Plasmonics https://doi.org/10.1007/s11468-019-00970-5 Sim-SPR: an Open-Source Surface Plasmon Resonance Simulator for Academic and Industrial Purposes Elton B. Costa1 · Eloise P. Rodrigues2 · Helder A. Pereira1 Received: 6 March 2019 / Accepted: 9 May 2019 © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract In this paper, an open-source simulation tool is proposed to evaluate the SPR effect considering a multilayer structure. The open-source simulator is called Sim-SPR and it follows the principles of software engineering. Furthermore, Sim-SPR is dedicated to analyze reflectance of prism-based SPR sensors using Otto’s configuration. It is important to emphasize that there is no available open-source simulation tool specifically built in this context in the literature. The Sim-SPR accuracy, efficiency, and reliability were analyzed by comparing our obtained results considering three different scenarios with two other simulation tools available in the literature, presenting minimal relative error. The results still include a sensitivity analysis of prism-based SPR sensors focusing on resonant angle. Keywords Biosensor · Open source · Otto’s configuration · Simulation tool · Surface plasmon resonance Introduction Surface plasmon resonance (SPR) is a physical effect in which the optical beam is reflected between a dielectric and a thin metal layer (noble metals), exciting a surface plasmon wave (SPW) at the other metal layer boundary [12]. For optical applications, SPR-based sensors become a leading technology due to diverse advantages, such as the following [7, 30]: (1) fast response; (2) small volume; and (3) high sensitivity to variations in the medium refractive index located close to metal thin film, for example. Elton B. Costa [email protected] Eloise P. Rodrigues [email protected] Helder A. Pereira [email protected] 1 Departamento de Engenharia Elétrica (DEE), Centro de Engenharia Elétrica e Informática (CEEI), Universidade Federal de Campina Grande (UFCG), Rua Aprı́gio Veloso, 882, Universitário, Campina Grande, Paraı́ba, 58429–900 Brazil 2 Programa de Pós-Graduação em Engenharia Elétrica (PPgEE), Centro de Engenharia Elétrica e Informática (CEEI), Universidade Federal de Campina Grande (UFCG), Rua Aprı́gio Veloso, 882, Universitário, Campina Grande, Paraı́ba, 58429–900 Brazil However, SPR-based sensors and instruments comprise a complex optical system design for practical uses. They have expensive optical components and materials besides of being necessary to take care in instrumental handling [23]. Therefore, simulation tools become an important apparatus before to construct SPR-based sensors and to optimize parameters aiming to reduce operational costs as well. There are a few simulation tools available in the literature that are used to analyze and to design SPR-based sensors, such as COMSOL Multiphysics [1] and Lumerical [2], for example, presenting themselves as robust simulation tools, but requiring expensive license costs and their source codes are unavailable for research improvements. In this paper, an open-source simulation tool is proposed to evaluate the SPR effect considering prism-based SPR sensors using Otto’s configuration based on a multilayer structure. The open-source simulator is called Sim-SPR1 and it is implemented in C++ language under the GNU Lesser General Public License, following the principles of software engineering. Furthermore, Sim-SPR is dedicated to analyze reflectance and sensitivity of prism-based SPR sensors, focusing on resonant angle. It is important to emphasize that there is no available open-source simulation tool specifically built in this context in the literature. Therefore, Sim-SPR becomes a pioneer open-source SPR simulator for academic and industrial purposes. Two simulation tools already consolidated and three different 1 For more information, interested readers are referred to https://github. com/eltonbrasil/SimSPR. Plasmonics Fig. 1 Two most popular metal-dielectric configurations to SPR optical excitation. a Otto [24]. b Kretschmann [18] Light source p-polarized light beam Position-sensitive detector Light source p-polarized light beam Prism Spacer Layer Metal Layer Position-sensitive detector Metal Layer Analyte kx kSPW Prism kx Plasmon wave kSPW Evanescent wave Plasmon wave Evanescent wave (b) (a) scenarios based on Otto’s configuration, both presented in the literature, were used to validate our obtained results and for comparison purpose. This paper is organized as follows: in “Surface Plasmon Resonance,” we discuss about the mathematical modeling of prism-based SPR sensors with multilayer structure, considering Fresnel equations. We present the state of the art of simulation tools available in the literature that consider SPR effect. Sim-SPR architecture, considered parameters, and its respective characteristics are presented in “Sim-SPR”. In “Simulation Scenarios,” we describe three different scenarios [16, 19, 27] and two simulation tools [1, 4], both available in the literature, to validate our obtained results and for comparison purposes. We still present the parameters used in our simulations to analyze the sensitivity of prism-based SPR sensors, focusing on resonant angle. In “Results,” we discuss about the obtained results and, in “Conclusions,” we give the conclusions. in which k0 = 2π λ represents the component of the incident light wave vector, λ the free space wavelength, m the metal complex dielectric constant (m = mr + j mi ) that depends on the wavelength, and na the sample refractive index (analyte). The coupling condition to excite a SPW occurs when the wave vector matches with the SPW, resulting a dip in the angular, or wavelength, variation of the reflected light. The coupling condition may be expressed by [11]: m n2a , (2) kx = np k0 sin(θSPR ) = k0 m + n2a Surface Plasmon Resonance in which kx is the wave vector, np the prism refractive index, and θSPR the resonant angle that excites the surface plasmon. According to Eq. (2), the coupling condition is satisfied only The plasmons excitation can be achieved through a coupler in multilayer structures which can be built on prism, grating, planar or cylindrical waveguide coated with a thin metal film [10]. For prism coupling, there are two most popular metal-dielectric configurations to SPR optical excitation: Otto [24] and Kretschmann [18], as shown in Fig. 1. In both metal-dielectric configurations (Otto and Kretschmann), the p-polarized light beam2 is reflected at the interface between a prism and a very thin metal layer, being captured by a position-sensitive detector. Consequently, the evanescent optical wave penetrates through the metal layer and it excites a SPW at the other metal boundary [11]. For Otto’s configuration, as shown in Fig. 1a, it is required that the metal surface must be separated from the prism by a spacer layer, in which the analyte solution flows above the metal surface. For Kretschmann’s configuration, as shown in Fig. 1b, a thin metal film is employed onto a glass surface. In both configurations (Otto and Kretschmann), there is a SPW propagating at the interface between a thin metal 2 The optical wave from a light source with the electric field direction parallel to the incidence plane. layer and a dielectric. The SPW propagation constant can be expressed by [11]: m n2a , (1) kSPW = k0 m + n2a if |mr | is higher than n2p n2a . n2p −n2a It occurs because when the wavelength decreases, |mr | approaches to the critical value and a SPW can not be excited [11]. Considering a prism-based SPR sensor with N layers, the reflected intensity of p-polarized light beam can be evaluated by the matrix method using Maxwell’s equations and Fresnel coefficients as follows [5, 7]: cos(βk ) − qik sin(βk ) , (3) Mk = −iqk sin(βk ) cos(βk ) in which Mk is the characteristic transfer matrix and itself represents the luminous propagation between layers, βk the phase factor, and qk the transverse magnetic incident light, given by the following equations [7]: (4) βk = k0 dk n2k − n2p sin2 (θi ), qk = n2k − n2p sin2 (θi ) n2k , (5) in which dk denotes the thickness, θi the incidence angle, and nk the metal layer refractive index which depends on the wavelength. The total characteristic transfer matrix is Plasmonics evaluated by multiplication of each Mk matrix for kth layer index as follows [7]: Mtotal = N−1 Mk . (6) k=1 The Fresnel reflection coefficient (r) of multilayers using Mtotal matrix terms can be evaluated by [7]: (M11 + M12 qN )q1 − (M21 + M22 qN ) r(θi , λ) = , (7) (M11 + M12 qN )q1 + (M21 + M22 qN ) in which M11 , M12 , M21 and M22 are elements of the total characteristic transfer matrix and q1 and qN are the transverse magnetic incident light for the first and the last layers, respectively. Consequently, the reflectance (R) of a multilayer structure is given by [7]: R = |r(θi , λ)|2 . (8) The reflectance can be evaluated considering two operating modes [11]: (1) angular interrogation mode (AIM) that considers the wavelength fixed while the incidence angle is changing and (2) wavelength interrogation mode (WIM) that considers the incidence angle fixed while the wavelength is changing. The appropriate resonant angle for exciting the SPR effect is given by [27]: n2a m 1 −1 θSPR = sin . (9) np n2a + m Furthermore, the prism refractive index can be computed using Sellmeier’s dispersion equation given by [8]: A1 λ2 A2 λ2 A3 λ2 + 2 + 2 , (10) np (λ) = 1 + 2 λ − B1 λ − B2 λ − B3 in which Ai and Bi (i = 1, 2, 3) are the Sellmeier coefficients associated to each material [8, 25]. In this paper, our analysis is focused on prism-based SPR sensors considering Otto’s configuration. Otto’s configuration is not as convenient as the Kretschmann’s because of the strong dependence of the surface plasmon coupling efficiency on the thickness of the dielectric spacer [27]. Besides that, Otto’s configuration requires very smooth surfaces for both the metal and the dielectric materials which are very difficult to be realized experimentally [31]. However, recent advances in microfabrication and thin film technology makes the fabrication of SPR biosensors based on Otto’s configuration feasible [6, 21]. Among other applications, SPR biosensors based on Otto’s configuration will be preferable in applications where direct contact with the metal surface is undesirable [6]. The use of Otto’s configuration for prism coupling brings some benefits to the applications in biosensing, such as the following [9]: (1) high-purity metal film can be preserved; (2) it is possible to use opaque substrates for the metal layer; (3) the degrading effect produced by the adhesion layer applied between the substrate and the metal film layer on the resonance curve quality factor (QF) does not occur in Otto’s configuration. As described in details in “Angular Interrogation Mode Sensor Sensitivity Analysis,” QF depends on the sensor sensitivity and the spectral width of the resonance curve. State of the Art of Simulation Tools Used for SPR-Based Sensors Analysis and Design Some simulation tools used for SPR-based sensors analysis and design are described in the literature [1–4, 13]. Therefore, some of these simulators do not make available their source codes and the cost of some respective licenses can be expensive. In this paper, we propose an open-source simulation tool to evaluate the SPR effect considering multilayer structures. Our proposal is dedicated to analyze reflectance and sensor sensitivity of prism-based SPR sensors using Otto’s configuration, focusing on resonant angle. For SPR-based sensors analysis and design, COMSOL Multiphysics uses the finite element method (FEM) to solve differential equations. The wave equation is given by [1]: ∇ × (∇ × E) − k02 mr E = 0. (11) Besides to solve Eq. (11) at the interface, the structure is divided into a mesh of elements with predefined sizes and the equation is applied element by element. The solution is evaluated from the field variation in the structure, being possible to generate the reflectance curves, verifying the resonance condition considering a variation of incidence angle. On the other hand, COMSOL Multiphysics demands high-performance computing, expense of longer running time, its source code is not available and its license is paid. Jamil et al. [14] used Lumerical’s finite-difference timedomain (FDTD) simulator [2] to optimize a SPR sensor based on Kretschmann’s configuration. It was analyzed the resonance curve’s full width at half maximum (FWHM) from a graphene-based SPR sensor. Jamil et al. [14] also monitored the performance of the SPR sensor by the FDTD Lumerical software as well as the bio-detection sensitivity. Lumerical also demands high-performance computing and it does not provide its source code for future improvements. In the field of renewable energy, solar cell, and electronic device simulations, Wenjun et al. [15] explored the impact of SPR effect on organic solar cell performance, considering optical coupling at an interface with silver nanoprisms, using Sentaurus device simulator [3]. Wenjun et al. [15] used a conventional organic photovoltaic structure implemented as simulation setup in the Sentaurus, with the aim to analyze the optimization of silver nanoprism sizes, reflectivity, and absorption. The impact of silver nanoprisms on short-circuit current was analyzed as well. It is important to observe that Sentaurus does not offer an open-source code. Plasmonics Table 1 State of the art of the simulation tools described in the literature used for SPR-based sensors analysis and design Simulation tool COMSOL [1] Lumerical [2] Sentaurus [3] WinSpall [4] PAME [13] Sim-SPR Reflectance analysis Sensitivity analysis Otto’s configuration Kretschmann’s configuration AIM WIM C++ language Python language N layers Free license Source code Optical fiber–based coupling Prism-based coupling X X X X X X – – X – – X X X X X X X X – – X – – X X X X X X X X – – X – – X X X – X X X – X – X X – – X X – – – X X – X X X X X – X X X – X – X – X X X – X Adam et al. [13] proposed the plasmonic assay modeling environment (PAME). It is an open-source application for modeling plasmonic systems of bulk and metallic films, also used for modeling plasmonic biosensors. It is implemented in Python programming language, there is a graphical interface that provides results in terms of graphs and its functional architecture is designed with integrated subprograms along with data analysis framework. PAME is presented as only one open-source application close to our purpose in this paper. While PAME uses optical fibers as a coupling method to design plasmonic biosensors, our proposal considers prism-based SPR sensors. WinSpall [4] is another software described in the literature used for simulations of SPR-based sensors. It is based on Fresnel equations considering multilayer structure. It is free and easy to use for thin film analysis using evanescent waves. It is developed by RES-TEC Solutions and it has been used as a good alternative to simulate resonance curves, operating with AIM mode. Therefore, WinSpall does not offer sensitivity analysis and does not provide its source code for future improvements [4]. SPR effect modeling implemented in MATLAB and Mathcad was presented in the literature as useful to determine parameters for designing optical sensors. Fontana [8] used Mathcad to determine the wavelength dependence of the optimum thickness for the maximum sensitivity of the SPR effect. In addition, Huang et al. [30] used MATLAB to design a prism-based SPR sensor based on Kretschmann’s configuration, considering AIM and WIM modes. However, all of these softwares require high-cost licenses to be used. Table 1 summarizes the main features of the simulation tools described in this section and brings a comparison with our proposal, evidencing the main features of the Sim-SPR. matrix, as evaluated by Eq. (6), considering a multilayer structure of prism-based sensor using Otto’s configuration. Sim-SPR considers the general case of plane wave interaction with a stack of N layers (N −1 interfaces). It uses features from the most recent C++ standards, benefiting from their well-developed C++ libraries, as Armadillo for linear algebra and a direct programming interface (DPI)3 to GNU Octave templates was developed to evaluate parameters using complex numbers. Interfaces are used to enable users to enter the required input parameters and to obtain the reflectance results. The numerical results of reflectance and resonance angle are saved in a structured data file. Algorithm 1 describes the Sim-SPR pseudocode. SimSPR initializes parameters, such as the following (lines 3 and 4): (1) incidence angle and (2) step-scale (for AIM mode). Between lines 6 and 8, the user selects the prismbased coupling configuration (in this paper, Otto’s configuration). Within lines 9 to 17, Sim-SPR reads parameters as refractive indexes and layers thickness for the metal and analyte layers, number of layers and wavelength. Then, reflectance class is instantiated to evaluate the reflectance. Subsequently (by using Eq. (8)), it is returned the reflectance value for each incidence angle, considering AIM mode (lines 18 to 24). Sim-SPR is structured on a verification environment. It assumes an unlimited number of layers and it imposes a limit to the incidence angle, as described in Algorithm 1, in which reflectance and sensitivity methods are instantiated (lines 18 to 27). Both methods provide an well-regulated algorithm, in which allows possible expansions. Sim-SPR 3 DPI Figure 2 shows the Sim-SPR sequence diagram. The SPR effect is evaluated based on the characteristic transfer is an interface which can be used to interface C++ with foreign languages. These foreign languages can be Octave, MATLAB, and Python as well as others. Plasmonics USER READ PARAMETERS AIM Evaluation data.txt AIM loop Minimum Reflectance Sensor Sensitivity Resonant Angle Fig. 2 Sim-SPR sequence diagram reflection coefficients (line 6), as described by Eq. (7). Once the reflectance curve as a function of the incident angle is generated, the point with the lowest reflectance level will be associated with an angle. Algorithm 2 describes the pseudocode to evaluate the reflectance. The reflectance is obtained from the evaluated Algorithm 3 describes the angular sensitivity evaluation pseudocode. The sensitivity method is governed only by three initialized parameters, such as the following: (1) na ; (2) np ; and (3) refractive index of the metal layer (nmetal ). Consequently, the output evaluated by Eq. (12) (line 3) is returned in degree per refractive index unit (◦ /RIU) (line 4). For improvement of the angular sensitivity results, Sim-SPR uses some features implemented by a multiprocessing programming in C++ using OpenMP library (line 2), in which is possible to run simulations in parallel for each refractive index of sensing medium shifts (na ). Plasmonics Welcome to Sim-SPR Number of Layers? Figure 3 shows a thread-friendly flowchart diagram considered on Sim-SPR. Each branch represents steps implemented on Sim-SPR, considering aspects of software engineering, which simplifies the process of extending its capabilities. Beside data processing in Fig. 3, it is presented the multiprocessing programming for sensitivity angular analysis. Extensive details about the Sim-SPR’s structure and its respective source code are available at its website.4 Otto Read Parameters Simulation Scenarios The Sim-SPR accuracy and efficiency were analyzed by comparing our obtained results considering three different scenarios presented in the literature [16, 19, 27] with two other softwares (COMSOL Multiphysics [1] and WinSpall [4]). Both simulation tools are well consolidated in the literature in the aspects of optimization, design and analysis of sensor devices and systems, as described in details in “State of the Art of Simulation Tools Used for SPR-Based Sensors Analysis and Design.” The “Scenario 1” to “Scenario 3” sections describe in details the three different scenarios considered in our simulations [16, 19, 27]. The first considers a prism-based sensor with three layers (N = 3) (Scenario 1), as shown in Fig. 4a [27]. The second is based on the thickness measurement of a dielectric layer on a metal surface (Scenario 2), as shown in Fig. 4b [16]. The third involves an experimental study focused on the characterization of a SPR-based sensor (Scenario 3), as shown in Fig. 4c [19]. All these scenarios are based on the Otto’s configuration and the parameters are described in Table 2. The results were obtained as a function of the incidence angle within the range of 30◦ < θi < 50◦ , with step-scale of 0.1◦ . Scenario 1 This hypothetical scenario was proposed by Sarid et al. [27] and it consists of three layers (N = 3), such as BK7 prism, having a gold film of 50 nm, separated by a well-defined air gap of 1000 nm with refractive index unitary (nair = 1), 4 https://github.com/eltonbrasil/SimSPR Data Processing Display Result Done Fig. 3 Sim-SPR algorithm flowchart using the excitation light beam wavelength of 800 nm, as shown in Fig. 4a. Scenario 2 This experimental scenario was proposed by Kaneoka et al. [16] to precise thickness measurement of a dielectric layer on a metal surface. It was considered a structure with five layers (N = 5), such as the following: (1) BK7 prism; (2) air gap of 300 nm with refractive index unitary (nair = 1); (3) polyvinyl alcohol (PVA) used as the dielectric core layer material; (4) gold film of 50 nm; and (5) BK7 substrate, as shown in Fig. 4b. The excitation light beam wavelength is set to be 632.8 nm and it was assumed that the PVA film had no light absorption, as shown in Fig. 4b. Plasmonics Fig. 4 Three different scenarios considered in our simulations. a Scenario 1 [27] (as described in “Scenario 1”). b Scenario 2 [16] (as described in “Scenario 2”). c Scenario 3 [19] (as described in “Scenario 3”) Gold Layer Air p-polarized light beam IR Laser (800 nm) Position-sensitive detector (a) IR Laser (632.8 nm) Position-sensitive detector p-polarized light beam PVA Gold Layer BK7 Gold Layer Air Quartz Prism BK7 Air kx kSPW Evanescent wave p-polarized light beam Prism BK7 IR Laser (975.1 nm) Position-sensitive detector (b) Scenario 3 This experimental scenario was proposed by Lee et al. [19] and it is an Otto chip device composed by a BK7 prism, having a gold film of 300 nm, separated from a quartz window surface by a well-defined air gap of 2200 nm. The excitation light beam wavelength is set to be 975.1 nm, as shown in Fig. 4c. Angular Interrogation Mode Sensor Sensitivity Analysis In this subsection, we present the parameters used in our simulations to analyze the sensitivity of prism-based SPR sensors focusing on resonant angle. These parameters are defined as follows: (1) sensor sensitivity (Sθ ); (2) detection accuracy (DA); and (3) quality factor (QF). For SPR-based sensors, sensor sensitivity (Sθ ) is evaluated by the ratio of the resonance angle displacement (θSPR ) and the analyte refractive index variation (na ) [11]: √ θSPR mr −mr = . (12) Sθ = na (mr + n2a ) mr (n2a − n2p ) − n2a n2p (c) According to Eq. (12), Sθ does not depend on the analyte thickness but with the respective values of prism and analyte refractive indexes. Consequently, Sθ can be given by [11]: Sθ = 1 θSPR ∼ . = na n2p − n2a (13) The detection accuracy is defined by the ratio of θSPR and the FWHM of the resonance curve. DA can be evaluated by [26, 29]: θSPR . (14) DA = FWHM Finally, the quality factor parameter depends on the sensor sensitivity, evaluated by Eq. (13), and the FWHM. QF can be given by [26, 28, 29]: Sθ . (15) FWHM QF is a figure of metric (FOM) used to assess the performance of plasmonic sensors [20]. However, QF has its limit to estimate the refractive index (RI) resolution (or detection limit) of a SPR sensor. The RI resolution depends directly on the detection noise (σ ) and inversely with the sensor sensitivity, given by Eq. (12). Besides not being proportional with FWHM, the relation between the RI QF = Table 2 Parameters used in the three different scenarios considered in our simulations: (a) Scenario 1 [27] (as described in “Scenario 1”); (b) Scenario 2 [16] (as described in “Scenario 2”); and (c) Scenario 3 [19] (as described in “Scenario 3”) Scenario 1 Reference [27] Scenario 2 Reference [16] Scenario 3 Reference [19] Wavelength λ = 800 nm np 1.5 Wavelength λ = 632.8 nm np 1.515 nPVA 1.5 ngold 0.172 + j 3.440 Wavelength λ = 975.1 nm np 1.5079 nquartz 1.4507 ngold 0.21516 + j 6.2835 ngold 0.23 + j 4.5 dair 1000 nm dgold 50 nm dPVA 310 nm dair 300 nm dgold 50 nm dquartz 50 nm dair 2200 nm dgold 300 nm Plasmonics Fig. 5 Reflectance as a function of the incidence angle using Sim-SPR (blue line solid), WinSpall (plus sign red line), and COMSOL Multiphysics (black cross line), considering. a Scenario 1 [27] (as described in “Scenario 1”). b Scenario 2 [16] (as described in “Scenario 2”). c Scenario 3 [19] (as described in “Scenario 3”) resolution and the SPR dip width is complicated involving pixel size of the detector (CCD or CMOS) and the distance between the detector and the SPR module [20]. In this paper, Sim-SPR does not consider the detection noise (σ ), consequently it does not evaluate the RI resolution. We only consider sensor sensitivity, detection accuracy and quality factor in the three different scenarios presented in the literature [16, 19, 27] to analyze the sensitivity of prism-based SPR sensors focusing on resonant angle. Results Figure 5 shows the reflectance as a function of the incidence angle using Sim-SPR (blue line solid), WinSpall [4] (plus sign red line), and COMSOL Multiphysics [1] (black cross line), considering (a) Scenario 1 [27] (as described in “Scenario 1”); (b) Scenario 2 [16] (as described in “Scenario 2”); and (c) Scenario 3 [19] (as described in “Scenario 3”). We can observe that the incidence angles that provided the lowest reflectance values (resonance angles) in all analyzed scenarios were very close to those obtained by COMSOL Multiphysics [1] and WinSpall [4]. The resonance angles obtained by Sim-SPR were also close to those obtained analytically, by evaluating with Eq. (9), and those provided by the references related to each respective scenario [16, 19, 27]. As described in Table 3, we can observe that all the values of the resonance angles (θSPR ) obtained by Sim-SPR and the simulation tools considered as comparison in this paper (COMSOL Multiphysics [1] and Winspall [4]) were close to those obtained analytically (by using Eq. 9) and those provided by the references related to each respective scenario [16, 19, 27]. It means that the results obtained by Table 3 Values of the resonance angle (θSPR ) obtained by: Analytically (Theorical), by evaluating with Eq. (9), Sim-SPR, WinSpall [4], COMSOL Multiphysics [1], and available in the reference related to each respective scenario [16, 19, 27] θSPR Scenario Theoretical Sim-SPR WinSpall COMSOL Reference (1) (2) (3) 43.10◦ 43.82◦ 42.20◦ 42.40◦ 44.67◦ 42.20◦ 41.06◦ 43.60◦ 42.30◦ 42.00◦ 42.00◦ 41.05◦ 43.00◦ 45.59◦ 42.40◦ Plasmonics Table 4 Relative error between the results provided by Sim-SPR and the results obtained by: (Case 1) Theoretical, by evaluating with Eq. (9), (Case 2) WinSpall [4], (Case 3) COMSOL Multiphysics [1], and (Case 4) the reference related to each respective scenario [16, 19, 27] Relative error(%) Scenario (Case 1) (1) (2) (3) 1.624 1.939 0 (Case 2) (Case 3) (Case 4) 3.263 2.454 0.236 0.952 6.357 2.801 1.395 2.017 0.471 Sim-SPR practically match with the experimental results [16, 19, 27] and the results obtained by the others simulation tools (COMSOL Multiphysics [1] and Winspall [4]). Table 4 describes the relative error between the results provided by Sim-SPR and the results obtained by: (Case 1) Theoretical, by evaluating with Eq. (9), (Case 2) WinSpall [4], (Case 3) COMSOL Multiphysics [1], and (Case 4) the reference related to each respective scenario [16, 19, 27]. We can observe that, in comparison with the resonance angle obtained analytically, by evaluating Eq. (9) (Case (1)), the maximum relative error obtained was 1.939%, referring to Scenario 2. With respect to the resonance angle provided by the references available in the literature [16, 19, 27], the maximum relative error was 2.017%, referring to Scenario 2. Regarding the simulation tools used as comparison in this Fig. 6 Reflectance as a function of the incidence angle, considering an analyte refractive index variation for the following scenarios. a Scenario 1 [27] (as described in “Scenario 1”). b Scenario 2 [16] (as described in “Scenario 2”). c Scenario 3 [19] (as described in “Scenario 3”) paper (COMSOL Multiphysics [1] and WinSpall [4]), the maximum relative error obtained with respect to COMSOL Multiphysics was 6.357 % in Scenario 2 whereas the relative maximum error obtained with respect to WinSpall was 3.263 %, for Scenario 1. Thus, compared with the results obtained analytically, by evaluating with Eq. (9), and the resonance angles provided by the respective references [16, 19, 27], Sim-SPR resulted in a maximum relative error approximately 2 %, confirming its accuracy, efficiency, and reliability to design and to analyze SPR-based sensors using Otto’s configuration in all scenarios described in details in “Scenario 1” to “Scenario 3”. Sensor Sensitivity Analysis In this subsection, we investigated the sensor sensitivity and the resonance angle variation by simulations using SimSPR. All the scenarios described in details in “Simulation Scenarios” were analyzed. The air was employed in all scenarios as refractive index sensing medium shifts within the range of 1.0 to 1.015 RIU with a short step-scale of 0.005. Figure 6 shows the reflectance as a function of the incidence angle, considering an analyte refractive index variation for the following scenarios: (a) Scenario 1 [27] (as described in “Scenario 1”); (b) Scenario 2 [16] (as described in “Scenario 2”); and (c) Scenario 3 [19] (as described in “Scenario 3”). The reflectance curve is used Plasmonics for comparison, in terms of resonance angle, to evaluate the sensor sensitivity. For each na , a resonant angle is obtained, as shown in Fig. 6. Thus, Sim-SPR returns pairs of data (na and θSPR ), in which it allows to determine the sensor sensitivity value of the multilayer structure for all scenarios described in this paper (“Simulation Scenarios”). Table 5 exhibits the results provided by Sim-SPR and the results obtained by WinSpall and COMSOL Multiphysics (sensor sensitivity, detection accuracy and quality factor) for all scenarios analyzed in this paper, considering a variation in the refractive index sensing of 0.005(na ). According to Table 5, the highest sensitivity is obtained by Scenario 1 and Scenario 3. Also, Scenario 3 promoted better results in terms of DA and QF. The reductions of DA and QF were due to their direct dependencies with the parameter FWHM, as described in details in “Angular Interrogation Mode Sensor Sensitivity Analysis.” A deeper reflectance curve with a narrow FWHM value provides better precision and detection accuracy while greater change in resonance angle causes a higher sensitivity [22]. Moreover, high resolution and minimum uncertainty of SPR-based sensors can be achieved when DA value is as high as possible [22]. The air gap thickness is an important parameter to enhance the SPR sensor sensitivity and, consequently, the parameters DA and QF. It occurs due to the fact of the air gap thickness directly affects the energy efficiency from the photon to the surface plasmon [27]. However, delicate adjustment of the air gap thickness can be difficult to achieve in practice in the Otto’s configuration, becoming this configuration not so popular as others configurations [27]. It is important to note that the sensor sensitivity is governed by the properties of the optical system. Thus, the choice of metal and prism also interferes with the displacement of the SPR curve from a minimal Table 5 Results obtained by Sim-SPR, WinSpall, and COMSOL Multiphysics (angular sensitivity, detection accuracy, and quality factor) for all scenarios analyzed in this paper, considering a variation in the refractive index sensing of 0.005(na ) Scenario Sim-SPR (1) (2) (3) WinSpall (1) (2) (3) COMSOL (1) (2) (3) Sθ (◦ /RIU) DA QF (RIU−1 ) 40 30.5 40 2 0.14 4 100 7.22 200 40.67 20 40.65 1.48 0.10 4.02 99.26 6.98 198 33 33 167 0.10 0.16 4.12 6.6 13.2 334 variation of the analyte layer. Until recently, it has been very difficult to directly compare the performance of sensors in terms of sensitivity, because the definitions for these relevant parameters differ [17]. It is worth mentioning that Sim-SPR is able to evaluate the sensor sensitivity parameter for any proposed arrangement of prism-based SPR sensors using Otto’s configuration. Conclusions In this paper, an open-source simulation tool is proposed to evaluate the SPR effect considering a multilayer structure. The open-source simulator is called Sim-SPR and it follows the principles of software engineering. Furthermore, SimSPR is dedicated to analyze reflectance of prism-based SPR sensors using Otto’s configuration. It is important to emphasize that there is no available open-source simulation tool specifically built in this context in the literature. Three different scenarios using Otto’s configuration and two others simulation tools available in the literature were used for comparison purpose and to validate our results in terms of resonance angle. The worst cases analysis resulted in (1) relative error of 1.939% (Scenario 2), when compared the Sim-SPR result with the result obtained analytically and (2) relative error of 2.017% (Scenario 2), when compared the Sim-SPR result with the values provided by the available experiments obtained through the references used in the literature. Angular sensitivities were obtained from 30.5 ◦ /RIU to 40.0 ◦ /RIU, considering a refractive index variation of 0.005 in all scenarios analyzed in this paper. Sim-SPR is an open-source simulation tool and provides new insights for possible applications in the field of biosensors analysis and design. Sim-SPR becomes a pioneer in the context of SPR simulation tools, presented as a robust and solid SPR simulator. 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