1. Introduction

Electroholographic three-dimensional (3-D) display technologies, a type of autostereoscopy (3-D viewable by unaided eyes), rely principally on diffractive phenomena to project distributions of electromagnetic radiation, and are hoped to offer the ultimate expression of synthetic realism [1]. However, canonical hypothetical autostereoscopic applications, such as interventional medical imaging, terrain visualization, and geophysics, still lack an electroholographic display with the display area, image fidelity, and compact packaging of mature 2-D display products. This is primarily due to the need for improvements in the performance and packaging of the light modulators underlying such display devices [1–4].

Approaches to light modulation for electroholography include pixelated electrically- or optically-addressed spatial light modulators (SLMs), acousto-optical modulators (AOMs), and systems relying on photorefractive polymers [2,4]. Pixelated SLMs, the most prevalent approach, usually have cm²-scale areas, relatively wide package borders, and pixels larger than visible wavelengths. These attributes result in displays which trade off area, viewing angle, frame rate, and package size [5]. AOMs, which convert electronic waveforms into regions of diffraction in the bulk or at the surface of a piezoelectric crystal, have shown promise for 3-D in several forms. Multi-channel bulk-mode AOMs in an arrangement with similarities to Scophony television generate interactive holograms but have required electromechanical scanners and large demagnification optics [6,7]. Surface acoustic wave (SAW) AOMs [8,9] exploit piezoelectrically-induced surface waves, are more easily arrayed, and can offer higher bandwidth than bulk AOMs for 3-D display [10,11]. In leaky-mode SAW AOMs, an applied electronic waveform creates a SAW which interacts with waveguided light in an interaction region, causing that light to “leak” a polarization-rotated optical signal into the modulator substrate bulk at angles corresponding to the waveform [9,11].

Two arrangements of leaky-mode SAW AOMs (hereinafter simply “SAW AOMs”) of particular promise for electroholographic displays are edge-emitting [11,12], in which the diffracted light exits a substrate edge, and an emerging class of surface-emitting SAW AOMs, as in Jolly et al. [13] and our reported device of Figs. 1(a) and 1(b). We describe their operation after a summary of their capabilities.

 

Fig. 1. (a) Side view of surface-emitting SAW AOM. TE light is in-coupled into the waveguide via a rutile prism (not to scale), and interacts with counter-propagating SAW pulses which cause TM light to “leak” into the substrate bulk at angle θ_DIP. A SAW typically penetrates one acoustic wavelength (approximately 10 µm in these devices) into the substrate, enabling an interaction with the optical wave confined to a surface waveguide of similar depth. The diffracted light is redirected towards the top modulator face by a 360 nm surface grating and exits at angle θ_AIR. A two-frequency-component SAW 1 yields diffracted optical signals depicted in black and dashed orange, and SAW 2 has one frequency component whose corresponding diffracted signal is depicted in black. (b) Isometric view, simplified for illustration by depicting a single spatial frequency SAW yielding a bundle of output rays. (c) Expected dip and exit signal trajectories for various values of f. (d) Modulated light exits the surface from a location along y as a function of the location and frequency spectrum of the pulse-illuminated SAW. These can be plotted in an angle-space parameterization.

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Surface-emitting SAW AOMs exhibit benefits of particular relevance to future handheld or desktop 3-D displays. First, the pixel pitch can be set by choice of fabricated waveguide spacing (z direction in Fig. 1), such as 0.02 mm, 0.1 mm, 1 mm, etc., and SAW waveform design along y, which is a continuous-time signal. A second benefit is the utility of the continuous linear holographic modulation along the modulator y axis to support a variety of fringe codings from the field of computational holography, such as holographic elements (hogels), small regions of “homogeneous [diffractive] spectrum” [14], or wavefront-curving wafels [15]. As a waveform is applied to the device, a linear hologram of appreciable length (order of cm, depending e.g. on SAW attenuation during propagation) can be partitioned. Third, due to this, the number of IDTs and in-coupling ports is greatly reduced compared to edge-emitting SAW AOMs. For example, this paper reports on producing the equivalent of 9 hogels from a single IDT and illuminator rather than 9 of each in a hypothetical edge-emitting equivalent.

Although the theory of operation of electroholographic displays is well known and reported elsewhere as cited above, we provide a high-level overview of electroholographic scene reconstruction for the reader's convenience. Figures 2(a) and 2(b) depict a system block diagram and light field generation scheme for a display reconstructing a 3-D scene, of which the ray paths for one real and one virtual representative scene point are shown. In a basic point-wise interpretation, point-like members of a 3-D scene are perceived when light is observed that followed a path that would have originated from those points. That is, physically-accessible (“real”) points reconstructed between the display and observer are formed by light converging from the system, and points behind the display (“virtual”) are a percept of diverging light.

 

Fig. 2. (a) and (b) In 3-D display applications, the channels of one or more surface-emitting SAW modulators reconstruct light fields in response to the frequency components of electronic signals as controlled by a computer or other controller, and possibly also as a function of illumination wavelength as described in this paper. The modulator(s), partitioned into rows, could be followed by a light field conditioning stage for: polarization-based extinction of TE (unmodulated) background light, horizontal field of view expansion (from, e.g., a micro-telescope array), and a vertical diffuser to widen the observers’ up-down head motion as is typical in a horizontal-parallax-only display. (c) and (d) Example design of a FOV expander; the principle of operation is described in the body of the manuscript.

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As explained in the body of this paper and as depicted in Figs. 2(a) and 2(b), scene-specific electronic waveforms and strobed illumination are applied under the control of a host PC or dedicated controller to an array of surface-emitting optical modulators. This paper focuses on the proof of operation of a single modulator channel, which, like other leaky-mode SAW modulators, requires only a linear polarizer to extract a holographically-modulated optical signal from unwanted background. However, when an array of modulators is instead employed as a display, a collection of downstream optical elements could be used to expand the horizontal field of view (FOV) to permit stereoscopic visualization with horizontal parallax, improve polarization-based contrast (as described), and broaden the vertical viewing window with a vertically-oriented directional diffuser. Such an optical group is here referred to as a light field conditioning stage. Figures 2(c) and 2(d) illustrate an example implementation of a FOV expander as a columnar array of micro-telescopes. In this example, the modulated light is incident on an array of vertical lenslets of one curvature akin to objective lenses, and exits from a plane of columnar “eyepieces” of a different curvature, with each group providing approximately −7× magnification. Although not employed in the experiments of this paper, which emphasize fundamental modulator behavior, such a device is a monolithic alternative to a design described in Hirsch et al. [16]. To provide even further FOV expansion, the illumination wavelengths can be modulated as described later in this paper.

Others in the field have reported on efforts towards surface-emitting electroholographic optical modulators. Jolly et al. [13,17] report progress towards, but not device-scale demonstration of, surface-emitting modulators fabricated with laser micromachining techniques that use volume hologram out-coupling features. Alternatively, McLaughlin et al. [18] of BYU fabricated and tested an arrangement whose out-coupler is a surface relief grating and directs light from an edge-emitting device into a surface-emitting device. In contrast to these, ours is a single-die modulator implementation compatible with mass-production techniques.

In this paper, we report to the authors’ knowledge the first demonstration of a monolithically-integrated, surface-emitting SAW modulator fabricated using lithographic techniques. In contrast to [13,17], it uses a backside, rather than volume, out-coupling grating, and in comparison to [18] does so in a single prism-coupled integrated optical device. To illustrate a reduction of required RF and optical inputs, 8 mm of electronically-defined diffracting regions (also referred to here as hogels or SAW bursts) were loaded into a single electrode on the device and illuminated with a single beam. Various partitions of the linear holograms are tested, ranging from a single 1 mm-scale diffractive beam-steering region to a group of 5 spaced-apart SAW bursts acting in parallel.

2. Leaky-mode SAW AOMs

As described elsewhere [8,9,19], a typical SAW AOM is an integrated optical device with an in-coupling structure for light, an optical waveguide, and an interdigital transducer (IDT) [20] fabricated on a piezoelectric surface or substrate. Light enters the optical waveguide via the in-coupling structure, such as a prism pressed against the modulator surface in proximity to the waveguide, or an etched in-coupling grating [12]. The waveguide is defined by effective refractive indices (n_eff) for the guided modes, which are greater than the surrounding material refractive index (n_substrate) at the input polarization. The IDT induces a Rayleigh wave piezoelectric response at the modulator surface whose propagation speed is ≅3,600–4,000 m/s in our devices, depending on the SAW frequency. In our device, the SAW is counter-propagating to the optical waveguided mode(s). Where the waveguided light and SAW overlap, the SAW acts as a grating. This interaction has two impacts on a resulting optical signal: a portion is rotated to the orthogonal polarization, and it is diffracted into the bulk of the substrate as leaky-mode light [9]. As in Fig. 1, the angular deflection θ_DIP of the polarization-rotated optical signal within the substrate is determined by: the free-space optical wavelength, n_eff of the guided mode in the waveguide, the SAW's temporal frequency component of interest (f), SAW velocity on the optical waveguide (v_SAW), and n_substrate experienced by the polarization-rotated signal. θ_DIP is given by the following expression and depicted in Fig. 1(a): θ_DIP = cos⁻¹[(k_guided + mk_SAW) / k_signal]. The k-vectors in this expression are given by k_guided = n_eff / λ₀, k_SAW = f / v_SAW, and k_signal = n_substrate / λ₀, where λ₀ is the free space optical wavelength, n_substrate is the refractive index at the signal polarization, and m is the diffraction order, where m = +1.

To illustrate the properties of a typical modulator, key quantities measured at 632.8 nm are provided. In x-cut, y-propagating LiNbO₃, TE-polarized input light (E-field in the y-z plane) interacts with the extraordinary substrate index n_e = 2.2022 and is guided into a desired optical waveguide mode such as n_{eff, TE1}, measured by a Metricon prism coupler to be 2.215 in our device. Driving the IDT from f = 250–400 MHz in the 5 mW regime induces SAWs having v ≅ 3,600–4,000 m/s along the waveguide, depending on f and on optical waveguide type and crystal cut (constant for our devices). The TM-polarized (E-field in the x-y plane) leaky-mode signal interacts with the ordinary substrate index n_o = 2.2865. Referring to Fig. 1(a), our surface-emitting devices operate at 640 nm and produce signals that travel at 5° < θ_DIP < 8° depending on waveguide mode and f.

3. Modulator design and methods

The piezoelectric material chosen for the modulator of Fig. 3 is x-cut lithium niobate (LiNbO₃). Optical waveguides are created along the crystal y-axis, 100 µm wide along z, via annealed proton exchange (APE) followed by reverse proton exchange (RPE) to increase the index of refraction along the crystal’s z-axis, enabling guiding of TE-polarized light propagating along the y-axis. Each waveguide has a corresponding IDT, typically measuring 620 µm along y in a chirped configuration with individual finger widths of 1.65–2.23 µm for broad RF response. The IDTs are patterned with a maskless aligner (Heidelberg Instruments MLA15) and deposited in Cr:Au. Background on IDTs is available in [20].

 

Fig. 3. (a) Device layout with aspects of the waveguides, IDTs, and backside out-coupling gratings shown. This experimental device has three columns of five IDTs. Only the first column was used in the scope of this paper. (b) Device photograph.

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Light diffracted within a leaky-mode SAW modulator typically travels at a near-glancing angle to the waveguide, requiring an out-coupling grating or other angle-changing feature to overcome TIR if emission from a broad surface, rather than an edge, is desired. While volumetric gratings as in [17] are advantageous for near-eye augmented reality displays due to their partial transparency, they are unnecessary for desktop and mobile systems. Referring to Fig. 4, we use a backside surface grating for better compatibility with high-volume wafer processing. The grating was designed by a hill-climbing algorithm wrapping the S⁴ Rigorous Coupled Wave Analysis (RCWA) package [21] with the metric of maximizing the diffracted power, with layout as shown in Fig. 4. The outgoing angle from the grating was set 12° off-normal to reduce reflection at the exit surface by the Brewster effect. The simulated efficiency of the as-fabricated geometry was 50%. The gratings were fabricated via electron beam lithography using spin-on glass resist (hydrogen silsesquioxane (HSQ)) paired with a charge dissipating agent.

 

Fig. 4. (a) The out-coupling surface grating fabrication goal is 135 nm-thick spin-on HSQ with a 135-165 nm line width and 360 nm period, backed with silver. (b) SEM image of a test grating on LiNbO₃.

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Figure 5 shows the device test geometry. To predict the anticipated device behavior, we calculated θ_DIP for sequential drive signals from 290 to 320 MHz, the diffraction of the out-coupling grating, and θ_AIR, the angle of exit refraction into air. An example “single-tone burst” waveform, e.g. Fig. 5(b) with tone duration 200 ns, induces a <1 mm SAW at a primary frequency, e.g. f = 290 MHz, that acts as a grating that outputs diffracted light along a first trajectory. A series of similar sequential waveforms with tone bursts spanning the frequency range causes calculated output rays to incrementally scan at 0.01°/MHz in air, as in the orange (upper) line of Fig. 1(c). Due to the reversed sign of our detector apparatus, defined in Fig. 5(a), the detector angle θ_LAB of the peak output optical power direction for each applied drive frequency f will appear as a curve of negative rather than positive slope, with a constant angular offset, as will be discussed regarding Figs. 6–7.

 

Fig. 5. (a) Top view of modulator characterization apparatus. The optical power detector is at the end of one of two rotating arms; observations are plotted with respect to arbitrary laboratory frame angle θ_LAB. For increasing applied single frequency f, an output ray turns in the direction shown. (b, c, d) Example SAW waveforms: one single-frequency burst (which results in an output ray whose trajectory corresponds to the frequency; vertical cut of Fig. 6(a) at 305 MHz), a series of four single-frequency bursts (resulting in four output rays at an angle θ_LAB; vertical cut of Fig. 6(b) at 305 MHz), and a series of four higher-frequency bursts (resulting in output rays at smaller θ_LAB; cut 319 MHz of Fig. 6(b).)

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Fig. 6. Detected optical power density, in units of nW/mm², as a function of applied waveform frequency and detector angle θ_LAB. (a) Interpreted as a series of vertical plot-cuts, a series of single-tone SAWs results in light changing trajectory as a function of SAW frequency. (b) 4 spaced-apart SAW bursts act as 4 spaced-apart gratings. (c) Observation of beam steering from a 9-hogel electrohologram having 5 SAW fringes and 4 zero-amplitude spaces. (d) Emitted light exits the AOM at the frequency-dependent θ_AIR, and is measured at two detector distances, r₁ = 95 mm and r₂ = 213 mm. Inverse ray tracing is used to determine the origin of the light along y and its trajectory θ_AIR from θ_LAB and r.

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Fig. 7. Timing of the laser and RF waveform triggers corresponding to the 9-hogel datamap of Fig. 6(c). In this example, there is no phase difference between the laser gating signal and the RF (IDT driver) gating signal. The light field can be translated along y with changes in Δφ.

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Given the ∼8 mm extent of the interaction region, between the prism and the IDT, the drive signal may be partitioned. In the example of the signals of Figs. 5(c) or 5(d), four single-frequency bursts are delivered to the modulator, behaving as four spaced-apart diffracting regions, which when illuminated produce four parallel, spaced-apart beams, with a trajectory controlled by the burst frequency.

4. Results and discussion

Our multi-channel SAW AOM is mounted on a PCB and wire bonded. To induce SAWs, a 50 Ω SMA jack on the PCB receives sinusoidal IDT drive waveforms of f = 280–320 MHz from a computer-controlled HP 4648D signal generator via 28 dB and 12 dB gain stages. TE-polarized light from a 40 mW 640 nm laser diode is passed through a polarizer (not shown) and in-coupled using a rutile prism pressed to the front face of the modulator with coupling spot ∼8 mm from the IDT. The prism-SAW AOM-PCB assembly is placed on a manual rotational stage to excite the desired waveguide mode, which, here, is the TE₁-like mode. An HP 8130A dual pulse generator gates the computer-controlled IDT drive signal to the modulator channel in synchrony with a laser strobe signal.

In Fig. 5(a), a TM-polarized output signal traverses the 1 mm-thick device, is redirected by the backside grating, exits the modulator surface, passes through a polarizer (not shown) to filter out unmodulated light, and is detected by a Thorlabs S130C slim photodiode detector behind an adjustable slit. To measure optical power output as functions of f and detector angle θ_LAB, the detector arm is incrementally rotated about an axis parallel to z by a computer-controlled rotary stage and f is ramped at each step. Henrie et al. [22] describe a linear version of a similar apparatus.

Motion of the SAW is implicitly frozen using short-pulse strobed light, an AOM illumination technique described in [13,23]. The pulse generator allows exploration of device behavior of various fringe lengths, spacings, and delays relative to the strobed illumination. The SAW traverses the 8-mm waveguide region between the prism and the IDT in 2.0-2.2 µs.

We first demonstrate the anticipated single beam emitter functionality of instances of SAW 1 of Fig. 1(a) spanning the circled operation points of the upper curve of Fig. 1(c). RF and laser pulse widths are 300 ns, the SAW-positioning laser delay is 700 ns, and the repetition rate is 1 µs. For each waveform frequency, the resulting emitted signals are plotted in vertical cuts of Fig. 6(a) for a 40 mW peak / ∼5 mW average laser power and 0.7 mm-width slit. The anticipated frequency dependence of each output signal's angle is observed in the negative slope of the plotted region, spanning ∼0.8° in θ_LAB space, the angle recorded by the detector, from 290 to 320 MHz for detector distance r₁.

We next demonstrate that a SAW partitioned into hogels can occupy the device, enabling the emission of multiple discrete optical signals as per Figs. 5(c) and 5(d). By setting the RF and laser pulse widths to 200 ns with a repetition period of 400 ns, i.e. less than the acoustic length of the modulator channel, four beams are emitted (vertical cut of Fig. 6(b)). Varying f of the hogels is observed to change the detected angle of the beams’ peak power, as expected, by regarding different vertical plot cuts of Fig. 6(c).

To further explore the ability of arbitrary space-partitioning of the SAW interaction region, we decrease the RF and laser pulse widths to 180 ns and the period to 360 ns, resulting in the 5 beams corresponding to “time slots” for 9 single-frequency hogels in Fig. 6(d). The pulse widths, period, offsets, and delay used to generate the 5-beam, 9-hogel case are shown in Fig. 7.

In a ray-optics approximation, our SAW AOM output from a small surface patch has two degrees of freedom: origin along y and trajectory in the x-y plane. For increased analytical precision, these must be separated from optical peak power data in θ_LAB space by obtaining data at two sensor distances (95 mm and 213 mm) and performing inverse raytracing with knowledge of modulator orientation, as depicted in Fig. 6(d). The experiment of Fig. 6(b) was run with the detector at two distances from the modulator. Through geometry and the values of θ_LAB of peak signal at r₁ and r₂, we find that for 294 < f < 320 MHz, θ_AIR from hogel 3 spanned |29.2-29.5°| = 0.3°, corresponding to 0.3°/26 MHz = 0.01°/MHz, in agreement with prediction. The edge-to-edge extent of these 7 hogels spans approximately 8 mm along y, considered for a single f to freeze the exit location. This result demonstrates that the entire length of the interaction region actively generates holographic fringes.

The duty cycle of the RF drive and laser strobe illumination is identical in this demonstration in order to improve the signal-to-noise ratio and determine the interaction length. In a display application, it is anticipated that the holographic SAWs will have a multi-component frequency spectrum and occupy a mm-to-cm length scale, and will be followed by a single pulse of strobe illumination when the SAW is at the desired location. This is elaborated elsewhere [13, section 2.4; 17, section 3]. Improved display brightness can be achieved in this case by utilizing a higher peak laser power to make up for the lower laser illumination duty cycle.

The IDTs utilized in these devices emit SAWs in both directions. No adverse effects due to SAW reflections are observed. The interaction between a SAW and the signal exiting the top surface of the modulator is expected to be negligible due to the short (µm-scale) interaction length. However, in a display, SAW absorbers and directional IDTs will be utilized to limit unwanted SAW propagation and reflections. An optimized application of this technology in a holographic display would use an in-coupling grating rather than a prism. Optical loss would thus be related to the grating efficiencies of the in-coupling and out-coupling gratings, and any internal reflections, rather than prism coupling efficiency.

The modest angular output subtense of this first device can be expanded in several ways, such as configuration for a 100 MHz or larger operational bandwidth. The surface grating's broadband response is compatible with beam-steering via optical wavelength tuning, a future direction that would allow dramatically wider output angles alongside electronic drive [24]. In that case, because θ_AIR is a strong function of illumination wavelength, a repeating sequence of perceptually indistinguishable colors would be chosen that result in coarse angular offsets of the RF-modulated light field outputs. For example, if a display were decomposed into emissive regions having a horizontal angular subtense of 60°, a user 30 cm away would perceive stereoscopic depth cues and motion parallax, the extent of which depends on the location of reconstructed scene points, the display size, and the user's interpupillary distance. Surface gratings similar to the one implemented impart 0.2° of angular offset per 1 nm illumination wavelength tuning. Therefore, 10° of addressability into air is spanned by 50 nm of wavelength tuning with 1° spacing to match the RF-based “fine modulation control,” e.g.: 630 nm, 635 nm, …, 675 nm. A modest angle-expanding stage of −6× thereby provides an avenue to a comfortably broad FOV.

In display applications, the SAWs will be composed of multiple frequency components and will be induced in modulator channels arrayed in two dimensions in each modulator device.

In this paper, we described the application of a surface grating on the backside of a SAW modulator to provide a surface-emitting AOM, holding linear holograms of at least 8 mm that can be synchronously illuminated. Output light scanned at 0.01°/MHz in air for single- and multi-hogel (partitioned) waveforms.