Abrupt phase change in graphene-gold spr-based biosensor

The performance of surface plasmon resonance (SPR) sensors can be different depending on which characteristic of the SPR sensor the amplitude or the phase is monitored. The phase sensitivity strongly depends on the geometry and the optical properties of the system. The existence of sharp changes in the phase spectrum variations is found as the thickness of SPR-supporting gold (dg) varies around a critical thickness (dc). In addition, the simulation results indicate that the phase sensitivity is divided into two regions so that phase sensitivity Sφ for region d g ≤ d c is greater than region dg > dc. It is demonstrated in condition of d g ≤ d c the phase sensitivity has a strong jump when the sensing medium refractive index lies within a certain interval, while the amplitude sensitivity has a monotonic shape. The phase analysis from another aspect exhibits that the phase maximum difference Δφmax towards the blank sample is sensitive to refractive index in a continuous interval. As a result, the phase detection interval is tunable by varying the gold thickness, which potentially is important for medical, biology and chemistry applications.


Introduction
Sensors based on SPR are powerful tools for real-time supervising of interactions in medicine, biology and chemistry analysis due to the enhancement of the surface sensitivity and accurate detection of the sensing medium molecules' reaction [1][2][3][4]. Surface plasmons (SPs) are collective oscillations of free electrons at the metal-dielectric interface [5]. Coupling of the incident light with SPs leads to the formation of a Surface plasmon polariton (SPPs), which propagate along the metal-dielectric interface and decays exponentially in a direction perpendicular to the interface [6,7].
Because of practical nature properties of gold metal such as stable, superior performance and good resistance to oxidation and corrosion is chosen as an active metal in the conventional SPR [8]. The most advantages of the use graphene layers can be pointed to large surface to volume ratio and the enhancement of biomolecular absorbance compared with gold, so a number of graphene layers are generated onto an optimized gold thin film to enhance the sensitivity of the SPR sensor [9][10][11]. Titanium is used as a supplementary adhesive layer to ensure strong contact between gold thin film and substrate glass [12,13].
In these sensors, the detection methods are performed based on the scanning of the wavelength and the angle of incident light. Under a resonance angle or wavelength of light incidence, the photon energy is transferred to a plasmon propagating over the interface of metal-dielectric and the intensity of reflected light reaches to minimum value [14][15][16]. Such amplitude-sensitive are useful for studies of many interactions, including relatively large molecules such as protein and DNA. Due to a physical limit in the detection of low molecular weight analytes by different sensor implementation with the wavelength or angular spectrum, the phase properties of light reflected under SPR reveal an important role in the detection [1,17].
In the study of the phase detection, the existence of a sharp phase jump under the some characterization of sensor such as the certain thickness and dielectric function of SPR-supporting metal [18][19][20]. The maximum value of phase jump and its curve strongly is depended on the refractive index (RI) of sensing medium [21,22]. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
In this study, we consider a Kretschmann configuration, including prism, titanium, gold, graphene and sensing medium. Owing to that the phase variations strongly affiliates to the shape, geometry and optical properties of the structure, any slight change in them leads to the variation in phase spectrum. It is presented that by varying the gold thickness (d g ) around the critical thickness (d c ), a sharp change occurs in the phase spectrum. According to the phase jump evens at the matched angle (q SPR ), it is further demonstrated that the maximum variation of phase with respect to the sensing medium refractive index (phase sensitivity,

Characterization of sensor in terms of phase and amplitude
The primary structure of the proposed SPR sensor as shown in figure 1 is consisted from five-layer prism, titanium, gold, graphene and sensing medium. Each medium is subscribed by a thickness d k , permittivity ò k and permeability μ k . The total reflectivity of the system is calculated based on Fresnel theory which for mulitilayer structure can be developed using transfer matrix method [27]. According to this method, the reflectance coefficient for p-polarized light can be given as follows: 21 22 here, N is the number of layers, β k and q k are the optically admittance and the phase factor, respectively that are characterized with the refractive index of prism n 1 and incident light angle θ in , are represented as: The total reflectivity for p-polarized incident light is given by: where, q 1 and q N are the phase factor of prism and sensing medium, respectively. By converting the equation (3) to polar form, the phase sensitivity that is defined as the ratio between the phase change and the refractive index variation of the Nth layer (sensing medium n s ) can be obtained as below: Because of the SPR highly sensitive to the variation of intensity amplitude, angle and spectrum width, we use the sensitivity S IAW that have introduced in our previous work [15] as following: here, S A , S I andD n denote the angular sensitivity, the intensity-amplitude sensitivity and the spectrum width, respectively. As mentioned in reference [28] the phase information improves detection with respect to the intensity one. In addition, it is found that with regard to refractive index change, the variations of the S j has a complex behavior compared to the S IAW ones. One can see that the S j shows an abrupt change towards n s , which strongly depends on the gold thickness. Investigation of phase detection from another aspect is clearly determined the maximum phase change Δj max is sensitive to a continuous interval of n s , whereas the amplitude sensitivity with respect to n s changes smoothly. Profiting from the abrupt change in S j or continuous change in Δj max , one can achieve a much better sensitivity.

Results and discussion
To compare the amplitude and phase sensitivities, we consider a graphene-gold SPR-based configuration with the fixed thicknesses of titanium and graphene 3 nm and 1.7 nm, respectively [15]. To investigate the effect of gold thickness on phase spectrum and its amplitude sensitivity, the thickness of gold is swiped from 30nm to 55 nm with step size of 5 nm. In order to see the typical phase response of the system, the refractive index in the sensing layer (n s ) varies from 1 RIU to 1.633 RIU at an optimized wavelength of 850 nm that can deliver the best sensitivity performance.  In order to detect the amplitude sensitivity and its comparison with phase sensitivity, the reflection spectrum curves of SPR sensor versus of θ in for various gold thickness extracted, as an example in figure 2(a), the reflection spectrum of 40 nm gold thickness has been plotted. As shown in figure 2(b), the logarithm of amplitude sensitivity in terms of n s delivers a same behavior for all the gold thicknesses. It is clearly seen from this figure that with increasing of the n s , first the sensitivity value decreases monotonically and then increases.
The optical phase detection of SPR sensor has been investigated experimentally and theoretically [29][30][31]. Their results show a strong dependence on sensor film thicknesses. According to their results the phase spectrum shows a same behavior for all metal thicknesses and sensing medium refractive indices. More accurate investigation of the phase detection indicates a different behavior with respect to previous works. Our simulation results show at a critical thickness of gold film, an abrupt phase change occurs in the phase spectrum. This novelty is high worthwhile in phase detection of SPR sensors. Figure 3(a) shows a typical phase response plot with regard to refractive index change for the d g =40 nm. As is observed for the sensing medium refractive indices in the interval n sA =1.370 to n sB =1.405 the evolution of the phase change with regard to varying n s is clearly identified. According to figure 3(b), the abrupt phase change causes the value of phase sensitivity at n sA and n sB strongly enhances. The appearance of local sharp peaks in S j promises to provide a more sensitive transduction to refractive index changes (red curve in figure 3(b)), in while the sensor performance is insensitive to amplitude measurement S IAW in these points (blue curve in figure 3(b)).
In order to examine the effect of gold thickness on sensor performance, we consider two regions d g >d c and  d d g c that the critical thickness (d c ) is 40 nm. In the case of  d d g c , the behavior of d g =35 nm is the same as the thickness of 40 nm but only the peak values of S j are shifted to n sA =1.145 and n sB =1.440, respectively. Further reduce the thickness to 30 nm explicitly indicates a different functional compared to d g =40 nm. As shown in figure 4(a), the behavior of phase spectrum is the same as the shape of step function (SSF) for all n s and the phase sensitivity has only a single sharp peak at n sC =1.450 (see figure 4(b)). As shown in figure 5(a), in condition of d g >d c the phase spectrum curves are modified away from SSF. Owning to figure 5(b) there is no sharp peak in S j curve, which as a result the phase sensitivity reduces towards previous case.  In the experimental measurements, before injection liquid samples inside the chamber the phase changes of the chamber must be determined. Usually for the study of evolution of phase change, the phase sensitivity of the system is calculated via the conventional relationship in equation (4). In this equation the sensitivity is found through a maximum value of phase difference between two consecutive phase spectrum. To better understand from the phase detection we introduce a different approach to phase interpretation. In this approach the chamber phase spectrum is used as the blank spectrum and the phase changes are measured with respect to it as follow: here, n 0 is the refractive index of blank sample which the air is considered as blank. In figure 6, the Δj max in terms of the n s for various gold thickness has been extracted. For  d d g c and in the interval of   n n n sA s sB , the Δj max has a maximum with certain detection width, while for d g >d c has a uniform behavior. The detection width of SPR sensor can vary with regard to the gold thickness.
The S j method the detection in the limited between n sA and n sB is determined by two sharp peaks, whereas the detection with later technique (Δj max ) occurs in a continuous interval. Therefore, by controlling the gold thickness and using two methods, S j and Δj max , the detection of experimental samples can be determined with better accuracy.

Conclusion
Phase measurements of the SPR sensors have been well modified and proven to provide highly sensitive to the geometry and the optical properties of the sensor structure. The phase sensitivity (S j ) based on phase difference between two adjacent phase spectrum shows a better sensitivity in the region of  d 40 nm g . It is found that for d g =30 nm a single peak appears at n sC =1.450. For d g =35 nm two peaks occur at n sA =1.145 and n sB =1.440, the peaks shift to n sA =1.370 and n sB =1.405 in d g =40 nm. In the region of d g >40 nm the S j does not exhibit any sharp peak. The maximum phase difference (Δj max ) with respect to the blank sample (n 0 ) occurs in a continuous detection width of n s . For d g =30 nm, the Δj max has continuously maximized at interval between n s =1.065 and n s =1.633. The detection width is limited to n sA =1.145 and n sB =1.440 in 35 nm gold thickness. The narrower detection width evens for critical gold thickness of 40 nm in the interval n sA =1.370 to n sB =1.405. Overall, by controlling the gold thickness and using two methods, S j and Δj max , the detection of experimental samples can be determined with high accuracy which is applicable in medical, biology and chemistry.

ORCID iDs
Jafar Mostafavi Amjad https:/ /orcid.org/0000-0002-0147-1299 Ramin Mohammadkhani https:/ /orcid.org/0000-0002-8542-1183 Figure 6. The phase measurement from the second point of view in which the maximum phase difference has been extracted for various d g . The Δj max exhibits different behavior by varying d g so that for  d d g c a strong detection width is yielded which adjustable with the gold thickness.