## Abstract

The perfect absorption of light in subwavelength thickness layers generally relies on exotic materials, metamaterials, or thick metallic gratings. Here we demonstrate that total light absorption can be achieved in ultrathin gratings composed of conventional materials, including relatively weakly absorbing semiconductors, which are compatible with optoelectronic applications such as photodetectors and optical modulators. We fabricate a 41 nm thick antimony sulphide grating structure that has a measured absorptance of $A=99.3\%$ at a visible wavelength of 591 nm, in excellent agreement with theory. We infer that the absorption within the grating is $A=98.7\%$, with only $A=0.6\%$ within the silver mirror. A planar reference sample absorbs $A=7.7\%$ at this wavelength.

© 2016 Optical Society of America

## 1. INTRODUCTION

Completely absorbing light within a layer of deeply subwavelength thickness, with zero reflection and zero transmission, is a challenge of both fundamental theoretical interest and of importance for practical applications such as photodetectors [1], optical switches, modulators, and transducers [2,3]. Total light absorption (TLA) can be achieved in two ways: by adiabatically introducing a complex refractive index change over the space of many wavelengths, or by creating a critically coupled resonance. While the first approach exhibits TLA across a broad bandwidth, it is inconsistent with the use of thin films [4]. The critical coupling condition required for resonant perfect absorption is typically satisfied over a modest bandwidth, but may be achieved in structures of subwavelength thickness.

Resonant perfect absorbers typically couple light into either a longitudinal standing wave in a homogeneous (or homogenized metamaterials) layer, as in Fig. 1(a) [1–3,5–11], or a sideways propagating surface plasmon polariton (SPP) on the surface of a corrugated metal, as in Fig. 1(b) [12,13]. TLA has also been demonstrated using plasmonic nanocomposites [14,15] and plasmonic metasurfaces [16–18]; however, plasmons are excited only by transverse magnetically (TM)-polarized light. The very strong absorption of unpolarized light has been achieved using crossed or biperiodic metallic gratings [12,18,19] and arrays of single layer doped graphene nanodisks [20]. The fabrication of metamaterial and nanoplasmonic structures is challenging because their minimum feature sizes are of the order of tens of nanometers at infrared and visible wavelengths. The use of metals also makes them incompatible with standard optoelectronic applications where a photocurrent must be extracted, although photodetection is possible based on hot electrons transferring over a Schottky barrier [18].

Here we experimentally demonstrate the total absorption of light in
lamellar gratings of deeply subwavelength thickness and provide a
comprehensive theoretical treatment of the phenomenon using the EMUstack
package [21–23] for numerical
simulations. Figures 1(c) and 1(d) show our theoretical and
experimental configurations respectively. In our experiments we show that
transverse electrically (TE)-polarized light, where the electric field is
along the grating rulings ($y$ axis in Fig. 1),
is totally absorbed in gratings composed of *relatively weakly
absorbing semiconductors* that have a complex refractive
index, $n={n}^{\prime}+\mathrm{i}{n}^{\prime \prime}$, with ${n}^{\prime \prime}\ll {n}^{\prime}$. Such materials are abundant in nature and are
compatible with optoelectronic applications. Furthermore, our structures
have minimum feature sizes close to 100 nm even when targeting visible
wavelengths, and can be patterned using standard techniques. We also show
numerically that TM-polarized light (magnetic field along the $y$ axis) can be totally absorbed in ultrathin gratings, and
that this requires metallic materials with ${n}^{\prime \prime}>{n}^{\prime}$ ($\mathrm{Re}(\u03f5)<0$), because it relies on the excitation of SPPs.

The paper is organized as follows: we began by reviewing the fundamental limits to absorption in ultrathin structures; in Section 2 we derive the conditions for TLA in uniform layers; in Section 3 we investigate absorption in gratings showing that TLA occurs at very different refractive indices than in uniform layers; in Section 4 we demonstrate TLA experimentally in weakly absorbing semiconductor gratings illuminated from one side; in Section 5 we show theoretically that TLA in ultrathin gratings can be achieved using a very wide range of materials; and we conclude in Section 6.

## 2. TOTAL LIGHT ABSORPTION IN ULTRATHIN LAYERS

Before investigating TLA in ultrathin gratings, we briefly examine TLA in homogeneous ultrathin films. An ultrathin structure (i.e., $|n|h\ll \lambda $, where $h$ is the layers thickness) can absorb at most 50% of the incident power when surrounded symmetrically by uniform media (refractive index $m$) and illuminated from one side [24–26]. This limit arises because the incident energy is equipartitioned between the two longitudinal modes of these structures: one has an even electric field symmetry [anti-node in the center of the layer, as in Fig. 2(a), line (i)]; the other has an odd symmetry [node in the center of Fig. 2(a), line (ii)] and, therefore, does not contribute to the absorption because it has negligible field inside the layer. The maximum absorption of $A=50\%$ occurs when the even mode is totally absorbed.

To increase the absorption beyond 50%, the excitation of the odd mode must
be suppressed; TLA requires that the structure either does not support an
odd mode, or for the excitation of the odd mode to be forbidden by the
symmetry of the incident field. With the odd mode not excited, TLA occurs
when the even mode is fully absorbed. In Fig. 1(a) the absorbing layer is illuminated from both
sides by coherent light of equal intensity, which totally suppresses the
excitation of the odd mode and excites a longitudinal standing wave across
the layer. This *coherent perfect absorption* (CPA)
configuration [2] produces $A=100\%$ with the same combination of $n$, $m$, and $h$ that produces $A=50\%$ when illuminated from one side.

#### A. Homogeneous (and Homogenized) Layers

Previous studies [2,10] have noted that TLA occurs in homogeneous layers when

where $r=(m-n)/(m+n)$ is the Fresnel reflection coefficient with normal incidence from the outside, and $\gamma ={e}^{\mathrm{i}n{k}_{0}h/2}$ is the change in phase*and*amplitude acquired by a mode with complex propagation constant $n{k}_{0}=2\pi n/\lambda $ upon propagating a distance $h/2$ [see Fig. 2(b)]. While Eq. (1) has been reported previously [2,10], its origin has not been completely clarified. Here we derive Eq. (1) in an intuitive, rigorous manner that generalizes to multimoded structures.

We note that Eq. (1) is consistent with critical coupling, where the loss rate of the resonance is set equal to the rate of incident energy (see Supplement 1 for derivation). Critical coupling has been used to analyze SPP-mediated TLA on corrugated metal surfaces [1]. Piper and Fan showed theoretically that a monolayer of graphene can achieve TLA when placed on top of a photonic crystal whose energy leakage rate matches the absorption rate of the graphene layer [27].

#### B. Derivation of Eq. (1)

In the symmetric configuration shown in Fig. 1(a), we can simplify our analysis by considering the properties of one half of the Fabry–Perot etalon with one incident beam. We begin with the resonance condition for a driven system in the presence of loss; with reference to Fig. 2(b) this is

where the first term represents a loop through the structure starting in the center of the layer (where the amplitude $b$ is marked), and the second term describes the contribution of the driving field to the resonance (also evaluated at the center). In the absence of a driving field ($a=0$), Eq. (2) reduces to the Fabry–Perot resonance condition, or, equivalently, the condition for a bound waveguide mode.For total absorption we require a further condition—the amplitude of the outgoing wave must vanish:

This expression also consists of two terms: the leakage from the resonant mode into the superstrate, and Fresnel reflection off the top interface. Finally, Eq. (1) is obtained by solving the simultaneous equations [Eqs. (2) and (3)], using the relationship $-r{r}^{\prime}+t{t}^{\prime}=1$ [28].#### C. Requirements on ${n}^{\prime}$ and ${n}^{\prime \prime}$

Rearranging Eq. (1) yields a transcendental expression for the complex refractive index required for TLA, which holds for structures of any thickness:

Focusing on ultrathin structures, we take the Taylor expansion of the tangent function in Eq. (4) for small arguments up to third order (derivation in Supplement 1). This yields which produces results consistent with the expression derived by Hägglund*et al.*(Eq. (3) in [10]). While Eq. (5) does not extend to the case where the substrate and superstrate have different refractive indices, its far simpler form allows us to obtain further insights.

Equation (5) reveals that TLA in ultrathin layers, where $\lambda /h\gg m$, is always possible in principle and requires ${n}^{\prime}\sim {n}^{\prime \prime}$ with ${n}^{\prime \prime}$ being slightly smaller. Furthermore, $|n|\propto \sqrt{\lambda /h}$ in these cases, which allows TLA to be achieved with only moderately large $|n|$ even with very small $h$. Figure 3 shows the absorption as a function of the real and imaginary parts of $n$, for a uniform film of thickness $h=\lambda /70$ arranged as in Fig. 1(a), and confirms that TLA occurs where ${n}^{\prime}\sim {n}^{\prime \prime}$. Throughout our simulations we take $m=1$.

Very few natural materials satisfy the condition ${n}^{\prime}\sim {n}^{\prime \prime}$, making TLA a truly unusual effect; examples include dyes [6] and the phase change material ${\mathrm{VO}}_{2}$ (when heated to precisely 342 K) [11]. TLA has also been demonstrated using metamaterials with subwavelength-sized meta-atoms (typically a combination of inductive and capacitive metallic elements) engineered to give an homogenized effective permittivity and permeability of $\mathrm{Re}({\u03f5}_{\mathrm{eff}})\approx 0$, $\mathrm{Re}({\mu}_{\mathrm{eff}})\approx 0$ on resonance [1,8,9], which is consistent with ${n}_{\mathrm{eff}}^{\prime}\sim {n}_{\mathrm{eff}}^{\prime \prime}$. The Taylor expansion used to derive Eq. (5) is accurate only when $n{k}_{0}h/2\ll 1$, which explains how CPA has also been demonstrated in thick ($nh/\lambda >385$) wafers of silicon at wavelengths where ${n}^{\prime \prime}$ is 3 orders of magnitude smaller than ${n}^{\prime}$ [2,7].

## 3. TOTAL ABSORPTION IN LAMELLAR GRATINGS

Having seen that TLA is difficult to achieve in uniform ultrathin layers, we now investigate how ultrathin gratings made of common materials can achieve TLA. We consider the volume gratings illustrated in Figs. 1(c) and 2(c), a fraction $f$ of which have refractive index $n$ and the remainder of which is air, illuminated at normal incidence. The period of the gratings $d$ is chosen so that multiple Bloch modes (each corresponding to superpositions of diffraction orders) propagate within the grating, but that only the specular diffraction order propagates away from the grating in the surrounding medium. These conditions require ${n}_{\mathrm{eff}}d>\lambda $ and $md<\lambda $, respectively, where ${n}_{\mathrm{eff}}$ of the grating is calculated using the linear mixing formula of the permittivity for TE polarization (the inverse linear mixing formula must be used for TM polarization).

The absorption of TE- and TM-polarized light in $h=\lambda /70$ thick lamellar gratings is shown in Figs. 4 and 5, respectively, where the gratings have $d=66\lambda /70$ and $f=0.5$. In comparing these to the results for a uniform layer of the same thickness (Fig. 3), we see that higher order diffractive grating modes drive TLA at dramatically different values of $n$ than for homogeneous layers, and that the required $n$ differs greatly between the polarizations.

#### A. TE-Polarized Light: Slab Waveguide Modes

For TE-polarized light, Fig. 4 shows that TLA occurs with refractive indices with ${n}^{\prime \prime}\ll {n}^{\prime}$ (far below the diagonal in Fig. 4), indicating that the gratings can be made of conventional, weakly absorbing semiconductors. We have established that TLA occurs due to the excitation of the fundamental TE leaky slab waveguide mode, which has no cutoff. Such guided mode resonances have previously been studied in detail for their broadband reflection properties [29–31]; however, TLA has not been reported using this effect. Examining the dispersion relation of the equivalent waveguide mode of the homogenized grating [32] indicates that the absorption peak at ${n}^{\prime}\sim 4$ corresponds to the waveguide mode being excited by the grating’s first reciprocal lattice vectors, $\pm G=\pm 2\pi /d$, whereas the peak at ${n}^{\prime}\sim 7$ is excited by $\pm 2G$. While the value of ${n}^{\prime}$ ensures that the guided mode is phase matched to the incident light, the corresponding ${n}^{\prime \prime}$ determines the absorption loss rate of the mode that must be equal to the mode’s radiative loss rate in order to fulfil the critical coupling condition and achieve TLA.

#### B. TM-Polarized Light: SPPs

The results for TM-polarized light (using the same gratings as in Fig. 4) are shown in Fig. 5. The refractive index that produces TLA has ${n}^{\prime \prime}>{n}^{\prime}$, i.e., $\mathrm{Re}(\u03f5)<0$, which implies a different underlying mechanism. TM-polarized light, unlike TE-polarized light, can excite SPPs that propagate in the $x$ direction, along the interface between the surrounding medium and a metallic grating, with $\mathrm{Re}(\u03f5)>0$ and $\mathrm{Re}(\u03f5)<0$, respectively. In ultrathin gratings, the SPPs of the top and bottom interfaces couple, producing two modes: the long range SPP (LRSPP) and the short range SPP (SRSPP), which is more lossy because it is more tightly confined within the absorber. TLA occurs due to the SRSPP because its dominant electric field component has an even symmetry in the $x\u2013y$ plane, whereas the LRSPP has an odd symmetry. The SRSPP creates a single absorption peak in Fig. 5 because its propagation constant is $\beta >0$, while $\mathrm{Re}(\u03f5)<0$.

## 4. EXPERIMENTAL DEMONSTRATION

We now present our experimental demonstrations of TLA of TE-polarized light using antimony sulphide (${\mathrm{Sb}}_{2}{\mathrm{S}}_{3}$) semiconductor gratings, placed above a metallic reflector, as illustrated in Fig. 1(d). TLA in this asymmetric configuration is driven by the same underlying physics as in Figs. 1(c), but allows for TLA with only a single incident beam and is experimentally far simpler. ${\mathrm{Sb}}_{2}{\mathrm{S}}_{3}$ was chosen as the absorbing layer because it is a stable semiconductor that can be deposited in thin films using thermal evaporation and it has a suitable refractive index and absorption coefficient (in its as-deposited amorphous form) to meet the TLA requirements close to $\lambda =600\text{\hspace{0.17em}}\mathrm{nm}$. We emphasize that the results of Section 3 demonstrate that TLA in ultrathin gratings is a general effect that can be achieved using a very wide range of common materials.

#### A. Fabrication

Figures 6(a) and 6(b) show SEM images of a fabricated grating structure on a polished Si wafer with light incident from air. From bottom to top, the structure consists of a 130 nm Ag reflector deposited by thermal evaporation, a ${h}_{s}=245\text{\hspace{0.17em}}\mathrm{nm}$ thick ${\mathrm{SiO}}_{2}$ spacer layer (refractive index ${m}_{s}$) deposited by plasma-enhanced chemical vapor deposition (PECVD), and a 41 nm thick amorphous ${\mathrm{Sb}}_{2}{\mathrm{S}}_{3}$ layer deposited by thermal evaporation. The grating was fabricated using electron-beam lithography to define a mask in a polymethyl methacrylate (PMMA) resist, followed by an inductively coupled plasma (ICP) etch using ${\mathrm{CHF}}_{3}$ gas. Further details of the deposition and processing conditions are provided in Supplement 1.

The ${\mathrm{SiO}}_{2}$ spacer layer is crucial for TLA in the asymmetric configuration because the light striking the absorber from below must be exactly in phase with the light incident from above to prevent the excitation of the odd mode. In the idealized case of an infinitesimally thick absorber and a perfect mirror [5], the required spacer thickness is ${h}_{s}=\lambda /4{m}_{s}$. However, at the wavelengths of interest in our demonstration, $\lambda \sim 600\text{\hspace{0.17em}}\mathrm{nm}$, Ag is an imperfect metal, which requires ${h}_{s}<\lambda /4{m}_{s}$ (details in Supplement 1). Figure 6(c) shows the $\mathrm{Re}({E}_{y})$ field component of the resonant optical mode in the asymmetric configuration, which is concentrated in the absorbing grating rulings.

We here focus on two 41 nm thick gratings, designed to achieve TLA at $\lambda =591\text{\hspace{0.17em}}\mathrm{nm}$ and $\lambda =605\text{\hspace{0.17em}}\mathrm{nm}$, which have $d=375\text{\hspace{0.17em}}\mathrm{nm}$, $f=72\%$, and $d=385\text{\hspace{0.17em}}\mathrm{nm}$, $f=75\%$, respectively. The measured refractive indices of ${\mathrm{Sb}}_{2}{\mathrm{S}}_{3}$ at these wavelengths are ${n}_{{\mathrm{Sb}}_{2}{\mathrm{S}}_{3}}=3.342+0.096\mathrm{i}$ and ${n}_{{\mathrm{Sb}}_{2}{\mathrm{S}}_{3}}=3.298+0.074\mathrm{i}$, respectively, corresponding to absorption coefficients of $\alpha =2.04\times {10}^{4}\text{\hspace{0.17em}}{\mathrm{cm}}^{-1}$ and $\alpha =1.54\times {10}^{4}\text{\hspace{0.17em}}{\mathrm{cm}}^{-1}$, and single-pass absorptances of $A=8.0\%$ and 6.1%.

#### B. Results

Optical reflection measurements were performed in a confocal microscope using a $20\times $, $\mathrm{NA}=0.4$ objective lens and a broadband supercontinuum light source. Reflected light was collected by a 100 μm core multimode fiber and coupled into a spectrometer for detection. The reflection spectrum from a planar, unpatterned region was compared to the spectrophotometer-measured reflectance of the same sample, and this was used to calibrate the reflectance from the patterned region. Measured (symbols) and simulated (curves) reflection spectra (Fig. 7) show excellent quantitative agreement especially in the wavelengths in the vicinity of the reflectance minima, for which they are calibrated.

The minimum measured reflectance is $0.7\pm 0.5\%$ at 591 nm, which corresponds to an absorption of $A=99.3\pm 0.5\%$ since the Ag mirror is sufficiently thick to prevent any transmission to the substrate. Although it is not possible to measure the absorption in the ${\mathrm{Sb}}_{2}{\mathrm{S}}_{3}$ and in the Ag separately, we can infer these values with some confidence from simulations given the excellent agreement between the modeled and measured results. The simulations indicate that, at $\lambda =591\text{\hspace{0.17em}}\mathrm{nm}$, the planar ${\mathrm{Sb}}_{2}{\mathrm{S}}_{3}$ film absorbs $A=7.7\%$, and the Ag mirror absorbs $A=0.3\%$ ($A=8.0\%$ total). After patterning the semiconductor layer, the calculated absorption increases to $A=98.9\%$ within the ${\mathrm{Sb}}_{2}{\mathrm{S}}_{3}$ grating and $A=0.6\%$ in the Ag [the simulated absorption spectrum of the Ag layer is shown in the inset in Fig. 7(c)]. We therefore infer $A=98.7\%$ in the experimentally realized ${\mathrm{Sb}}_{2}{\mathrm{S}}_{3}$ grating. For the second grating, the maximum absorption at $\lambda =605\text{\hspace{0.17em}}\mathrm{nm}$ is $A=97.4\pm 0.5\%$, which we infer is $A=96.6\%$ in the ${\mathrm{Sb}}_{2}{\mathrm{S}}_{3}$ grating. This is an even larger increase relative to the planar sample ($A=6.1\%$ at $\lambda =605\text{\hspace{0.17em}}\mathrm{nm}$) because the absorption coefficient of ${\mathrm{Sb}}_{2}{\mathrm{S}}_{3}$ decreases noticeably with increasing wavelength, from $\lambda =591\text{\hspace{0.17em}}\mathrm{nm}$ to $\lambda =605\text{\hspace{0.17em}}\mathrm{nm}$.

## 5. GENERALITY OF TLA EFFECT

Having shown that TLA can be achieved experimentally and numerically using a specific material, we now investigate what range of material parameters are compatible with TLA in ultrathin gratings. To do this we consider gratings with a range of $\u03f5h/\lambda $ values and numerically optimize the $d$ and $f$ of the grating such that the absorption is maximized. Our optimizations were carried out in terms of $\u03f5h/\lambda $ because we established that the properties of ultrathin lamellar gratings depend on only this parameter. The relation $|n|\propto \sqrt{\lambda /h}$ therefore applies to both homogeneous layers and gratings. Our proof of this property, presented in Supplement 1, involves reducing the finitely conducting lamellar grating formulation [33] to the grating layer formulation of Petit and Bouchitté [34] in the limit of infinitesimal thickness, and is consistent with the formulation of perfectly conducting zero thickness gratings [35].

The results of the optimization for TE- and TM-polarized light are shown in Figs. 8(a) and 8(b), respectively. Here the colored contours show the maximum absorption obtained at each value of $\u03f5h/\lambda $, and the black dashed curves indicate the $\u03f5h/\lambda $ of ultrathin layers of common materials across the visible spectrum, $350\text{\hspace{0.17em}}\mathrm{nm}<\lambda <800\text{\hspace{0.17em}}\mathrm{nm}$. The dashed curves in Fig. 8(a) correspond to $h=\lambda /30$ layers of CdTe, InP, and GaAs (left to right), and to $h=41\lambda /605$ layers of ${\mathrm{Sb}}_{2}{S}_{3}$ (furthest right). The values of our experimental demonstrations in ${\mathrm{Sb}}_{2}{S}_{3}$ at $\lambda =591\text{\hspace{0.17em}}\mathrm{nm}$, 605 nm are marked by a magenta triangle and circle, respectively. In Fig. 8(b) meanwhile, the dashed curves show the values for $h/\lambda =1/20$ thick layers of Cu, Au, and Ag [36] (top to bottom), across the same visible wavelength range. Comparing these trajectories with the optimized absorption indicates that TLA can be achieved across almost the whole visible spectrum. The positions of the dashed curves expand/contract radially from the origin when the $h/\lambda $ ratio is decreased/increased.

While Figs. 8(a) and 8(b) show that TLA can be achieved with a wide range of $\u03f5h/\lambda $ values, we show in Supplement 1 that the absorption bandwidth depends linearly on the material’s loss tangent ($\mathrm{Im}(\u03f5)/\mathrm{Re}(\u03f5)$), for $\mathrm{Im}(\u03f5)/\mathrm{Re}(\u03f5)$ as large as 2. For larger loss tangents the 95% bandwidth saturates at approximately $\mathrm{\Delta}\lambda /{\lambda}_{0}=0.6$.

#### A. Theoretical Analysis of Absorption in Gratings

To analyze TLA in gratings we examine the coupling coefficients between the grating modes and the plane waves of the surrounding medium [Fig. 2(c)]; for example, ${t}_{00}$ is the coupling coefficient of the incident specular plane wave with the “fundamental” grating mode (labeled BM0), while ${r}_{01}^{\prime}$ describes the reflection of the fundamental grating mode into the “higher order” grating mode (labeled BM1). We consider the case of normal incidence upon a grating in which only two modes propagate, whose amplitudes are ${c}_{0}$, ${c}_{1}$; when more modes propagate (such as at non-normal incidence) the expressions generalize with scattering matrices representing the coupling among all propagating modes.

In the case of two propagating modes, the resonance condition of BM1 is given by

#### B. Comparison between Polarizations

A striking difference between Figs. 4 and 5 is that there is no absorption peak due to the excitation of the fundamental TM waveguide mode in Fig. 5, even though this mode also has no cutoff. This is because the field of this mode is concentrated almost totally within the air surrounds in ultrathin structures, with only very little field inside the absorber, which is expressed in a modal effective index of the mode being ${n}_{\mathrm{eff}}\simeq 1$ [37]. This field distribution prevents the mode from contributing noticeably to the absorption and also means the mode is very weakly excited, because there is a negligible overlap between the guided mode and the incident field. The analysis using Eq. (7) leads to the same conclusion; the phase of ${r}_{11}^{\prime}$ is approximately 0 and $\pi $, for TE and TM, respectively, corresponding to a node and an anti-node of the electric field close to the grating’s interface [38]. In order to observe an absorption peak for TM-polarized light in gratings with ${n}^{\prime \prime}<{n}^{\prime}$, the refractive index range must be increased to $|n|\approx 40$, which is unrealistic, or the thickness of a structure with ${n}_{\mathrm{eff}}^{\prime}\sim 5$ must be increased to $h>100\text{\hspace{0.17em}}\mathrm{nm}$, at which point the structure is no longer ultrathin.

## 6. CONCLUSION AND DISCUSSION

We have shown theoretically and experimentally that ultrathin gratings made of a wide range of weakly absorbing semiconductors can absorb nearly 100% of TE-polarized light. We also showed theoretically that TM-polarized light can be totally absorbed in ultrathin gratings made of metals. We measure a peak absorptance of $A=99.3\pm 0.5\%$ at $\lambda =591\text{\hspace{0.17em}}\mathrm{nm}$, in a structure with a 41 nm thick ${\mathrm{Sb}}_{2}{\mathrm{S}}_{3}$ grating, where $A=98.7\%$ within the grating. Our findings show that the total absorption of shorter visible wavelengths can be straightforwardly achieved by using thinner gratings or materials with smaller $\u03f5$. Our gratings are far simpler to design and fabricate than existing ultrathin perfect absorbers that rely on exotic materials and metamaterials, and may be generalized to achieve TLA of both polarizations simultaneously by using biperiodic structures. Ultrathin perfect absorbers made of weakly absorbing semiconductors may be used in optoelectronic applications such as photodetectors, where the use of semiconductors provides the possibility of extracting a photocurrent or measuring the photoresistivity.

## Funding

Australian Renewable Energy Agency (ARENA); Australian Research Council (ARC) (CE110001018).

## Acknowledgment

We acknowledge the assistance of Y. Osario Mayon with FIB and ellipsometry measurements and X. Fu with the reflectance measurements. Computational resources were provided by the National Computational Infrastructure, Australia, and the NeCTAR Research Cloud, Australia. Experimental facilities were provided by the Australian National Fabrication Facility and Centre for Advanced Microscopy at the Australian National University. This work was supported by the Australian Renewable Energy Agency and by the Australian Research Council Discovery Grant and Centres of Excellence (CE110001018) Schemes.

See Supplement 1 for supporting content.

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**37. **When the dispersion relation of the TM mode remains close to the
light line for all but very large transverse wavevectors, which
are not excited by gratings with $d\sim \lambda $.

**38. **Consistent with the phases of the TE and TM Fresnel coefficients of
a homogeneous interface at angles of incidence just beyond total
internal reflection (equivalent transverse wavevector as BM1).