1. Introduction
Conventional illumination systems are typically designed to provide either directional or diffuse illumination, spot or flood lighting, using a fixed optical path through collimating or diffusing optics. In settings where the required type of illumination varies, light energy could be used more efficiently if the source could adapt to provide illumination consistent with the user’s immediate need. For example, in home or office lighting the user may want to switch between directional task lighting to illuminate a workspace and diffuse lighting to illuminate an entire room.
Previous work on planar solar concentrators has demonstrated efficient, highconcentration designs that use a two dimensional lens array positioned above a micropatterned waveguide [
44. J. H. Karp, E. J. Tremblay, and J. E. Ford, “Planar microoptic solar concentrator,” Opt. Express 18(2), 1122–1133 (2010). [CrossRef] [PubMed]
]. The addition of a moveable lens array above the waveguide allows the concentrator to adapt to changing sun angle [
55. J. M. Hallas, K. A. Baker, J. H. Karp, E. J. Tremblay, and J. E. Ford, “Twoaxis solar tracking accomplished through small lateral translations,” Appl. Opt. 51(25), 6117–6124 (2012). [CrossRef] [PubMed]
]. The same physical structure can be adapted for a versatile illuminator by reversing the direction of light propagation, and reoptimizing the design for the light source and output constraints.
Fig. 2 Section of the array showing a collimated beam when the arrays are aligned (a), a
redirected beam when the arrays are translated (b), and a diverging beam when the arrays are
rotated (c).
Aligning the lenslet and extraction arrays with the extraction features located at or near
the focal plane of the lenses produces a collimated output beam [
Fig. 2(a)]. Laterally translating the lens array relative to the extraction array
steers the overall beam by steering all individual beams in the same direction, as shown in
Fig. 2(b). Relative rotations between the two arrays
alter the overall divergence of the beam by steering the individual beams in a
‘spiral’ of different directions, as shown in
Fig.
2(c). In
Fig. 2 the divergence angle of the light
extracted from the waveguide has been restricted, because lateral offsets between the arrays
would otherwise induce unwanted crosstalk as light spills into adjacent lenses. This crosstalk
leads to side lobes in the emitted pattern, which are undesireable for most applications.
The same functionality can be achieved using an array of pointlike LED sources directly behind the lens array, which would eliminate the complexity of edge coupling and waveguiding. However, a waveguidebased design has the advantages that it 1) allows a thinner form factor and simplifies electrical routing and heat sinking by moving the LED sources to the edges of the waveguide; 2) clears the aperture opposite to the lens array from LEDs, wiring, and heat sinks, allowing the use of higher performing reflective lenses, discussed in Section 2.1; and 3) allows the coupling, waveguiding, and extraction structures to perform the necessary angular and spatial mapping of the real sources into an effective array of pointlike sources. While the efficacy (electrical to luminous conversion efficiency) and emittance (spatial power density) of LED dies typically scale inversely with die size within one class of LEDs, socalled ‘high power’ LEDs with apertures larger than 2mm currently have higher performance in terms of emittance than do small package LEDs with apertures less than 1mm. From conservation of radiance, edge coupling a smaller number of high power LEDs will produce a brighter beam than a large number of small LEDs located directly behind the lens array. This edge coupling approach will be adaptable as LED technology improves, up to the point when the emittance of small aperture LEDs matches that of large aperture LEDs, which would warrant the direct array approach.
The thin form factor of the planar illuminator allows conformal mounting to flat surfaces with little or no recessing, making it ideal for retrofitting ceiling fixtures. Further, control over light from a relatively large aperture can be achieved with relatively short range mechanical motion compared to traditional designs. Control over a similar amount of light energy would require an array of traditional luminaires, with each element having its own actuation mechanism. Conventional actuation mechanisms require motion in 3 dimensions, either by moving a lens with radial and axial freedom with respect to the source or by gross actuation of the entire luminaire including the source and heat sink. The planar illuminator uses precise shortrange 2D motion of one optical component to achieve the same degree of control.
In the following section we will present an analytic model of each element of the system, then in Section 3 combine the elements to obtain an overall system model, and determine the potential performance of optimal designs. In Section 4 we describe an experimental fullscale ‘proof of principal’ prototype, and compare its performance to the model. We conclude in Section 5 with some comments on future directions of this technology.
2. System design
Typical performance metrics for illumination systems include optical efficiency, efficacy, luminous emittance, and pattern uniformity. In our system, we are also concerned with the beam steering and divergence ranges conditional on the degree of crosstalk between adjacent lenses. We would also like the system to scale efficiently to large aperture sizes for high flux applications. Here we describe a simple analytic model for each element of the system, beginning at the output where we discuss lens performance, then moving to waveguiding and extraction, and finishing with the source and coupling methods.
2.1 Beam steering and diverging
The maximum steering angle, minimum divergence angle, and degree of crosstalk of emitted light are driven by two parameters: the lenslet F/# (focal length over aperture diameter) and the divergence of light exiting the waveguide. From geometrical optics, using the paraxial lens approximation, the maximum steering angle with zero geometrical crosstalk is given by:
where
θ2 is the half divergence angle of the effective source immersed in refractive index
n. Maximizing the steering angle corresponds to minimizing the lens F/# and the divergence angle of the effective source. Also from geometrical optics, we can write the minimum divergence angle due to the spatial extent of the effective source as:
where
wfacet is the full width of the effective source and
f is the focal length of the lens. For a small minimum divergence angle, corresponding to a tightly collimated output beam, the lateral extent of the source needs to be small with respect to the focal length of the lens.
2.2 Light guiding and extraction
The extraction features act as the effective sources for the lenses by intercepting and redirecting light propagating in the waveguide toward the lens array. Light may be extracted from the waveguide using reflection, refraction, diffraction, or diffuse scattering. Flat faceted features are desirable because they have broadband performance (unlike dispersive gratings) and conserve angular divergence (unlike diffusers or curved facets). The conservation of angular divergence is crucial for minimizing crosstalk and generally keeps the system more étenduelimited, leading to more efficient designs.
The waveguide confines light by TIR for a sufficient angular spectrum, allowing light to be
efficiently distributed to the extraction sites. The type of waveguide determines the
relationship between the waveguide thickness and the dimensions of extraction features. We
considered two waveguide designs. One is a constant cross section and ‘constant mode
volume’ (CMV) waveguide [
Fig. 4(a)] where light
is shared between extraction sites, and the other is a laterally tapered ‘stepped mode
volume’ (SMV) waveguide [
Fig. 4(b)] where each
extraction site adiabatically truncates the modal volume [
77. D. T. Moore, G. R. Schmidt, and B. L. Unger, “Concentrated photovoltaic stepped planar light guide,” in International Optical Design Conference, Technical Digest (Optical Society of America, 2010), paper JMB46P. [CrossRef]
].
Fig. 4 Constant (a) and stepped (b) mode volume waveguide illustrations for N = 5 extraction
sites. Each section as drawn supplies light to one row of lenses above the waveguide (not
shown).
In the CMV geometry, light makes multiple passes through the waveguide and extraction is fundamentally nonuniform. We model the percentage of light energy extracted at a facet as the ratio between the facet cross section and the waveguide cross section. This model ignores shadowing effects, which is valid when the divergence is relatively large and the facets are relatively small with respect to their period. First, we determine the facet cross section ‘
σf,’ which is the cross sectional area of the facet seen by the average waveguide mode. By the reasoning presented above for the SMV waveguide, we set the facet angle
γ to 45°. Constraining the base dimensions of the facet to be square (
wfacet x
wfacet) to produce a symmetric beam using a rotationally symmetric lens, the facet cross section is just the product of the facet width and height, where the height is half the width:
σfγ=45∘=wfacet2/2. We then write the distributed absorption and extraction per lens aperture as:
where
D is the full lens aperture and
α is the absorption coefficient of the waveguide material. Modifying the BeerLambert law, where
j runs from 1 to
N facets, the output power at the
jth facet is given by:
where
P0 is the power coupled into the waveguide,
η2and
η1 are the reflection efficiencies from the end of the waveguide and the source, respectively, and
N is the total number of extraction sites in the section of waveguide. By symmetry, we consider a section of waveguide that is one lens aperture wide and half the total system aperture long, taking
η2=1 and
η1=ηcoupler2RLED, where
ηcoupler is the coupler efficiency (discussed in Section 2.3) and is modeled as being equivalent in both forward and reverse directions and
RLED is the percentage of light recycled by the LED. The incident light recycled by a typical die is about 50% [
88. J. K. Kim, T. Gessmann, H. Luo, and E. F. Schubert, “GaInN light emitting diodes with RuO_{2}/SiO_{2}/Ag omnidirectional reflector,” Appl. Phys. Lett. 84(22), 4508–4510 (2004). [CrossRef]
] and the phosphor efficiency can be as high as 70% per pass [
99. H. Luo, J. K. Kim, E. F. Schubert, J. Cho, C. Sone, and Y. Park, “Analysis of highpower packages for phosphorbased whitelightemitting diodes,” Appl. Phys. Lett. 86(24), 243505 (2005). [CrossRef]
]. The total recycling efficiency can be approximated by two passes through the phosphor and one reflection from the die, which gives 25% total recycling efficiency. The total extracted power can be determined by evaluating the sum:
where we consider the term on the right hand side which scales the input power
P0 to be the average extraction efficiency ‘
ηext,’ referred to later in Section 3. In the CMV geometry the relationship between waveguide and facet dimensions is:
for
γ = 45° in order for the facet to fit within the waveguide. Here, unlike for the SMV waveguide, there is no fixed geometrical relationship between facet geometry, number of facets, and waveguide length.
Recalling from
Eq. (2) that minimizing the divergence of emitted light corresponds to minimizing
wfacet, we find that by the geometry of the SMV waveguide [
Eq. (3)] and by the desire for high extraction efficiency in the CMV waveguide [
Eq. (6)], we would like to minimize the waveguide thickness ‘
twg’ in both cases.
2.3 Light sources and couplers
White LEDs currently have superior luminance and efficacy compared to other broadband sources. From conservation of radiance, the brightness at the output of any passive optical system is limited by the brightness of the source. Consequently, LEDs with the highest luminance are desirable because they provide more optical power with the same étendue. These ‘high power’ LEDs have die sizes exceeding 2mm in width and typically obey Lambert’s cosine law, leading us to calculate the fraction of Lambertian power in a beam of half angle θ1 to be:
For example, a Lambertian emitter output clipped at θ1 = ± 71.65° still contains 90% of the total power. Having such a clearly defined beam divergence simplifies étendue calculations.
To a high degree of accuracy, we can approximate both collimator designs as conserving étendue, so for two square apertures:
where
h1 and
h2 are the full widths of the source and exit apertures and
θ1 and
θ2 are the half divergence angles of light entering and exiting the collimator, respectively.
3. Systemlevel analytic model and optimization
Systemlevel optimization of the planar illuminator is difficult in standard optical design software because of the complex geometries and merit functions. We developed an analytic model based on equations from imaging and nonimaging optics to give an intuitive optimization approach that provided more confidence than a ‘black box’ method. The designs resulting from the analytic optimization were modeled in Solidworks and ray traced with nonsequential Monte Carlo analysis using Zemax to insure the accuracy of the analytic model. A truly ‘optimal’ solution is predicated on a detailed list of applicationspecific constraints and performance metrics. Without the information needed for a quantitative merit function, we optimized according to qualitative ideas of wellbalanced performance.
3.1 Design 1: constant mode volume with faceted coupler
The first design aims for manufacturability at the cost of performance by using the faceted coupling structure and a constant mode volume waveguide. The coupler is compatible with injection molding and the waveguide with roll processing of glass or plastic sheets.
From
Eqs. (9) and
(12), setting
θ=0 for the CMV waveguide geometry, we arrive at an implicit
transcendental equation for
θ2:
where we recast
M=(h1sinθ1)/(twgsinθ2) using
Eqs. (9) and
(10) so that the optimization problem is
constrained to 4 dimensions:
{twg,σf,F/#,N}, with the remaining variables fixed by design constraints. The
optimization algorithm maps the design space by iterating through these 4 dimensions and
numerically solving
Eq. (16) over a grid of
points in the space. For each point in
{F/#,N} space, an optimal point in
{twg,σf} space is found by maximizing a weighted sum of normalized maximum
steering angle and normalized system efficiency [
Fig.
9(a)].
Fig. 9 CMVF design space for 25% of target emittance. (a) Optimization metric for
N=60, F/#=0.75. (b) Maximum beam steering angle in {F/#,N} space. (c) Optical efficiency in {F/#,N} space. Note that the axes are rotated 90°
counterclockwise from (b) to (c) to clearly illustrate the data.
The maximum steering angle is given by
Eq.
(1) and the overall optical system efficiency is the product of all efficiency terms in
Eq. (16). We discarded solutions for which the
minimum half divergence angle [
Eq. (2)] is
greater than a design limit of 5° and for which extraction deviation is greater than 1%,
where the deviation is given by
maxj{Pext,total−NPext,j/Pext,total} using
Eqs. (5) and
(6).
Figures 9(b) and
9(c) show the corresponding optimums mapped from
{twg,σf} to
{F/#,N} space. There is a clear tradeoff between efficiency and maximum steering angle, which also depends on the target emittance. Higher emittance values drive both the maximum steering angle and efficiency down. High emittance requires a low aspect ratio
M to maintain a high spatial power density, which either requires a thick waveguide or a small intermediate aperture [
Eq. (10)]. To maintain the same minimum divergence angle for the same lens F/# when the waveguide is made thicker, the facet dimension must be held constant [
Eq. (2)], meaning the extraction efficiency decreases [
Eq. (6)]. The other alternative, shrinking the intermediate aperture
h2, means that for the same beam efficiency [
Eq. (8)], the divergence angle of coupled light increases [
Eq. (9)], which both lowers the maximum steering angle [
Eq. (1)] and lowers the coupler efficiency [
Fig. 6]. Similar balancing forces are present when trying to push the maximum steering angle or the optical system efficiency as well.
The physical structure was modeled in Solidworks and imported into Zemax for ray trace analysis.
The full system has a 2x2 foot aperture consisting of 120x120 lenslets and 4 source LEDs. The
model consisted of a full 3 dimensional structure where rays were stored after being traced
through the coupler and relaunched into the waveguide to save repetitive tracing through the
coupler. A sufficient number of rays were traced to achieve ergodicity. The far field
directionality was simulated as a function of lateral offset [
Fig. 11(a)] and the divergence as a function of rotation about the center of the array
[
Fig. 11(b)]. The collimated beam can be steered
± 45° maintaining over 35% optical efficiency, and can be diverged from ±
5° to ± 60° maintaining about 43% optical efficiency. Most of the loss
comes from the faceted coupler, which has a relatively large aspect ratio of
M=22. We see good agreement between the analytic model, which assumes
a tophat beam intensity profile characterized by
ψ and
φ, and the Zemax simulation in
Fig.
11(a).
Fig. 11 Far field directivity (a) and divergence (b) simulations of the optimal CMVF design, with
total optical efficiency plotted on the lefthand plane (dashed blue). Part (a) shows good
agreement between the Zemax (black) and analytic (red) models. Part (b) shows the Zemax
model (black) on a log scale.
Higher efficiencies can be reached if the minimum divergence requirement is relaxed, as this enables a reduction in the aspect ratio of the coupler, an increase in waveguide thickness, and a corresponding increase in facet size. This allows coupler efficiency to be increased without reducing extraction efficiency. Similarly, relaxing the uniformity requirement increases the extraction efficiency, which also increases overall system efficiency.
3.2 Design 2: stepped mode volume with curled coupler
Fig. 13 Single section wireframe model of optimal SMVC design.
This design benefits greatly from a nearly ideal coupling structure and extraction
mechanism. The 1.475x10
^{4} lux target emittance could be met while retaining a useful
portion of the design space. We chose an optimal design with
N=20,
F/#=0.5, and
twg=0.761mm [
Fig. 13]. Like the
CMVF design, this design also used a reflective lens array to achieve the necessary F/#. This
yielded a predicted maximum steering angle of ± 60° and a minimum divergence
angle of about ± 5°.
Fig. 14 Far field directivity (a) and divergence (b) simulations of optimal SMVC design, with
total optical efficiency plotted on the lefthand plane (dashed blue). Part (a) shows good
agreement between the Zemax (black) and analytic (red) models. Part (b) shows the Zemax
model (black) on a log scale.
The full system has a 2x2 foot aperture consisting of 40x40 lenslets and 6 source LEDs.
We used the same modeling technique discussed in Section 3.1 to simulate the system
performance. The result of the Zemax simulations, shown in
Fig.
14, confirm that the system can steer the beam ± 60° while maintaining
over 75% optical efficiency and diverge the beam from ± 5° to essentially
hemispherical illumination maintaining about 80% optical efficiency. The main source of loss in
this design came from Fresnel reflections. To reach higher efficiencies the optics could be
antireflection coated, at an increased manufacturing cost.
A third design using a constant mode volume waveguide with a curled coupler (CMVC) was optimized and simulated and occupied a middleground between the previously discussed CMVF (35% optical system efficiency) and SMVC (75% optical system efficiency) designs in both manufacturability and performance. The optimal CMVC design emitted 1.22x10^{4} lux and could steer the beam ± 60°, operating above 62% optical system efficiency, and could diverge the beam from ± 5° to hemispherical illumination.
4. Prototype fabrication and characterization
The modeled systems in Section 3 used optimized components to achieve high system performance. To demonstrate the concept and compare model with measurement, we constructed a prototype system using commercially available or easily fabricated components. Because alignment tolerances scale with component size, the physical scale of parts was the driving factor in determining our choice of components.
We used F/1.04 refractive Fresnel lenses molded from poly methyl methacrylate (PMMA) available in 4x4 arrays measuring 3x3 inches. To reduce F/# and increase steering range we increased the lens power by stacking two lens layers for a final F/0.7 lens, measured in the PMMA waveguide. The Fresnel lenses were oriented so that the grooved sides were both facing away from the source. For the extraction features, we used 1mm diameter steel ball bearings epoxied into hemispherical recesses machined into the waveguide. The spherical symmetry of the bearings translates into relaxed alignment tolerance and a higher degree of repeatability compared to flat facets, which would require precise 3 dimensional alignment. The spatial extent of the 1mm diameter hemispheres gives a 3.2° half divergence angle of emitted light. For the waveguide, we used a 2.54 mm thick planar sheet of PMMA, where the thickness was chosen to produce uniform and efficient extraction. A 10.6 mm thick PMMA substrate was glued to the bottom of the lens array to minimize the air gap between the waveguide and lens structure while keeping the total optical distance between lens and extraction feature equal to the focal length. We found that an air gap of 100300 μm between the lenses and waveguide was sufficient to minimize undesirable divergence, and could be achieved using a small number of thin Teflon spacers distributed across the system aperture.
The curled and faceted couplers discussed previously provide a relatively collimated and axially symmetric angular spectrum, which is ideal for use with flat facets. However, when using spherical extraction features, there is no need for the illumination to be collimated or axially symmetric due to the scattering properties of a sphere. From an étendue perspective, the spheres are more efficiently illuminated by light with a larger divergence angle and a higher spatial power density. Additionally, the extraction efficiency of spherical facets was found to increase when light propagates with a large average angle with respect to the waveguide plane, so long as the TIR condition is obeyed. Based on these observations, we used a linear array of closelyspaced 0.43 mm thick LEDs attached to a 1D CPC to reduce the divergence in the plane normal to the waveguide while allowing full divergence in the plane of the waveguide. The CPC bar was attached to the waveguide at a 36° angle with respect to the waveguide plane. The CPC couplers were machined out of polycarbonate and vapor polished to produce a specular surface finish, and later sputtered with 1 micron thick silver reflector (measured to be >85% efficient) to increase reflectivity in regions of the CPC that were not TIR limited. The LEDs were chosen for their thin form factor, allowing adequate collimation defined by the 1D étendue relation, and for their high flux of 4.38 lm from a 2.3x0.3 mm aperture. The LEDs were reflowsoldered onto a printed circuit board (PCB) while using an alignment fixture machined from FR4 to register the LEDs to about 200 μm positional tolerance. This tight alignment tolerance allowed efficient interface with the CPC coupler.
4.2 Full aperture system
Fig. 19 Simulation (left column) and measurement (center column) of onaxis, offaxis, and
diverged spots 3 meters from the aperture. The right column shows the corresponding view of
the aperture from an angle.
Fig. 20 Near field directionality (a) and divergence (b) of the prototype system 3 meters from the
aperture. Part (a) shows the analytic model (red), Zemax model (black), and measurements
(blue). Part (b) shows the Zemax model (black) and measurement (blue) on a log scale.
Qualitative [
Fig. 19]] and quantitative [
Fig. 20 measurements were taken 3 meters from the system
aperture using a camera and calibrated photodiode, respectively, demonstrating good agreement
with both the semianalytic and Zemax models. The tophat profile beam calculated with the
semianalytic model was mapped from polar far field space to physical space using simple
radiometric calculations. The scattering of light from Fresnel zone transitions accounts for
the main discrepancy between model and measurement. From lens cross section measurements the
zone transitions were estimated to obscure about 30% of the clear lens aperture, accounting for
the reduction in central beam power and resultant increase in the noise pedestal surrounding
the beam. This effect becomes more pronounced as the beam is steered to more extreme angles.
This also explains the behavior observed for extreme rotations, where we find the system acts
more like a diffuse emitter instead of preferentially ‘spreading out’ the light
according to the Zemax model.
Polar integration of the illuminance line scan measurements yields a total output of 98 lm,
corresponding to an optical system efficiency of 7.6%, which agrees well with the simulated
optical efficiency of 7.56%. The major source of loss in the prototype came from the high
absorption coefficient of the PMMA waveguide, measured and simulated to be 0.5
m
^{−1}. Zemax simulations showed that using a BK7 waveguide with an absorption
coefficient of 3x10
^{−4} m
^{−1} (used in the optimized
theoretical designs) would increase the overall optical system efficiency of the prototype to
31%. Secondary sources of loss in the prototype were coupling mirror loss, waveguide surface
scattering, and small misalignments in the couplers and lens array. While the prototype system
is highly inefficient compared to optimal designs, the consistency between measurement, model,
and simulation indicates that the predicted high efficiencies for optimized designs [
Table 1] are credible. This agreement also supports the
accuracy of the analytic model in representing the system during design and
optimization.
Table 1. System Efficiencies and Loss Mechanisms 

5. Conclusion
We showed how a planar waveguide illuminator with periodically patterned extraction features and lens array can be used to control both the directionality and divergence of light output using shortrange mechanical motion.
The system performance depends on a large number of variables, which led us to develop an analytic model compatible with the two coupling and two waveguiding designs considered in order to perform systemlevel optimization. The analytically optimized designs were ray traced in Zemax and the resulting performance was in good agreement with the analytic model. We found that the optimal design used a stepped mode volume glass waveguide and curled coupler. This design could steer a collimated beam over ± 60° and diverge the beam from ± 5° to fully hemispherical illumination, while maintaining over 75% optical efficiency, for a total output of 4800 lumens from a 2x2 foot aperture.
We constructed a proofofprinciple prototype from commercially available components which successfully demonstrated both the beam steering and diverging principle in a 2x2 foot aperture embodiment. Although the optical efficiency of the device was only 7%, good agreement between the measurement, Zemax simulation, and analytic model was established, supporting the predictions of high efficiency and high output power in optimal designs which used fully custom optical components. The next step would be to fabricate an efficient system using the optimized optical structures, and using electrical controllers to allow remote actuation.
In future research, the same basic concept could be extended to provide a thin energy efficient flat panel display where light energy is actively directed toward one or more users, whose position may be tracked using a video camera and facetracking software. Given accuracy sufficient to selectively illuminate each of the user’s eyes, this approach may be used for multiuser glassesfree 3D display.