Abstract
We propose a general, easytoimplement scheme for broadband coherent perfect absorption (CPA) using epsilonnearzero (ENZ) multilayer films. Specifically, we employ indium tin oxide (ITO) as a tunable ENZ material, and theoretically investigate CPA in the nearinfrared region. We first derive general CPA conditions using the scattering matrix and the admittance matching methods. Then, by combining these two methods, we extract analytic expressions for all relevant parameters for CPA. Based on this theoretical framework, we proceed to study ENZ CPA in a single layer ITO film and apply it to alloptical switching. Finally, using an ITO multilayer of different ENZ wavelengths, we implement broadband ENZ CPA structures and investigate multiwavelength alloptical switching in the technologically important telecommunication window. In our design, the admittance matching diagram was employed to graphically extract not only the structural parameters (the film thicknesses and incident angles), but also the input beam parameters (the irradiance ratio and phase difference between two input beams). We find that the multiwavelength alloptical switching in our broadband ENZ CPA system can be fully controlled by the phase difference between two input beams. The simple but general design principles and analyses in this work can be widely used in various thinfilm devices.
Introduction
Coherent perfect absorption (CPA) occurs due to the interference of two counterpropagating beams, which leads to complete absorption of light in an absorbing medium^{1,2,3,4}. It is also known as a timereversed laser or an antilaser. It was first demonstrated in a FabryPerot cavity with a wavelengthscale silicon slab. Incident light is trapped in a cavity, bouncing back and forth, until it is completely absorbed and converted to heat or other form of energy. Later, CPA was studied for various nanostructures and subwavelength thin films^{5,6,7,8,9,10,11}, and was measured recently for graphene and conducting thin films^{12,13}. However, the CPA structures so far are mostly limited to singlefrequency operation, and are hard to be extended to a broadband structure  especially in the high, optical frequency region.
Here, we propose a new broadband CPA scheme based on epsilonnearzero (ENZ) multilayer films. ENZ thin films can be a versatile platform for strong field confinement and for the enhancement of lightmatter interactions^{14,15,16}. Recently, it was found that unidirectional perfect absorption can occur in ultrathin, lowloss ENZ layers^{17,18,19}. Furthermore, at ENZ wavelengths (i.e. Re(ε) = 0), the normal component (E_{⊥}) of the electric field can become very strong in a deeply subwavelength film (following the boundary condition ε_{1}E_{1⊥} = ε_{2}E_{2⊥}). This strong field enhancement in ENZ films was also used to enhance nonlinear harmonic generation or control light absorption electrically in a cavity^{20,21}. Interestingly, for very lowloss (Im(ε) ~ 0) dielectric films, it was reported that multilayers of high and low index films can be designed for unidirectional perfect absorption with field enhancement^{22}.
In our previous theoretical and experimental works, we used ITO as a nearinfrared (nearIR) ENZ material, and demonstrated perfect absorption in an ultrathin ITO film. In these works, an ITO film was coated on a reflective substrate (or we worked in the attenuated total reflection condition) in order to suppress the transmission. In this case, by finding the destructive interference condition of reflected light, we could achieve unidirectional perfect absorption (i.e. having a single input beam)^{23}. The ENZ wavelengths of ITO films depend on doping levels that can be controlled during the film growth, and thus tunable perfect absorption could be achieved without any structural patterning. Moreover, by using an ITO multilayer of different ENZ wavelengths, we experimentally demonstrated ultrawideband perfect absorption in the nearIR^{24}. Inspired by previous studies, here we propose a general strategy for broadband, bidirectional CPA based on planar, unpatterned films. Again, we use an ITO thin film as an ENZ layer, and find broadband CPA conditions in the nearIR region. Finally, we use this broadband ENZ CPA for multiwavelength alloptical switching in the telecommunication window. In our analysis, we also fully account for the effects of the substrate. Therefore, we consider realistic configurations for our analysis. This method can be also readily extended to other frequency ranges using different ENZ materials (e.g. it can be extended to mid and farinfrared using doped semiconductors). Our work shows that ENZ multilayer films provide a very flexible platform for highfrequency, broadband CPA.
In this paper, we first derive the CPA conditions using the scattering matrix and the admittance matching methods separately. Herein, we show that these two CPA analysis methods are equivalent. By combining these two methods, we extract not only the structural parameters of the CPA system, such as thin film thicknesses and incident angles, but also the input beam parameters, such as the amplitude ratio and phase difference between the two input beams. We also show that the broad ENZ wavelength band in the effective dielectric constant of the ITO multilayer film is important in achieving broadband CPA. Finally, we investigate multiwavelength optical switching in our broadband CPA system consisting of an ITO multilayer sandwiched between two ZnSe prisms with 45° incident angles. It is also verified that our analytic calculations agree well with numerical simulations. The design principles and analyses used here can be widely applied to various nanophotonic devices and components, such as optical switches, modulators, filters, sensors, and thermal emitters.
Theoretical Framework
Scattering Matrix Method
We first obtain general conditions for CPA using the scattering matrix method. CPA occurs when the determinant of the scattering matrix of an absorbing medium becomes zero. This is a very general condition that can be applied to either a structured medium or an unpatterned film. The schematic diagram of CPA in an absorbing medium of complex refractive index N_{f} = n − ik (dielectric constant ) is shown in Fig. 1(a). The monochromatic time harmonic convention, e^{iωt}, is used in this paper. The optical system consists of two ports; one on the left of the medium and the other on the right. Port 1 has the input and out fields E_{1} and O_{1} in the +z and −z directions, respectively, in the nonabsorbing incident medium of a refractive index n_{0}. Similarly, Port 2 has the input and out fields E_{2} and O_{2} in the −z and +z directions, respectively, in the nonabsorbing substrate medium of a refractive index n_{s}. The substrate (n_{s}) and incident (n_{0}) media are the output media for E_{1} and E_{2}, respectively. Then the relationship between the output and input fields can be expressed using a scattering matrix as
where the scattering matrix [S] is defined as
The elements of the scattering matrix are as follows: and are the reflection and transmission coefficients, respectively, of the incident field E_{1}, and and are the reflection and transmission coefficients, respectively, of the incident field E_{2}^{25,26}. The reflection phases are φ_{ρ1} and φ_{ρ2}, and the transmission phases are φ_{τ1} and φ_{τ2}.
Since CPA occurs when O_{1} = O_{2} = 0 (i.e. the determinant of scattering matrix [S] must be zero), the CPA condition is given by
This can be, in turn, rewritten as
and
where . In deriving Eqs (4) and (5), the principle of the reversibility of and φ_{τ1} = φ_{τ2} were employed. The definitions of the admittances η_{0}, η_{f}, and η_{s} in each medium for the TE and TM waves are presented in Supplementary Information (Supplementary Note A)^{26,27}.
By taking into account the amplitude ratio and phase difference between the two input beams, Eq. (1) can be expressed as
where φ_{12} = φ_{2} − φ_{1} is the phase difference between the two input beams, and the input irradiances at Port 1 and 2 are defined respectively as and , where is the admittance of the vacuum. Then, the output irradiance P_{out1} in the incident medium of Port 1 can be written as
where Δ_{1} = φ_{ρ1} − φ_{τ} + φ_{12} is the interference phase, and we assumed E_{1} = 1. Similarly, the output irradiance P_{out2} in the substrate becomes
where .
Since P_{out1} = P_{out2} = 0 at CPA (i.e. complete destructive interference) occurs in Eqs (7) and (8), the input beam requirements, namely, the irradiance ratio and phase shift, can be respectively derived to be
and
Equation (9), which is equivalent to Eq. (4), is related to balancing of the amplitudes between two output beams. Then, the output irradiances become
and
If φ_{ρ2} = φ_{ρ1} or φ_{ρ1} + π in Eq. (10) (i.e., if φ_{12} = 0 or π), then P_{out1} = P_{out2} = 0, which is “twoport” CPA. If φ_{12} = 0, the two input beams are called symmetric, whereas if φ_{12} = π, they are antisymmetric. Equations (11) and (12) indicate that CPA can be used as a sinusoidal optical switch or modulator if φ_{12} is varied. We may tune φ_{12} to make either P_{out1} = 0 or P_{out2} = 0, yielding “oneport” CPA. The output irradiances and absorptance (A) in the figures presented herein were normalized with respect to the total input irradiance (P_{in1} + P_{in2}): .
Admittance Matching Method
Now we consider CPA conditions using the admittance matching method that can be applied to unpatterned films. This will be eventually used in the next section when we design a nearIR CPA system with ITO multilayers.
When CPA occurs with O_{1} = O_{2} = 0 in Fig. 1, only one incident beam exists in each medium: E_{1} in the incident medium (n_{0}) and E_{2} in the substrate (n_{s}). Since the waves in the two media are counterpropagating, the magnetic field direction in the substrate should be reversed in the opposite direction to that in the incident medium (i.e., H →−H) if the electric field direction is the same. Then the admittance of the substrate can be defined as −η_{s} when CPA is present^{28}. The negative admittance does not mean a negative index.
Therefore the forward admittance of the film starting from (−η_{s}, 0) can be calculated using the transfer matrix method (TMM) as follows:
where B and C are the normalized electric and magnetic fields, respectively, in the incident medium, and the optical phase thickness is defined as . And N_{f} = n − ik, d, and η_{f} are the complex refractive index of the film, physical thickness, and admittance of the thin film, respectively^{26}. Snell’s law is valid here: , where θ_{0}, θ, and θ_{s} are the incident angle, transmitted angle in the film, and transmitted angle in the substrate, respectively. The surface admittance of the film at z_{1} is given by
Then, CPA occurs when
where η_{0} is the admittance of the incident medium. From Eqs (13) ~ (15), the CPA condition for an absorbing thinfilm layer can be derived to be
If the backward admittance matching is traced from η_{0} to −η_{s} using −δ in Eq. (13), the same CPA condition as Eq. (16) can be obtained. For a freestanding film in air at normal incidence, Eq. (16) is identical to Eqs (4, 7 and 14) in Refs 1, 7 and 8, respectively.
The structural parameters of thin films exhibiting CPA, such as their materials, thicknesses, and the incident light angles in the two media, can be determined from Eq. (16). They can be also obtained graphically using the admittance diagram^{23,28}. In the next section, we will use the admittance diagram to determine the CPA parameters for ITO thin films. The elements of the scattering matrix in Eq. (2) are obtained in Supplementary Note A. It is also shown therein that Eq. (16), which was derived using admittance matching, is equivalent to Eq. (3), obtained from the scattering matrix. Thus, the relationship between the reflection and transmission coefficients can be expressed as
and
Then, the CPA condition of Eq. (3) for a single layer can be expressed as
indicating that two input beams have even and odd phases. Also, the input beam parameters for singlelayer CPA (more specifically, the irradiance ratio and phase shift given in Eqs (9) and (10)) can be respectively expressed by
and
If a single absorbing layer cannot complete this admittance matching between the substrate and the incident medium, another phasematching dielectric layer can be added to complete the trajectory of the admittance locus for Eq. (15) in the admittance matching diagram, in which case the phase shift of Eq. (21) is not necessarily 0 or π^{28}.
In our previous work on unidirectional perfect absorption, we showed that the admittance matching condition (Eq. (15)) can be satisfied in an ultrathin, lowloss ENZ film for ppolarized oblique incidence of light^{23,24}. This can be directly extended to bidirectional CPA based on ENZ films, using the negative admittance for a substrate. Moreover, employing an ENZ multilayer film, we can achieve broadband CPA. This will be discussed more in the next section using ITO films.
ENZ CPA can be also understood as critical coupling, as explained in Supplementary Notes B and C. Since ENZ CPA is caused by resonant plasmon absorption, we can rewrite the admittance matching condition of Eq. (16) as the phase matching condition for transverse resonance in the film:
where κ_{f} is the transverse wavevector in the film, 2φ_{0} and 2φ_{s} are the reflection phases at the incident mediumfilm and filmsubstrate interfaces, respectively, and m is the order of a resonance mode. Eq. (22) indicates that once the critical coupling condition is satisfied for an ENZ film, two counterpropagating waves in the absorbing film interfere constructively, behave like an inhomogeneous guided mode in the film, and are totally absorbed as the mode propagates in the film.
Results
The ENZ wavelengths of ITO films in the nearIR region can be controlled by doping levels. In our previous work, broadband perfect absorption with unidirectional illumination was experimentally realized using an ITO multilayer film^{24}. In this work, we again use ITO as a tunable ENZ material. More specifically, we use two ITO films (ITO1, ITO2) as nearIR ENZ materials, whose ENZ wavelengths (i.e. Re(ε) = 0) are 1435 nm (ITO1) and 1605 nm (ITO2), as shown in Fig. 1(b) ^{29}.
ENZ CPA in a Singlelayer ITO Thin Film and Its Application to Alloptical Switching
We start with a CPA structure including a single ITO layer (ITO1). We assume different materials for the incident and substrate media (i.e. an asymmetric structure), as shown in Fig. 2(a). We will first find CPA parameters graphically using the admittance matching diagram^{26,28,30}, and then compare them with the general CPA conditions derived from the scattering matrix method.
The admittance diagram in Fig. 2(b) shows the admittance matching results for [GlassITO1ZnSe] at a wavelength of 1424 nm; the forward locus of the modified admittance of the ENZ ITO film starts at the negative modified admittance of (−1.05, 0) for the ZnSe substrate, makes a large circle in the clockwise direction corresponding to the film thickness of 23.13 nm, and arrives at a positive modified admittance of (1.50, 0) for the glass^{28}. The incident angles were determined to be 70° in the glass and 35.2° in the ZnSe substrate.
The absorption spectrum of [GlassrITO1ZnSe] is calculated using the transfer matrix method (TMM), and is shown in Fig. 2(c), revealing CPA (A = 1) at 1424 nm, which is slightly shorter than the ENZ wavelength of 1435 nm. The same behavior was also observed in our previous study on unidirectional perfection absorption in ITO films^{23}. It can be understood in this way: since CPA occurs due to critical coupling to a radiative mode in the ENZ thin film, CPA should follow the dispersion of this mode, which lies slightly above the ENZ frequency (Re(ε) = 0). Therefore, CPA occurs at a slightly shorter wavelength than the ENZ wavelength.
The elements of the scattering matrix in Eq. (2) were also calculated in Fig. 2(d). It can be seen that (red) occurs at 1424 nm and 1446 nm and that (blue) occurs at 1424 nm. The CPA wavelength at 1424 nm, which satisfies both Eqs (4) and (5) and is shown in the inset of Fig. 2(d), was also used to obtain the admittance matching in Fig. 2(b), implying that Eq. (16) is equivalent to Eq. (3) for the singlelayer CPA. We obtained also the input beam parameters; the irradiance ratio and phase shift between the two input beams were determined from Eqs (9) and (10) to be and φ_{12} = 0°, respectively.
If we apply Eq. (22) for this ENZ CPA at 1424 nm (TM wave), we obtain the subwavelength waveguide characteristics of ENZ CPA as follows; the vertical wavevector of ENZ CPA is κ_{f} = (0.55 − i6.15) × 10^{6} m^{−1}, the order is m = 0, and the effective index of a propagating ENZ CPA wave is N_{eff} = 1.41. We find that the electric field decreases rapidly in the transverse direction, and the ultrathin subwavelength thickness obtained from the admittance matching of Eq. (16) is in good agreement with the zeroth order of Eq. (22), implying that ENZ CPA occurs due to critical coupling to a propagating wave in the longitudinal direction along the film.
Now, we use this ENZ CPA for alloptical switching. The 2D contour maps of P_{out1} and P_{out2} are shown as functions of the relative phase shift φ_{12} and the incident wavelength in Fig. 3. Firstly, twoport CPA (i.e., O_{1} = O_{2} = 0) is observed at λ = 1424 nm, φ_{12} =0° in both Fig. 3(a,b). Secondly, oneport CPA with O_{1} = 0 occurs at λ = 1446 nm, φ_{12} = −16° in Fig. 3(a), whereas oneport CPA with O_{2} = 0 at λ = 1446 nm, φ_{12} = 24° in Fig. 3(b). The oneport CPA at 1446 nm can be explained as follows: Though the output irradiances are given by Eqs (11) and (12) due to at 1446 nm as shown in Fig. 3(d), the phase change is either Δ_{1} = 0° or Δ_{2} = 0° depending on how the external phase shift φ_{12} is controlled.
The twoport CPA optical switch at 1424 nm is shown as a function of the phase shift φ_{12} in Fig. 3(c): the “ON” state (O_{1} = O_{2} = 0) is apparent at φ_{12} = 0°, and the optical switching effects are same in both ports. Optical switching behaviors at 1446 nm are also evident in Fig. 3(d). At φ_{12} = −16° the “ON” state (O_{1} = 0) appears in Port 1, whereas the “OFF” state (O_{2} ≠ 0) occurs in Port 2, while at φ_{12} = 24° the optical switch state is reversed. Equation (4) has two solutions at different wavelengths: one for twoport CPA and the other for oneport CPA. The optical switching phenomena in [GlassITO1ZnSe] CPA are summarized in Table 1.
Broadband ENZ CPA in ITO Multilayers
Extending the previous ITO singlelayer study, we now propose a broadband ENZ CPA system and apply it to multiwavelength alloptical switching. As shown in Fig. 4(a), we consider an ITO double layer sandwiched between two ZnSe prisms (i.e. [ZnSeITO1ITO2ZnSe]), and fix the incidence angles as 45° in the both ZnSe prisms (n_{0} = n_{s} = 2.45). This configuration was chosen to realize nearIR broadband CPA while keeping the structure as simple as possible. We can broaden the bandwidth further by increasing the number of ITO layers. The ENZ wavelengths (i.e. Re(ε) = 0) of each ITO film are 1435 nm for ITO1 and 1605 nm for ITO2 (Fig. 1(b)). As we did in the previous section, we will first find CPA parameters graphically using the admittance matching diagram, and then compare them with the general CPA conditions derived from the scattering matrix method.
The admittance diagram shows that the forward modified admittance locus of ITO1 (blue line) at a TMwave wavelength of 1550 nm starts at (−2.45, 0) in Fig. 4(b), while the backward modified admittance (red line) begins at (+2.45, 0). The intersection of two loci of ITO1 and ITO2 at (−1.35, −2.05) indicates ITO1 and ITO2 thicknesses of 14.22 nm and 20.13 nm, respectively. Furthermore, the irradiance ratio and phase shift between the two input beams were determined from Eqs (9) and (10) as and φ_{12} = 1°, respectively. This method is a simple and intuitive means of determining the structural parameters in Eq. (15) for ENZ thin films exhibiting CPA, such as the thinfilm materials, thicknesses, and the incident angles in media.
The normalized output irradiances log(P_{out1}) and log(P_{out2}) were calculated and are shown in Fig. 5(a). The broadband range of CPA with >99% absorptance is apparent in 1443~1576 nm, and two CPA dips are evident at 1466 nm and 1550 nm in the CPA band. The CPA conditions were calculated using Eqs (4) and (5) and are plotted as a function of wavelength in Fig. 5(b). Four wavelengths with are evident: 1381 nm, 1463 nm, 1550 nm, and 1683 nm, and three wavelengths with are apparent: 1474 nm, 1497 nm, and 1550 nm. The band with and is between 1443 and 1576 nm, which is consistent with the broad CPA band shown in Fig. 5(a). In addition, the CPA wavelength satisfying both CPA conditions simultaneously was found to be 1550 nm; perfect admittance matching occurs at this wavelength, as shown in Fig. 5(b).
Since the thicknesses of the ITO1 and ITO2 layers are much less than the wavelength , the effective dielectric constant (ε_{eff}) of the ITO double layer can be calculated using the effective medium approximation^{24,31}:
where f is the ratio of ITO1 layer thickness to the total thickness. Figure 5(c) shows the real and imaginary parts of ε_{eff} for the two ENZ ITO layers. Its real part Re(ε_{eff}) is close to zero over the broad spectral region from 1443–1576 nm, indicating that the broadband ENZ regime was obtained. Using ε_{eff}, the CPA spectrum was calculated, and Fig. 5(d) shows that the broad ENZ wavelength region corresponds closely to the broad CPA regime. Again, broad CPA (i.e., radiative mode) occurs at broad Re(ε_{eff}) slightly larger than zero and at shorter wavelength regime than the ENZ wavelength (1585 nm) of the effective layer at Re(ε_{eff}) = 0.
Since ENZ absorption is caused by radiative resonant plasmons, Eq. (S23) of TCMT in Supplementary Note D can be applied to determining the damping constants of ENZ resonances at CPA. The absorption spectra of [ZnSeITO1(14.22 nm)ZnSe] and [ZnSeITO2(20.13 nm)ZnSe] calculated by TMM and fitted by TCMT are shown in Fig. 5(d).
It is evident that both methods yield the same CPA wavelengths at 1429 and 1594 nm. The broad CPA spectrum of [ZnSeITO1ITO2ZnSe] that was calculated by the TMM was also fitted by the sum of two Lorentzian spectra using Eq. (S15) in Supplementary Note B. We then obtained an equivalent CPA spectrum for [ZnSeITO1ITO2ZnSe], which is slightly narrower than the simple summation of the two spectra and which corresponds closely to that calculated by the TMM. Then, we determined the intrinsic and radiative damping constants of [ZnSeITO1ITO2ZnSe] structure to be Γ_{i} = Γ_{r} = 8.1 × 10^{13} rad/s in the broad CPA spectrum, indicating that the broadband ENZ CPA is the coupling of the two resonant CPAs in the ENZ ITO layers.
We also numerically simulated the same [ZnSeITO1ITO2ZnSe] structure, and verified that our analytic results agree well with the finitedifference time domain (FDTD) simulations. We show field profiles for our CPA structure too. For more details on numerical simulations, see Fig. S1 in Supplementary Information.
Multiwavelength Alloptical Switching
Finally, we investigate the optical switching of the broadband CPA of [ZnSeITO1ITO2ZnSe]; P_{out1} and P_{out2} are shown on 2D contour maps as a function of the relative phase shift φ_{12} and incident wavelength in Fig. 6(a,b), respectively. Firstly, broadband CPA greater than 99% absorptance is observed in the 1443 ~ 1576 nm wavelength range at 1° phase shift (horizontal blue area, O_{1} = O_{2} = 0, i.e. twoport CPA) in Fig. 6(a,b); the bandwidth is ~133 nm in spectrum and the phase shift range is −5 ~ 7°. Secondly, the narrowband oneport CPAs are also evident: the oneport CPAs with O_{1} = 0 are found at λ = 1381 nm, φ_{12} = 46° and λ = 1683 nm, φ_{12} = −55° (tilted blue area) in Fig. 6(a), whereas the oneport CPAs with O_{2} = 0 are evident at λ = 1381 nm, φ_{12} = −44° and λ = 1683 nm, φ_{12} = 57° in Fig. 6(b).
The twoport broadband CPA optical switching at 1550 nm is shown as a function of φ_{12} in Fig. 6(c), and the “ON” state (O_{1} = O_{2} = 0) is apparent in both ports at φ_{12} = 1°. Similarly the broadband optical switching is evident at wavelengths of 1443~1576 nm at φ_{12} ≈ 1°. The optical switching of oneport CPA at 1381 nm and 1683 nm is shown in Fig. 6(d,e), respectively. At 1381 nm, the “ON” state with O_{1} = 0 appears at φ_{12} = 46°, whereas the “ON” state with O_{2} = 0 appears at φ_{12} = −44°. Similarly at 1683 nm, the “ON” state with O_{1} = 0 appears at φ_{12} = −55°, whereas the “ON” state with O_{2} = 0 appears at φ_{12} = 57°. Thus, the oneport optical switching of the narrowband CPA at 1381 nm and 1683 nm depends on the phase shift, and the twoport optical switching of the broadband CPA at 1443 ~ 1576 nm at φ_{12} = 1°. The multiwavelength optical switching behaviors in narrowband and broadband [ZnSeITO1ITO2ZnSe] CPA device are summarized in Table 2.
We also investigated the incident angle dependence of the broadband CPA spectrum, which is shown in Fig. S2. As the incident angle increases from 44.5°–49°, the bandwidth between two CPA dips at 1466 nm and 1550 nm narrows, keeping the center wavelength middle in the band, until a single, merged broad resonance appears.
Discussion
We want to clarify the difference between previous CPA proposals and our broadband CPA scheme. Previous CPA proposals were mostly based on nanostructured films. In those cases, elaborate multiple resonances in nanostructures may be employed to achieve broadband CPA. But, this can complicate the device structure and fabrication procedure. In contrast, we use simple, planar ENZ films, where optical properties can be easily controlled during the film growth (e.g. tuning film thicknesses and doping levels). Our approach simplifies the device fabrication and also facilitates the chipscale integration with other optical components.
We notice that Ref. 8 also reported on CPA based on ultrathin films. It studied two cases: Woltersdorff thickness and plasmon thickness. The former corresponds to a lowfrequency region (DC to ~1 THz). The latter corresponds to the ENZ regime (i.e. Re(ε) = 0). Figure 6 in Ref. 8 shows strong absorption over a broad nearIR region in an ultrathin tungsten film. But, as studied in Refs 23 and 32, normalincidence perfect absorption in an ultrathin film can happen only in a very lossy (large Im(ε) > 1) film. It is hard to achieve this in other lowloss (small Im(ε) < 1) materials. However, in our CPA scheme, perfect absorption can occur in a lowloss, ultrathin ENZ film, thanks to critical coupling at the ENZ wavelength^{23,24}. Moreover, this can be easily extended to broadband CPA using ENZ multilayer films. Therefore, ENZ materials provide a very general, flexible platform for highfrequency, broadband CPA. We believe that many CPA devices can benefit from our approach.
In summary, we proposed the broadband ENZ CPA system based on tunable ITO thin films, and investigated its application to multiwavelength alloptical switching in the nearIR region. We derived general CPA conditions first, using the scattering matrix and admittance matching methods separately, and demonstrated their equivalence for thinfilm CPA. Then, we designed a [ZnSeITO1ITO2ZnSe] structure exhibiting the broadband CPA at 45° incident angles in two ZnSe prisms. We found that the admittance matching method could extract not only the structural parameters, such as layer thicknesses and incident angles in media, but also input beam parameters, such as the power ratio and phase difference between two input beams. Finally, we analyzed multiwavelength optical switching in our broadband ENZ CPA system. We can broaden the bandwidth further by increasing the number of ENZ layers. The same method can be also readily extended to other frequency ranges using different ENZ materials. Our proposal and theoretical analysis can provide design principles and guidelines for thinfilm CPA devices, which can find various applications in optical switches, modulators, filters, sensors, and thermal emitters.
Additional Information
How to cite this article: Kim, T. Y. et al. General Strategy for Broadband Coherent Perfect Absorption and Multiwavelength Alloptical Switching Based on EpsilonNearZero Multilayer Films. Sci. Rep. 6, 22941; doi: 10.1038/srep22941 (2016).
References
 1
Chong, Y. D., Ge, L., Cao, H. & Stone, A. D. Coherent Perfect Absorbers: TimeReversed Lasers. Phys. Rev. Lett. 105, 053901 (2010).
 2
Gmachl, C. F. Suckers for light. Nature 467, 37–39 (2010).
 3
Noh, H., Chong, Y., Stone, A. D. & Cao, H. Perfect coupling of light to surface plasmons by coherent absorption. Phys. Rev. Lett. 108, 186805 (2012).
 4
Wan, W. et al. TimeReversed Lasing and Interferometric Control of Absorption. Science 331, 889 (2011).
 5
Zhang, J., MacDonald, K. F. & Zheludev, N. I. Controlling lightwithlight without nonlinearity. Light Sci. Appl. 1, 1–5 (2012).
 6
Kang, M., Chong, Y. D., Wang, H.T., Zhu, W. & Premaratne, M. Critical route for coherent perfect absorption in a Fano resonance plasmonic system. Appl. Phys. Lett. 105, 131103 (2014).
 7
Chen, T., Duan, S. & Chen, Y. C. Electrodynamics analysis on coherent perfect absorber and phasecontrolled optical switch. J. Opt. Soc. Am. A 29, 689–694 (2012).
 8
Pu, M. et al. Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination. Opt. Express 20, 2246–2254 (2012).
 9
DuttaGupta, S., Martin, O. J. F., Gupta, S. D. & Agarwal, G. S. Controllable coherent perfect absorption in a composite film. Opt. Express 20, 1330 (2012).
 10
Zhang, J. et al. Coherent perfect absorption and transparency in a nanostructured graphene film. Opt. Express 22, 12524 (2014).
 11
Fan, Y. et al. Tunable midinfrared coherent perfect absorption in a graphene metasurface. Sci. Rep. 5, 13956 (2015).
 12
Li, S. et al. Broadband perfect absorption of ultrathin conductive films with coherent illumination: Superabsorption of microwave radiation. Phys. Rev. B. 91, 220301(R) (2015).
 13
Rao, S. M., Heitz, J. J. F., Roger, T., Westerberger, N. & Faccio, D. Coherent control of light interaction with graphene. Opt. Lett. 39, 5345–5347 (2014).
 14
Engheta, N. Persuing nearzero response. Science 340, 286–287 (2013).
 15
Jun, Y. C. et al. EpsilonNearZero Strong Coupling in MetamaterialSemiconductor Hybrid Structures. Nano Lett. 13, 5391−5396 (2013).
 16
Campione, S., Brener, I. & Marquier, F. Theory of epsilonnearzero modes in ultrathin films. Phy. Rev. B 91, 121408(R) (2015).
 17
Jin, Y., Xiao, S., Mortensen, N. A. & He, S. Arbitrarily thin metamaterial structure for perfect absorption and giant magnification. Opt. Express 19, 11114–11119 (2011).
 18
Feng, S. & Halterman, K. Coherent perfect absorption in epsilonnearzero metamaterials. Phys. Rev. B 86, 165103 (2012).
 19
Luk, T. S. et al. Directional perfect absorption using deep subwavelength low permittivity films. Phys. Rev. B 90, 085411 (2014).
 20
Luk, T. S. et al. Enhanced third harmonic generation from the epsilonnearzero modes of ultrathin films. Appl. Phys. Lett. 106, 151103 (2015).
 21
Park, J. Kang, J.H., Liu, X. & Brongersma, M. L. Electrically tunable epsilonnearzero (ENZ) metal film absorbers. Sci. Rep. 5, 15754 (2015).
 22
Ndiaye, C., Lemarchand, F., Zerrad, M., Ausserre, D. & Amra, C. Optimal design for 100% absorption and maximum field enhancement in thinfilm multilayers at resonances under total reflection. Appl. Opt. 50, C382–C387 (2011).
 23
Badsha, M. A., Jun, Y. C. & Hwangbo, C. K. Admittance matching analysis of perfect absorption in unpattern thin films. Opt. Comm. 332, 206–213 (2014).
 24
Yoon, J. et al. Broadband EpsilonNearZero Perfect Absorption in the NearInfrared. Sci. Rep. 5, 12788 (2015).
 25
Collin, S. Nanostructure arrays in freespace: optical properties and applications. Rep. Prog. Phys. 77, 126402 (2014).
 26
Macleod, H. A. In ThinFilm Optical Filters 4th edn, Ch. 2, 42–61 (CRC Press, 2010).
 27
Yeh, P. In Optical Waves in Layered Media, Ch. 5, 112–114 (John Wiley & Sons, 2005).
 28
Macleod, H. A. Optical absorption, Part 2. Bulletin (Society of Vacuum Coaters, Issue Fall) 13, 28–33 (2013).
 29
Optical Constants of Electronic Materials and Transparent Conductors (280–2500 nm): URL https://windows.lbl.gov/materials/chromogenics/N&Kcoverpage.html (Date of access: 28/12/2015).
 30
Essential Macleod Thin Film Software (2015). Thin Film Center Inc, Tucson, AZ, USA. URL http://www.thinfilmcenter.com/.
 31
Sun, L. & Yu, K. W. Strategy for designing broadband epsilonnearzero metamaterials. J. Opt. Soc. Am. B 29, 984–989 (2012).
 32
Park, J., Kim, S. J. & Brongersma, M. L. Condition for unity absorption in an ultrathin and highly lossy film in a GiresTournois interferometer configuration. Opt. Lett. 40, 1960–1963 (2015).
Acknowledgements
This work was supported by the Basic Science Research Program through a National Research Foundation of Korea grant funded by the Ministry of Education (NRF 2013R1A1A2007348). YCJ acknowledges the support from NRF grants (No. 2015001948, NRF2014R1A1A2054108).
Author information
Affiliations
Contributions
T.Y.K., M.A.B., J.Y. and S.Y.L. performed simulations and modeling. Y.C.J. and C.K.H. conceived the idea and wrote the manuscript. C.K.H. supervised all aspect of the project. All authors reviewed the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Rights and permissions
This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
About this article
Cite this article
Kim, T., Badsha, M., Yoon, J. et al. General Strategy for Broadband Coherent Perfect Absorption and Multiwavelength Alloptical Switching Based on EpsilonNearZero Multilayer Films. Sci Rep 6, 22941 (2016). https://doi.org/10.1038/srep22941
Received:
Accepted:
Published:
Further reading

Ultrathin multiband coherent perfect absorber in graphene with highcontrast gratings
Optics Express (2020)

Coherent perfect absorption in unpatterned thin films of intrinsic semiconductor
Journal of Optics (2020)

Flexible silver nanowire/carbon fiber felt metacomposites with weakly negative permittivity behavior
Physical Chemistry Chemical Physics (2020)

Tunable dualband amplitude modulation with a double epsilonnearzero metasurface
Journal of Optics (2020)

Dynamical Control of Broadband Coherent Absorption in ENZ Films
Micromachines (2020)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.