sensors Article
Enhancement of Long-Range Surface Plasmon Excitation, Dynamic Range and Figure of Merit Using a Dielectric Resonant Cavity Phitsini Suvarnaphaet †
ID
and Suejit Pechprasarn *,†
College of Biomedical Engineering, Rangsit University, Pathum Thani 12000, Thailand;
[email protected] * Correspondence:
[email protected]; Tel.: +66-2-997-2200 (ext. 1469) † These authors contributed equally to this work. Received: 14 June 2018; Accepted: 17 August 2018; Published: 22 August 2018
Abstract: In this paper, we report a theoretical framework on the effect of multiple resonances inside the dielectric cavity of insulator-insulator-metal-insulator (IIMI)-based surface plasmon sensors. It has been very well established that the structure can support both long-range surface plasmon polaritons (LRSPP) and short-range surface plasmon polaritons (SRSPP). We found that the dielectric resonant cavity under certain conditions can be employed as a resonator to enhance the LRSPP properties. These conditions are: (1) the refractive index of the resonant cavity was greater than the refractive index of the sample layer and (2) when light propagated in the resonant cavity and was evanescent in the sample layer. We showed through the analytical calculation using Fresnel equations and rigorous coupled wave theory that the proposed structure with the mentioned conditions can extend the dynamic range of LRSPP excitation and enhance at least five times more plasmon intensity on the surface of the metal compared to the surface plasmon excited by the conventional Kretschmann configuration. It can enhance the dip sensitivity and the dynamic range in refractive index sensing without losing the sharpness of the LRSPP dip. We also showed that the interferometric modes in the cavity can be insensitive to the surface plasmon modes. This allowed a self-referenced surface plasmon resonance structure, in which the interferometric mode measured changes in the sensor structure and the enhanced LRSPP measured changes in the sample channel. Keywords: long-range surface plasmon polariton; short-range surface plasmon polariton; dielectric resonant cavity; multiple reflections; plasmonic; surface plasmon resonance sensor; instrumentation
1. Introduction Surface Plasmon Resonance (SPR) has been a powerful scientific tool for biological protein kinetic studies [1–4]. The SPR sensing platforms are usually implemented based on the optical configuration proposed by Kretschmann-Raether in 1968 [5,6]. That same year, Otto also proposed an optical configuration that allowed the SPR to be excited on a bulk gold surface [7]. The Otto configuration has not been exploited much in biosensing applications since the structure requires a very narrow spacing gap (less than a wavelength spacing height) between the coupling prism and the bulk plasmonic metal. It has been very well established that double plasmonic metal interfaces such as: (1) insulatormetal-insulator (IMI) structures [8] or (2) metal-insulator-metal (MIM) structures [9–11] can support two plasmonic modes, so-called, long-range surface plasmon polaritons (LRSPP) and short-range surface plasmon polaritons (SRSPP) [12]. These LRSPP and SRSPP modes have been experimentally verified by several groups including Lee et al. [13] and Slavík et al. [14]. The LRSPP mode has several preferable features over the SRSPP mode including (1) it can be excited at a lower incident k-vector (lower angle and lower incident wavelength) and (2) it has a higher figure of merit (FoM). The FoM
Sensors 2018, 18, 2757; doi:10.3390/s18092757
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is a quantity used tolower measure the detection performance, a ratio of the(FoM). sensitivity to the (lower angle and incident wavelength) and (2) it hasrelative a higherto figure of merit The FoM full-width half maximum (FWHM) of the reflectance dip position in SPR biosensing platform. This is a quantity used to measure the detection performance, relative to a ratio of the sensitivity to the is half maximum of thelocal reflectance dip position in SPR biosensing is due full-width to the change of the SPR(FWHM) signal upon refractive index changes. Thus theplatform. narrow This reflection due to the change ofof the SPR signal upon local refractive index changes. Thus[15]. the narrow reflectionFoM dip and enhancement the sensitivity improves the FoM of SPR sensors The enhanced dip and enhancement of thein sensitivity improves the FoM SPR sensors [15]. Theetenhanced FoM has the has proven itself very useful biosensing platforms andofapplications. Khan al. [16] reported proven itself very useful in biosensing platforms and applications. Khan et al. [16] reported the implementation of an interdigitated capacitor (IDC)-based glucose biosensor with high detection implementation of an interdigitated capacitor (IDC)-based glucose biosensor with high detection − 7 sensitivity of 10 refractive index units (RIU) and wide dynamic range for fast response and recovery sensitivity of 10−7 refractive index units (RIU) and wide dynamic range for fast response and recovery in which the limit of detection reached nanomolar concentration. Zhen et al. [17] has reported an in which the limit of detection reached nanomolar concentration. Zhen et al. [17] has reported an ultra-sensitive plasmonic biosensor having the detection sensitivity down to 10−18 molar concentration ultra-sensitive plasmonic biosensor having the detection sensitivity down to 10−18 molar of ssDNA sensingofbyssDNA nanostructures goldhybridized thin film. Yu et thin al. [11] have concentration sensing byhybridized nanostructures gold film. Yu recently et al. [11]proposed have the side-coupled Fabry-Perot cavity as Fabry-Perot a resonator for ultrahigh wavelength selection.wavelength Wu et al. [18] recently proposed the side-coupled cavity as a resonator for ultrahigh haveselection. reportedWu theettheoretical MIM plasmonic structures a ringstructures resonator. al. [18] haveperformance reported the of theoretical performance of MIMwith plasmonic with The LRSPP and SRSPP modes occur due to a hybridization between the two bound SPR modes a ring resonator. on two metal surfaces. This modes lower occur excitation of course, reduces of using The LRSPP and SRSPP due toangle, a hybridization between thethe tworequirement bound SPR modes two metalaperture surfaces. This excitation of course, reduces the requirement usinghowever, high highon numerical (NA)lower objective lensangle, to excite the LRSPP [19]. The LRSPPofdoes, numerical aperture (NA) objective lens to excite the LRSPP [19]. The LRSPP does, however, still have still have two main issues. Firstly, it does have a very limited dynamic range since it can only two main issues. Firstly, itindices does have a very limited dynamic rangemetal since itlayer can only excited Secondly, when be excited when refractive sandwiching the plasmonic are be similar. refractive indices sandwiching the plasmonic metal layer are similar. Secondly, although the LRSPP although the LRSPP reflectance dip is much narrower than the conventional Kretschmann SPR, the dip reflectance dip is much narrower than the conventional Kretschmann SPR, the dip sensitivity in sensitivity in refractive index sensing is much less. The longer propagation length of LRSPP can offer a refractive index sensing is much less. The longer propagation length of LRSPP can offer a larger larger detection area of the binding sample region allowing the LRSPP to be more sensitive than the detection area of the binding sample region allowing the LRSPP to be more sensitive than the conventional SRSPP [12]. conventional SRSPP [12]. The The insulator-insulator-metal-insulator (IIMI) structure for LRSPP excitation was first introduced insulator-insulator-metal-insulator (IIMI) structure for LRSPP excitation was first by Abelès and Lopez–Rios in 1974 [20]. The major differences for the IIMI structure [13,14,20] reported introduced by Abelès and Lopez–Rios in 1974 [20]. The major differences for the IIMI structure by others andreported this paper are that interested in the IIMI as shown in Figure 1 under certain [13,14,20] by others andwe thisare paper are that we are interested in the IIMI as shown in Figure conditions (1) thewhich refractive ofrefractive the dielectric cavity (nresonant 1 underwhich certainwere: conditions were:index (1) the indexresonant of the dielectric cavitythan (n0) the 0 ) was larger was larger than index ofregion the sensing (n3);where (2) thethe k-vectors where the light refractive index of the refractive sensing sample (n3 ); sample (2) the region k-vectors light propagated in the propagated in the dielectric cavity were evanescent in the sample region. dielectric cavity were evanescent in the sample region.
Figure 1. The proposed IIMI structure. The The incident incident medium was a semi-infinite glass Figure 1. The proposed IIMI structure. medium(Region (Region0)0) was a semi-infinite glass substrate refractive index 0 servingas asan an incident incident medium. cavity (Region I) was substrate withwith refractive index n0nserving medium.The Theresonant resonant cavity (Region I) was made a dielectric layer with refractive index 1 and thickness d1. The plasmonic medium (Region made of a of dielectric layer with refractive index n1nand thickness d1 . The plasmonic medium (Region II) II) was a noble metal layer with refractive index n 2 and thickness d2. The sample medium (Region III) was a noble metal layer with refractive index n2 and thickness d2 . The sample medium (Region III) was also the dielectric layer with refractive index n3 which was the sample channel of the proposed SPR sensor.
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The thickness of the dielectric cavity considered here ranged from 0.5 to 4 µm, which is much thicker than the LRSPP structures reported in the literature. Thus the proposed structure served as a resonator allowing multiple reflections inside the cavity and interferometric modes. By matching the k-vectors of the resonant cavity and the LRSPP, these conditions can enhance the properties of the LRSPP excitation, dynamic range and FoM in SPR sensing applications. To the best of the authors’ knowledge, these features of the LRSPP excited through the dielectric resonant cavity have never been reported before. 2. Structure and Simulation Methods 2.1. Simulation Methods The multi-layer type structure shown in Figure 1 was analysed using a transfer matrix approach for Fresnel equations [21]. The following variables were used throughout the paper: rp and tp are the reflection coefficient and transmission coefficient for p-polarization and s-polarization, respectively. Rigorous coupled wave theory [22] has been implemented to determine the mode profiles in the structure and stored optical power per unit length in the resonant cavity. Ex , Ey and Ez are the electric fields along the x-, y- and z-axes, respectively. Hx , Hy and Hz are the magnetic fields along the x-, yand z-axes, respectively. The axes were defined as indicated in Figure 1. 2.2. Terms and Definitions There are several definitions for figure of merit (FoM) [23]. The commonly used FoM that is defined to evaluate the dip position measurement in SPR systems [15], which is also used in this paper and defined as: S FoM = (1) FWHM where FoM is the figure of merit for dip position measurement. S is the sensitivity term. In the SPR biosensing platforms, the sensitivity is herein defined in term of dkx,resonance /dnsample for bulk sensitivity where the kx,resonance is the k-vector position of the resonant mode along the x-axis and the nsample is the refractive index of the bulk sample medium. FWHM is the full-width half maximum of the reflectance dip. The width of the dip is measured at 0.5 intensity level of the reflectance curve. Dynamic range (D) is defined as the range of refractive indices that the plasmonic reflectance dip intensity is below 0.25. The illumination k-vector in this paper is presented as a normalized k-vector, k k x = no sin θ0 or numerical aperture (NA). f ree−space
3. Results and Discussion 3.1. LRSPP and SRSPP Before looking at the IIMI plasmonic structure, let us consider the case where we only had pure plasmonic modes in a three homogenous-layer structure, when either d1 was treated as 0 nm or n0 equalled n1 . The structure was a thin plasmonic gold layer with thickness d2 sandwiched by two semi-infinite dielectric media with refractive indices of n0 and n3 . Gold has been chosen in this study since it is suitable for biological sensor fabrication because gold is chemically stable, inductive and non-toxic to biological samples [3,24]. The refractive index of gold is 0.18344 + 3.4332i at 633 nm free-space wavelength (λ) extracted from Johnson and Christy [25]. Note that we have compared and discussed the performance of silver with refractive index of 0.056206 + 4.2776i [25] as reported and shown in Figure S1 and Table S1 in the Supplementary Information (SI). The silver results tell the same story as the gold results. The results are therefore omitted from the main manuscript. Figure 2a–c shows ln(|rp |2 ) for different values n0 ranging from 1.29 (Teflon™ AF2400 [26]), 1.33 and 1.3616 (potassium fluoride: KF [27]), respectively, when n3 was fixed at 1.33. It is important to point out that the n0 sinθ 0 range in the calculation was 1.33 to 1.52. This made the sinθ 0 greater than 1 indicating
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as the gold results. The results are therefore omitted from the main manuscript. Figure 2a–c shows ln(|rp|2) for different values n0 ranging from 1.29 (Teflon™ AF2400 [26]), 1.33 and 1.3616 (potassium fluoride: KF [27]), respectively, when n3 was fixed at 1.33. It is important to point out that the n4 0of sinθ 0 Sensors 2018, 18, 2757 17 range in the calculation was 1.33 to 1.52. This made the sinθ0 greater than 1 indicating that the SPR modes shown here were excited by an evanescent wave and the structure required a higher coupling that themedium SPR modes were excited by ancondition. evanescent and structure required a index or ashown gratinghere to satisfy the k-vector Ofwave course, if the another higher refractive higher coupling index medium or a grating to satisfy the k-vector condition. Of course, if another coupling layer had been added to the structure, this would form an IIMI structure. The higher refractive modes coupling hadcan been added to the structure, formmodes an IIMI structure.in interferometric in layer the IIMI unavoidably interact withthis the would plasmonic explained The modes in the calculations IIMI can unavoidably interact the plasmonic explained theinterferometric later section. These Fresnel have enabled us towith identify the mode modes coupling strength inand the the laterk-vector section.positions These Fresnel calculations have enabled us to identify the mode coupling strength for the pure SRSPP and pure LRSPP modes without any influence from and k-vector positions for the pure SRSPP and pure modes without any influence from the the coupling layer. It has been very well established thatLRSPP the LRSPP exists under certain conditions, the coupling It has been very well established the LRSPP metal, exists under conditions, which are (1)layer. the refractive indices, which sandwichthat the plasmonic have tocertain be similar [12] and which are plasmonic (1) the refractive which the plasmonic metal, haveused to be similar [12] and (2) the metalindices, thickness is sandwich usually thinner than the metal in Kretschmann (2) the plasmonicFigure metal 2b thickness usually thinner metal usedindices in Kretschmann configuration. configuration. showedis that when the nthan 0 andthe n3 refractive were perfectly matched, Figure 2b showed that when n0 and n3 refractive indices matched, the coupling the coupling strength for thethe both LRSPP (symmetric mode)were andperfectly SRSPP (asymmetric mode) were strength both LRSPP (symmetric mode) SRSPP (asymmetric mode) similar.coupling On the similar. for Onthe the other hand, when they wereand mismatched, the LRSPP hadwere a stronger other hand, to when they were mismatched, thethan LRSPP a stronger coupling to with the SRSPP compared the SRSPP when n0 was lower n3 ashad shown in Figure 2a in acompared comparison Figure when n was lower than n as shown in Figure 2a in a comparison with Figure 2c. The separation in 2c. The0 separation in k-vector space between the two SPP modes was wider when the plasmonic gold 3 k-vector space twowhen SPP modes waswas wider when the 75 plasmonic goldSPP wasmodes thin. On the otherto was thin. On between the otherthe hand, the gold thicker than nm the two combined hand, when the gold thicker than 75 nm the two modes combined a single The LRSPP a single mode. Thewas LRSPP k-vector appeared at aSPP larger k-vector valuetowith the mode. larger n 0 refractive k-vector appeared at aof larger k-vector value the larger The thickness thebe index. The thickness the gold d2 and the with refractive indexnsandwiching the plasmonic gold of will 0 refractive index. gold d2 and the index sandwiching the plasmonic gold be employed a key parameter employed as arefractive key parameter to vary the k-vector positions of will the two plasmonicasmodes in the next tosection. vary the k-vector positions of the two plasmonic modes in the next section.
Figure2.2.Comparison Comparisonof ofcoupling couplingstrength, strength, ln|r ln|rpp||22, ,ofofLRSPP where n0n=0n=1 and Figure LRSPPand andSRSPP SRSPPininthe thecase case where n1 d1 =d10 =nm considered as pure plasmonic modes forfor (a)(a) n0 n=0 n=1 n=11.29; (b)(b) n0 n=0n=1 n = 11.33 andand n0 n = 0n=1 = and 0 nm considered as pure plasmonic modes = 1.29; = 1.33 Other parameters areare λ λ = =633 and nn33 == 1.33; 1.33;(d) (d)Normalized Normalized n11.3616. = 1.3616. Other parameters 633nm, nm,nn2 2==0.18344 0.18344 ++ 3.4332i 3.4332i and ”𝑘 " /𝑘 attenuation coefficients for the cases in (a–c). The solid red curves in (a–c) were the 𝑓𝑟𝑒𝑒−𝑠𝑝𝑎𝑐𝑒 attenuation coefficients k sp𝑠𝑝 /k f ree −space for the cases in (a–c). The solid red curves in (a–c) were the solutionstoto Equation LRSPP mode anddashed the dashed red curves the solutions formode. SRSPP solutions Equation (2) (2) for for LRSPP mode and the red curves are theare solutions for SRSPP mode.
Stegeman and Burke [28] have reported a dispersion relation for the two plasmonic modes for asymmetric metal waveguide [29], which is given by: tanh(k z2 d2 )(ε 0 ε 3 k2z2 − ε22 k z0 k z3 ) − ε 2 k z2 (ε 0 k z3 + ε 3 k z0 ) = 0
(2)
the permittivity of the region 0, II and III. These permittivity values can be determined by
2 n22
and
0 n02 ,
3 n32 .
Equation (2) allows us to solve for complex surface plasmon k-vector: Sensors 2018, 18, 2757
where ksp is the complex surface plasmon k-vector, where
k sp
kx ksp ksp iksp , 5 of 17
is the real part of the complex surface
plasmon k-vector and k is the attenuation coefficient. kx is the k-vector along the x-axis, which is where kz0 , kz2 , and kz3 arespthe k-vectors along the z-axis in the region 0, II and III. ε 0 , ε 2 and ε 3 are the 2 n0 region 0, permittivity and These permittivity canmedium be determined by εin n20 , ε 21.=The n22 0 = given by of the theIII. incident angle in thevalues incident as shown Figure sin 0 . 0II is and ε 3 = n23 . 00 solutions Equationk sp (2) allows ustotothe solve for complex surface k x =red k sp curves = k0sp + normalized Equation (2) were shownplasmon in Figurek-vector: 2a–c as solid forikthe sp , where ksp is the complex surface plasmon k-vector, where k0sp is the real part of the complex surface solutions to the Equation (2) for LRSPP and dashed red 00 curves for the SRSPP. The normalized k sp plasmon k-vector and k sp is the attenuation coefficient. kx is the k-vector along the x-axis, which is given 2πn the cases described in Figure 2a–c is shown in Figure 2d. The attenuation loss for the LRSPP was 0 by λ sin θ0 . θ0 is the incident angle in the incident medium as shown in Figure 1. The normalized k0sp much lower than the SRSPP. It was dependent mostly on the thickness of the metal, not the coupling solutions to the Equation (2) were shown in Figure 2a–c as solid red curves for the LRSPP and dashed refractive red curvesindex. for the SRSPP. The normalized k0sp solutions to the Equation (2) for the cases described in Figure 2a–c is shown in Figure 2d. The attenuation loss for the LRSPP was much lower than the SRSPP. n1 n3 index. IIMI Structuremostly for LRSPP Excitation through Couplingrefractive It3.2. was dependent on the thickness of theEvanescent metal, notWave the coupling 3.2. IIMI LRSPP Excitation throughwas Evanescent Wave Coupling n3 1 ≤surface TheStructure couplingfor refractive index of 1.3616 not sufficient to excite nthe plasmon modes. It was, therefore, essential to provide a higher refractive index coupling media such as the glass The coupling refractive index of 1.3616 was not sufficient to excite the surface plasmon modes. substrate with the refractive index of 1.52. This glass substrate did not only provide the sufficient kIt was, therefore, essential to provide a higher refractive index coupling media such as the glass vector to excite therefractive surface plasmons, also provided the interferometric second substrate with the index of but 1.52.it This glass substrate did not only modes provideand thethe sufficient dielectric layer can also serve as a resonant cavity. These interference fringes were formed by the k-vector to excite the surface plasmons, but it also provided the interferometric modes and the second n dielectric layer can also serve as a resonant cavity. These interference fringes weren0formed by the direct direct reflection from the first interface between the region 0 and the region I, rp 1 , and the multiple n0 | n 1 reflection from the first interface between the region 0 and the region I, r p , and the multiple reflected n1 here n3 case, reflected as in depicted the 1 of calculated 1.34 was calculated as an beams as beams depicted Figure in 1. Figure For the1.n1For ≤n n1 of here 1.34 n was as an example. 3 case, In this case, interferometric mode k-vectors the below k-vectors the two of SPthe modes example. Inall this case, all interferometric modeappeared k-vectors below appeared theof k-vectors two as SP shown modes in asFigure shown3.in Figure 3.
Figure 3. Responses showed |rp|2 for λ = 633 nm n0 = 1.52, n1 = 1.34 with thickness d1 and n2 = 0.18344 Figure 3. Responses showed |rp |2 for λ = 633 nm n0 = 1.52, n1 = 1.34 with thickness d1 and n2 = 0.18344 3.4332iwith withthickness thicknessdd2,,nn3 == 1.34 1.34 (a) (a) dd2 == 150 150 nm nm (b) (b) dd2 == 60 60 nm nm and and (c) (c)dd2 == 30 30 nm. nm. The The colored colored ++3.4332i 2 3 2 2 2 curves shown in these figures were the interferometric mode positions calculated using Equation (3) curves shown in these figures were the interferometric mode positions calculated using Equation (3) and the two plasmonic modes calculated using Equation (2). ‘A’ and ‘B’ were labeled as plasmonic and the two plasmonic modes calculated using Equation (2). ‘A’ and ‘B’ were labeled as plasmonic modescalculated calculatedusing usingEquation Equation(2). (2).‘C’, ‘C’,‘D’ ‘D’and and‘E’ ‘E’are arelabelled labelledas asinterferometric interferometricmodes. modes. modes
These interferometric mode positions can be calculated using the asymmetric Fabry Perot cavity resonant mode number [30], which is given by: n | n2 | n3
2k z1 + Phase(r p1 n |n
n |n |n
n | n0
) + Phase(r p1
) = 2Mπ
(3)
where Phase(r p1 0 ) and Phase(r p1 2 3 ) are the phase of reflection coefficients for p-polarization for the light travelling the region I to the region 0 and the region I to the region II and the region III, respectively. M is the resonant mode number, M = 0, 1, 2, 3, . . . . The 0th order did not have a cut-off k-vector unlike the other higher order modes [31] and it can excite the LRSPP mode. The interferometric mode positions matched very well with the Fresnel
where
n n
n n n 2 3
Phase(rp 1 0 ) and Phase(rp 1
) are the phase of reflection coefficients for p-polarization
for the light travelling the region I to the region 0 and the region I to the region II and the region III, respectively. M is the resonant mode number, M = 0, 1, 2, 3, …. Sensors 2018, 18, 2757 6 of 17 The 0th order did not have a cut-off k-vector unlike the other higher order modes [31] and it can excite the LRSPP mode. The interferometric mode positions matched very well with the Fresnel simulations. The interferometric not deep very indicating deep indicating gold layer cannot simulations. The interferometric dipsdips werewere not very that thethat goldthe layer cannot provide 2 2 provide loss sufficient for the interferometric modes. |rp| of responses the IIMI sufficient for theloss interferometric modes. Figure 3a–cFigure shows3a–c |rp |shows responses the IIMI of structure structure with different gold thicknesses. The two plasmonic modes were excited through attenuated with different gold thicknesses. The two plasmonic modes were excited through attenuated total total internal reflection (ATR) evanescent wave,the where was evanescent in the region I after internal reflection (ATR) evanescent wave, where lightthe waslight evanescent in the region I after n0 sinθ 0 0sinθ0The of 1.34. The two plasmonic modechanged k-vectorswhen changed when the goldchanged thickness ofn1.34. two plasmonic mode k-vectors the gold thickness as changed predictedas predicted Figure 3. The dielectric cavity heighta dcrucial 1 played a crucial role in the mode plasmonic mode from Figurefrom 3. The dielectric cavity height d1 played role in the plasmonic coupling. cannot be too high because of the shortofpenetration of the evanescent Figure It coupling. cannot beIttoo high because of the short penetration the evanescent wave. Figure wave. 4 showed the 4 showed the phase transition through the gold layer of the two plasmonic modes labelled ‘A’ and ‘B’ phase transition through the gold layer of the two plasmonic modes labelled ‘A’ and ‘B’ in Figure 3b. in Figure 3b. The LRSPP had an anti-phase pattern at the two interfaces of the gold layer as shown The LRSPP had an anti-phase pattern at the two interfaces of the gold layer as shown in Figure 4ain Figure 4a the an SRSPP had an in-phase phase pattern at the gold interfaces. whereas thewhereas SRSPP had in-phase phase pattern at the gold interfaces.
Figure Phaseprofiles profilesofofEExx in in rad rad for 0 = 1.4156, n1 = Figure 4.4.Phase for (a) (a) LRSPP LRSPP mode modelabelled labelled‘A’ ‘A’ininFigure Figure3b: 3b:n0nsinθ 0 sinθ 0 = 1.4156, with d1 =d360 nm, n2 = 0.18344 + 3.4332i with d2 = 60 nm and n3 = 1.34 and (b) SRSPP mode labelled n11.34 = 1.34 with 1 = 360 nm, n2 = 0.18344 + 3.4332i with d2 = 60 nm and n3 = 1.34 and (b) SRSPP mode ‘B’ in Figure 3b: n 0sinθ 0= 1.513, 1 = 1.34 with d1 = 175 nm, n2 = 0.18344 + 3.4332i with d2 = 60 nm and n3 labelled ‘B’ in Figure 3b: n0 sinθn 0 = 1.513, n1 = 1.34 with d1 = 175 nm, n2 = 0.18344 + 3.4332i with = 1.34. d2 = 60 nm and n3 = 1.34.
3.3.LRSPP LRSPPExcited ExcitedbybythetheDielectric DielectricResonator Resonatorn1 n> 3.3. n3n3 1 InIn this n3 . There was a range of k-vectors that the light thissection, section,letletususlook lookatatthe thecase casewhere wheren1 n> 1 n3 . There was a range of k-vectors that the light was a propagating wave in the region I and evanescent in the region III. The range was the k-vectors was a propagating wave in the region I and evanescent in the 2 region III. The range was the k-vectors with n0 sinθ 0 between n3 and n1 . Figure 5a,b showed |r p | for the IIMI structure with n0 = 1.52, with n0sinθ0 between n3 and n1. Figure 5a,b showed |rp|2 for the IIMI structure with n0 = 1.52, n1 = 1.39 n1 = 1.39 (lithium fluoride: LiF [27]) with thickness d1 and n2 = 0.18344 + 3.4332i with thickness d2 and (lithium fluoride: LiF [27]) with thickness d1 and n2 = 0.18344 + 3.4332i with thickness d2 and the last the last dielectric medium n3 = 1.34 for different gold layer thicknesses d2 = 30 nm and d2 = 20 nm, dielectric medium n3 = 1.34 for different gold layer thicknesses d2 = 30 nm and d2 = 20 nm, respectively. respectively. These figures were the cases when before the LRSPP k-vector matched to the range of These figures were the cases when before the LRSPP k-vector matched to the range of interferometric interferometric mode k-vectors and when they matched. mode k-vectors and when they matched. Consequently, the interferometric modes dissipated the light power more efficiently through the Consequently, the interferometric modes dissipated the light power more efficiently through the plasmon coupling and appeared as very deep and narrow reflectance dips at 0 intensity level as shown plasmon coupling and appeared as very deep and narrow reflectance dips at 0 intensity level as in Figure 5b. It is interesting to note that the LRSPP excited by the 0th order interferometric mode is, shown in Figure 5b. It is interesting to note that the LRSPP excited by the 0th order interferometric of course, excited by a propagating wave mode inside the region I. Therefore the LRSPP can be excited mode is, of course, excited by a propagating wave mode inside the region I. Therefore the LRSPP can at any cavity thickness d1 as if the thickness allows the interferometric mode. This makes the device conveniently practical to fabricate. Not only the 0th order (M = 0) interferometric mode can excite the LRSPP, but also the other higher order interferometric modes if they were within the LRSPP k-vector range as shown in Figure 5b. In addition to the 633 nm wavelength, the other wavelengths of SPR excitation in the near-infrared region, i.e., 785 nm and 1024 nm were also presented and discussed in the SI.
be excited at any cavity thickness d1 as if the thickness allows the interferometric mode. This makes the device conveniently practical to fabricate. Not only the 0th order (M = 0) interferometric mode can excite the LRSPP, but also the other higher order interferometric modes if they were within the LRSPP k-vector range as shown in Figure 5b. In addition to the 633 nm wavelength, the other wavelengths of SPR excitation in the near-infrared region, i.e., 785 nm and 1024 nm were also Sensors 2018, 18, 2757 7 of 17 presented and discussed in the SI.
Figure5.5.Simulation Simulation results results for for λ= 633 = 633 nm, = 1.52, 1.39with withthickness thicknessd1d1and andnn2 2==0.18344 0.18344++ Figure nm, n0 n=0 1.52, n1n=1 =1.39 3.4332iwith withthickness thicknessdd2 2and andnn3 3==1.34. 1.34.(a) (a)|r|rp p||22 when when dd22 == 30 30 nm nm and and(b) (b)|r |rpp||22 when d22 = 20 nm nm (c) (c) 3.4332i Phase(rpp))in inrad radwhen whend2d2==30 30nm nmand and(d) (d)Phase(r Phase(r p ) in rad when d 2 = 20 nm. The colored curves shown Phase(r ) in rad when d = 20 nm. The colored curves shown in p 2 in (a,b) interferometric mode positions calculated using Equation (3) and LRSPP mode (a,b) are are the the interferometric mode positions calculated using Equation (3) and the the LRSPP mode
Figure 6a 6a shows shows the the|H |Hy||22 field field distributions distributions of of the the LRSPP LRSPP excited excited by by the the evanescent evanescent wave wave Figure y coupling labelled ‘C’ in Figure 5a. There was no standing wave inside the resonant cavity only the coupling labelled ‘C’ in Figure 5a. There was no standing wave inside the resonant cavity only the re-radiated leaky leaky LRSPP LRSPP wave wave leaked leaked their their power power back back through through the the cavity. cavity. Figure Figure 6b,c 6b,c shows shows the the re-radiated |H y|22 field distributions of the LRSPP excited by the 1st order (M = 1) and the 0th order (M = 0) |Hy | field distributions of the LRSPP excited by the 1st order (M = 1) and the 0th order (M = 0) interferometric modes modes labelled labelled ‘D’ ‘D’ and and ‘E’ ‘E’ in inFigure Figure5b. 5b. There Therewas wasthe the1st 1storder orderTM TM1guided guidedmode mode interferometric 1 patterninside insidethe theresonant resonant cavity in Figure 6b and the fundamental 0th order TM0 guided pattern cavity in Figure 6b and the fundamental 0th order mode mode TM0 guided mode mode pattern in Figure 6c. The sharpness LRSPP dips excited by the resonant cavity depended on pattern in Figure 6c. The sharpness LRSPP dips excited by the resonant cavity depended on the cavity the cavityd thickness d1. Figure 5c,d shows the phase profiles of Figure 5a,b. The gradient of phase thickness 1 . Figure 5c,d shows the phase profiles of Figure 5a,b. The gradient of phase transitions for transitions for the interferometric modes depended onofthe the resonant the interferometric modes depended strongly on thestrongly thickness thethickness resonantof cavity. For the cavity. cavity For the cavity thickness less than 1 m, the phase gradients of all the interferometric modes thickness less than 1 µm, the phase gradients of all the interferometric modes were shallower thanwere the shallower than the LRSPP as shown in Figure 5a and became much sharper when the thickness LRSPP as shown in Figure 5a and became much sharper when the thickness increased. This feature increased. feature to excite the LRSPP with the sharpness reflectance allowed usThis to excite theallowed LRSPP us with the different sharpness ofdifferent the reflectance dip,ofinthe other words, dip, in other words, it allowed us to vary the FWHM of the LRSPP mode. We will illustrate that it allowed us to vary the FWHM of the LRSPP mode. We will illustrate that not only the FWHM can not be only the by FWHM can be adjustedbut by it the cavity thickness, also gives different dip refractometric adjusted the cavity thickness, also gives different but dip itrefractometric sensitivity. These will be sensitivity. These be fully quantified in the next section. fully quantified in will the next section. For fabricating consideration, the structure with such thin gold film around 20 nm to 30 nm, the gold films are likely to have some defects such as gold islands [32]. There are several research groups working on ultra-thin gold film fabrication. Kossoy [33] have achieved an artifact-free 5.4 nm gold film. Another issue that we need to consider is that for all the simulations presented in this paper, the gold layers were treated as a uniform bulk gold layer. There is no standard threshold and criteria for the thinnest thickness gold film that can be still treated as bulk gold. There are several research articles
For fabricating consideration, the structure with such thin gold film around 20 nm to 30 nm, the gold films are likely to have some defects such as gold islands [32]. There are several research groups working on ultra-thin gold film fabrication. Kossoy [33] have achieved an artifact-free 5.4 nm gold film. Another issue that we need to consider is that for all the simulations presented in this paper, the Sensors 2018, 18, 2757 8 of 17 gold layers were treated as a uniform bulk gold layer. There is no standard threshold and criteria for the thinnest thickness gold film that can be still treated as bulk gold. There are several research articles reporting an abnormal optical the thickness is below 15 reporting optical transmission transmissionthrough throughaathin thingold goldfilm filmwhen when the thickness is below nmnm [34,35]. Laref et al. [36] have reported that thethe complex permittivity of gold does depends on the 15 [34,35]. Laref et al. [36] have reported that complex permittivity of gold does depends on thickness of the gold filmfilm when thethe gold film is ultrathin
