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Film display holograms typically diffract light over a wide enough view-angle to be viewed, directly, without intervening optics. However, all holographic video displays (with the exception of eye-tracked systems) must use optics beyond the hologram surface to overcome the challenges of small display extent and low diffraction angle by using some form of demagnification and derotation (i.e. angle magnification and optical multiplexing). We report a leaky mode waveguide spatial light modulator with sufficiently high angular diffraction to obviate the need for demagnification in scanned aperture systems. This high angle was achieved by performing a number of experiments to determine the depth of the annealed, proton-exchanged waveguide which corresponded to a maximized diffracted angle. Diffraction sweeps were recorded in excess of 19.5° (corresponding to only 70 MHz of input bandwidth) for 632.8 nm light which is above the 15° required for direct view display. Device geometries are proposed which might achieve greater than 20° of total angular sweep for red, green, and blue light.
© 2016 Optical Society of America
1. Introduction
Spatial light modulators are limited to low diffraction angles relative to those of traditional film holography as it is difficult to fabricate active pixels to match the scale of the smallest holographic fringes (<1 μm feature size). At a minimum, to achieve a direct-view holographic display with both binocular parallax and motion parallax, the display would have to be capable of diffracting light over an angle of 15° as shown in Fig. 1(a). The modulators currently used in holographic displays (pixelated spatial light modulators and acousto-optic modulators) are currently incapable of achieving this angle of deflection and instead rely on demagnification and derotation to achieve wide angles and large extents (see Fig. 1(b)). Pixelated modulators, such as liquid crystal spatial light modulators, illuminated normal to the modulator surface would require a pixel size of 1.2 μm to deflect 632.8 nm light over this angle. Such a pixel density is beyond the current state of the art. Once such devices are created and connectivity (fan-out) issues are resolved, the resulting pixel density of >1 Mpixel/mm2 will make necessary a drive solution with extremely high bandwidth (such a display with 120 cm2 would require a drive bandwidth of 360 Gpixels/s). An acousto-optic modulator, illuminated at the Bragg angle, would require a similar minimum acoustic fringe size which, in a slow-shear mode tellurium dioxide acousto-optic modulator with an acoustic velocity of 617 m/s, would require a signal with an RF bandwidth of 255 MHz which lies well outside its capacity (currently these modulators are limited to bandwidths of approximately 70 MHz). Lithium niobate bulk wave modulators are capable of much higher bandwidths, but they also possess higher acoustic velocities (∼4000 m/s) so that a 15° deflection would require a signal bandwidth in excess of 1.65 GHz per acoustic channel. In order to avoid the computational complexity associated with these high bandwidths and the fabrication complications associated with physically small diffractive features, it would be desirable to have a modulator which could achieve high angular deflection with low drive bandwidth and relatively large diffractive features.
Fig. 1 a) 15° is needed for eye to view a static hologram with both stereopsis and motion parallax at a standard viewing distance of 500 mm from the hologram. b) 3° deflection of a typical spatial light modulator adds the need for a telescope to increase the view angle to 15° by utilizing the two lenses of different focal length. The light is also optically multiplexed via a scanner. c) Our fabricated device with deflection of larger than 15° used in the holovideo without demagnification (the focal length of both lenses is the same). d) It is now possible to multiplex devices physically to enable direct-view architectures.
In this work we report a leaky-mode guided-wave modulator capable of deflecting 632.8 nm light over an angle above 19.5° scattering off of acoustic structures with a minimum period of approximately 7 μm driven by an RF signal only 70 MHz in bandwidth. This result shows a six-fold increase over the current state of the art for scanned aperture holovideo displays. To the best of our knowledge this result also represents the highest scanned angle per period for all spatial light modulators. Further improvements in device geometry will make it possible to achieve aggregate deflections in excess of 20 ° for green and blue light as well.
Holographic video displays utilize spatial light modulators to encode holographic wavefronts. Typically these modulators are limited in their angular deflection to a few degrees. For example, the first two generations of scanned-aperture holographic video displays [1–5] utilized acousto-optic Bragg cells with an RF bandwidth of 50 MHz and a corresponding angular sweep of 3°.
Waveguide light modulators have been introduced as an alternative to acousto-optic Bragg cells and pixelated modulators for holographic video displays. They advance the state-of-the-art bulk wave modulators by providing a low-cost, highly parallel, high-bandwidth design with unique capabilities such as the ability to rotate the polarization of the signal light, the ability to control color in the frequency domain and the ability to deflect light over a greater angle for a given grating period [6–9]. This last advantage is a result of the nonlinear nature of the grating equation shown in Eq. (1). A grating illuminated from a glancing angle will have orders that deflect at higher relative angles than light entering normal to the grating (see Fig. 2(b,c)).
Fig. 2 Leaky-Wave device physics. a) TE light enters the waveguide as a high-order guided mode, then, interacts anisotropically with the surface acoustic wave. The result of this interaction is that a portion of the guided light is polarization rotated and therefore no longer guided. The light then exits the waveguide as TM-polarized leaky-mode light. b) Light illuminating a grating at the normal deflects less than light which illuminates the grating from glancing angles (as is the case for light interacting with a grating in a waveguide) c) This graphic shows the k-space diagram for the cases of normal and near-colinear illumination which enable widely disparate deflections given the same grating period.
This increase grows further as the light exits the high-index waveguide substrate and enters the air according to Snell’s law [see Eq. (2)] as shown in Fig. 2(a).
where θ1, θin, m, λ, and Λ are respectively angle of incident light, angle of diffracted light in the substrate, integer value, wavelength of light, and grating period. where θout, nair, and nsub are respectively angle of light exiting the substrate, refractive index of air, and refractive index of the substrate. This increased angle appears to come at the cost of point spread function. As the angle of incidence approaches the grating parallel the apparent aperture of the grating is reduced even as the pattern itself is effectively foreshortened. The result is that as the deflected angle increases the output spot size increases, likely to preserve space-bandwidth product.Previous efforts have resulted in further optimization of the frequency control of color in these devices [6–9]. Currently scanned aperture holography systems are built with target view angles between 15°–30°. This has required the use telescopes which demagnify the acoustic image up to ten times. A modulator with the ability to sweep angles in excess of 15° would make possible holographic displays with little or no need for demagnification. In this work, an effort is made to improve the angular behavior of guided wave modulators by characterizing the change in angular bandwidth with respect to a key fabrication parameter: waveguide depth. The goal is to identify guided to leaky mode transitions that are both efficient and wideband and to identify the maximum achievable deflection angle for leaky mode transitions in proton-exchanged waveguide systems.
1.1. Theory
When surface acoustic waves (SAW) produced by the interdigital transducers (IDTs) hit the TE-guided light, light is coupled into TM-leaky mode which is no longer guided and it exits the substrate. According to couple mode theory, the coupling coefficient is defined and calculated as following [10]:
where ω, εo, En, Eν, and Δεr are respectively temporal frequency of light, the permittivity of free space, electrical field of guided mode, electrical field of leaky mode, and change in dielectric coefficient in proton-exchanged lithium niobate due to SAWs. Therefore, based on the behavior of Δεr, coupling coefficient change. Rust and Strake [11] have calculated Δεr for lithium niobate and proton-exchanged lithium niobate which is a piezoelectric media through solving the electromechanical wave equations [12–14]. Figure 3 shows the modulation amplitude of the offdiagonal dielectric tensor element, Δεr, for a specific proton-exchanged device which is mainly responsible for the conversion of TE-guided modes to TM-leaky modes in proton-exchanged lithium niobate function with respect to the depth.Fig. 3 Modulation amplitude of the offdiagonal dielectric tensor element, Δεr, for a specific proton-exchanged device which is mainly responsible for the conversion of TE-guided modes to TM-leaky modes in proton-exchanged lithium niobate. [From Rust and Strake, PADERBORN UNIV (GERMANY FR) (1992). [11]]
It is known that inside a multimode waveguide, the higher modes have more external evanescent fields and based on the Δεr Rust et al. calculated, the fields outside of the waveguide are more strongly coupled into the TM-leaky mode so coupling coefficient and consequently diffraction efficiency of those higher modes is higher. This is proved theoretically by Rust and Strake in [11].
1.2. Fabrication
For this study eight devices are fabricated with different proton-exchange timing which result in devices with different waveguides of different depth. Figure 4 depicts the fabrication of a completed device. First a layer of aluminum (200 nm) is coated on a 9 mm x 15 mm X-cut Y-propagating lithium niobate sample and then is patterned using Heidelberg uPG-01 to be proton-exchanged inside a pure Benzoic acid bath. Once the device is proton-exchanged and annealed at 375°C for 45 minutes the sample is etched by the aluminum etchant and then cleaned in Piranha acid and Isopropanol (IPA). 200 nm aluminum is coated on the cleaned sample and then patterned again to put the the interdigital transducers (IDTs) on the sample. The sample is then polished with multiple polishers and cleaned with Piranha acid and IPA. The device is then mounted on a piece of glass slide next to PCB boards and then wire bonded. The wideband IDTs are designed with an impedance of 50 ohms at the target center frequency of 400 MHz. The IDT was chirped to cover a band from 350 MHz to 450 MHz, though less efficient SAW generation continues beyond these frequencies [15].
Fig. 4 Fabrication process. a) The slab waveguide is created via proton exchanging the device. The interdigital transducers are written on the aluminum side of the sample. The light interaction length in this device is 4 mm. b) The smallest spacing (p) between the fingers is 6.54 (μm) and the maximum is 9.74 (μm). Width (W) and length (L) of the IDTs are 100 (μm) and 800 (μm) respectively. c) The index profile of the device. neg, nog, nes, and nes are the ordinary and extraordinary refractive indexes of the waveguide and the substrate
Table 1 shows eight samples. The first four columns give the device label, proton exchange time, waveguide depth, and number of guided modes respectively. The fifth column identifies the highest guided mode. In this experiment, the guided to leaky mode transition originating at the highest guided mode was used in all red and green experiments. In blue experiments, the guided to leaky mode transition originated from the second highest guided mode (as shown in column six). Waveguide depth and the proton-exchange time are related through the following equation.
where d, D, and t are the waveguide depth, acid diffusion length, and proton exchange time respectively.
Table 1. Mode characteristics of different devices with different waveguides’ depth. The first four columns shows the device label, proton exchange time, waveguide depth, and number of guided modes respectively. The fifth column identifies the highest guided mode leaky mode transition and the sixth column gives the guided to leaky mode transition originated from the second highest guided mode.
2. Testing and experiment
The testing of these samples was performed by mounting each sample in a custom, semiautomatic characterization apparatus [15] which sweeps the RF input with and sample the optical output in angle. From this data we can map input frequency to output angle and determine the RF and angular bandwidth of each device as depicted in Fig. 5.
The lasers used in this work have the following specifications: red (diode, 632.8 nm), green (diode, 554 nm), blue (diode, 445 nm).
3. Results
The primary result of this work, as shown in Fig. 6 is showing proton-exchanged leaky mode devices with angular deflection of 19.5° for red light (15.6°, and 11° respectively for Green, and Blue). This angular output maps to an input of 70 MHz giving a 3.5 MHz per degree of deflection compared to 16.7 MHz per degree of deflection for traditional high-deflection TeO2 slow shear Bragg modulators. There are 3 guided modes in sample Y2 (TE0, TE1, and TE2) which the highest guided mode is TE2. Transitions from TE2 to the leaky mode have an angular bandwidth in excess of 19° (for red). This angular output along with the angular output for sample Y3 forms the local and global maxima for the highest order transition for all depths.
Fig. 6 Angular Bandwidth. For example, for red, the highest guided mode in sample Y2 is TE2. Transitions from TE2 to the leaky mode have an angular bandwidth in excess of 19°. This angular output along with the angular output for sample Y3 forms the local and global maxima for the highest order transition for all depths
The data shown in Fig. 7 follows a trend that is not linear and not monotonic. Instead, it follows a curve with three extrema. This supports the assumption of a waveguide region with depleted piezoelectric and electro-optic properties. A depleted waveguide region gives rise to a modulation function like the one shown in Fig. 3 which, when integrated (see Eq. (3)), leads to the path with multiple extrema like those in Fig. 7.
4. Conclusion and Future work
In this study a leaky mode modulator with high angular bandwidth of 19.5° and moderate RF input 70 MHz is presented. This result occurs at a depth of 1.1401 μm which demonstrates optimal angular deflection for not only red input light, but for green and blue input lights as well. The principle conclusion from these results is that it is possible to fabricate high order leaky mode devices with angular bandwidths more than six times greater than the TeO2 modulators traditionally used in scanned aperture holographic video displays. The angular bandwidth for red and green input light is sufficiently high to obviate the need for demagnification entirely (>15°). Blue light also showed relatively high angular output at the optimal waveguide depth. However, blue was somewhat anomalous in this study as its most efficient transition was not the highest, but instead, the second highest guided to leaky mode transition. This may have been due to the fact that the blue transition usually occurs at higher frequencies than the red and green transitions. It is possible that the highest order transition for blue did not fit within the sample transducer’s 350–450 MHz range. Additional experiments might better determine the maximum potential angular output of blue light. By reducing or eliminating the need for demagnification, high order leaky mode devices promise to greatly advance the effort to create relatively simple, low-cost holographic video displays.
Future work includes the creation of a bilateral device which will effectively double the angular output reported here. The angular output of the waveguide leaky mode modulators is unilateral, creating only positive or negative angles of deflection as shown in Fig. 8(a). A sandwich of these devices would provide both positive and negative angles, effectively doubling the angular deflection (see Fig. 8(b)). A single sample could have waveguide devices fabricated on both sides of the substrate. In this case a monolithic device would produce both positive and negative angles from a single device aperture as depicted in Fig. 8(c).
Fig. 8 Method of doubling the deflection angle. a) Unilateral angular output from one device. b) Bilateral angular output from two devices glued together (both positive and negative angles). c) Bilateral angular output with one monolithic device having waveguide and IDTs at both sides of the sample.
Funding
Air Force Research Laboratory contract FA8650-14- C-6571; DAQRI LLC
References and links
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