-absorbing particles in the solution that can be held next to the interdigitated electrodes is determined by the electrolytic capacitance of the interface of the electrode and charge of the particles in the solution. Under normal circumstances, for molecules such as dye ions, the electrolytic capacitance of the dye/electrode interface is too low to substantially alter the reflectance of this interface [10]. Nanoporous films with large surface areas can be used to increase the effective capacitance; however, they are expensive to manufacture and difficult to pattern into interdigitated designs. The electrophoretic diffraction approach was a precursor to the work reported here. In particular, this paper describes a significant improvement that eliminates the need for nanoporous conductive materials. We have identified a system in which the interface between indium-tin oxide (ITO) and a solution of 7470

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methylene blue (MB) ions dissolved in water exhibits supercapacitive qualities. This increases the effective capacitance without requiring a nanoporous coating. 2. Background

To understand this improved approach, it is helpful to briefly review four key physical concepts: the Debye length, electrolytic capacitance, supercapacitance, and total internal reflection (TIR). In an electrolyte (a solvent that contains dissolved ions), the charge of the dissolved ions is screened by a layer of solvent molecules. This layer is known as the Debye layer. The radius of this solvent shell is known as the Debye length, λD , and can be estimated using the Debye formula: s εo εr kB T ; λD  2q2e I

(1)

where εo is the electric constant, εr is the dielectric constant of the solvent, kB is Boltzmann’s constant, T is the temperature of the electrolyte, qe is the charge of an electron, and I is the ionic strength of the electrolyte (ions∕m3 ). An electrolytic capacitor consists of two electrodes in contact with an electrolyte. When an electrical potential difference is applied between the electrodes, each electrode acts as a capacitor, where one side of each capacitor is the electrode and the other side is a thin layer of ions in the electrolyte surrounding the electrode. The concentration of the ions in the electrolyte adjacent to the electrode drops exponentially with distance from the electrode, with a characteristic length equal to the Debye length [11]. The electrolytic capacitance of each electrode/electrolyte interface can be estimated by assuming the ions next to the electrodes form one side of a capacitor and are separated from the electrode (the other side of the capacitor) by the Debye length. The capacitance can then be estimated as C

εo εr A ; λD

(2)

where A is the area of the electrode exposed to the electrolyte and λD is the Debye length. Supercapacitors typically have 10–100 times the capacitance of ordinary electrolytic capacitors. Several different methods can be used to achieve such capacitance. The simplest method is to increase the effective surface area of the electrode in contact with the electrolyte by coating the surface with a material having a high surface-area, such as activated carbon or carbon nanotubes. This increases the surface area in contact with the electrode by a factor of 50 or more. A second method achieves enhanced capacitance through reversible electrochemical reactions between the electrolyte and the electrode surface [11], through chemical activations, oxidations with acids or bases, polymer deposition, or

by using an electrochemically active molecule [12]. Some supercapacitors combine both methods, either by using a different method on each electrode or by using both methods on the same electrode. An example of a supercapacitor that uses two different methods is a carbon nanotube film with a conductive polymer deposited on the nanotubes [13]. In terms of optics, TIR occurs when light strikes the interface between two media at an angle larger than a critical angle with respect to the normal to this interface. This angle, derived from Snell’s law, is given by   n θc  a sin 2 ; (3) n1 where θc is the critical angle, n1 is the index of refraction of the first medium, and n2 is the index of refraction of the second medium. The intensity of the reflected light depends on the absorptive properties of the second medium and can be calculated from the Fresnel equations as the absolute square of the electric field amplitude reflection coefficient. The experiments described in this paper use s-polarized light. The reflected intensity for this polarization is r   2    n1 Cosθi  − n2 1 − n1 Sinθi  2  n2    r Rs   2  ; (4)   n Cosθ   n 1 − n1 Sinθ     1 i 2 i n2 where Rs is the intensity of the reflected light for s-polarization, and θi is the angle in the first medium between the incident light beam and the normal to the interface. The intensity of light that reflects by TIR from an interface can be calculated using Eq. (4) as long as the angle of incidence and the two indices of refraction of the two media are known. If the two media are not light absorbing (they have real indices of refraction), the reflected intensity for incident angles exceeding the critical angle required for TIR will be 1. If one of the media has light-absorbing characteristics (it has a complex index of refraction), then the reflected intensity will be less than 1. When the second medium has light-absorbing characteristics, for example a solution of dye molecules dissolved in water, the real component of the index of refraction is largely independent of dye concentration but the imaginary component of the index of refraction is not. The imaginary component can be calculated using the Beer–Lambert law [14]: κ

ρσλo ; 4π

3. Electrically Controlled Diffraction

Light-absorbing particles can be moved by electrophoresis into and out of the region next to an interface where light is undergoing TIR, thus causing the intensity of the reflected light to be electrically controlled. This approach can be used to influence a pattern of diffracted light. This method for controlled diffraction requires the patterning of a transparent conductive film on a transparent substrate into two interdigitated electrodes, as depicted in Fig. 1. When no potential difference is applied between the interdigitated electrodes in contact with a light-absorbing species suspended or dissolved in a transparent liquid, the light that reflects from the electrode/liquid and substrate/liquid interfaces diffracts due to the spatially periodic reflectance. When a potential difference is applied between the two interdigitated electrodes, the light-absorbing species is moved by electrophoresis next to one of the electrodes. The increased concentration of light-absorbing material in these regions reduces the reflectance of every second grating line, and therefore the reflectance of the grating acquires a spatially periodic component with twice the spatial period of the electrodes. This results in diffraction that sends light to angles between those associated with the spatial periodicities of the original interdigitated grating (Fig. 2). As already mentioned, the fraction of light that is absorbed at the electrode/electrolyte interfaces is determined by the number of light-absorbing particles present in the region adjacent to the electrodes and the fraction of light absorbed per particle. Two common types of light-absorbing particles are pigment particles and dye ions. Typical pigment particles have an advantage because they have, per unit of charge, several orders of magnitude more absorption than dye ions. Experiments with pigments have demonstrated more than 80% attenuation of TIR [15]. The drawback to using pigment particles is that they tend to irreversibly agglomerate over time. Electrophoretic devices using these particles have limited lifetimes and they require complicated electrical driving

(5)

where κ is the imaginary component of the index of refraction for the electrolyte, ρ is the concentration of dye ions in the electrolyte, σ is the absorption cross section of the dye ions, and λo is the wavelength of the light in a vacuum.

Fig. 1. Schematic for two interdigitated electrodes, where conductive transparent film is shown in black. 1 November 2013 / Vol. 52, No. 31 / APPLIED OPTICS

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Fig. 2. Electrically controlled diffraction using controlled TIR. Light strikes the glass/liquid and electrode/liquid interfaces at the critical angle and undergoes TIR. In (a) the reflected light diffracts to angles associated with the spatial periodicity of the interdigitated electrodes. In (b) a potential is applied between the interdigitated electrodes, which changes the reflectance from the interdigitated electrodes, and new diffraction peaks are created that depend on twice the spatial periodicity of the interdigitated electrodes.

schemes [16,17]. In contrast to pigment particles, dye molecules do not agglomerate, but their absorption to net charge ratio is much lower. A typical amount of reversible light absorption at an interface consisting of a standard electrode, such as ITO, and a typical dye, such as MB, is about 1% of the total light [10] in contrast to the 80% attenuation achieved using pigment particles. Materials typically used in supercapacitive surfaces could be used to attract more dye ions next to an optical interface to achieve higher absorption, but most of these materials are not optically transparent, and are therefore not useful for this purpose. However, there are some techniques for producing supercapacitance that are not incompatible with light transmission. For example, supercapacitance has been achieved with transparent electrodes using enhanced effective surface areas that arise from carbon nanotube films, zinc antimonate nanoparticle films, and porous ITO films made using glancing angle deposition (GLAD) [9]. Such films showed a substantial increase in capacitance compared to planar films; however, the techniques used to create the films are expensive and the films are difficult to pattern into fine interdigitated designs. To our knowledge, supercapacitance has not previously been achieved with transparent electrodes that use reversible electrochemical reactions. Under certain circumstances, however, the dye MB has been shown to enhance the capacitance of carbon nanotube films using a reversible oxidation-reduction reaction [18]. We investigated whether such a reaction could be used to create supercapacitance between ITO and MB. We found that MB dissolved in water is electrochemically active with ITO, effectively achieving 7472

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supercapacitance. Preliminary experimentation verified that the capacitance was influenced by a number of factors. For instance, the interface of MB and gold films was found to also have increased capacitance. Another common dye, Victoria Blue [19], however, did not exhibit enhanced capacitance with ITO or gold. Several other factors affected the capacitance of the MB-H2 O∕ITO interface, including dye concentration and temperature. While a thorough investigation of the exact requisite conditions for enhanced capacitance was not studied in detail here, it may be appropriate to do so in a future study. We found that MB dissolved in water, at a concentration of 1.317 · 1026 molecules∕m3 (0.22 M), reproducibly achieved supercapacitance with ITO, so this MB-H2 O∕ITO interface was the focus of the experiments described here. To study the capacitance of this interface, we developed a characterization system for measuring the change in intensity of diffractive orders caused by electrostatic manipulation of dye concentration by means of this proposed form of enhanced capacitance. 4. Experimental Design

The experimental setup consisted of three main components: interdigitated electrodes on a substrate, the surrounding optical system, and the circuitry used to apply controlled time-varying voltages and measure the results. The design included three electrodes, with two forming the interdigitated array, and the third being a separate large-area counter electrode. The interdigitated electrodes were fabricated by lithographically patterning an approximately 15 nm thick coating of ITO on glass. Figure 3 shows the design for these two electrodes. The separate electrode was given a much larger area to offset the differences in electrolytic capacitance between ITO and the two different ions dissolved in the water so that the capacitance was determined by the grating electrodes and was not limited by the third separate electrode. When dissolved in a solvent, MB dye molecules dissolve into

Fig. 3. Top view of the pattern of interdigitated ITO electrodes (shown in black) made using lithography on glass. White space represents glass, i.e., places where ITO has been removed by a lithographic etch process.

two ions, positively charged, light-absorbing dye ions (here labeled MB ) and negatively charged chlorine ions (Cl− ). We have found that MB ions do form a supercapacitor on ITO, but the chlorine ions do not. The total capacitance of an electrolytic capacitor is equal to the capacitance of two capacitors in series, so the relatively small capacitance of the interface of ITO and chlorine ions in water (here denoted Cl-H2 O∕ITO) compared to the ITO and MB ions in water (here denoted MB-H2 O∕ITO) limits the total capacitance. Supercapacitors that use electrochemically active ions avoid this limitation by using a large-surface-area secondary electrode that typically consists of activated carbon or carbon nanotubes. In our design, the third electrode for this same purpose consisted of ITO on glass and had a surface area exposed to the solution that was 150 times greater than that of the interdigitated electrodes. A test cell was made with these ITO-coated glass pieces by placing 1 mm spacer beads between them and sealing the edges of the ITO coated pieces using a silicone sealant [20]. A solution of 1.317 · 1026 molecules∕m3 (0.22 M) MB dissolved in distilled water was then injected into the 1 mm cell gap using a syringe. A prism was placed on top of the cell and maintained in optical contact with the glass surface using index-matched oil. The prism caused the beam of an incident 650 nm, 3 mW laser to refract such that it intercepted the glass/ITO and H2 O∕ITO interfaces at an angle for which it would undergo TIR (Fig. 4). The angle of the incident laser beam in the glass, as measured from the surface normal of the glass and H2 O∕ITO interfaces, was 63.5°  0.2°, which was 2° greater than the critical angle of 61.5°. Electrical contact with the three ITO electrodes was made with copper wires bonded to the ITO using silver conductive epoxy [21]. Light that underwent TIR at the H2 O∕ITO and glass∕H2 O interfaces was diffracted to angles associated with the spatial periodicity of the interdigitated electrodes. A new diffraction pattern, with angles associated with twice the spatial periodicity of the

interdigitated electrodes, was created by moving dye ions by electrophoresis into the region next to one of the two interdigitated electrodes. The concentration of dye ions was controlled by applying a potential difference between the interdigitated electrodes. For the sake of simplicity, we will henceforth refer to the potentials of the interdigitated electrodes in reference to the third, counter-electrode, considered to have zero potential. The first-order diffraction peak of the new diffraction pattern was the focus of this experiment as it showed the greatest contrast in intensity for different potentials applied to the interdigitated electrodes. The intensity of this peak was modulated by applying a selected positive voltage to one of the interdigitated electrodes, and an equal and opposite voltage to the other. A schematic representation of the system used to apply voltages to the electrodes is shown in Fig. 5. In preliminary experiments, it was observed that any significant asymmetry in the electrical treatment of the two interdigitated electrodes resulted in an irreversible residual diffraction pattern at the same angle as the desired signal. We hypothesized that this was either due to damage to one of the electrodes or due to ions adhering asymmetrically to the interdigitated electrodes. To minimize this problem, the voltage sequences applied to the two electrodes were designed to ensure that each electrode experienced the same electrical potential history and so that neither electrode experienced a large initial voltage pulse. The magnitude of the voltages applied in these patterns was increased from 0 to 1 V over 25 cycles, and then was decreased back to 0 V over an additional 25 cycles. The voltages between the interdigitated ITO electrodes and the grounded large area electrode were applied for 0.5 s. There was an approximately 80 s period between applied DC pulses where all electrodes had zero potential. This allowed the solution to return to its original state. These times were determined experimentally to give the best results based on preliminary testing. The voltage sequence applied to one of the two interdigitated electrodes is depicted in Fig. 6. The voltage sequence applied to the other interdigitated

Fig. 4. Side view of the diffraction grating cell and prism. The ITO-coated glass with the interdigitated pattern is on top with the glass holding the large surface-area ITO electrode beneath it. The two different glass pieces are separated by spacer beads and edge-sealed with silicone adhesive.

Fig. 5. Schematic representation of the system used to apply voltages (not to scale). Voltages applied to the two interdigitated electrodes, with respect to the grounded counter-electrode, were equal and opposite. The current to each electrode was monitored by measuring the voltage across the 900 Ω series resistors. 1 November 2013 / Vol. 52, No. 31 / APPLIED OPTICS

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Fig. 7. Gray-scale digital photograph of the diffraction pattern from the diffraction grating cell.

Fig. 6. Voltage sequence applied to one of two interdigitated ITO electrodes. Each voltage level was applied for 0.5 s and was followed by an 80 s period during which all electrodes were electrically connected to allow the system to return to its original state.

electrode is not shown, but it was always of the opposite sign and equal in magnitude to the voltage applied to the first interdigitated electrode. 5. Experimental Results

To interpret the strength of the diffraction peaks, we divided the measured luminous flux by that of the light incident on the diffraction grating. For the latter, rather than measure the flux of the source directly and estimating the portion reaching the grating, which would have been reduced by various imperfections in the components, we instead measured the flux of light reflecting from the cell when it was filled with air (no dye or water present). This gave the total amount of light incident on the grating less the small amount of light absorbed by the grating itself or scattered by physical imperfections in the grating. For the sake of simplicity, we will henceforth refer to this measured flux as the total light striking the grating. By normalizing measured intensities to this value, the slight absorption in the grating and any imperfections were factored out of the measurements. To measure the flux of each diffraction peak, as described above the entrance port of an integrating sphere was moved to the location of each diffraction peak reflecting from the cell and the received flux was in turn measured with an attached silicon photodiode [22]. The sum of the signals from the photodiode for every diffraction peak, measured when the cell was filled with air, was used to normalize all future measured signals. The flux of the diffraction peaks were then measured again after a solution of 1.317 · 1026 molecules∕m3 (0.22 M) of MB dissolved in water was injected via syringe into the cell. Figure 7 shows a gray-scale digital photograph of a white diffusing screen onto which the diffraction pattern was directed. The voltage sequences described in Fig. 6 were applied in order to modulate the intensities of the diffraction peaks caused by the new diffraction pattern 7474

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(described in Section 4). The data acquisition system recorded applied voltages, the voltages across resistors in series with the interdigitated electrodes, and the intensity of the new first order diffraction peak. The intensity of the new first order diffraction peak, shown in Fig. 8, dramatically increased at applied potentials above 0.6 V, up to a maximum intensity just below that of the original first order diffraction peak. The peak diffraction efficiency measured was 0.75%. Previous electrophoresis-based electrically controlled diffraction methods have measured diffraction efficiencies of typically around 0.39% [23]. It is worthwhile to note that no attempt was made to increase the speed of the changes in intensities of the diffraction peak shown in Fig. 8. Instead, for these experiments, the emphasis was on experimental simplicity and measurement accuracy. For this reason, the sequence had large time periods between applied potentials to give the solution ample time to return to its original state and 900 Ω resistors were placed in series to give more accurate measurement of the current flow. It should be possible to achieve a much faster response by reducing the series resistance, applying larger fields, and/or reducing the time periods between applied potentials.

Fig. 8. Intensity of the new first order diffraction peak normalized to the total light striking the grating in response to the applied voltage sequence shown in Fig. 6. The intensity of the diffraction peak remains near zero at applied potentials below 0.6 V. The greatest intensity corresponds to 0.75% of the light incident on the grating, or equivalently 3.4% of the total light reflecting from the grating.

Table 1.

Period Period Period Period

1 2 3 4

Charge Transfer through the Two-Electrode Electrolytic Cella

1 V 0V −1 V 0V

178 μC −36.2 μC −414 μC 350 μC

a The net charge transfer during four characteristic time periods:

(1) when 1 V voltage difference was applied across the cell, (2) when the voltage difference was returned to zero, (3) when a −1 V voltage difference was applied across the cell, and (4) when the voltage difference was again returned to zero. The cell had unequal electrode areas of 8 · 10−6 m2 and 4 · 10−4 m2 . A positive voltage attracts Cl− ions to the smaller electrode and a negative voltage attracts MB to the smaller electrode.

The voltage drops across the resistors connected in series with the interdigitated electrodes were measured to determine the current passing through the resistors during the experiment. An integration of the measured current as a function of time was used to determine the total charge that flowed through the series resistors during different time periods of the experiment. However, the interpretation of these integrated charges was complicated by the three-electrode design of the cell. Rather than attempt to understand the charge transfer in the three electrode cell, a two-electrode cell was constructed for the purpose of analyzing charge transfer. The two-electrode cell was equivalent to the threeelectrode cell in all but one aspect: the top piece of ITO-coated glass was not patterned into two interdigitated electrodes but was instead left as a single nonpatterned electrode. A voltage difference alternating between 1 V and −1 V was applied to this cell and the electric current through the cell was measured and integrated to calculate the net charge transfer during different time periods of the experiment. These net charge transfer amounts are shown in Table 1. The magnitude of the net charge transfer through the cell was greater during the periods of applied voltage difference (i.e., when charging the capacitor) than during the periods of zero potential difference (when discharging the capacitor). Generally, this is a sign of a leaky capacitor—one in which there is charge transfer via a conductive path from one electrode to another, in addition to that associated with the charging of the capacitor. Such charge transfer is said to arise from faradaic current [24]. The equivalent circuit representation for electrolytic capacitors having faradaic current is depicted in Fig. 9 [25]. Charge transfer between the electrodes and the electrolyte can be modeled as a parallel resistor, referred to as the leakage resistance. The net effect is

Fig. 9. Equivalent circuit representation for an electrolytic capacitor. The series resistance primarily depends on the resistance of the electrolyte. The parallel resistance, sometimes referred to as the leakage resistance, depends on several factors such as chemical reaction rates and mass transfer rates.

that only a portion of the charge transfer through the cell represents charge stored at the electrode/ electrolyte interface. In the absence of any electrochemical reactions, the expected stored charge could be calculated using Eq. (2). For the concentration of MB in H2 O used in these experiments, the Debye length was calculated to be 6.51 · 10−10 m, and the expected electrolytic capacitance per unit area was estimated to be 1.09 F∕m2 . Taking into account the net effective capacitance of the series connection of the capacitance associated with each of the two electrodes, we would expect a cell with such interfaces to have a capacitance of 8.6 · 10−6 F. In reality the observed capacitance was 3.6 · 10−5 F when a positive voltage difference and 3.5 · 10−4 F when a negative voltage was applied. Based on the electrode areas and the series capacitance formula, it is simple to show that the capacitance per unit area of the Cl-H2 O∕ITO interface must be approximately 4.5 F∕m2, a value that is somewhat higher than might be expected but could possibly be explained by surface roughness of the ITO at the atomic scale. In contrast, the corresponding capacitance per unit area for the MB-H2 O∕ITO interface is 52.5 F∕m2. This is significantly larger than what one would expect to see if the mechanism for charge storage were simple electrolytic capacitance. This suggests that the mechanism for charge storage involves electrochemical reactions. 6. Diffraction Peak Simulations

The expected intensities of the diffraction peak measurements described in the previous section were estimated by an analytical calculation based on the Huygens–Fresnel principle [26] and calculated with Mathematica, a computational software program [27]. The result of this calculation gave the theoretical diffraction peak intensities based on the parameters of the diffraction grating, which included the indices of refraction of all materials, the physical dimensions of the grating, and the thickness of the increased concentration of MB dye ions next to one of the two interdigitated electrodes. The diffraction peak intensities were also estimated numerically using a program that solves for 1 November 2013 / Vol. 52, No. 31 / APPLIED OPTICS

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Fig. 10. Conceptual depiction of model used to calculate the diffraction peak intensities when the cell was filled with air. The width and thickness of the ITO comprising the interdigitated electrodes (labeled “ITO Width” and “ITO Thickness,” respectively) were set to match the experimentally observed diffraction pattern.

Fig. 12. Conceptual depiction of setup used to calculate the diffraction peak intensity with an electrode energized. In this case, the total diffraction grating spacing is 20 μm. The imaginary component of the solution surrounding one of the two interdigitated electrodes (labeled κ 2 ) and the thickness of this layer were set to match the experimentally observed diffraction pattern.

stable solutions of Maxwell’s equations in a diffraction grating to calculate diffraction peak intensities [28]. Figures 10–12 depict the conceptual representations of the gratings modeled with the computational software that were used to recreate the experimental results. Several of the parameters of the grating used in these calculations, such as the diffraction grating pitch (10 μm), the index of refraction of glass (1.51), and the index of refraction of ITO (1.93), were known values. The width and thickness of the interdigitated electrodes, the index of refraction of the MB∕H2 O solution in the bulk of the cell, and the thickness and imaginary component of the index of refraction of the solution near the interdigitated electrodes were not known with a high degree of certainty. These values were therefore adjusted in the model to match experimental measurements. The Huygens–Fresnelbased calculation was used to find the values of these quantities that best fit the experimental data by minimizing the sum of the squared differences between calculated and experimentally measured diffraction peak intensities. The squared differences were weighted by the experimental uncertainties for each measured diffraction peak. The computational model was then used as a secondary check to make sure both models were in agreement.

The diffraction peak intensities of three different diffraction gratings were calculated. The model for the first grating is shown in Fig. 10. This model was used to estimate the diffraction peak intensities for the cell when it was filled with air. In this case, the width and thickness of the interdigitated electrodes used for this calculation were set to match experimental measurements. The ITO width was set to 6.5 μm, and the ITO thickness was fit to 13.6 nm [Delta Technologies, the manufacturer of the ITO coated glass used for these gratings, estimates a thickness of 15–30 nm for the sheet resistance of ITO used for this experiment (70–100 Ω∕sq:) [29], so this was reasonable]. A comparison of the calculated intensities using these dimensions and the experimentally measured intensities is shown in Table 2. To evaluate the model, we calculated the chi-squared statistic and then estimated the probability of the model having a statistic this large or larger (known as a p-value). For the six experimental measurements taken, one would expect a chi-squared statistic value of around 5 or 6. The chi-squared value we obtained for these fits, 19.8 (p-value 0.003), indicated the model was not complete. This is not surprising, as the model does not factor in things such as surface roughness or

Table 2. Measured Diffraction Peak Intensities versus Calculated Intensities and the Differences between These Values (Δ) for the Cell Filled with Aira

Order Measured Intensities Calculated Intensities 0th 1st 2nd 3rd 4th 5th Fig. 11. Conceptual depiction of setup used to calculate the diffraction peak intensities for the case where the cell was filled with a solution consisting of 1.317 · 1026 molecules∕m3 MB dissolved in water. The imaginary component of the solution (labeled κ 1 ) was set to match the experimentally observed diffraction pattern. 7476

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0.960  0.001 0.0151  0.0009 0.0033  0.0002 0.00005  0.00003 0.0009  0.0001 0.00035  0.00004

0.961 0.0151 0.0028 0.00011 0.0010 0.00024

Δ 0.001 0.0000 0.0005 0.00006 0.0001 0.00011

a The calculated diffraction peak intensities were estimated using a Huygens–Fresnel-based calculation and were checked using a computational program that solves for stable solutions of Maxwell’s equations in a grating to calculate diffraction peak intensities. The chi-squared value for this fit was 19.8 (p-value 0.003).

imperfections of the glass or ITO film. Nevertheless, the results seem reasonable overall. The second case that was modeled was the intensity of the diffraction peaks when the cell was filled with a solution consisting of 1.317 · 1026 molecules∕m3 of MB dissolved in water (no voltages applied between electrodes). In this case, the imaginary component of the index of refraction of the solution (labeled κ1 in Fig. 11) was set to minimize the sum of the squared differences between the calculated and experimental measurements. The setup for this model is shown in Fig. 11. The sum of the squared differences was smallest when this imaginary index was 0.103, which, using Eq. (5) and the absorption cross section for MB of 2.396 · 10−20 m2 [30], corresponds to an ionic concentration for MB of 8.31 · 1025 ions∕m3. The concentration used for these experiments was 1.317 · 1026 molecules∕m3 . The differences in these concentrations is likely due to the linking of MB ions into dimers and trimers of MB at high concentrations [31,32], which were not accounted for in the model. Comparisons of the calculated intensities and the measured intensities for the case where the cell was filled with MB∕H2 O solution are given in Table 3. The chi-squared statistic value for this fit of 30.7 (p-value 3 · 10−5 ) was larger than for the previous fit. This relatively large value could be due to a thin layer of adsorbed ions on the substrate surface that was not accounted for in the model. Though the model is not perfect, the results seem reasonable. Finally, the intensity of the new first order diffraction peak was modeled when 1 V was applied to the interdigitated electrodes. The highest measured intensity of the new diffraction peak was 0.75% of the laser light incident on the grating, or equivalently 3.40% of the total light diffracted from the grating. This new diffraction intensity under this condition was evaluated in the numerical model and the amount of dye present was adjusted to match the observed intensity. In this case there were two parameters used for fitting: the imaginary component of the index of refraction for the layer of solution surrounding the interdigitated electrode attracting MB ions (labeled κ 2 in Fig. 11) and the thickness of this layer (labeled “MB Thickness”). The index of refraction around the electrode attracting chlorine ions was left Table 3. Measured Diffraction Peak Intensities versus Calculated Diffraction Peak Intensities and the Differences between These Values (Δ) for the Cell Filled with 1.317 · 1026 molecules∕m3 of MB Dissolved in Watera

Order Measured Intensities Calculated Intensities 0th 1st 2nd 3rd 4th 5th a

0.201  0.007 0.0069  0.0003 0.0016  0.0002 0.00002  0.00003 0.00055  0.00003 0.00026  0.00006

0.182 0.0082 0.0016 0.00006 0.00060 0.00016

Δ 0.019 0.0013 0.0000 0.00004 0.00005 0.00010

The chi-squared value for this fit was 30.7 (p-value 3 · 10−5 ).

unchanged in the model, as the capacitance of this interface was much less than for the interface attracting MB ions. Prior experimentation also indicated the reflectance from the interface attracting chlorine ions remained primarily unaltered when these ions were attracted to this interface. This indicated a negligible change in the imaginary component of the index of refraction surrounding this interface. The setup used for the case where a 1 V potential was applied between the interdigitated electrodes is shown in Fig. 12. There was a range of imaginary index and layer thickness values that could be used in the model to match the measured new diffraction peak intensity. The layer thicknesses ranged from 10 nm to as much as 150 nm. The imaginary component of the complex index for these layers ranged from 0.25 to 1.14. The amount of charge needed to create these layers of increased MB concentration ranged from 2 to 6 C∕m2 . The maximum layer thickness estimate is an important result, as it indicates that this method is in fact scalable to submicrometer size scales, allowing for light deflection to larger angles than other methods. The minimum thickness estimate from these fits is also important as it is thicker than the Debye length estimated from Eq. (1) (1 nm), an indicator that simple electrolytic capacitance could not achieve the results observed here. The model also found that the total amount of light from the cell decreased, though the total flux of diffracted light remained approximately constant, which is consistent with increased absorption at one of the interdigitated electrodes. The amount of charge per unit area estimated to be stored at this interface, based on the measured capacitance of the MB-H2 O∕ITO interface shown in Table 1 and the series capacitance formula, was 52.5 C∕m2 . The large difference between the estimated amount of charge stored at the interface and the amount of charge needed to create the measured diffraction peak intensity based on the analytical model could be a result of additional ions other than MB present at the interface (and having smaller absorption cross sections). Spectroscopic analysis of the electrolyte’s absorption cross section would need to be performed to further elucidate the chemical composition of the charge being stored on the electrode. 7. Conclusion

Electrically controllable diffraction is a promising method for controlling the deflection of a light beam. We achieved controllable diffraction by moving dye ions, by means of electrophoresis, into and out of the region surrounding one of two ITO electrodes in an interdigitated design. A new diffraction pattern, associated with twice the spacing of the interdigitated electrodes, was created and then removed by controlling the local density of these dye ions next to these electrodes. We measured the intensity of one of the new diffraction peaks to reversibly reach an intensity corresponding to 3.4  0.1% of the total diffracted light. 1 November 2013 / Vol. 52, No. 31 / APPLIED OPTICS

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The amount of light deflected to these new peaks could be increased in a number of ways. Since we estimate the thickness of the layer of ions attracted near the electrodes to be on the order of tens of nanometers, the electrode sizes could potentially be scaled down to the wavelength of light, removing all diffraction peaks except the peaks created when a potential is applied between the electrodes. Blazing such a grating could be used to remove one of these two new peaks, leaving only one diffraction peak that can be switched on and off. The mechanism through which the dye ions were controlled was probably not due solely to doublelayer capacitance, but also involved reversible current flow from the electrode to the electrolyte. An electrochemical analysis of these reactions warrants further study. This work represents an improvement for electrophoresis-based electrically controlled diffraction. It achieved a higher diffraction efficiency than previous work, without the need for expensive and difficult-topattern nanoporous materials. It is superior to other methods for electrically controlled diffraction because it has the potential to be scaled down to submicrometer size scales, enabling a larger angular operating range than is possible with other methods. This method for controlled diffraction has potential applications in telecommunications, free space communications, industrial laser drilling or cutting, and in holographic data storage. References 1. G. Keiser, “A review of WDM technology and applications,” Opt. Fiber Technol. 5, 3–39 (1999). 2. V. Nikulin, M. Bouzoubaa, V. Skormin, and T. Busch, “Modeling of an acousto-optic laser beam steering system intended for satellite communication,” Opt. Eng. 40, 2208–2214 (2001). 3. T. Chao, J. Hanan, G. Reyes, and H. Zhou, “Holographic memory using beam steering,” U.S. Patent 7251066 B2 (31 July 2007). 4. J. Younse, “Mirrors on a chip,” IEEE Spectrum 30, 27–31 (1993). 5. A. Clark, “A variable spacing diffraction grating created with elastomeric surface waves,” M.Sc. thesis (University of British Columbia, 1997). 6. P. Mach, P. Wiltzius, M. Megens, D. Weitz, K. Lin, T. Lubensky, and A. Yodh, “Electro-optic response and switchable Bragg diffraction for liquid crystals in colloid-templated materials,” Phys. Rev. E 65, 031720 (2002). 7. S. Valyukh, I. Valyukh, and V. Chigrinov, “Liquid-crystal based light steering optical elements,” Photon. Lett. Pol. 3, 88–90 (2011). 8. D. Resler, D. Hobbs, R. Sharp, L. Friedman, and T. Dorschner, “High-efficiency liquid-crystal optical phased-array beam steering,” Opt. Lett. 21, 689–691 (1996). 9. P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, J. Huizinga, and L. Whitehead, “Variable diffraction gratings using nanoporous electrodes and electrophoresis of dye ions,” Proc. SPIE 6645, 66450K (2007). 10. P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, T. Dunbar, J. Huizinga, and L. Whitehead, “Application of

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Electrically controlled diffraction employing electrophoresis, supercapacitance, and total internal reflection.

The reflectance of a surface can be altered by controlling the concentration of dye ions in a region adjacent to an optically transparent and electric...
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