Complete terahertz absorber: coupled topological like structure, spaced graphene and magneto-optic effect

The work examines terahertz (THz) broadband absorbers for unit topological structure (UTS) with spaced graphene. This study examined the transmission and absorption of the proposed structure without and with graphene at each dielectric interface. The UTS absorbed more light while using a cascade structure with a structural index (n) and adjusting dielectric thicknesses (Δ). Absorption increased significantly with an external magnetic field (B). The objective for a complete THz absorber is achieved with average absorption, A¯ = 0.8093 by a modified structure with n = 5, applying an external magnetic field, B = 10.7 T, Fermi level, E F = −0.48 eV, and manipulating the thickness parameter Δ.

T erahertz (THz) photonics [1][2][3] has experienced a significant surge in attention in recent years. Tis evolved spectrum (0.1 THz to 10 THz) has a broad range of applications, including imaging, 4,5) telecommunications, 2,6) spectroscopy, 7) and many more.8,9) The role of THz absorbers, which are specialized tools for capturing and controlling electromagnetic waves in the THz frequency range, has been greatly practiced in the mentioned applications.Out of different perspectives on the design of such absorbers, one of its kind makes use of photonic crystals (PCs) [10][11][12] special features, which are periodic structures that can influence the propagation of electromagnetic waves.In addition to PCs, these structures also include materials such as chalcogenides, metals, and graphene and their special characteristics.13) However, due to the extraordinary physical, chemical, and electrical properties of graphene, 14) it's widely recommended for this purpose, as well as to maintain the structure in an alldielectric configuration.
Spaced graphene with quarter-wave dielectric plate photonic lattices has great potential to absorb a broad range of frequencies, 15,16) whereas it can still be improved with a structural arrangement.Recently, a broadband absorber was presented by Mahesh et al. 17) by practicing a random-like unit cell stack with graphene sandwiched at each unit cell interface.Although the structure looks simple from a fabrication point of view, it will not be easy to grow.Therefore, a different perspective on structural design can be a solution for designing broadband absorbers.One of the ways is by using a topological structure, 18) which may solve the purpose.
One-dimensional (1D) topological structure 18,19) is a periodic stack of unit cells that have two distinct structures, namely

-and
--.Here, A and B may be any kinds of material and are designed as a quarter-wave plate. 20)A 2 and B 2 are made of the same material and the corresponding thicknesses are calculated for a condition of λ 0 /8. 21)The stack structures --

( ) and
) , in which N and M are the number of repetitions, provide the same bandgaps. 22)The stacked structure of --

(
) can provide highly localized states within the bandgap regions, leading to perfect transmission.This is because of the Zak phase 22,23) and arises when the sum of the Zak phases of previous bands has a phase difference of mod 2 p ( ). 22,23) This structure can confine terahertz waves, improving their interaction with light-absorbing materials and reducing undesired leakage.This makes terahertz wave absorption more efficient and dependable than periodic or random structures.Due to their highly localized state, the topological structures are more favorable and are employed as perfect narrow-band absorbers by placing the graphene at the interface of the distinct structures.However, such a structure in spaced graphene can also enhance absorption.Moreover, the spaced graphene topological structure is more uniform and easy to grow as compared to the random one. 17)Therefore, in this study, a one-dimensional topologically spaced graphene structure is used with an expectation of sharp enhancement of average absorption in the entire THz frequency range.
To achieve the objective, a modified topological structure is considered.The modified structure is described as is the unit topological structure (UTS), and n is a positive integer denoted as the structural index.A and B represent the constituent materials silicon dioxide (SiO 2 ) and titanium dioxide (TiO 2 ) with refractive indices of n A = 1.45 and n B = 2.3, respectively. 24)The thickness of the layers is calculated from the designed wavelength, λ 0 = 60 μm.This letter studies numerically the features of transmission (T), reflection (R), and absorption(A) using a 4 × 4 transfer matrix method. 25,26)The absorption of the UTS can be calculated by A = 1 − T − R. 26) The above structure provided zero absorption because of the absence of an absorbing medium.By including graphene (G) at each interface, the structure is in view ) and becomes absorbent.The permittivity of graphene is calculated from the Drude model, 27) which is a function of magnetic field B, polarization, and Fermi level E F .The schematic views of basic UTS without graphene and with graphene are represented in Figs.1(a) and 1(b), respectively.
To examine the proposed structure first, the transmission properties of UTS without graphene (solid orange line) and with graphene (solid green line) are illustrated in Fig. 1(c) with B = 0 and E F = −0.34eV. Figure 1(c) shows that the inclusion of graphene drastically decreases the transmission spectra because of the improved light-matter interaction between the localized waves and graphene.To gain a deeper insight, an investigation of the proposed structure's absorption characteristics is necessary.This analysis will focus on the impact of increasing the structural index n to 2. Figure 2(a) represents the proposed structure for n = 2, i. e. , UTS-G-UTS, which is denoted as 2-UTSs.Note that from here onward, UTS stands for UTS with graphene.Additionally, a thickness parameter δ i,j = 1( + , − )Δ modifies the thicknesses of all layers in the second structure of 2-UTSs rather than just cascading; thus, i and j represent the materials A and B, respectively, and Δ values range from -1 to 1. 052005-2 © 2024 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd Δ (solid red line).It is clearly understood that by cascading two UTS, the absorption was enhanced in the lower and mid-THz regions, and the average absorption, A of 2-UTSs, reached 0.5662.This is caused by the number of graphene layers as well as the enhanced light-matter interaction in the specific frequency region.However, the absorption at higher THz decreases because of the bandgap provided by the stratified, spaced graphene structure.To nullify the effect of the bandgap, the inclusion of uniform variation in thickness was introduced in the form of δ, as discussed above.The impact of δ is examined with a step size of 0.01 and found that at Δ = −0.3, the A is maximum, which is equal to 0.5717.It is observed that the bandgap is not much affected by the thickness variation because of its robust nature. 16)owever, a marginal increase in the absorption spectra is observed on the blue side of the photonic bandgap.
Although graphene possesses a bandgap, an external magnetic field perpendicular to the graphene layer can provide a configurable bandgap.The bandgap suppresses terahertz waves and promotes their absorption.This magnetic field-created adjustable bandgap can increase spaced graphene structure absorption for terahertz wave manipulation by overcoming intrinsic graphene characteristics. 28)herefore, the proposed structure is examined in the presence of an external magnetic field for its strength and polarization.The objective is to investigate the magneto-optic 29) properties of graphene that is used for left and right circularly polarized 26) (LCP and RCP) magnetic fields with a step size of 0.01 T. The maximized value is plotted in Fig. 2(c) compares the absorption spectra of UTS (solid blue line), 2-UTSs (solid black line), and 2-UTSs with Δ (solid red line) in the presence of an LCP magnetic field with B = 10.7 T. It is evident that by introducing a magnetic field, the absorption was amplified in the blue THz region, especially the region protected by a graphene-induced bandgap with an absorption trade-off.Moreover, it could be noted that A = 0.5848, 0.7387, and 0.7440 for UTS, 2-UTSs, and 2-UTSs with Δ at Δ = 0.7, respectively.
The above outcomes show that n has a significant impact on the average absorption, and with the help of such a parameter, the goal of A may be achieved.Increasing the structural index n up to 5 is investigated here to understand its effect.This strategy leverages the cascading effect of UTSs, where each UTS amplifies the absorption of the previous one.We compared the A of 2-to 5-UTSs with varying thicknesses by Δ to understand this effect.Figure 3(a) shows the A of the proposed structure for different n configurations without the presence of an external magnetic field.As discussed earlier, the maximum of A =0.5717 for 2-UTSs occurs at Δ = −0.3.This indicates that for this specific thickness variation, the resonant coupling between the UTS and light is optimized, leading to enhanced absorption.Similarly, the maximum of A =0.6383 for 3-UTSs is observed at Δ = −0.5, while for 4-and 5-UTSs, the maximum of A = 0.6656 and 0.6813, respectively, are observed at the same value of Δ = −0.5.This suggests that as the number of UTS layers increases, the optimal thickness variation for achieving peak absorption may shift to slightly larger values.Figure 3(b) displays the average absorption for various UTS configurations with an applied magnetic field.Interestingly, the high A for different numbers of UTS layers occurred at distinct thickness variations: Δ = 0.7 and 0.5 for 2-UTSs and 3-UTSs, respectively, and Δ = −0.5 for both 4and 5-UTSs.Notably, the maximum of A exhibited a gradual 052005-3 © 2024 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd rise with the increasing number of layers, reaching 0.7740, 0.7814, 0.7966, and 0.8016 for 2, 3, 4, and 5-UTSs, respectively.The mentioned high average absorption may be achieved due to the external magnetic field and variability in thickness configuration by influencing the UTS resonant coupling.However, the increase in A is not significant with an increase in n from 4 to 5.This is due to the saturated absorption provided by the proposed structure at E F = −0.34eV.The change in E F may increase in A , which can easily be achieved with the help of an external electric field.
To maximize the A of the proposed structure, the previously described approach of varying the Fermi level E F within the range of −2 eV to 2 eV. 30)Figure 3(c) illustrates the A of 2-(solid black line) and 5-UTSs (solid green line) versus E F without any influence of the external magnetic field.From Fig. 3(c), it is evident that for the 2-UTSs system, the maximum A is 0.7364 at E F = −1.65 eV.Similarly, for the 5-UTSs system, the maximum A is 0.7457 at E F = −1.29 eV.This high absorption is achieved because of the E F , and the surface conductivity of graphene eventually influences its optical response.This tunability of the Fermi level presents an effective strategy for fine-tuning the UTS to achieve optimal average absorption.It could be noted that the maximum of A is symmetrically shifted on both sides, but we are considering the hole doping case, i. e. , the downward Dirac point of graphene.On the other hand, it is evident from Fig. 3(d) that the average absorption spectra are not symmetrical in the case of an applied magnetic field and always provide the maximum A in the case of hole-doped graphene.The 2-UTSs system is provided with the maximum A of 0.7764 when E F = −0.95eV.Whereas the maximum A =0.8093 is achieved for 5-UTSs with a nominal E F = −0.48eV, which is the lowest doping level structure and provides the maximum absorption corresponding to all the considered cases.This minimal doping structure can be effectively realized with the currently available state-of-the-art research facility.
In the above context, the absorption spectra of 5-UTSs and 5-UTSs with Δ are illustrated in Fig. 4 for 5-UTSs with Δ, whereas it only reaches 15 a.u.for 5-UTSs.This is due to the improved resonant coupling caused by changing the thickness of the UTS, which has made the light interact with it more strongly.Graphene will be particularly affected by electric fields at resonance frequencies.These observations emphasize the crucial role of resonant coupling in manipulating light-matter interactions within both the original 5-UTSs and their variations in thicknesses.Because of the improved contact, electrons in the UTSs are more likely to be driven to higher energy levels by the electric field.The distribution of the electric field was more uniform due to reduced light-matter interaction in the higher THz region.
This letter suggests a new direction of research by introducing the concept of UTS and analyzing how topological events affect the absorption properties of UTS when graphene is introduced at each interface.Increasing the number of UTS layers, changing the dielectric thicknesses, adding a magnetic field, and altering the Fermi level of graphene with an external gate voltage effectively enhance the UTS's absorption properties.Resonant coupling is crucial for optimizing light-matter interaction inside the UTS, as shown in the study.The findings suggest the potential for creating customizable THz broadband absorbers through the combination of spaced graphene and UTSs.The hybrid technique shows promise for use in terahertz devices, sensors, and communication systems, as well as significant progress in controlling electromagnetic waves.Future advancements in terahertz technology can be achieved through further research and enhancement of these absorbers.Nevertheless, comprehending the fundamental principles provides vital insight into their prospective functionality.
Figure 1(d) compares the absorption of the 4-layer periodic stack with graphene (solid pink line) i.e., (A − G − B − G − A − G − B) and UTS with graphene (solid blue line) and resembles a high rise in absorption.It can be noted that average absorption A for the entire THz range jumps from 0.285 to 0.3954.This is because of the number of graphene layers and the resonant wavelengths formed by the 8 0 l plates.

Fig. 1 .Fig. 2 .
Fig. 1.Schematic representation of unit topological structure (a) without graphene, (b) with graphene, (c) comparison of transmission spectra between the UTS without graphene and with graphene, and (d) comparison of absorption spectra between the UTS and periodic structure with graphene.

Fig. 3 .
Fig. 3. (a) Comparison of average absorptions of 2-to 5-UTSs versus Δ without B. (b) Comparison of average absorptions of 2-to 5-UTSs versus Δ, with LCP magnetic field, B = 10.7 T. (c) Comparison of average absorptions of 2-and 5-UTSs versus Fermi level E F without B (d) comparison of average absorptions of 2-and 5-UTSs versus Fermi level E F with LCP magnetic field, B = 10.7 T.
(a).The solid violet line and solid orange line represent the absorption spectra of 5-UTSs and 5-UTSs with Δ, respectively, and for both cases, E F = −0.34eV.The solid brown line represents the absorption spectrum of 5-UTSs with Δ when E F = −0.48eV.It can be noted that the average absorption is remarkably increased by the 5-UTSs with Δ and E F = −0.48eV, especially for the three frequency regions, i.e., 3.038, 5.881, and 9.332 THz.However, a decrease in absorption at 1.93 THz.To evident an increase in absorption, a study was conducted to investigate the squared electric field intensity (|E| 2 ) inside the UTS. Figure 4(b) represents the |E| 2 along the z-axis of structures for 5-UTSs and Fig. 4(c) represents the same but for 5-UTSs with Δ.The 5-UTSs and 5-UTSs with Δ exhibit distinct absorption peaks at specific frequencies, indicating amplified electric field intensity due to resonant coupling with photonic modes.It could be noted that the maximum field enhancement at resonance frequencies rises to 34 a.u.