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Abstract
Recently, broadband optical Tamm states (OTSs) in heterostructures composed of highly lossy metal layers and all-dielectric one-dimensional (1D) photonic crystals (PhCs) have been utilized to realize broadband absorption. However, as the incident angle increases, the broadband OTSs in such heterostructures shift towards shorter wavelengths along the PBGs in all-dielectric 1D PhCs, which strongly limits the bandwidths of wide-angle absorption. In this paper, we realize a broadband omnidirectional OTS in a heterostructure composed of a Cr layer and a 1D PhC containing layered hyperbolic metamaterials with an angle-insensitive photonic band gap. Assisted by the broadband omnidirectional OTS, broadband wide-angle absorption can be achieved. High absorptance (A > 0.85) can be remained when the wavelength ranges from 1612 nm to 2335 nm and the incident angle ranges from 0° to 70°. The bandwidth of wide-angle absorption (0°-70°) reaches 723 nm. The designed absorber is a lithography-free 1D structure, which can be easily fabricated under the current magnetron sputtering or electron-beam vacuum deposition technique. This broadband, wide-angle, and lithography-free absorber would possess potential applications in the design of photodetectors, solar thermophotovoltaic devices, gas analyzers, and cloaking devices.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical absorption plays a crucial role in various devices, such as photodetectors [1,2], solar thermophotovoltaic devices [3], gas analyzers [4], and cloaking devices [5]. If one could concentrate the electric field in lossy materials, optical absorption can be effectively enhanced [6–17]. As a kind of optical interface states, optical Tamm state (OTS) has attracted great researchers’ interest since its unique resonant property [18–23]. OTS can exist in one-dimensional (1D) heterostructure composed of a metal layer and an all-dielectric 1D photonic crystal (1D PhC) [19,20,24–28]. The physical mechanism of OTS can be briefly explained as follow. The metal layer and the all-dielectric 1D PhC act like 2 optical mirrors. As the sum of the reflection phases of the metal layer and the all-dielectric 1D PhC becomes integral multiple of 2π, the 1D heterostructure can be viewed as a Fabry-Perot cavity, leading to OTS. Assisted by OTS, the electromagnetic field can be concentrated around the interface between the metal layer and the all-dielectric 1D PhC [29–33]. Therefore, the optical absorption can be greatly enhanced since the metal layer possesses Ohmic loss. Over the past decade, researchers have realized narrow-band absorption at different wavelength ranges in heterostructures composed of noble metal layers (such as Ag, Au and Pt) and all-dielectric 1D PhCs [34–37]. However, it is known that the Ohmic losses of noble metals are not too high [38]. The Q factors of OTSs in heterostructures composed of noble metal layers and all-dielectric 1D PhCs will be quite high, which strongly limits the bandwidths of absorption [34–37]. In order to achieve broadband absorption, various lithography-required micro-structures have been proposed [39–51]. Here, we briefly introduce three kinds of typical micro-structures for broadband absorption. The first one is the metal-dielectric-metal structure consisting a metallic top layer (composed of metallic resonators with different sizes), a dielectric layer and a metal bottom layer [39–43]. The second one is the tapered hyperbolic metamaterial array [44–48]. The third one is the multilayer metallic resonator arrays with different sizes [49–51]. The key of broadband absorption in the above three kinds of micro-structures is to combine multiple narrow-band absorption with different peak wavelengths together, which greatly expands the bandwidth of absorption. Nevertheless, the lithography technique is needed in the fabrication process, which greatly increases the complexity and the cost of the fabrication process.
In recent years, researchers realized a kind of low-Q OTS called broadband OTS in 1D heterostructure composed of a highly lossy epsilon-negative material layer (such as TiN, Cr and W) and an all-dielectric 1D PhC [52–54]. Owing to the high Ohmic loss of the epsilon-negative material layer, the resonant width of the OTS is effectively expanded. Therefore, assisted by low-Q OTS, broadband absorption can be realized. Such heterostructures are complete 1D structures, which do not require the lithography technique. However, the wavelength range of the absorption band is strongly related to the incident angle of light. The underlying reason is that the photonic band gap (PBG) in all-dielectric 1D PhC is strongly related to the incident angle according to the Bragg interference mechanism [55–58]. Hence, the absorptance cannot be kept high in wide ranges of the wavelength and the incident angle. In other words, the bandwidth of wide-angle absorption (0°-70°) is still limited [52–54]. Recently, researchers realized a kind of special PBG called angle-insensitive PBG in 1D PhC containing layered hyperbolic metamaterials (HMMs) [59–61]. Different from angle-sensitive PBG in all-dielectric 1D PhC, angle-insensitive PBG in 1D PhC containing layered HMMs does not shift as the incident angle changes, which provides us a possibility to realize broadband omnidirectional OTS.
In this paper, we realize a broadband omnidirectional OTS in a 1D heterostructure composed of a highly lossy metal layer (Cr) and a 1D PhC containing layered HMMs with an angle-insensitive PBG. Assisted by the broadband omnidirectional OTS, broadband wide-angle near-infrared absorption can be achieved. In detail, high absorptance (A > 0.85) can be remained when the wavelength ranges from 1612 nm to 2335 nm and the incident angle ranges from 0° to 70°. The bandwidth of wide-angle absorption (0°-70°) reaches 723 nm, which is much broader than those in [52–54]. Besides, the proposed absorber is a lithography-free 1D structure which can be easily fabricated under the current magnetron sputtering [62] or electron-beam vacuum deposition technique [57]. This broadband, wide-angle, and lithography-free absorber would possess potential applications in the design of photodetectors, solar thermophotovoltaic devices, gas analyzers, and cloaking devices.
2. Design of angle-insensitive PBG in 1D PhC containing layered HMMs
Before studying the broadband omnidirectional OTS, we first design a near-infrared angle-insensitive PBG in a 1D PhC composed of alternating layered HMMs and isotropic dielectrics based on the phase variation compensation theory in [59]. For the conventional isotropic dielectric, the iso-frequency curve is a closed circle [63]. Therefore, the propagating phase along the periodic direction within the isotropic dielectric ${\phi _{\textrm{Dielec}}} = {k_{\textrm{Dielec}{\textrm{,}_{}}z}}{d_{\textrm{Dielec}}}$ decreases with the increase in the incident angle. However, for the HMM, the iso-frequency curve is an open hyperbola [63]. Therefore, the propagating phase along the periodic direction within the HMM ${\phi _{\textrm{HMM}}} = {k_{\textrm{HMM}{\textrm{,}_{}}z}}{d_{\textrm{HMM}}}$ increases with the increase in the incident angle. If the phase variations with the incident angle within the isotropic dielectric and the HMM can be compensated, the propagating phase within the unit cell ${\phi _{\textrm{Unit cell}}} = {\phi _{\textrm{Dielec}}} + {\phi _{\textrm{HMM}}}$ will be insensitive to the incident angle, leading to an angle-insensitive PBG [59]. The designed 1D PhC can be denoted by [(CD)2B]N, as shown in Fig. 1(a). (CD)2 represents the subwavelength TiO2/indium tin oxide (ITO) multilayer which can be viewed as an HMM layer. B represents the isotropic dielectric Si layer. The refractive indices of dielectrics TiO2 and Si can be obtained from experimental measurements: ${n_\textrm{C}} = 2.72$ and ${n_\textrm{B}} = 3.48$ [64]. The relative permittivity of ITO can be described by the classical dispersion formula containing a Drude term and a single oscillator [65]
Fig. 1. (a) Schematic of the designed 1D PhC containing layered HMMs. The 1D PhC can be denoted by [(CD)2B]N, where (CD)2 represents the layered HMM mimicked by a subwavelength TiO2/ITO multilayer and B represents the isotropic dielectric Si layer. (b) Two components of the effective relative permittivity of the subwavelength TiO2/ITO multilayer (CD)2 as a function of the wavelength.
According to the effective medium theory [63,66], 2 components of the effective relative permittivity tensor of the TiO2/ITO multilayer (CD)2 can be determined by
Now, based on the transfer matrix method [68], we calculate the reflectance spectra [under transverse magnetic (TM) polarization] of the designed 1D PhC [(CD)2B]N at different incident angles 0°, 30°, 60° and 70°, as shown in Fig. 2(a). The periodic number is chosen to be N = 4. The substrate medium is selected to be a kind of transparent glass (BK7) with the refractive index ${n_\textrm{S}} = 1.515$ [69]. At normal incidence, a PBG ranging from 1553 nm to 2581 nm (2 edges of the PBG are extracted from the reflectance dips) is opened around the designed Bragg wavelength ${\lambda _{\textrm{Brg}}} = 1819$ nm. Interestingly, in contrast to the conventional blueshift PBGs in all-dielectric 1D PhCs [55–58], as the incident angle increase from 0° to 70°, 2 edges of the designed PBG are both insensitive to the incident angle. To clearly see the angle-dependent property of the PBG, we also calculate the reflectance spectra (under TM polarization) of the 1D PhC [(CD)2B]4 as a function of the incident angle, as shown in Fig. 2(b). One can clearly see that the PBG is angle-insensitive, indicating that an angle-insensitive PBG is realized. The wavelength range of the omnidirectional PBG is from 1570 nm to 2549 nm. The bandwidth of the omnidirectional PBG reaches 979 nm.
Fig. 2. (a) Reflectance spectra (under TM polarization) of the 1D PhC [(CD)2B]4 at different incident angles 0°, 30°, 60° and 70°. (b) Reflectance spectra (under TM polarization) of the 1D PhC [(CD)2B]4 as a function of the incident angle.
3. Broadband wide-angle absorption based on broadband omnidirectional OTS
In this section, we realize a broadband omnidirectional OTS based on the designed broad angle-insensitive PBG in Section 2. In order to realize a broadband OTS, we choose a Cr layer to constitute the 1D heterostructure since its high Ohmic loss in the near-infrared region [64]. We give the measured data (extracted from Ref. [64]) of the real and the imaginary parts of the relative permittivity of Cr [$\textrm{Re} ({\varepsilon _\textrm{M}})$ and ${\mathop{\rm Im}\nolimits} ({\varepsilon _\textrm{M}})$] as a function of the wavelength, as shown by the black circles in Fig. 3(a) and the red circles in Fig. 3(b), respectively. Then, we utilize the polynomial functions to fit the real and the imaginary parts of the relative permittivity of Cr. The corresponding fitting curves are also shown by the blue solid line in Fig. 3(a) and the green solid line in Fig. 3(b), respectively. The fitting polynomial functions can be written as
Fig. 3. (a) Real and (b) imaginary parts of the relative permittivity of Cr as a function of the wavelength.
Then, we put a Cr layer in front of the designed 1D PhC [(CD)2B]4 to constitute the 1D heterostructure to realize a broadband OTS. Furthermore, in order to realize higher absorptance, an impedance matching layer (Si layer) is put on the top of the Cr layer [54]. The 1D heterostructure can be denoted by IM[(CD)2B]4, as schematically shown in Fig. 4(a). Here I and M represent the impedance matching layer (Si layer) and the metal layer (Cr layer), respectively. The thickness of the Cr layer is set to be ${d_\textrm{M}} = 35$ nm to obtain an OTS. The thickness of the impedance Si layer is optimized to be ${d_\textrm{I}} = 114$ nm to obtain high absorptance. The substrate medium is also selected to be a kind of transparent glass (BK7) with the refractive index ${n_\textrm{S}} = 1.515$ [69]. We calculate the absorptance spectrum (under TM polarization) of the proposed 1D heterostructure IM[(CD)2B]4 at normal incidence, as shown in Fig. 4(b). One can see that within the wavelength of the PBG, the absorptance is quite high. In detail, the absorptance is higher than 0.90 in the wavelength range from 1595 nm to 2624 nm, which is shown by the purple shadow region. In order to confirm that the broadband absorption originates from the broadband OTS, we calculate the electric field distributions |E| of the heterostructure at normal incidence at 2 different wavelengths ${\lambda _1} = 1800$ nm and ${\lambda _\textrm{2}} = 2200$ nm based on the transfer matrix method [68], as shown in Figs. 4(c) and 4(d). The maximum electric field is normalized [Max(|E|) = 1]. At the wavelength ${\lambda _1} = 1800$ nm or ${\lambda _\textrm{2}} = 2200$ nm, the electric field is concentrated around the Cr layer. Besides, the envelope of the electric field decays exponentially in the 1D PhC. Therefore, the electric field distribution shows that the broadband absorption originates from the broadband OTS [53]. It should be noted that even if the electric field in the impedance matching layer is stronger, it will not contribute to the absorptance since the impedance matching layer is lossless.
Fig. 4. (a) Schematic of the proposed 1D heterostructure IM[(CD)2B]4. (b) Absorptance spectrum (under TM polarization) of the 1D heterostructure IM[(CD)2B]4 at normal incidence. (c) and (d) Electric field distributions in the 1D heterostructure IM[(CD)2B]4 at normal incidence at 2 different wavelengths λ1=1800 nm and λ2=2200 nm.
Next, we investigate the angle-dependent property of the broadband absorption. Figure 5(a) gives the absorptance spectra (under TM polarization) of the 1D heterostructure IM[(CD)2B]4 at different incident angles 0°, 30°, 60° and 70°. To clearly see the angle-dependent property of broadband absorption, we also calculate the absorptance spectrum (under TM polarization) of the 1D heterostructure IM[(CD)2B]4 as a function of the incident angle, as shown in Fig. 5(b). One can see that assisted by the angle-insensitive PBG in the 1D PhC, the broadband absorption shows excellent angular tolerance. Even at a large incident angle (70°), the absorption is also broadband. High absorptance (A > 0.85) can be remained when the wavelength ranges from 1612 nm to 2335 nm and the incident angle ranges from 0° to 70°. The bandwidth of wide-angle absorption (0°-70°) reaches 723 nm, which is much broader than those in Refs. [52–54]. In Refs. [52–54], the bandwidths of wide-angle absorption are smaller than 200 nm since the broadband OTSs are angle-sensitive. Figures 5(c) and 5(d) show the calculated electric field distributions |E| of the heterostructure at 2 different incident angles $\theta = 0^\circ$ and $\theta = 70^\circ$ at the wavelength $\lambda = 1800$ nm. The maximum electric field is normalized [max(|E|) = 1]. At the incident angle $\theta = 0^\circ$ or $\theta = 70^\circ$, the electric field is concentrated around the Cr layer. Besides, the envelope of the electric field decays exponentially in the 1D PhC. Therefore, the electric field distribution shows that the broadband wide-angle absorption originates from the broadband omnidirectional OTS. We achieve broadband wide-angle absorption in a lithography-free 1D structure, which can be easily fabricated under the current magnetron sputtering [62] or electron-beam vacuum deposition technique [57].
Fig. 5. (a) Absorptance spectra (under TM polarization) of the 1D heterostructure IM[(CD)2B]4 at different incident angles. (b) Absorptance spectrum (under TM polarization) of the 1D heterostructure IM[(CD)2B]4 as a function of the incident angle. (c) and (d) Electric field distributions in the 1D heterostructure IM[(CD)2B]4 at 2 different incident angles θ = 0° and θ = 70° at the wavelength λ = 1800 nm.
Actually, the proposed heterostructure contains 2 kinds of lossy materials: Cr and ITO. Hence, here we analyze the absorptance ratio between the Cr layer and the PhC (with 8 ITO layers) according to the electric field distribution in the heterostructure. According to Ref. [13], the power dissipation density (PDD) of the incident light is proportional to the imaginary part of the lossy material and the square of the electric field, which can be expressed as
where $|{E(z)} |$ represents the electric field at the position z. According to the transfer matrix method [68] and Eq. (8), the PDD distribution of the heterostructure can be calculated, as shown in Fig. 6. The incident angle and the wavelength are set as $\theta = 0^\circ$ and $\lambda = 1800$ nm. The maximum PDD is normalized [max(PDD) = 1]. One can see that the PDD is much more concentrated within the Cr layer compared with that within the ITO layer since the following 2 reasons. One is the imaginary part of the relative permittivity of Cr is much larger than that of ITO. The other is that the electric field within the Cr layer is larger than that within the ITO layer. PDD within the Si and TiO2 layer is exactly 0 since Si and TiO2 are lossless materials.Fig. 6. PDD distribution in the heterostructure IM[(CD)2B]4 at normal incidence at the wavelength λ = 1800 nm.
Then, the absorbed power of the Cr layer ${\alpha _{\textrm{Cr}}}$ is proportional to the integral of the PDD within the Cr layer
Similarly, the absorbed power of the PhC ${\alpha _{\textrm{PhC}}}$ is proportional to the integral of the PDD within 8 ITO layers
Based on Eqs. (8)–(10), we can obtain the absorptance ratio between the Cr layer and the PhC $K = {{{\alpha _{\textrm{Cr}}}} / {{\alpha _{\textrm{PhC}}}}}$ under parameters $\theta = 0^\circ$ and $\lambda = 1800$ nm is 16.8, indicating that the absorptance within the PhC is much smaller than that within the Cr layer. From Fig. 5(a), the total absorptance under parameters $\theta = 0^\circ$ and $\lambda = 1800$ nm is 0.906. Based on Eq. (11), the respective absorptances of the Cr layer and the PhC can be calculated as 0.855 and 0.051.
Finally, we calculate the absorptance ratio between the Cr layer and the PhC in the wavelength range from 1612 nm to 2335 nm at the incident angles $\theta = 0^\circ$ and $\theta = 70^\circ$, as respectively shown by the black and green solid lines in Fig. 7. One can see that the absorptance ratio between the Cr layer and the PhC is larger than 10 in the wavelength range from 1725 nm to 2335 nm at the incident angles $\theta = 0^\circ$ and $\theta = 70^\circ$. Therefore, we can finally conclude that the broadband wide-angle absorption is mainly contributed to the absorptance of the Cr layer.
Fig. 7. Absorptance ratio between the Cr layer and the PhC in the wavelength range from 1612 nm to 2335 nm at the incident angles θ = 0° and θ = 70°.
4. Conclusion
In conclusion, we realize a broadband omnidirectional OTS in a 1D heterostructure composed of a highly lossy metal layer (Cr layer) and a 1D PhC containing layered HMMs with an angle-insensitive PBG. Assisted by the broadband omnidirectional OTS, we achieve broadband wide-angle absorption. High absorptance (A > 0.85) can be remained when the wavelength ranges from 1612 nm to 2335 nm and the incident angle ranges from 0° to 70°. The bandwidth of wide-angle absorption (0°-70°) reaches 723 nm. By calculating the power dissipation density distribution, we find that the broadband wide-angle absorption is mainly contributed to the absorptance of the Cr layer. The designed absorber is a lithography-free 1D structure, which can be easily fabricated under the current magnetron sputtering or electron-beam vacuum deposition technique. This broadband, wide-angle, and lithography-free absorber may be useful in the design of photodetectors, solar thermophotovoltaic devices, gas analyzers, and cloaking devices.
Funding
National Natural Science Foundation of China (11947065, 61805064); Natural Science Foundation of Jiangxi Province (20202BAB211007); Natural Science Foundation of Shandong Province (ZR2020LLZ004); Guangdong Province University Youth Innovative Talents Program of China (2019KQNCX070); Natural Science Foundation of Guangdong Province (2021A1515010050); Interdisciplinary Innovation Fund of Nanchang University (2019-9166-27060003); Start-Up Funding of Guangdong Polytechnic Normal University (2021SDKYA033).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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