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Abstract
Wavelength-selective light absorption and the related switching operations are highly desired in optical devices. Herein, we report the approach for ultra-high quality (Q) graphene perfect optical absorption, which possesses impressive performance in switching manipulation. A record-breaking Q-factor (up to 105) is observed, suggesting one or two orders of magnitude larger than that of the conventional graphene absorbers. The ultra-low external leakage loss rate of quasi-bound states in the continuum (BIC) resonator and the ultra-low intrinsic absorption loss rate in the resonant mode volume are the main contributions for the ultra-high Q perfect absorption. By introducing a Kerr nonlinear medium, spectral relative intensity can be changed from 0 to 100% when an ultra-low pump light with the intensity of only 5 kW cm−2 is used. After a rather slight tuning of the refractive index (Δn = 5×10−4) for the resonators, the absorption contrast ratio reaches 31 dB. The switching related spectral wavelength shift sensitivity is up to 915 nm/RIU and the figure of merit (FOM) is 50 833. These features confirm the ultra-high tunability and switching manipulation. It is believed that the ultra-high Q-factor absorption offered by all-dielectric configuration provides plentiful potential applications for graphene-based devices in the all-optical switch, modulator, notch filter, etc.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Graphene is a monolayer of hexagonally arranged carbon atoms, which has attracted increasing attention due to its fascinating material properties for nano-electronics and nano-photonics [1–3]. Previous studies of graphene had emphasized potential advantages to optoelectronic [4,5], such as atomical thickness [6], high mechanical strength [7], extremely high carrier mobility [8] and thermal conductivity [9]. Moreover, the conductivity of graphene can be easily controlled by applying a gate voltage [10], which is a fascinating advantage in contrast to traditional 3D bulk crystals in optoelectronic devices. Thus, these unique attributes of graphene are gradually placing it as a frontier in modern optics [11,12].
Although graphene interacts so strongly with light that a one-atom thick single layer can absorb 2.3% of the incident light in visible and near infrared [13], the absorption efficiency is still not effective enough for optoelectronic devices. Therefore, substantially improving light absorption of graphene is a prerequisite for its widespread applications. To improve the light absorption [14,15], a considerable amount of researches have been done to confine light within single or few layers of graphene, such as by using the Fano resonance [16], guided-mode resonance [17], surface plasmon [18–20], bound states in the continuum (BIC) [21], etc. For example, Lin et al. demonstrate an extremely broadband graphene metamaterial with approximately 85% absorptivity [22]. Zhu et al. proposed a photonic structure with two unpaterned dielectric layers for complete optical absorption by self-interference mode [23]. Yang et al. achieved almost 100% absorptivity via the surface waves by a simple graphene-based structure with purely dielectric planner configuration [24]. Meng et al. realized perfect graphene absorption in the mid-infrared region by exciting graphene surface plasmons in a Si-based diffraction grating structure [25]. However, these studies did not provide much attention to reduce absorption bandwidth, which is the key factor of many optoelectronic devices. The absence of feasible approach and physical mechanism for ultra-narrowband graphene absorption inevitably limits the insight into high-Q spectral absorption and further hampers the applications on the graphene-based optoelectronic devices.
Generally, the significant factor to achieve ultra-narrowband perfect absorption is to realize the ultra-low external leakage loss rate and ultra-low intrinsic absorption loss rate simultaneously [26–28]. Due to the lack of plasmons in the visible and near infrared band [3], various methods [14–27] were employed to enhance absorption by placing graphene in a resonator, which leaded to negative control of the intrinsic absorption loss rate in the system and inevitably limited the achievement of narrowband spectrum absorption. More recently, an effective method to reduce intrinsic absorption loss rate was investigated by Long et al., a high-Q (20000) graphene absorption system is achieved by exciting guided mode resonances (GMR) of distributed Bragg reflector (DBR) [29]. Based on this mechanism, Lee et al. proposed an ultra-narrowband graphene perfect absorber and investigated the fabrication-tolerant of this system [30]. Therefore, the mechanism (GMR of DBR) provides a new perspective for realizing ultra-low intrinsic absorption loss rate. On the other hand, there is always a lack of effective method to reduce the external leakage loss rate, which inevitably limits the realization of ultra-high Q absorption.
In recent years, the research of BIC has attracted a lot of attention [31–33]. BIC is a theoretical mathematical object which has an infinite high Q factor and an infinite lifetime [34,35]. Meanwhile, optical BICs are natural high-Q resonators, which provide new opportunities for the development of many high-Q optical devices. In addition, there is another attractive regime in the vicinity of the BIC, called “quasi-BICs”, at which very high Q resonances are still attainable [36–38]. The external leakage loss rate of the quasi-BIC resonator provides a new mechanism for the realization of ultra-high Q graphene absorbers. For example, Zhang et al. designed the BIC based graphene optical absorber with high Q-factor ∼2000 [21]. However, the Q is still not high enough due to the negative control of intrinsic absorption loss rate. In general, it still remains a challenge to realize the ultra-low external leakage loss rate and ultra-low intrinsic absorption loss rate simultaneously, which still hampers the realization of ultra-high Q perfect absorption for graphene and other 2D materials.
In this work, a dielectric configuration assisted continuous unpatterned monolayer graphene system is proposed to theoretically and numerically investigate for the achievement of the ultra-high Q graphene absorber. A record-breaking Q-factor (up to 106 106) is observed, delivering a significant performance leap for high Q graphene absorber within the visible and near infrared regimes. In our design, both the external leakage loss rate and intrinsic absorption loss rate can be effectively suppressed. The sharp resonances, which originate from DBR, lead to high Q absorption of graphene. Moreover, the ultra-high Q property of this system shows enormously high fabrication tolerance. Intriguingly, without making any changes to the structure parameters, the system exhibits unique additional absorption mechanism by introducing the oblique incidence light. We further develop the approach and achieve high performance switching manipulation by introducing nonlinear dielectric within DBR. The spectral relative intensity change from 0 to 100% can be achieved by just 0.2 eV chemical potential or 5 kW cm−2 pump light. Such graphene-based platform provides plentiful potential applications for graphene-based optoelectronic devices, and paves a novel method to achieving ultra-high Q-factor absorption for other 2D materials, as well as representing a new design paradigm for more compact, functional, and integrated components.
2. Structural scheme and graphene model
The proposed configuration is schematically depicted in Fig. 1. A continuous graphene monolayer is placed between the dielectric grating and DBR layers. The DBR structure is composed of 5 pairs of dielectric A and dielectric B. The thicknesses of A and B are ha and hb, respectively. A dielectric film with thickness of hs is set on the top of the DBR layer. The dielectric grating is composed of periodic nanowires, in which the diameter of nanowires is D and the spacing between adjacent nanowires is W. The refractive index of A and B are na = 1.44 and nb = 3.47, respectively. A TE-polarized plane electromagnetic wave is used as the light source. Finite-difference time-domain method is employed for simulating the optical properties. In the simulation, periodic boundary conditions are applied in the x direction, and the perfectly matched layer absorbing boundary conditions are employed along the z direction. The thickness of monolayer graphene is 0.34 nm. The minimum mesh size inside the graphene layer is 0.1 nm and gradually increases outside the graphene.
The surface conductivity of monolayer graphene ${\sigma _{graphene}}$, which comprises the contributions of both intraband term ${\sigma _{{\mathop{\rm int}} ra}}$ and interband term ${\sigma _{{\mathop{\rm int}} er}}$, can be given by Kubo formula [39]:
3. Result and discussion
3.1. Ultra-high quality graphene perfect absorption
Figure 2 shows the absorption spectrum for proposed ultra-high Q graphene perfect absorber under normal incidence. It is observed that the absorptivity of monolayer graphene is significantly enhanced at λ1 = 1345.5 nm, λ2 = 1390.9 nm, λ3 = 1509.5 nm, λ4 = 1606.4 nm and λ5 = 1673.9 nm. Two near perfect absorption peaks reach 96.6% at λ1 and 95.8% at λ4. Meanwhile, the full width at half maximum (FWHM) of the five absorption peaks are Δλ1 = 0.96 nm, Δλ2 = 1.5 nm, Δλ3 = 0.15 nm, Δλ4 = 0.018 nm and Δλ5 = 8 nm, respectively. Specifically, the FWHM of λ1, λ3 and λ4 are all less than 1 nm, suggesting an excellent single wavelength selective absorption performance, which is desirable in many optoelectronic applications. To the best of our knowledge, the Q-factor ($Q = {\lambda _0}/\Delta {\lambda _0}$) of λ4 is with Q4 of 89244, which breaks the previous records for the Q-factor of graphene-based absorbers [14–24,29,30,41,42] under the same situation and reveals a huge leap in the narrow-band high Q absorption in graphene system.
Fig. 2. Absorption spectrum of the proposed ultra-high Q graphene perfect absorbers. Geometrical and physical parameters: The diameter of Si nanowires is D = 2R = 740 nm, the spacing between adjacent nanowires is W = 200 nm, the thickness of dielectric film is hs = 320 nm, the parameters of DBR are ha = 206 nm and hb = 108 nm, respectively.
In order to have a quantitative understanding of the formation mechanism of absorption peaks, we further carry out the study on the absorption behavior within a framework of temporal coupled-mode theory (CMT). In this system, the transmission light is forbidden due to photonic band effect caused by DBR [15,43–45]. For a resonator with a resonant frequency ω0, the absorptivity of the system can be described by CMT [41,46]:
To get a qualitative understanding of the mechanism for absorption peaks, the electric field distributions are shown in Figs. 3(a)–3(e). At λ1 and λ5, the fields are mainly trapped in the areas around the nanowires [Figs. 3(a) and 3(e)], indicating the excitation of the GMRs from nanowiers. Interestingly, it is observed that the incident waves are well localized within the DBR [Figs. 3(b)–3(d)]. Although the electromagnetic field around graphene is enhanced, it is very weak compared with that in DBR. This is different from previous graphene absorbers [14–24]. More importantly, absorption enhancement at these modes and the high Q absorption at λ4 indicate an attractive mechanism of graphene absorption enhancement: GMRs of DBR. Graphene has typically been placed in a resonator to enhance graphene absorption in previous studies [14–24], which resulted in negative control of the intrinsic absorption loss rate of the resonance. In this work, graphene is on the corn edge of a resonator, the absorption rate of graphene can be well adjusted, which then helps us to achieve ultra-high Q perfect absorption. In order to determine the generation of GMRs of DBR, we put a prism on DBR to excite GMRs [as shown in Fig. 3(h)] [43–45]. It can be clearly seen that three dips are generated in the transmission spectrum when the incident angle increases, revealing that GMRs exist in DBR in this system [Fig. 3(i)]. The wave vector of GMRs in DBR can be obtained by the following formula:
where ${K_{\textrm{gm}}}$ denotes the wave vector of the guided mode of DBR; ${K_p}$ denotes the wave vector of incident light in the prism, which calculated as ${K_p} = 2\pi nf/c$ (n, f and c are refractive index of the prism, frequency of the incident light and velocity of the incident light in vacuum).Fig. 3. (a)-(e) The distribution properties of electric field at λ1 - λ5, respectively. (f), (g) The electric field distribution around graphene for λ3 and λ4, respectively. (h) Schematic of the excitation of guided mode in DBR via a prism. (i) Transmission spectra of DBR as a function of the frequency and incident angle. Mi (i = 1, 2, 3) is related to the ith-order of the guided mode in the DBR.
To better understand the mechanism of high-Q absorber, the absorption spectral curves for these modes are plotted as a function of the distance (hs) between graphene and DBR. As shown in Fig. 4, with the increase of hs, the linewidth of the resonances (λ2, λ3 and λ4) disappears and the Q factor increases quickly. Moreover, the Q curves diverge, which manifests the formation of BICs. Interestingly, with the increase of hs, the decline rate of Q-factor is slowed down after the system passed BIC point [Figs. 4(d)–4(g)]. This is owing to the loss rate reduced by the increase of hs [29,30], thus affecting the decline of Q-factor. As shown in Fig. 4(f), although the absorption rate is not high enough, the Q-factor of λ3 reaches 2×105, showing that BICs make a huge increase in the Q-factor of the system. It is clear that the Q-factors become infinite at the absorption peaks near the BICs point, which demonstrate the effectively suppress of the external leakage loss rate of this system. Meanwhile, the increased distance between graphene and the resonator weakens the electromagnetic field distribution around graphene, resulting in the inhibition of the intrinsic absorption loss rate of the system. It can be emphasized that, this system effectively suppress external leakage loss rate and intrinsic absorption loss rate simultaneously.
Fig. 4. Absorption responses of the absorber under different hs for (a) λ2, (b) λ3, (c) λ4. BICs are highlighted by white circles. Due to the ultra-narrow bandwidths of absorption peaks, the color bar ranges from 0 to 0.2 is used to better display absorption characteristics. (d-g) Q-factor as a function of hs for λ2, λ3 and λ4.
From CMT theory, the FWHM of absorption peaks can be obtained by Eq. (5):
where $\delta = 1/{\tau _{rad}}$ and $\gamma = 1/{\tau _{abs}}$ are described as intrinsic absorption loss rate and external leakage loss rate. Combined with electric field distribution diagram and the formation of BICs, the cause of ultra-high Q absorption can be explored. The incident light is strictly limited within DBR, resulting in a very low external leakage loss rate. Meanwhile, the electromagnetic field around graphene is relatively small, leading to low absorption loss rate. From Eq. (7), the combination of $\delta$ and $\gamma$ results in a very narrow bandwidth of the absorption peak, and causes the ultra-high Q graphene absorption.Figure 5 shows the absorption under different geometrical parameters, except as indicated, the geometric parameters are fixed to the default values. As shown in Fig. 5(a), an increase of 5 nm in the nanowires radius leads to 15.5 nm redshift for the absorption peak (λ4). The high absorption and narrowband feature for these modes can be maintained during the red-shift process when the radius of the nanowire is increased. In particular, as shown in Fig. 5(a), the average Q-factor of λ4 is 90 783 with the maximum of 98 278 and the minimum of 87 792, which shows a high stability during the tuning of nanowire's radius. For the high Q mode, the electric field is mainly oscillating in DBR, which is attributed to the periodic modulation of the refractive index. Meanwhile, the weak electromagnetic field around nanowires also indicates the tiny effect of nanowires radius on Q-factor. Figure 5(b) demonstrates that an increase in the distance between adjacent nanowires leads to redshift for the absorption peaks (λ2-λ4). Compared with it, the other two peaks (λ1, λ5) almost unchanged. These result demonstrate that the difference between the two absorption modes (GMR of gratings and GMR of DBR). The spectral positon of ultra-high Q absorption peaks is sensitive to the structure parameters of the grating, showing tunable wavelength selection absorption prosperity.
Fig. 5. (a) Absorption responses for the absorber under different cylindrical radius. (b) Absorption responses for the absorber under different spacing between adjacent nanowires.
Furthermore, the absorption properties are investigated under a slight oblique incident light. From Fig. 6(a), it is clearly observed that λ1 and λ5, which mainly originate from GMR in nanowires, remain unchanged at oblique incidence. On the other hand, λ2, λ3 and λ4 exhibit frequency splitting and a substantial shift of resonance as the increase of angle. When light is incident on the periodic array of nanowires, the momentum-matching condition between the resonant modes and inplane wavevectors of the incident light can be described by Bragg’s coupling equation [46–48]:
where K0 is the wavevetor of the incident light with an incident angle θ, Gx and Gz are the Bragg vectors, i and j are integers indicating the orders of the scattering event. In our case, Gz is ignored based on the infinite range in the z direction. According to Eq. (8), the resonant frequency scattered by ${\pm} {G_x}$ occurs for light at oblique incidence, which has caused one branch redshift and the other blueshift. As shown in Fig. 6(e), in the range of incidence angle is from 0° to 2°, these peaks position shows a good linear variation. For example, the position of λ4a can be defined as:${\lambda _{4a}} ={-} 14.8\theta + 1606.4$. This also provides a way to quantitatively tune the absorption spectrum.Fig. 6. (a) Absorption spectrum for the absorber as a function of incident angle. The radius of nanowires is 370 nm. Due to the ultra-narrow bandwidths of absorption peaks, the color bar ranges from 0 to 0.2 is used to better display absorption characteristics. (b) Absorption spectrum for the absorber with the angle of incidence to be 1°. Q-factor as a function of incident angle for (c) λBIC1, (d) λBIC2. (e) The peaks position as a function of incident angle.
As shown in Fig. 6(b), there are eight absorption peaks that exceed 80%, demonstrating a remarkable absorption property with multiple resonant absorption modes under oblique incidence. More importantly, the Q value of λ4a is as high as 106 106, showing a remarkably enhanced Q value in comparison with that under normal incidence. Interestingly, two modes emerged suddenly (λBIC1 and λBIC2), suggesting the existence of a new mechanism in this system. The Q-factor of λBIC1 and λBIC2 are shown in Figs. 6(c), 6(d). Both of them diverge at the Γ point, which manifests the formation of symmetry-protected BICs [34,35]. Symmetry-protected BIC appears at the Γ point under normal incidence due to the symmetry incompatibility with the outgoing field [49–51]. More importantly, without the need to make any changes to the structure parameters, the novel multispectral light absorption is emerged on this platform by tuning the angle of incidence. To evaluate the performance of the proposed graphene-based absorber, the spectral properties supported by other similar structures are listed in the Table 1. It is observed that this system simultaneously exhibits two main advantages including the multiple resonances and the remarkable high-Q factors. This confirms that the absorption mechanism is superior to others in graphene related high-Q spectral absorption, which therefore would provide an impressive approach to achieve high-Q absorption for 2D-materials.
Table 1. Comparison of proposed absorber with similar plans.
3.2. High performance switch manipulation
Next, we investigate the modulation of the absorption via tuning the chemical potential of the graphene. As shown in Fig. 7(a), the spectral absorption curves show noticeable changes when the chemical potential Ef is varied from 0.35 eV to 0.60 eV. All the absorption peaks disappeare when Ef is 0.60 eV. To gain insights into the effect of absorption regulation mechanism of graphene, the real and imaginary parts of the surface conductivity are exhibited in Figs. 7(c), 7(d). The real part of the surface conductivity, which represents the intrinsic loss of graphene, is gradually approaching zero as chemical potential increase. Therefore, by increasing chemical potential Ef, graphene can be transformed from lossy material to lossless material. When Ef is equal to 0.6 eV, the system can be considered as a total reflector due to the absence of lossy material. We further carry out the investigation of modulation depth, which is defined as $|{A - {A_0}} |/{A_0}$ (${A_0}$ is the absorption at Ef = 0.35 eV, and ${A_{}}$ is the corresponding absorption for the other values of Ef). The modulation depths of λ3 and λ4 are plotted in Fig. 7(b). It is observed that the modulation depth varies from almost zero to nearly 100% with a slight change in chemical potential Ef (from 0.35 eV to 0.55 eV), which demonstrate excellent modulation property [14–24].
Fig. 7. (a) Absorption responses for the absorber under different chemical potential of graphene. (b) Modulation depth of λ3 and λ4 under different chemical potential. Real (c) and imaginary (d) parts of the of the complex surface conductivity at different chemical potential.
As shown in Fig. 8(a), when the refractive index of A is varied from 1.440 to 1.454 in step of 0.002, obvious red-shifts for absorption peaks are observed. With increasing na, almost linear red-shifts for absorption peaks are observed. For instance, at λ4, the peak position can be defined as ${\lambda _4} = 915n + 288$. The sensitivity S, as the definition of $S = \delta \lambda /\delta n$, is up to 810 nm/RIU and 915 nm/RIU for λ3 and λ4 respectively. The FOM of λ3 and λ4 achieve 5400 and 50833 respectively, indicating the significant spectral shift to the refractive index change. These properties show excellent spectral response to the refractive index, which provide us with inspiration for designing all-optical switches.
Fig. 8. (a) Absorption responses for the absorber under different na. (b) Absorption peaks positions as a function of na. Difference intensity spectrum (c) and contrast radio (d) of the structure with na of 1.4405 contrast to the case with na = 1.4400.
Metamaterials make it possible to controlling light propagation by structuring the constituents of composite materials [52–54]. Moreover, controlling light propagation with light is essential in all-optical signal processing for applications in optical communications [55–57]. All-optical devices are based on various types of optical nonlinearities and have been proposed and demonstrated under numerous designs. For example, Hu et al. reported low-power all-optical switching based on a composite material made of organic chromophore and polymer, where the nonlinear refractive index was only with the order of 10−7 cm2/W. The intensity of the pump light was 110 kW cm−2 [58]. Zhang et al. constructed multi-component nanocomposite with large and ultrafast optical nonlinearity based on 1-(3-methoxycarbonyl)- propyl-1-phenyl-(6,6)C61 (PCBM) and silver nanoparticles. The nonlinear refractive index was only of the order of 10−7 cm2/W, and the intensity of the pump light was 70 KW/cm2 [59]. Meanwhile, Fig. 8(c) presents the difference intensity spectrum of the system after a tuning of na from 1.4400 to 1.4405. Spectral relative intensity change can be achieved from 0 to 100% by ultra-small increasing of na. 10log10(A1.4400/A1.4405) is defined as the absorption contrast ratio. As shown in Fig. 8(d), the absorption contrast ratio at λ4 is 31 dB, suggesting an ultra-high switching efficiency. Excellent nonlinear medium and spectral variation are the key factors to realize low-power optical switching. In this work, these impressive spectral properties show great improvement to the others for applications in all-optical switches [58–61]. Moreover, in the study of all-optical switch for this high-Q absorber, dielectric A is employed as the Kerr nonlinear medium, and we choose its Kerr coefficient n2 = 10−7 cm2/W. The refractive index of nonlinear dielectric can be defined as $n = {n_0} + {n_2}I$ (I is the intensity of the pump light). As shown in the insets of Fig. 8(a), the refractive index of nonlinear dielectric can be modulated by adding pump light. The refractive index is changed 5×10−4 with increasing I to 5 kW cm−2, obvious spectral relative intensity change is observed as shown in Fig. 8(c). More important, the intensity of the pump light was only 5 kW cm−2, which is at least one order of magnitude less than that of previous reports [58–63].
In general, the absorption performance of the proposed graphene absorber can be tuned by gate voltage and pump light, respectively. Spectral relative intensity change from 0 to 100% can be achieved by tuning the chemical potential with the value of 0.2 eV or adding pump light for the nonlinear medium with the intensity of 5 kW cm−2. Remarkable optical switch manipulation is achieved by both the electric and optical tuning, which will hold potential in the design of graphene-based optical switch.
4. Conclusion
In summary, we have proposed a feasible approach to significantly improve the performance of ultra-high quality graphene perfect absorbers. A record-breaking Q-factor (up to 105) is obtained, delivering a significant performance leap for high Q graphene absorber. The BICs and GMRs of DBR are the main reasons for the ultra-high quality absorption, which pave a novel method to achieve ultra-high Q absorption for 2D materials. Furthermore, we demonstrate the realization of high-performance of switch manipulations via the electric method by tuning chemical potential of the graphene with the scale of 0.2 eV or via the optical process by adding the pump light with the ultra-low intensity of 5 kW cm−2 to the nonlinear medium. These findings will hold potential applications in the design of graphene-based devices, including all-optical switch, optoelectronic modulator and detector, ultra-narrowband selective filter, etc.
Funding
National Natural Science Foundation of China (62065007, 11804134, 11664015, 51761015, 11974188); Natural Science Foundation of Jiangxi Province (2018ACB21005, 20182BCB22002, 20181BAB201015, 20202BBEL53036, 20202BAB201009).
Disclosures
The authors declare that they have no competing interests.
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