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Abstract
Thermal radiation has applications in numerous fields, such as radiation cooling, thermal imaging, and thermal camouflage. Micro/nanostructures such as chiral metamaterials with polarization-dependent or symmetry-breaking properties can selectively emit circularly (spin) polarized polarization waves. In this paper, we propose and demonstrate the spinning thermal radiation from two twisted different anisotropic materials. Taking industrial polymer and biaxial hyperbolic material α-MoO3 as an example, it is found that broadband spinning thermal radiation can be obtained from 13 µm to 18 µm. The spin thermal radiation of the proposed twisted structure originates from the combined effect of polarization conversion of circularly polarized wave and selective absorption of linearly polarized wave by the top and bottom layers of anisotropic materials, respectively. Besides, the narrowband spinning thermal radiation with 0.9 circular dichroism is achieved at wavelength of 12.39 µm and 18.93 µm for finite thickness α-MoO3 due to the epsilon-near-zero mode, and the magnetic field distribution can confirm the phenomenon. This work achieves broadband and narrowband spin thermal radiation and significantly enhances circular dichroism, which may have applications in biological sensing and thermal detection.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Thermal radiation is propagated in the form of electromagnetic waves and possesses various basic properties of electromagnetic waves, such as spectral properties and polarization properties [1–4]. Naturally occurring thermal radiation is random and unpolarized. In general, most studies on thermal radiation consider the linear polarization, including transverse magnetic (TM) and transverse electric (TE) waves [5–7]. Artificial microstructures such as gratings and photonic crystals can produce different responses to TE and TM wave, which is critical in applications like thermal management and thermal imaging [8]. In contrast, spin polarized (circularly polarized) wave has obtained extensive attention in chiral optics [9–11] and spin-controlled nanophotonics [12], where its spin angular momentum is harnessed for engineering spin-dependent light-matter interactions at nanoscale. Recently, the research on micro/nano chiral structures has demonstrated the engineering of spinning thermal radiation. In addition to its fundamental interest, spinning thermal radiation may also find application in thermal detection [13–15].
As we all know, the spin polarized wave can be selectively emitted by chiral structures [16]. Circular dichroism (CD) is one of the most representative and powerful parameters for characterizing spinning thermal radiation. However, the CD of natural materials is extremely weak due to the mismatch between the spatial expansion of the molecular wave function of natural structures and the excitation wavelength [17]. Thus, the development of spin thermal radiation in the field of detection and sensing has been somewhat hindered. In comparison, the emergence of metamaterials provides an effective solution to this problem [18–22]. Chiral metamaterials refer to artificially designed periodic subwavelength structures that can efficiently couple incident wave and respond differently to circularly polarized waves. For instance, Kong et al. proposed a chiral metamaterial structure with Γ-shape arranged nanocrystals for achieving the giant CD [23]. So far, many two- dimensional (2D) or three-dimensional (3D) chiral metamaterials have been designed to enhance spin thermal radiation [24–28]. Although chiral metamaterials can effectively improve the CD, the subwavelength nanostructures always increase the complexity of structure fabrication.
Recently, researchers have turned their attention to twisted structures both theoretically and experimentally, especially those composed of two-dimensional materials such as graphene and black phosphorus [29–33]. Interlayer interactions in twisted structures can enhance lots of properties, including optical and electronic properties [34]. Inspired by recent discoveries of novel electronic and photonic properties in twisted structures, there has been a surge of interest in exploring exotic properties in those structures. It has been demonstrated that twisted structure allows for active control of thermal radiation [34]. For example, Zhang et al. achieved controlled thermal radiation using twisted bilayer graphene, which has potential applications in stealth [32]. Besides, Wu et al. proved that the twisted bilayer anisotropic material molybdenum trioxide α-MoO3 can realize a strong CD with 0.89 [30]. However, using twisted structures of the identical anisotropic materials to achieve spin thermal radiation has more restrictions on the materials.
Here, we demonstrate that the spinning thermal radiation can be generated by twisting two different anisotropic materials. The proposed structure composes of one quarter-wave plate (QWP) and α-MoO3 substrate, which removes the material constraints in generating spin thermal radiation. Firstly, the absorption of linearly and circularly polarized waves is discussed for semi-infinite α-MoO3. It can be found that selective absorption and polarization conversion will produce broadband spin thermal radiation. Furthermore, we investigate the case of finite thickness α-MoO3 to achieve narrowband spinning thermal radiation at epsilon-near-zero point [35,36], and explain the physical mechanism by magnetic field distribution. This work significantly improves circular dichroism and achieves broadband and narrowband spin thermal radiation, allowing greater freedom in regulating circular dichroism.
2. Theory and method
The proposed structure consists of one quarter-wave plate (QWP) and α-MoO3 substrate. The QWP is a birefringent film with permittivity ${\varepsilon } = ({2.25,\textrm{ }2.56,\textrm{ }2.25} )$. The permittivity is chosen according to the available polymers in industry [37]. It is noted that the angle between the optical axis of the QWP and the y-axis is 45° in the calculation.
The α-MoO3 is a biaxial hyperbolic material, whose permittivity tensor can be expressed as [38]
The real parts of the permittivity components of α-MoO3 are shown in Fig. 2. One can see that ${\varepsilon _{xx}}$ is negative in the 10.3-12.2 µm, while ${\varepsilon _{yy}}$ is negative in the 11.8-18.34 µm.
In this work, we only consider the radiation in the normal direction. Supposing the magnetic field and electric field in the α-MoO3 slab are respectively [39–41]
andOne can get
Equation (6) can be decoupled into
As shown in Fig. 1, the TM wave has magnetic field along the y-axis and electric field along the x-axis, while the TE wave has electric field along the y-axis and magnetic field along the x-axis. Equation (7) and Eq. (8) indicate no coupling between TM wave and TE wave. Besides, the TM is related to the ${\varepsilon _{xx}}$, while the TE is related to the ${\varepsilon _{yy}}$. As shown in Fig. 2, ${\varepsilon _{xx}}$ and ${\varepsilon _{yy}}$ have opposite signs. The different signs of ${\varepsilon _{xx}}$ and ${\varepsilon _{yy}}$ means the absorption of TM and TE can be completely different, which will be shown in the next section. If the absorption of TM wave is close to unity, while that of the TE wave is close to zero, then the semi-infinite α-MoO3 will emitter TM wave, and the TM wave will be converted into RCP by the QWP. However, if the absorption of TE wave is close to unity, while that of the TM wave is close to zero, then the object will emit TE wave, and the TE wave will be converted into LCP by the QWP. Therefore, the proposed design can be used to generate spinning thermal radiation. The 4*4 transfer matrix method is used to calculate the reflection, transmission, and absorption of linearly and circularly polarized waves, which has been introduced in detail in our published papers [30,32].
Fig. 1. The proposed structure to generate spinning thermal radiation, which consists of one quarter-wave plate and α-MoO3 substrate. The α-MoO3 substrate can emit TE wave or TM wave, while the quarter-wave plate can rotate the linearly polarized waves into circularly polarized waves.
3. Results and discussion
Firstly, the absorption of TM wave and TE wave is investigated. Figure 3 shows the absorption of TM wave and TE wave for semi-infinite α-MoO3. It is clear that the absorption of TM wave is small in the band where ${\varepsilon _{xx}}$ is negative, while that of TE wave is small in the band where ${\varepsilon _{yy}}$ is negative. The absorption of TM and TE waves is small in the band where ${\varepsilon _{xx}}$ and ${\varepsilon _{yy}}$ are negative. At wavelength of 11 µm, the absorption of TE wave is close to unity, while that of TM wave is small, as much as 0.05, indicating the semi-infinite α-MoO3 has strong selective absorption for those two linearly polarized waves. At this wavelength, there is ${\varepsilon _{xx}} ={-} 3.069 - j0.167$ and ${\varepsilon _{yy}} = 1 - j0.029$, which means that the incident TM wave will be greatly reflected, and the incident TE wave will be greatly absorbed. According to our theory, it is possible to be used to realize spinning thermal radiation.
At the wavelength of 11 µm, the thickness of the QWP should be 13.75 µm. The absorption of the whole structure under different hand-ness circularly polarized waves are shown in Fig. 4. One can see that the absorption of RCP and LCP are greatly different, especially at wavelength of 11 µm. According to Kirchhoff’s law, the emission equals the absorption. It means that the proposed structure can generate spinning thermal radiation. Besides, it can be seen that broadband spinning thermal radiation can be found in the range of 13 µm to 18 µm. Besides, the hand-ness of the circularly polarized wave in this band is in contrast to that at wavelength of 11 µm to explain this phenomenon.
Fig. 4. (a) The absorption of LCP and RCP for the QWP atop the semi-infinite α-MoO3. (b) The transmission of LCP and RCP waves, including TM and TE components.
As shown in Fig. 3, the absorption of TE wave is high in this range, and it can be changed into LCP wave. As shown in Fig. 4(b), the polarization conversion is broadband. Broadband selective absorption and broadband polarization conversion will generate broadband spinning thermal emission.
The absorption of LCP and RCP at wavelength of 11 µm is shown in Fig. 5 for different incident angle θ and azimuthal angle φ. One can see that high absorption of LCP can be obtained when the incident angle is smaller than 60°, and the absorption of RCP is always small when the incident angle is smaller than 60°, regardless of the azimuthal angle.
Fig. 5. The absorption as a function of incident angle θ and azimuthal angle φ at wavelength of 11 µm: (a) LCP; (b) RCP.
We have shown that broadband spinning thermal radiation can be generated. However, narrowband spinning thermal radiation can also be generated. Following the same process, we firstly design the selective absorbers. One of the simple structures is one film atop the metal substrate with thickness of 0.2 µm. As shown in Fig. 2, ${\varepsilon _{xx}}$ and ${\varepsilon _{yy}}$ have epsilon-near-zero (ENZ) points. Previous studies have shown that perfect absorption is possible to be realized at those points [35,36]. Figure 6(a) shows the absorption of TM and TE waves for α-MoO3/Ag structure. By optimizing the thickness of the α-MoO3, perfect absorption at wavelength of 12.39 µm and 18.93 µm is realized when the thickness of the α-MoO3 film is 0.4 µm. The permittivity of the Ag is described using the Drude model, i.e., ${\varepsilon _{Ag}} = {\varepsilon _\infty } - {{\omega _p^2} / {({{\omega^2} + j\omega \Gamma } )}}$, with ${\varepsilon _\infty } = 3.4$, ${\omega _p} = 1.39 \times {10^{16}}\textrm{ rad/s}$ and $\Gamma = 2.7 \times {10^{13}}\textrm{ rad/s}$ [42].
Fig. 6. (a) The absorption of TM and TE wave for α-MoO3/Ag structure. The thickness of α-MoO3 is 0.4 µm. (b) The distribution of the magnetic field for incident TM and TE waves along the z-axis at wavelength of 12.39 µm.
To investigate the selective absorption at wavelength of 12.39 µm, the distribution of the normalized magnetic field is shown in Fig. 6(b). One can see that when the incident light is TM wave, the magnetic field is greatly enhanced at the interface between the α-MoO3 film and Ag substrate, resulting in perfect absorption and small reflection. However, when the incident light is TE wave, the magnetic field at the interface between the air and α-MoO3 film is close to 2, indicating that the incident light is almost reflected, and thus the absorption is negligible. At wavelength of 18.93 µm, the situation is switched, and the distribution of magnetic field is similar to that shown in Fig. 6(b). One can see that the strongest position of the magnetic field is located at the interface of α-MoO3 and Ag. It can be found from Fig. 2 that the real parts of the permittivity components of α-MoO3 are close to 0 at wavelength of 12.39 µm, which can excite ENZ mode, resulting in the enhancement of the magnetic field. Besides, the magnetic field decays away from the dielectric film while the electric field is both enhanced and confined in the film due to the vanishing dielectric constant [35,36,43]. Therefore, the magnetic field distribution presents such a phenomenon, and the distribution of magnetic field can well explain the selective absorption shown in Fig. 6(a).
The narrowband selective absorption at wavelength of 12.39 µm can be used to realize narrowband spinning thermal radiation. The thickness of the QWP should be 15.49 µm at this wavelength. The absorption of the RCP and LCP waves for QWP/α-MoO3/Ag is shown in Fig. 7. The thicknesses of QWP and α-MoO3 are 15.49 µm and 0.4 µm. One can see that the difference in absorption for RCP and LCP can be as high as 0.9 at wavelength of 12.39 µm and 18.93 µm, indicating that the proposed structure can generate narrowband spinning thermal radiation. The FWHM at wavelength of 12.39 µm is about 0.16 µm, which means that the proposed structure may have applications in thermal detection [44].
Fig. 7. The absorption of LCP and RCP waves for QWP/α-MoO3/Ag structure. The thicknesses of QWP and α-MoO3 are 15.49 µm and 0.4 µm, respectively.
4. Conclusions
In this work, we have shown that spinning thermal radiation can be generated in twisted anisotropic materials. One of the anisotropic materials is used for realizing polarization conversion between linearly polarized waves and circularly polarized waves, while the other is used for selective absorption for TM and TE waves. The combination between them can generate spinning thermal radiation. Taking industrial polymer and biaxial hyperbolic material α-MoO3 for example, broadband and narrowband spinning thermal radiation is realized at wavelength of 12.39 µm and 18.93 µm. We believe that the results of this study have potential applications in the fields of biosensing and heat detection.
Funding
National Natural Science Foundation of China (52106099); Natural Science Foundation of Shandong Province (ZR2020LLZ004).
Disclosures
The authors declare no conflicts of interest.
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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