Tunable absorption characteristics in multilayered structures with graphene for biosensing

Graphene derivatives, possessing strong Raman scattering and near-infrared absorption intrin-sically, have boosted many exciting biosensing applications. The tunability of the absorption characteristics, however, remains largely unexplored to date. Here, we proposed a multilayer con¯guration constructed by a graphene monolayer sandwiched between a bu®er layer and one-dimensional photonic crystal (1DPC) to achieve tunable graphene absorption under total internal re°ection (TIR). It is interesting that the unique optical properties of the bu®er-graphene-1DPC multilayer structure, the electromagnetically induced transparency (EIT)-like and Fano-like absorptions, can be achieved with pre-determined resonance wavelengths, and furtherly be tuned by adjusting either the structure parameters or the incident angle of light. Theoretical analyses demonstrate that such EIT- and Fano-like absorptions are due to the interference of light in the multilayer structure and the complete transmission produced by the evanescent wave resonance in the con¯guration. The enhanced absorptions and the huge electrical ¯eld enhancement e®ect exhibit potentials for broad applications, such as photoacoustic imaging and Raman imaging.


Introduction
Two-dimensional materials have been intensely investigated for their wide applications in biomedicine. 1,2 Speci¯cally, the unique properties of graphene have enabled applications in numerous technological areas. As an example, the fast and broadband optical absorption features of graphene have bene¯ted many novel optoelectronic and biosensing applications. 3,4 The desired properties of graphene in these applications mainly include three aspects. First, strong optical absorption from the graphene layers is sought for as it is directly related to the performance of imaging camera, 5 coherent absorption, 6 photoacoustic imaging, 7 and photothermal therapy applications. 8,9 To overcome the low absorption challenge of single-layer graphene, many approaches have recently been proposed, such as one-dimensional photonic crystal (1DPC), 10 microcavity with mirrors, 11 the gratings 12 and the graphene ribbon array. 13 Second, di®erent absorption line shapes are desired. In the above-mentioned structures, light recycle of photon interference at a resonant wavelength is the basic principle to increase the absorption, causing all absorbing responses to have Lorentzian line shapes. In fact, the phenomenon of electromagnetically induced transparency (EIT) found in quantum optical systems has been realized in classical optical structures such as microtoroid, 14 metamaterials, 15 and terahertz waveguide 16 for applications of sensor,¯lter, slow light, and logic processing. Also, all optical analog EIT has been experimentally achieved by 1D coupled photonic crystal microcavities. 17 On the other hand, Fano resonance with asymmetric line shape is widely investigated in plasmonic systems for its high sensitivity and¯gure of merit. 18 Third, tunable optical absorption in the near-infrared regime and multi-wavelength operation is desired in graphene-based devices 19,20 ; the tunability and multi-wavelength operation allow good match with the laser sources of di®erent wavelengths, while the resultant electrical¯eld enhancement at desired position can be applied for surface-enhanced Raman scattering (SERS)-based biosensing. 21 In con¯gurations reported earlier, 22 however, it is challenging to tune the absorption properties after the structure is fabricated.
In this work, we propose a con¯guration of a graphene monolayer sandwiched between a bu®er layer and 1DPC multilayer. The resultant tunable multichannel absorption property is investigated under the total internal re°ection (TIR) condition. Meanwhile, by utilizing the evanescent wave resonance in the 1DPC, the EIT-like and Fano-like absorption is implemented at desired resonance wavelengths due to the interference of light in the proposed con¯guration. It is shown that the absorption characteristics of the con¯guration, including the absorption peak positions, widths, intensities, number of the peaks, and the interval between adjacent peaks, are all adjustable without engineering the graphene monolayer. Such a property may¯nd wide use to improve the performances of graphene-based devices and furtherly extend their applications in biosensing.

Structure Model and Principle
Similar to the EIT phenomenon in an atomic system, in our con¯guration two \atoms" should be constructed, including one broadband \Atom 1" (bright state) being absorbed and one narrowband \Atom 2" (dark state) being transmitted. The EITlike and Fano-like absorption then can be obtained by detuning the central wavelength of the narrowband transmission peak from that of the broadband absorption. The characteristics of such two-atom con¯guration, i.e., the bu®er-graphene-1DPC multilayer structure, are discussed herein with a schematic shown in Fig. 1. In this system, \Atom 1" realizing the broadband absorption is constructed by designing a multilayer structure producing light interference. The complete absorption is achieved in such a multilayer structure that contains a layer of graphene as the absorption material. On the other hand, the transmission and the re°ection of the whole structure are separately engineered to be zero based on the TIR and destructive interference experienced by the re°ected light at all layer interfaces, 23 and the position of the broadband absorption peak can be optimized with the help of the transfer matrix method. 24 As for \Atom 2", the narrowband transmission is enabled by a periodic structure like the 1DPC that produces the evanescent wave resonance. A perfect narrowband transmission is obtained when the evanescent wave resonance is formed in the low-index dielectric layers under the TIR. In an in¯nite periodic dielectric multilayers (BC) N alternately composed by a layer of high refractive index (B) and a layer of low refractive index (C), the propagation of light satis¯es the following equation based on the Bloch theory 25 : where z is the Bloch vector normal to the layer interfaces of periodic dielectric multilayers (BC) N , k zb ¼ k 0 n b cos( b ) and k zc ¼ k 0 n c cos( c ) are the z components of the wave vector in layers B and C, k 0 is the wave vector in air, n b and n c are the refractive indexes, b and c are the incident angles, d b and d c are the thickness of layer B and C, respectively. If the period of 1DPC is¯nite, the transmission peak number and z have the following relation 25 : for period number N, the values of z corresponding to the transmission peaks (light propagating from left to right) are just ðN À 1Þð=dÞ/N, Thus, when the material and structure parameters are determined, the position of perfect transmission peak can be solved through Eq. (1). The absorption characteristics of the onedimensional dielectric multilayers can be investigated based on the above-mentioned transfer matrix method. 24,25 The propagation of light in the one-dimensional multilayer structure with homogeneous materials can be expressed with the production of the matrices for each layer. The transmission matrix for jth layer can be written as where d j is the thickness, k zj ¼ k 0 n j cos( j ) is the z component of the wave vector, n j is the refractive index, j is the incident angle, q j ¼ ffiffiffiffiffiffiffiffiffiffiffi " j = j p cos j for TE wave and q j ¼ ffiffiffiffiffiffiffiffiffiffiffi j =" j p cos j for TM wave, " j is the permittivity, and j ¼ 1 is the permeability of the jth layer. Matrix M 0 for the whole structure equals to the successive production of the matrices of each layer. The transmission and re°ection coefcients of the whole structure can be respectively calculated from M 0 as: where m 11 , m 12 , m 21 , and m 22 are the elements of M 0 , q in and q out are the admittance coe±cients of the input and output materials, respectively. The transmission and re°ection then can be calculated

Results and Discussion
To illustrate the validity of the above principle, a typical bu®er-graphene-1DPC multilayer structure EG(BC) 2 is presented for achieving the EIT-like and Fano-like absorption performance. The two half-sphere prisms are used to couple light based on a model proposed by Kretschmann. 26 The advantage of using such a scheme is that the polarization response of the con¯guration can also be investigated if needed. It should be pointed out that prisms of other shapes, such as triangular 27 and half-cylinder, 28 can also be used. The structure parameters are set as follows: the thickness of the G layer d g ¼ 0:34 nm and its optical refractive index n g ¼ 3 þ iC 1 /3, where C 1 ¼ 5:446 m À1 , 3 the refractive indexes of B and C layers are respectively n b ¼ 3:48 and n c ¼ 1, and the bu®er layer E is a low-index layer with a refractive index n e ¼ 1.
Speci¯cally, the optimal thicknesses of B, C and E layers in the structure EG(BC) 2 are separately d b ¼ 269 nm, d c ¼ 500 nm, and d e ¼ 220 nm, which are selected to get the perfect absorption of the structure by making the transmission and re°ection to be zero under TIR in mid-infrared electromagnetic region. The size of the con¯guration in the transverse directions theoretically can be in¯nite. 29 For practical fabrication, according to the reported works, one-dimensional multilayered con¯guration of centimeter long in the transverse directions can work for investigations within an area $ 100 Â 100 m 2 . 30,31 In addition, the graphene monolayer with a practical area of $ 0:5 Â 0:5 mm 2 has been experimentally reported. 32 Figure 2 shows the absorption (A), re°ection (R), and transmission (T ) of the two composited \atoms" (EGBC and BCBC) as well as the whole structure EG(BC) 2 with incident angle ¼ 60 under TE polarization. From Fig. 2(a), a highly enhanced broadband absorption is observed in the structure EGBC comparing with the 2.3% absorption of graphene monolayer. In Fig. 2(b), the perfect transmission is achieved when the evanescent resonance is formed in the BCBC structure; both absorption and re°ection are zero at the resonant wavelength ¼ 1439 nm. And, as shown in Fig. 2(c), the EIT-like absorption is achieved by EG(BC) 2 structure at the dark state wavelength ¼ 1439 nm. This con¯rms that the formation mechanism of the EIT-like absorption is the combination of the highly enhanced absorption caused by the light interference in the EGBC multilayer and the narrowband perfect transmission caused by the evanescent wave resonance in the 1DPC. This principle to get the EIT-like absorption is di®erent from those reported in the references. 14-17 Moreover, the position and the width of the absorption tip (dark state) can be adjusted by altering the thickness of layer B and C, respectively.
As displayed in Fig. 3, the positions of the absorption tips occur redshift as increasing d b (Fig. 3  (a)), and the widths of the absorption tips decrease as increasing the thickness d c (Fig. 3(b)). In addition, the number of the absorption tips and the interval between adjacent tips can also be changed by varying the periodic number N and the thickness of the C layer in the middle unit of the 1DPC (denoted as defect layer F), respectively, as shown in Fig. 4. From Fig. 4(a), there are N À 1 absorption tips for 1DPC with N periods. From Fig. 4(b), the interval between the adjacent absorption tips increases with reduced thickness of the defect layer d f . And the Fano-like absorption is gradually obtained (for d f smaller than about 400 nm) during the increase of the wavelength detuning between the two \atoms". Moreover, the in°uence of di®erent thicknesses d f of the defect layer F on the spectrum response has also been checked in the structure EG(BC) m BF(BC) m (the total period N ¼ 2m þ 1, m ¼ 2, 3). It is noted that the case for m ¼ 1 is given in Fig. 4(b). It is found that that the number of the tips is 2m when the thickness of F is 500 nm. With increased d f , the number of tips gradually changes to m main sessions. The interval between the main sessions is de¯ned as the \external interval", and the interval between the two tips within each main session is referred to as the \internal interval". Therefore, the external intervals decrease and the internal intervals increase with reduced d f . As shown in Fig. 5, the absorption of the structure EG(BC) 2 can be changed by adjusting either the thickness of the bu® layer E or the incident angle of light. From Fig. 5(a), an optimized thickness d e ¼ 220 nm is found to obtain the complete absorption of \atom 1". The perfect transmission caused by the evanescent wave resonance always exists in the structure and is almost independent of the thickness d e . From Fig. 5(b), a tradeo® is found between the maximum value of the absorption and the width of the absorption tip. That is, with increased incident angle, the absorption decreases linearly but the tip becomes narrower. The angularsensitive response of the proposed structure is a signi¯cant advantage for designing a good performance directional¯lter and sensor. For example, the angular-sensitive response is calculated to be $ 70 nm/degree, i.e., $ 4010 nm/radian, for wavelength from 1100 nm to 1800 nm, with an incident angle from 55 to 65 .
Moreover, the con¯guration can work in both near-infrared and visible regimes. By properly changing the materials and the geometry parameters of the con¯guration, the operation wavelength can be transited. At the same time, as demonstrated above, the structure parameters can be selected to make the central wavelength of \atom 2" a little far from that of \atom 1", which will result in a Fano-like absorption. Figure 6(a) shows single Fano-like absorption at visible region, and the number of the absorption peaks can be changed by varying the period number N of structure BC. Same as the case of EIT, there are N À 1 peaks for period number N. Figure 6(b) shows the absorption responses of structure EG(BC) 6 are linear and havē ve ultra-narrow Fano-like absorption peaks. The full width at half maximum Á is about 9 pm for the middle peak at ¼ 670:54 nm, which corresponds to the quality factor of 7:45 Â 10 4 calculated from /Á. It is very useful for designing of highsensitive sensor and ultra-narrowband¯lter. Moreover, for the Fano-like absorption, the electrical eld distribution in the structure is also calculated to investigate the in°uence of the wavelength detuning of \atom 2" from that of \atom 1" . Figures 6(c) and 6(d) show the electrical¯eld distributions for the absorption peaks in Fig. 6(a) with Lorentzian and Fano-like shapes, respectively. It is observed that the con¯nement area of electrical¯eld has obviously been changed from the cavity close to the graphene layer to a more distant one. This con¯rms that the EIT-like or the Fano-like absorption peak is formed through the interference between the two cavities of \atom 1" and \atom 2". The huge electrical¯eld enhancement with a magnitude of over 1:4 Â 10 4 means the SERS enhancement factor beyond of 3:8 Â 10 16 , which can be potentially applied for single-molecule detection. 33 Furthermore, when the nonlinear property of the material is considered, the bistable absorption can be obtained. 34 Figures 7(a) and 7(b) show the nonlinear performances in the cases of EIT-like and Fano-like absorption, respectively. Obviously, the bistable behaviors are observed for both the absorption and re°ection curves. As shown in Fig. 7 (a), with a set of suitable structure parameters, the absorption dip of the EIT-like absorption occurs at ¼ 1118 nm. With increased input light intensity, a nearly zero ($ 10 À4 ) absorption arrives at threshold about 10 kW/cm 2 . Whereas, in Fig. 7(b), the complete absorption arrives at ¼ 670:53 nm with a threshold of 0.8 MW/cm 2 . The much low bistable thresholds show their great potential advantages for the design of all optical switching and logical circuits.
In principle, the EIT and the Fano-like absorption also can be theoretically explained by the coupled mode model. For the structure of EG-(BC) Nþ1 , the N individual \atoms" are characterized by the energy amplitudes of the cavities which are denoted by the energy amplitude array a¼ [a 1 ,a 2 , . . ., a N À 1 , a N ] T , where a q (q ¼ 1,. . ., N) represents the energy amplitude in the q th cavity. We assume that the input power is P in , then the input array s ¼ [Àj i P 1=2 i , 0, . . ., 0, 0] T . The time evolution of the energy amplitude a(t) has the following form 35 : where i represents the normalized coupling coe±cient between the incident layer and the \bright" cavity; z (z ¼ 1, . . ., N À 1) are those between the adjacent cavities, respectively; Á! q ¼ 2Áf q is the angular frequency detuning from the resonance angular frequency ! q of the qth cavity. The coupling matrix M is expressed as: where 2 L;q /2 ¼ 1/ L;q is the decay rate came from the intrinsic loss, and 2 i /2 ¼ 1/ i is the decay rate coupled to the incident layer. The absorption amplitude of the system is given by: where the normalized detuning of angular frequency q ¼ Á! q /! q; Q L;q ¼ ! q L;q /2, and Q i ¼ ! q i /2 are the quality factors related to the intrinsic loss and the incident coupling loss, Q c;q ¼ ! q c;q /2 represents the quality factors of the cavity related to the coupling loss for the qth cavity, respectively. By using Eq. (7), for a typical system with three coupled cavities, Fig. 8 exhibits an EIT-like absorption with two tips, agreeing well with the result in Fig. 4(a). It demonstrates that this model can also be used for inverse design. That is, for a given line shape calculated by the transfer matrix method, the coupling coe±cients and the detuning wavelength of the individual cavity in a coupled resonator structure can be¯tted and extracted by the coupled mode model. This builds a link between the desired spectral property and the geometric parameters for the design of the device with the characteristic of EIT-like absorption. This can be potentially applied for absorption-based imaging as targets with varied refractive index response can be located in the bu®er or B sensing layer.
It should be clari¯ed at this point that the captioned manuscript focuses on numerical simulation as the¯rst step of the project to make sure of the feasibility and optimum design. That said, experiments have been planned and under preparation. In the following, the fabrication of the structure is brie°y discussed herein. For multiple graphene layers, researches have reported the realization of enhanced absorption between two dielectric materials. 23 For monolayers, there are studies positioning the graphene monolayer in a microcavity to form a photodetector, 3,36 which may be used as reference in fabrication. Speci¯cally, when silicon and air materials are used (e.g., Figs. 1-5), the silicon-air¯lter can be fabricated using the method in Ref. 37. The graphene monolayer can also be fabricated through a suspended structure. 38 When other dielectric materials are used (e.g., Fig. 6), the multiple dielectric layers can be fabricated through plasma-enhanced chemical vapor deposition (PECVD) 3,39 or spin-coating. 32 Note that imperfections, such as twisted or folded regions, are inevitable during fabrication, which will reduce the performance of the spectrum response obtained in numerical simulation. That said, recent developments in the¯eld have allowed for fabrication of large-area continuous and uniform graphene monolayers. 40,41 For example, graphene monolayers of $ 3:5 Â 1:5 cm 2 have been achieved. 40 Lastly, but not the least, the following dielectric material parameters will be considered in fabrication: for the silicon-air con¯guration in near-infrared as shown in  Fig. 6(a). The nonlinear refractive index of layer C is n c2 ¼ 2:5 Â 10 À15 m 2 /W in both calculations. Fig. 8. Absorption of a system with three cavities. The simulation parameters are set as Q L;1 ¼ 5 Â 10 4 , Q L;2 ¼ 1 Â 10 8 , Q L;3 ¼ 1 Â 10 8 , Q i ¼ 2 Â 10 3 , and Q c;1 ¼ Q c;2 ¼ Q c;3 ¼ 2 Â 10 4 .
Figs. 1-5, silicon with n ¼ 3:48 will be used for prism and B layer (E, F, and C layers are air); 42 for the multiple dielectric layers in Fig. 6, SiO 2 (quartz) with n ¼ 1:55 will be used for B layer, but nanoporous SiO 2 with a low-refractive-index material n ¼ 1:23 [44] will be used for C layer; 43 for nonlinear application in Fig. 7, silicon with n ¼ 3:48 will be used for prism and B layer, and polydiacetylene 9-BCMU organic material with n ¼ 1:55 and high nonlinear coe±cient n c2 will be used for C layer. 45

Conclusions
In summary, to achieve tunable absorptions characteristics for biosensing, a bu®er-graphene-1DPC multilayer structure is proposed to obtain the EITlike and the Fano-like absorptions in the nearinfrared regime. The absorption property of the structure can be tuned by changing the geometric or physical parameters of the designed con¯guration and the incident angle of light. The tunable multichannel EIT-like and Fano-like absorptions may be applied for designing of various biosensing devices, such as sensor,¯lter, modulator, optical tagging, thermal detecting, optical switching and all-optical diode. [46][47][48] Moreover, the structure with EIT-like and Fano-like absorption in visible and near-infrared regimes can potentially be extended to infrared and even terahertz spectrum for more applications in biosensing.