Optical Broadband Angular Selectivity

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Science  28 Mar 2014:
Vol. 343, Issue 6178, pp. 1499-1501
DOI: 10.1126/science.1249799

Optical Angular Selection

A monochromatic electromagnetic plane wave is typically characterized by three properties: its frequency, its polarization, and its propagation direction. While the selection of light signals based on the first two properties has been studied in depth, selection based on direction is relatively unexplored but equally important. Shen et al. (p. 1499) demonstrate a simple approach that provides narrow-angle selectivity over a broad range of wavelengths using heterostructured photonic crystals that act as a mirror for all but a narrow range of viewing angles where the crystals are transparent. Such angular selection should find a number of applications in, for example, high efficiency solar energy conversion, privacy protection systems, or high signal-to-noise detectors.


Light selection based purely on the angle of propagation is a long-standing scientific challenge. In angularly selective systems, however, the transmission of light usually also depends on the light frequency. We tailored the overlap of the band gaps of multiple one-dimensional photonic crystals, each with a different periodicity, in such a way as to preserve the characteristic Brewster modes across a broadband spectrum. We provide theory as well as an experimental realization with an all–visible spectrum, p-polarized angularly selective material system. Our method enables transparency throughout the visible spectrum at one angle—the generalized Brewster angle—and reflection at every other viewing angle.

The ability to control light has long been a major scientific and technological goal. In electromagnetic theory, a monochromatic electromagnetic plane wave is characterized (apart from its phase and amplitude) by three fundamental properties: its frequency, its polarization, and its propagation direction. The ability to select light according to each of these separate properties would be an essential step in achieving control over light (Fig. 1).

Fig. 1 Illustration of light selection on the basis of its fundamental properties.

(A) Frequency selectivity provides control over transmission or reflection of different frequencies. Photonic crystals (such as omnidirectional mirrors) can select light in specific frequency bandwidths. (B) Polarization selectivity provides control over the transmission or reflection of different polarizations. An ideal polarizer selects light with a specific polarization. (C) Angular selectivity provides control over the transmission or reflection of incident angles; so far, achieving broadband selectivity has remained elusive.

Tremendous progress has been made toward both frequency selectivity and polarization selectivity. Frequency selectivity (Fig. 1A) can be obtained, for example, by taking advantage of photonic band gaps in photonic crystals (15). Polarization selectivity (Fig. 1B) is accomplished, for example, by means of a “wire grid” polarizer (6) or by exploiting birefringent materials (7, 8). Methods based on interference and resonance effects have been explored for angular selectivity, but they have limited applications because they are sensitive to frequency.

An angularly selective material system should ideally work over a broadband spectrum. Such a system could potentially play a crucial role in many applications, such as high-efficiency solar energy conversion (9, 10), privacy protection (11), and detectors with high signal-to-noise ratios. Some progress has been made toward achieving broadband angular selectivity by means of metallic extraordinary transmission (12, 13), anisotropic metamaterials (14), combined use of polarizers and birefringent films (11), or geometrical optics at micrometer scale (15). The first two of these mechanisms are difficult to realize in the optical regime; the other two work only as angularly selective absorbers.

Here, we introduce a basic principle to achieve optical broadband angular selectivity. Our result rests on (i) the fact that polarized light transmits without any reflection at the Brewster angle, (ii) the existence in photonic crystals of band gaps that prevent light propagation for given frequency ranges, and (iii) the band gap–broadening effect of heterostructures. First, we prove our fundamental idea theoretically for a single polarization and oblique incident angles, and also for both polarizations and normal angle of incidence. Second, we experimentally demonstrate the concept in the case of all–visible spectrum, p-polarized light. The demonstrator is transparent for all colors at one viewing angle and highly reflecting at every other viewing angle.

We begin by considering a simple quarter-wave stack with periodicity a, relative permeability μ of μ1 = μ2 = 1, and relative permittivities ε of ε1 and ε2. In such a system, monochromatic plane waves with frequency ω propagate only in certain directions; propagation in other directions is not allowed because of destructive interference (3). Another way to look at this is through the photonic band diagram shown in Fig. 2A: Modes that are allowed to propagate (so-called extended modes) exist in the shaded region; no modes are allowed to propagate in the white regions (known as band gaps). In the photonic band diagram, modes with propagation direction forming an angle θi with respect to the z axis in Fig. 2 (in the layers with dielectric constant εi) lie on a straight line represented by Embedded Image, where ky is the y component (as defined in Fig. 2) of the wave vector k and c is the speed of light; for general propagation angle θi, this line will extend through the regions of the extended modes as well as through the band gap regions.

Fig. 2 Theoretical illustration.

(A) Extended modes (shaded regions) for off-axis propagation vectors (0, ky, kz) in a quarter-wave stack with two materials having ε1 = 1 and ε2 = 2, respectively. The green region indicates modes with E fields polarized in the yz incidence plane (p-polarized). The dashed black line corresponds to the Brewster angle θB in both layers. (B) Schematic layout of a simple quarter-wave stack. (C) The same plot as in (A), but with ε1 = μ1 = 1, ε2 = μ2 = 2, and for both p- and s-polarizations. (D and F) Extended modes for an ideal heterostructure with (m, n) → ∞. (E) Schematic layout of the heterostructure stacking mechanism. (G) P-polarized transmission spectrum of 50 quarter-wave stacks at various periodicities. Each quarter-wave stack consists of 10 bilayers of {ε1 = 1, ε2 = 2} materials. The periodicities of these quarter-wave stacks form a geometric series ai = a0ri–1 with a0 = 200 nm and r = 1.0212, where ai is the periodicity of ith stack. See (20) for a more detailed discussion of this stacking process. (H) P- and s-polarized transmission spectrum for a structure that has the same number of stacks and layers per stack as in (G), but with a0 = 140 nm and r = 1.0164, and with different material properties: ε1 = μ1 = 1, ε2 = μ2 = 2.

However, for p-polarized light, there is a special propagation angle, known as the Brewster angle θB, for which the extended modes exist regardless of ω (dashed line in Fig. 2A) (8, 16):Embedded Image (1)where θB is the Brewster angle in the layers with dielectric constant ε1. At θB, p-polarized light is fully transmitted for all frequencies at both interfaces (from ε1 to ε2 layers and from ε2 to ε1 layers). This condition is not sufficient to achieve angular selectivity; we also need to remove all the extended modes in other propagation directions. Because the location of the band gap scales proportionally to the periodicity of the quarter-wave stack, the effective band gap can be enlarged when we stack quarter-wave stacks with various periodicities together (1719). The details of this process are illustrated in fig. S1 (20). As a proof of principle, in Fig. 2D we plot the band diagram of an ideal structure with ε1 = 1 and ε2 = 2 and the number of quarter-wave stacks approaching infinity. By doing this with a finite system of 50 stacks (10 bilayers in each stack), we can achieve an angularly selective range of less than 2° and a frequency bandwidth of ≥54%, similar to the size of the visible spectrum (Fig. 2G).

For s-polarized light, as there is no Brewster angle, this construction behaves as a dielectric mirror that reflects over a wide frequency range and over all incident angles (fig. S2) (20).

The mechanism above provides both angular selectivity and polarization selectivity, and is therefore useful in many applications. For example, in most optically pumped lasers, the pumping light comes in with a specific polarization and at one specific angle. A cavity built with both angularly selective and polarization-selective mirrors will allow the pumping light to get through, while at the same time trapping all the light with other propagation directions and polarizations inside the cavity.

The restriction on the polarization can be lifted by releasing the conventional requirement that μ1 = μ2 = 1. During the past decade, it has been demonstrated that metamaterials have the potential to achieve ε = μ ≠ 1 in a broad frequency range (2123). Consider two media with ε1 = μ1 ≠ ε2 = μ2; under those circumstances, there is no reflection at the interface at normal incidence because the two media are impedance-matched, where the impedance Z is defined as Embedded Image. The off-axis reflectivity can be calculated directly from the generalized Fresnel equations (8):Embedded Image (2)andEmbedded Image (3)where the subscripts i and r denote incident light and reflected light, respectively, and the subscripts ⊥ and || indicate the direction of the electric field E with respect to the plane of incidence. When Zi = Zt, the reflectivities for s- and p-polarized light become identical. In particular, the Brewster angle is the same for both polarizations (θB = θi = θr = 0°). As a proof of principle, we plot the band diagram of a quarter-wave stack with ε1 = μ1 = 1 and ε2 = μ2 = 2 in Fig. 2C. As in the previous case, we can broaden the band gaps by stacking quarter-wave stacks with various periodicities together (Fig. 2F); this approach gives rise to ultra-broadband angular selectivity at normal incidence for both polarizations (Fig. 2H).

Other than using photonic band gaps to remove unwanted extended modes, there might exist even more optimized ways to forbid light from propagating in unwanted directions: The narrowness of angular selectivity can be optimized using numerical tools (17, 24) to further enhance the performance of the material system. Examples of optimizations based on three different physical mechanisms are shown in fig. S3 (20).

To show the feasibility of the method described above, we present an experimental realization for the ε1 ≠ ε2, μ1 = μ2 = 1 case. The sample was fabricated with the bias target deposition (BTD) technique (25) at 4Wave Inc. using SiO21 ≈ 2.18, μ1 = 1) and Ta2O52 ≈ 4.33, μ2 = 1) on a 2 cm × 4 cm fused silica wafer (University Wafer Inc.). The sample consists of 84 layers in total (Fig. 2E). There are six bilayer stacks (m = 6), each bilayer stack consisting of seven bilayers (n = 7), with the thicknesses of each layer equal in a given stack. The periodicities of the six bilayer stacks form a geometric series with ai = a0ri–1 for the ith stack, where a0 = 140 nm and r = 1.165. For index-matching purposes, the whole sample was immersed into a colorless liquid with dielectric constant εliquid = ε1 = 2.18 (Cargille Labs) (Fig. 3A). The sample could work in the air by adding a coupling prism or by using a porous material for ε1 that has a lower refractive index, such as aerogel (26).

Fig. 3 Experimental setup and observation.

(A) Schematic layout of the experimental setup. The system is immersed in a liquid that is index-matched to Embedded Image. (B) Normal incident angle setup. The sample behaves as a mirror and reflects the image of the camera. (C) θi = 30° setup. The sample behaves as a mirror and reflects the image of MIT cups in the lab. (D) θi = θB = 55° setup. The sample becomes transparent for the entire visible regime for p-polarized light. (E) θi = 70° setup. The sample behaves as a mirror and reflects the figurine placed at the corner of the table. In (B) to (E), a polarizer is installed on the camera so that it detects only p-polarized light.

The sample is transparent (up to 98%) to p-polarized incident light at θB = 55° (Fig. 3D); the angular window of transparency is about 8°. It behaves like a mirror at all other incident angles over the entire visible spectrum (Fig. 3, B, C, and E). For s-polarized incident light, the sample behaves like a mirror at all angles (fig. S2) (20). The p-polarization transmittance of the sample in the visible spectrum was measured using an ultraviolet-visible spectrophotometer (Cary 500i); a p-polarizer was used to filter the source beam. The experimentally measured result agrees with the rigorous coupled wave analysis (RCWA) (27) simulation prediction (Fig. 4), which includes the measured dispersion of materials (index variation < 1.3% for SiO2 and < 6.2% for Ta2O5 over the wavelength range from 400 to 700 nm). In the experimental measurements, the peak transmittance at θB becomes lower at shorter wavelengths (Fig. 4, lower panel) because the wavelength is getting closer to the dimensional tolerance of fabrication. Movie S1 is a video recording of the full process with the sample rotating 90° in this experimental setup.

Fig. 4 Simulation and experimental measurement.

Comparison between the p-polarized transmission spectrum of the RCWA simulation (27) (top) and the corresponding experimental measurements (bottom). The value of transmission is indicated by the color bars.

Our method has a number of attractive features, including simplicity, narrow angle selectivity, scalability beyond optical frequencies, and reproducibility on large scales. Furthermore, this method can be implemented in other wave systems that have Brewster angle analogs, such as acoustic and elastic waves. A natural next step would be to examine materials whose magnetic permeability is similar to their dielectric constant, so as to reach angular selectivity in both polarizations.

Supplementary Materials

Figs. S1 to S3

Reference (28)

Movie S1

References and Notes

  1. See supplementary materials on Science Online.
  2. Acknowledgments: We thank P. Rebusco for critical reading and editing of the manuscript, J. J. Senkevich for advice on fabricating the sample, and C.-W. Hsu for valuable discussion. Supported in part by the Army Research Office through the Institute for Soldier Nanotechnologies under contract W911NF-13-D0001. The fabrication part of the effort, as well as M.S. (in part), were supported by the MIT S3TEC Energy Research Frontier Center of the U.S. Department of Energy under grant DE-SC0001299.
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