Open Access
Add to BibSonomy
Abstract
Two-dimensional chirped-pitch crossed surface relief gratings (CP-CSRGs) were fabricated on azobenzene-functionalized thin films using a simple two-step procedure. The resulting gratings had a constant pitch in one direction and a varying (chirped) pitch in the orthogonal direction. They were coated with silver and tested for their ability to change the polarization of surface plasmon resonance (SPR) signals, when placed between crossed polarizers. It was observed that several different bandwidths of SPR wavelengths are excitable using a single device, making CP-CSRGs suitable as next generation SPR-based sensors. The SPR wavelengths shifted as much as 10.5 nm/mm along the chirped grating, and a maximum sensitivity of 778.6 nm/RIU was obtained when detecting the refractive index change of various concentrations of aqueous sucrose solutions.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Surface plasmon resonance (SPR) -based sensors have attracted attention in recent years due to their precision and their suitability to be built in compact and inexpensive devices that can have high detection resolution and sensitivity, while enabling real-time sensing [1–5]. As such, SPR-sensors have been implemented as biosensors in medical diagnostics [6], food safety detection [7] and DNA hybridization [8]. SPRs are free-electrons density fluctuations occurring at the interface between two materials exhibiting different signs of the real part of their dielectric permittivity, typically a metal and a dielectric. SPRs are optically induced when incident light photons are phase-matched to the plasmon wave vector along the interface [9,10]. They can be excited using the Otto [11] or Kretschmann [12] configurations by taking advantage of the evanescent wave from total internal reflection inside a prism adjacent to a metallic layer. Surface relief gratings (SRGs) are an easier way to excite SPRs since the additional light momentum provided by the grating vector can be used to phase-match and couple incident light photons to the SPR [13]. When using diffraction gratings, several parameters can affect the SPR excitation wavelength and these include the grating pitch, the dielectric permittivities of the metal and the dielectric, as well as the light polarization and incidence angle [14].
A SRG’s pitch can be chosen during its fabrication process to theoretically enable the excitation of a specific SPR wavelength. Experimentally, when a constant-pitch one-dimensional grating is coated with a thin layer of gold or silver, a narrow bandwidth of SPR wavelengths is excited, instead of a single wavelength, due to the dispersive nature of the boundary materials. When polychromatic white light, polarized along the grating vector, is incident on the metallic grating, a SPR will be excited and it can be detected as a positive peak in transmission or a negative peak in reflectance. This occurs because the metal layer becomes more transparent at the SPR wavelength. When a water-based solution is placed over the metallic grating, the SPR wavelength will shift, from a baseline SPR signature of pure water, according to a change in the refractive index of the solution. Since SPR signals occur experimentally in a fairly narrow wavelength bandwidth, they can be used as a powerful tool for detecting small changes in the refractive index of a dielectric water-based solution. Hence, they are prime candidates for applications in sensing [16,17].
Surface relief diffraction gratings are easily inscribed on azobenzene-functionalized thin films using a Direct Laser Interference Patterning (DLIP) technique. Azobenzene-containing materials undergo trans to cis photo-isomerization at an absorbing light wavelength [18]. When exposed to a laser interference pattern, this microscopic phenomenon will enable macroscopic changes in the film’s surface mainly due to pressure waves from the azobenzene molecules migrating from high to low light irradiance regions. Therefore, the interference pattern will be imprinted in surface relief on the azobenzene film. Various shapes of nanostructures or diffraction gratings can be inscribed by exposing the azobenzene film to a laser interference pattern of the desired shape and structure. For instance, circular [19] and non-uniform surface relief gratings [20] have been fabricated in our group.
Furthermore, DLIP on azobenzene films allows for the fast, consistent and accurate fabrication of other nano-engineered gratings including crossed and chirped (variable-pitched) gratings [21]. Crossed surface relief gratings (CSRGs) are two-dimensional gratings that are fabricated by exposing the azobenzene film to a constant-pitch interference pattern, and then turning the sample by 90 degrees and making a second exposure to the same interference pattern. CSRGs allow for plasmonic energy exchange between the two superimposed gratings, as explained elsewhere [21,22]. When a CSRG, having two superimposed orthogonal gratings with identical pitch, is placed between crossed linear polarizers, it will rotate the incident light polarization at the common SPR wavelength only, hence enabling the measurement of only the plasmonic signal in transmission. Therefore, a very high signal-to-noise ratio can be achieved with plasmonic CSRGs since they eliminate all the incident polychromatic light, except at the narrow SPR bandwidth where polarization conversion has occurred. Our group was successful in using CSRGs for the fabrication of very accurate biosensors for the detection of proteins [21] and bacteria [23]. These sensors had a maximum sensitivity of 647 nm/RIU, a resolution on the order of 10−6 RIU and were successfully used to detect a minimum concentration of 105 CFU/ml of E. Coli bacteria in a water-based solution. A single plasmonic chirped grating, where the grating pitch increases regularly along the grating vector, has also been proven in the past to widen the SPR wavelength bandwidth when illuminated in its entirety [24]. Another unique advantage of chirped gratings is their unique ability to produce SPRs at different wavelength bandwidth depending on the area of the grating being illuminated.
In this work, we fabricate novel nanostructures consisting of chirped-pitch crossed surface relief gratings (CP-CSRGs) and we use them as wavelength-selective sensors having the ability to generate SPR signals at different wavelengths, using the same fabricated device. These CP-CSRGs are the resulting nanostructures from the orthogonal superposition of a constant-pitch sinusoidal grating and a chirped-pitch grating, having a regularly increasing pitch along its grating vector. This unique sensor allows for real-time tunability for the detection of very small refractive index changes in a water-based solution, with a very high signal-to-noise ratio. Since CSRGs can only generate a SPR at a unique narrow wavelength bandwidth, they are limited for use at specific light wavelengths. However, CP-CSRGs are capable of operating at user-specific wavelengths depending on the location on the sample being illuminated, while maintaining the high sensitivity of a crossed grating.
2. Fabrication
The azobenzene solution containing a 3 wt.% of Disperse Red 1 azobenzene molecular glass (Solaris Chem, Montreal, Canada) to dichloromethane was spun coated on Corning 0215 soda lime glass microscope slides (Corning, New York, USA) with dimensions of 38 x 38 mm2 by 1 mm thickness. These glass slides were cleansed of dust and oils before the spin coating process to ensure a quality thin film deposition. Approximately 300 μm of azobenzene solution was deposited on each clean glass slide and spun coated at 1100 rpm for 30 seconds using a Headway Research spin-coater (Headway Research Inc., Texas, USA). This resulted in the deposition of an azobenzene thin film, having an approximate thickness of 250 nm, as measured using a Dektak II profilometer (Veeco Instruments Inc., New York, USA). The thin film was then dried and annealed in an oven at 95 degrees Celsius for 30 minutes.
The gratings were inscribed onto the azobenzene layer using a 532-nm wavelength Coherent Verdi V5 diode-pumped laser. Figure 1(a) illustrates the fabrication steps of the CP-CSRGs. In Fig. 1(b), the 532-nm laser beam passes through a spatial filter, a collimating lens, a quarter-wave plate and an iris, before being incident on a Lloyd mirror setup that is used to create an interference pattern onto the azobenzene sample. The grating’s pitch and depth are controlled by the Lloyd mirror angle and the exposure time respectively. The quarter-wave plate is used to achieve circular laser polarization. This polarization has been found to be optimal for SRG inscription on azobenzene films. The Lloyd mirror setup creates a constant light interference pattern that, when incident on the azobenzene film, creates a constant-pitch, sinusoidal surface relief grating in the form of a half-disc. The CP-CSRGs were fabricated by exposing the same azobenzene film to two different exposures, each having a different interference pattern. Both exposures were carried out at an initial 312 mW/cm2 irradiance with the Lloyd mirror angle set to generate a 550-nm constant-pitch interference pattern. The first inscription was for a constant-pitch linear grating and the exposure time was 120 secs. During the first exposure, the cylindrical lens, seen in Fig. 1(b) in the direct laser path, was removed. For the second orthogonal grating inscription, the sample was rotated 90 degrees from its original position and a cylindrical lens, having a 4-mm diameter, was positioned 38 mm away from the sample. The second exposure only lasted for 60 secs. This exposure time was optimized to attempt having almost equal modulation depths of the two superimposed orthogonal gratings. This is not an easy task since the laser irradiance changes due to the presence of the cylindrical lens. Finally, the fabricated CP-CSRG were in the shape of a half-disc with an approximate 25 mm2 area and they were coated with a 60-nm layer of silver using a Bal-Tec SCD 050 sputter coater.
Fig. 1 Illustration of DLIP inscription of CP-CSRGs onto an azobenzene film. a) The step-by-step process of the device fabrication starting with the spin coating of the azobenzene glass, then the imprinting of the gratings, and finally the coating of the grating with a silver layer, b) the optical setup used to inscribe the gratings onto the azobenzene film and c) an AFM image of the CP-CSRG.
The metallic CP-CSRGs were imaged using a Dimension Edge Atomic Force Microscope (AFM) (Bruker, Massachusetts, USA). The AFM tip scanned the surface using peak-force tapping mode, on a 5 x 5 μm area, with a scan rate of 1 Hz per line. The collected images were then corrected and fitted by a built-in 2D plane fit function in the AFM software. Several images were taken on each CP-CSRG at distance intervals 0.5 mm from one edge of the chirped grating vector to the opposing edge 4 mm away. A sample AFM image, taken at the 3.5 mm mark on a CP-CSRG, is presented in Fig. 1(c). All the AFM images were analyzed using the Bruker NanoScope Analysis software program to obtain numerical values of the localized pitch and depth of several locations on each CP-CSRG. The measurement uncertainty for these values is approximately 5 nm.
The SPR light spectrum was acquired in transmission mode using a fiber optic CCD spectrometer (Edmund Optics Inc., New Jersey, USA). Measurements were obtained using the experimental setup illustrated in Fig. 2. An Oriel Corp. halogen lamp (Newport Corporation, California, USA) was used to generate the white light that passed through a square aperture and then a variable neutral density filter and an iris. Then, the light passed through a horizontal linear polarizer, whose transmission axis was set to be parallel to the grating vector of the chirped grating. The polarized light was then focused to a 1 x 1 mm2 spot size onto a small area of the metallic CP-CSRG using a convex lens with 20 cm focal length. A SPR was generated by the chirped grating at the desired wavelength and the plasmonic energy was re-radiated by the orthogonal constant-pitch grating in the orthogonal light polarization, as explained elsewhere [22]. Subsequently, the transmitted light through the device was re-collimated by another identical lens and it passed through another polarizer whose transmission axis was set to be perpendicular to that of the first polarizer. This effectively cancelled all the non-SPR transmitted light and only the polarization-converted SPR light was incident on the spectrometer. Finally, the tunability of this CP-CSRG sensor was tested by removing the white lamp source and substituting it with two different low-power probe lasers having 632.8 nm and 532 nm wavelength. These lasers were collimated and made incident on various locations on the CP-CSRG. Spectroscopic measurements were taken at 1 mm intervals along the chirped grating vector.
The sensitivity of the CP-CSRG sensor was obtained by measuring the SPR spectrum and analyzing the corresponding SPR wavelength shift in 5 different aqueous sucrose solutions, having sucrose weight concentrations of , , , and in purified water. An example of representative SPR plots of the light transmission as a function of wavelength can be found elsewhere [21]. Each sucrose solution’s refractive index was measured using an Abbe refractometer (Shanghai Optical Instruments, China) to quantify the refractive index / sucrose solution correlation. For the SPR sensing, a polydimethylsiloxane (PDMS) well of approximately 2 mm thickness was positioned over the CP-CSRG and each solution was deposited individually on the sensor while using a cover glass for the PDMS well. The SPR signal was acquired in transmission at varying locations across the chirped grating as previously explained.
3. Results and discussion
Figure 3 displays information collected using the AFM scans on the surface properties of a CP-CSRG along a varying linear distance along the chirped grating vector. In Fig. 3(a), the two superimposed gratings’ pitch is measured from 0 to 4 mm at 0.5 mm intervals. As expected, the vertical grating has a constant pitch, while the horizontal grating exhibits a pitch variation from left to right at a rate of c.a. 10 nm/mm. The wide range of pitches available on the CP-CSRG provide a potential for sensing at various light wavelengths. At normal incidence, the theoretical SPR wavelength is given by the following equation [15]
where is the pitch of the grating, n is the refractive index of the dielectric and is the real part of the permittivity of the metal. Based on the measured CP-CSRG pitches in Fig. 3(a), a SPR should be theoretically excited at a silver / pure water interface at a wavelength range between c.a. 717 nm and 766 nm at locations from 0 mm and 4 mm respectively along the chirped grating vector. In these calculations, the refractive index of water was taken to be 1.33 and the real part of the permittivity of the silver layer was taken to be −24.3 and −28.3 at the wavelengths of 717 nm and 766 nm respectively [25]. In Fig. 3(b), the modulation depth of the constant-pitch and chirped-pitch gratings is plotted at various locations along the chirped grating vector. A maximum depth difference of c.a. 53 nm and a minimum depth difference of c.a. 6 nm were obtained at 1.0 mm and 3.5 mm respectively. This depth variation is most likely associated with the Gaussian nature of the inscribing laser beam, as well as the irradiance re-distribution by the cylindrical lens along the collimated laser beam path. The modulation depth of our gratings was optimized through trial and error in order to obtain the strongest SPR polarization conversion signal between the crossed gratings. Furthermore, it is known that the grating depth can affect the SPR signal strength and could potentially lead to plasmonic bandgaps in the SPR spectrum [26]. Hence, if a grating is too deep, the SPR bandwidth will widen, and this will eventually lead to a loss of resolution when these gratings are used as sensors. If the grating depth is too low, the SPR signal will be too weak. Therefore, an optimization process was done by fabricating and testing several CP-CSRGs with different relative modulation depths between the crossed gratings. The data shown in Fig. 3 is that of the optimized device.Fig. 3 AFM analysis of the CP-CSRG at varying points along the chirped grating vector, a) depicts the change in the gratings’ pitch and b) depicts the change in the gratings’ modulation depth.
The SPR signal from the CP-CSRG was obtained at varying bulk refractive index of sucrose solutions. The sensitivity of the device would be represented by the nanometric shift of the SPR wavelength divided by the refractive index unit (RIU) change. Five solutions of increasing sucrose concentration in pure water were tested. The refractive indices of each solution were measured to be 1.3325, 1.3396, 1.3460, 1.3530, and 1.3580 for 0%, 5%, 10%, 15%1 and 20% wt.% of sucrose concentration respectively. The measured SPR wavelength shift as a function of linear distance along the chirped grating vector are presented in Fig. 4(a) using sucrose solution concentrations varying from 0% to 20%. From this figure, the SPR wavelength shift was calculated to be 9.7 nm/mm, 9.6 nm/mm, 10.5 nm/mm, 10.4 nm/mm, and 10.5 nm/mm at 0%, 5%, 10%, 15% and 20% wt.% of sucrose concentration respectively. On average, the SPR signal shifted by 10.1 nm/mm along the chirped grating vector. Also, the SPR wavelength shift was plotted as a function of the sucrose concentration at various locations along the sample, as seen in Fig. 4(b). The bulk sensitivities at 0 mm, 1 mm, 2 mm, 3 mm, 4 mm linear distance along the chirped grating vector were calculated from this figure and they were 532.7 nm/RIU, 745.7 nm/RIU, 538.0 nm/RIU, 619.2 nm/RIU and 778.6 nm/RIU respectively. The difference in bulk sensitivity at different locations on the CP-CSRG is most likely related to the varying modulation depths of the gratings. Regardless, these measurements highlight the potential use of this device as a tunable sensor. Furthermore, when using polychromatic incident light, the CP-CSRG enabled the optimization of the greatest plasmonic energy exchange between the two gratings, which in turn, gave an observed sensitivity of 778.6 nm/RIU at 4 mm distance along the chirped grating vector. This constitutes one of the highest sensitivities reported to date for grating-based sensing.
Fig. 4 SPR signal and sensing performance of a CP-CSRG. a) The SPR wavelength shift across the chirped grating with an average of 10 nm/mm at increasing sucrose concentration solutions and b) the SPR wavelength shift per refractive index unit increase along the chirped grating.
To further highlight the utility of the CP-CSRGs as tunable sensors, wavelength-selective SPR measurements were undertaken using two different low-power probe lasers. The monochromatic nature of the laser beam allows for the excitation of only a single SPR wavelength. Therefore, unless the conditions in Eq. (1) are satisfied, a SPR will not be excited.
These monochromatic SPR measurements, shown in Fig. 5, showcase the wavelength tunability of the CP-CSRG device. With a pure water solution over the gratings, a 532-nm green laser and a 632-nm red laser were used separately to probe SPR excitations on various locations along the chirped grating vector, in lieu of the white light source. The SPR signal intensity is plotted as a function of a narrow wavelength range and as a function of the incident light location along the chirped grating vector. The maximum SPR signal was observed at the 2-mm grating location for the green laser, while the maximum SPR signal was observed at the 5-mm grating location using the red laser. This indicates that the SPR is being excited at different locations on the device depending on the incident light wavelength.
Fig. 5 Normalized SPR signal strength as a function of wavelength and location on the CP-CSRG for a) 532-nm green laser and b) 632-nm red laser.
4. Conclusion
Two-dimensional chirped-pitch crossed surface relief gratings (CP-CSRGs) sensors were fabricated on azobenzene thin-films by superimposing a constant-pitch grating with a variable (chirped) pitch grating in the orthogonal direction. When coated with a layer of silver, the fabricated CP-CSRG device was successfully used as a tunable plasmonic sensor. Using a transmission-based optical set-up, when the CP-CSRG was placed in between two crossed polarizers, the incident light polarization was rotated only at the SPR wavelength, while eliminating all the background light noise. Due to the varying pitch of the second superimposed grating, the generated SPR wavelengths can be tuned depending on the location along the chirped grating vector of the CP-CSRG. The maximum observed SPR wavelength shift was 10.5 nm/mm. Furthermore, the bulk sensitivity of the CP-CSRG was measured using five different aqueous sucrose solutions at varying refractive index and a maximum sensitivity of 778.6 nm/RIU was obtained. Finally, the CP-CSRG sensor’s SPR wavelength tunability was demonstrated using two different monochromatic light beams and it was shown that SPR from the different monochromatic beams can be excited on different locations on the device.
Funding
Natural Sciences and Engineering Research Council of Canada (NSERC) (RGPIN-2015-05743 and RGPIN-201-05138); Canada Foundation for Innovation Leaders Opportunity Fund Program (31967).
Acknowledgments
RGS acknowledges funding from Natural Sciences and Engineering Research Council of Canada (NSERC) RGPIN-2015-05743. CE acknowledges funding from Natural Sciences and Engineering Research Council of Canada (NSERC) RGPIN-201-05138 and Canada Foundation for Innovation Leaders Opportunity Fund Program (No. 31967).
References
1. J. G. Gordon II and S. Ernst, “Surface plasmons as a probe of the electrochemical interface,” Surf. Sci. 101(1–3), 499–506 (1980). [CrossRef]
2. A. K. Sharma, R. Jha, and B. Gupta, “Fiber-optic sensors based on surface plasmon resonance: a comprehensive review,” IEEE Sens. J. 7(8), 1118–1129 (2007). [CrossRef]
3. W. B. Lin, N. Jaffrezic-Renault, A. Gagnaire, and H. Gagnaire, “The effects of polarization of the incident light-modeling and analysis of a SPR multimode optical fiber sensor,” Sens. Actuator A-Phys. 84(3), 198–204 (2000). [CrossRef]
4. Q. Wang and W.-M. Zhao, “Optical Methods of Antibiotic Residues Detections: A Comprehensive Review,” Sens. Actuator B-Chem. 269(15), 238–256 (2018). [CrossRef]
5. M. Soler, P. Mesa-Antunez, M.-C. Estevez, A. J. Ruiz-Sanchez, M. A. Otte, B. Sepulveda, D. Collado, C. Mayorga, M. J. Torres, E. Perez-Inestrosa, and L. M. Lechuga, “Highly sensitive dendrimer-based nanoplasmonic biosensor for drug allergy diagnosis,” Biosens. Bioelectron. 66(15), 115–123 (2015). [CrossRef] [PubMed]
6. Q. Wang and W.-M. Zhao, “A comprehensive review of lossy mode resonance-based fiber optic sensors,” Opt. Lasers Eng. 100, 47–60 (2018). [CrossRef]
7. S. D. Mazumdar, M. Hartmann, P. Kämpfer, and M. Keusgen, “Rapid method for detection of Salmonella in milk by surface plasmon resonance (SPR),” Biosens. Bioelectron. 22(9-10), 2040–2046 (2007). [CrossRef] [PubMed]
8. F.-C. Chien, J.-S. Liu, H.-J. Su, L.-A. Kao, C.-F. Chiou, W.-Y. Chen, and S.-J. Chen, “An investigation into the influence of secondary structures on DNA hybridization using surface plasmon resonance biosensing,” Chem. Phys. Lett. 397(4–6), 429–434 (2004). [CrossRef]
9. S. A. Maier, “Excitation of surface plasmon polaritons at planar interfaces,” in Plasmonics: fundamentals and applications, S. A. Maier, (Springer, 2007), pp. 39–52.
10. J. Homola and M. Piliarik, “Surface plasmon resonance (SPR) sensors,” in Surface plasmon resonance based sensors, J. Homola, (Springer, 2006), pp. 45–67.
11. A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. A Hadrons and Nuclei 216(4), 398–410 (1968). [CrossRef]
12. E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A 23(12), 2135–2136 (1968). [CrossRef]
13. L. Lévesque and P. Rochon, “Surface plasmon photonic bandgap in azopolymer gratings sputtered with gold,” J. Opt. Soc. Am. A 22(11), 2564–2568 (2005). [CrossRef] [PubMed]
14. R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21(22), 1530–1533 (1968). [CrossRef]
15. J. Homola, I. Koudela, and S. S. Yee, “Surface plasmon resonance sensors based on diffraction gratings and prims couplers: sensitivity comparison,” Sens. Actuator B-Chem. 54(1–2), 16–24 (1999). [CrossRef]
16. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuator B-Chem. 54(1–2), 3–15 (1999). [CrossRef]
17. E. M. Munoz, S. Lorenzo-Abalde, A. González-Fernández, O. Quintela, M. Lopez-Rivadulla, and R. Riguera, “Direct surface plasmon resonance immunosensor for in situ detection of benzoylecgonine, the major cocaine metabolite,” Biosens. Bioelectron. 26(11), 4423–4428 (2011). [CrossRef] [PubMed]
18. P. Rochon, E. Batalla, and A. Natansohn, “Optically induced surface gratings on azoaromatic polymer films,” Appl. Phys. Lett. 66(2), 136–138 (1995). [CrossRef]
19. J. Leibold, P. Snell, O. Lebel, and R. G. Sabat, “Design and fabrication of constant-pitch circular surface-relief diffraction gratings on disperse red 1 glass,” Opt. Lett. 39(12), 3445–3448 (2014). [CrossRef] [PubMed]
20. N. Swanson and R. G. Sabat, “Inscription and analysis of non-uniform diffraction gratings in azobenzene molecular glass thin films,” Opt. Express 26(7), 7876–7887 (2018). [CrossRef] [PubMed]
21. S. Nair, C. Escobedo, and R. G. Sabat, “Crossed surface relief gratings as nanoplasmonic biosensors,” ACS Sens. 2(3), 379–385 (2017). [CrossRef] [PubMed]
22. R. G. Sabat, N. Rochon, and P. Rochon, “Dependence of surface plasmon polarization conversion on the grating pitch,” J. Opt. Soc. Am. A 27(3), 518–522 (2010). [CrossRef] [PubMed]
23. S. Nair, J. Gomez-Cruz, Á. Manjarrez-Hernandez, G. Ascanio, R. G. Sabat, and C. Escobedo, “Selective uropathogenic E. Coli detection using crossed surface-relief gratings,” Sensors (Basel) 18(11), 3634–3646 (2018). [CrossRef] [PubMed]
24. E. Bailey and R. G. Sabat, “Surface plasmon bandwidth increase using chirped-pitch linear diffraction gratings,” Opt. Express 25(6), 6904–6913 (2017). [CrossRef] [PubMed]
25. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
26. W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996). [CrossRef] [PubMed]
