Theoretical and experimental studies were undertaken to investigate the grating-coupled excitation of multiple surface-plasmon-polariton (SPP) waves guided by the periodically corrugated interface of a metal and a chiral sculptured thin film (STF). The rigorous coupled-wave approach was adapted to calculate the absorptance spectrum of a structure comprising a chiral STF atop a rectangular metallic grating when that structure is illuminated by a linearly polarized plane wave whose wavevector lies wholly in the corrugation plane. The incidence direction could be either normal or oblique with respect to the thickness direction of the structure. High-absorptance bands for both - and -polarized incident plane waves were found to be correlated with the SPP wavenumbers calculated from the solution of the underlying canonical boundary-value problem, indicating that multiple distinct SPP waves can be excited at a specific frequency. The resistive-heating thermal evaporation technique was used to deposit chiral STFs of zinc selenide on gold gratings made by electron-beam lithography, and transmittance and reflectance spectra of the fabricated structures were measured in a variable-angle spectroscopic system in order to qualitatively validate the theoretical understanding. Several high-absorptance bands were found to be almost unaffected by the number of periods of the chiral STF. The existence of these bands indicated that as many as three distinct SPP waves were excited at a specific frequency in several spectral regimes by - and/or -polarized incident light.
© 2017 Optical Society of America
The surface-plasmon-polariton (SPP) wave is an electromagnetic wave guided by the planar interface of a metal and a dielectric material [1,2]. The fields of the SPP wave are confined to the vicinity of the interface and are therefore very sensitive to small changes in the constitutive properties near the interface. This characteristic of SPP waves is exploited in (i) highly sensitive and label-free sensors for detecting chemicals [3–6] and (ii) microscopes with subwavelength resolution to obtain images of objects with very low contrast, without the use of dyes or markers [7–9]. Applications of SPP waves are on the horizon in the area of communications as well [10–13].
Most researchers on SPP waves consider the partnering dielectric material to be homogeneous. The solution of time-harmonic Maxwell equations then quickly shows that only one SPP wave can propagate in a specific direction along the interface at a fixed frequency [2,3,6]. Furthermore, this SPP wave is constrained to be polarized.
Multiple SPP waves of the same frequency but propagating with different propagation speeds, attenuation rates, and spatial profiles would be very desirable. The existence of multiple isofrequency SPP waves propagating along a specific direction in the interface plane is possible if the dielectric partnering material is periodically nonhomogeneous in the direction normal to the interface plane. This has been established both theoretically  and experimentally [14–16].
Of the possible periodically nonhomogenous dielectric materials for the excitation of multiple surface waves, sculptured thin films (STFs) with chiral morphology are easy to fabricate [17,18]. An STF is an assembly of parallel and identical nanowires that can be fabricated by directing a collimated vapor flux at a planar substrate under conditions of controlled temperature and pressure. This fabrication technique is called physical vapor deposition . If the substrate is held fixed during the fabrication process, columnar thin films comprising straight nanowires grow . If the substrate is rotated at a steady rate about an axis passing normally through it, the nanowires are helical and the film is a chiral STF [17,18].
The theory of excitation of multiple SPP waves guided by a planar metal/chiral-STF interface was established  for the prism-coupled configuration, which is commonly used to launch SPP waves for optical sensing and microscopy [3–9]. Also, multiple SPP waves guided by a planar metal/chiral-STF interface were launched and detected experimentally [22–24].
The prism-coupled configuration offers ease of the excitation of SPP waves. The only requirement is that the refractive index of the prism must be sufficiently high [3,25]. In particular, that refractive index must be higher than the ratio of the real part of the wavenumber of the SPP wave of interest and the free-space wavenumber [15,21–24]. The grating-coupled configuration  offers an alternative approach without the need of any prism, and therefore can potentially excite all possible SPP waves. Therefore, we set out to investigate the excitation of SPP waves guided by the metal/chiral-STF interface in the grating-coupled configuration.
In this paper, the theory and the experimental confirmation of exciting multiple SPP waves guided by the periodically corrugated interface of a metal and a chiral STF for the grating-coupled configuration are reported. The corrugations are taken along the axis, the grating is invariant along the axis, and the axes of the helical nanowires of the chiral STF are parallel to the axis of a Cartesian coordinate system. The organization of this paper is as follows: Section 2 adapts the formulation  of the canonical boundary-value problem underlying SPP-wave propagation guided by a planar metal/chiral-STF interface, provides the theoretical procedure to solve for the plane-wave response of a structure containing a periodically corrugated interface of a metal and a chiral STF, and presents numerical results obtained for both theoretical problems. Section 3 describes the procedures to fabricate a structure comprising a chiral STF deposited on a metal grating and to measure the remittances of that structure, and concludes with experimental data that indicate the excitation of multiple SPP waves. The paper concludes with some remarks in Section 4.
An time dependence is implicit in Section 2, with as the angular frequency, as time, and . The free-space wavenumber, the free-space wavelength, and the intrinsic impedance of free space are denoted by , , and , respectively, with being the permeability and the permittivity of free space. Vectors are in boldface, column vectors are in boldface and enclosed within square brackets, dyadics are underlined twice, and matrices are underlined twice and square-bracketed. The position vector is denoted by , where , , and are the Cartesian unit vectors.
2. THEORETICAL WORK
A. Constitutive Parameters of a Chiral STF
A cross-sectional scanning-electron micrograph of a chiral STF is shown in Fig. 1. Clearly, the chiral STF is an assembly of parallel nanohelixes. Macroscopically, a chiral STF may be modeled as a unidirectionally nonhomogeneous continuum with the relative permittivity dyadic 
B. Canonical Boundary-Value Problem
In order to set up the canonical boundary-value problem of SPP-wave propagation, let the half-space be occupied by a metal with relative permittivity and the half-space by a chiral STF, as shown schematically in Fig. 2. Suppose that the SPP waves propagate parallel to the unit vector , , and attenuate as .
The electromagnetic field phasors in the metal may be written as
The field representation in the region requires the definition of auxiliary field phasors and as follows:1) yields two algebraic and four differential equations. These equations yield the -matrix ordinary differential equation 7) in order to compute the matrix that appears in the relation  9) and (10) yields the identity
Satisfaction of the usual four boundary conditions across the interface amounts to enforcement of the equality  , where the column 4-vector can be obtained using Eqs. (3) and (4). All four boundary conditions can be compactly represented as
C. Grating-Coupled Configuration
Solution of the canonical problem yields values of the SPP wavenumber as well as spatial profiles of the fields associated with each SPP wave. However, as discussed in Section 1, the grating-coupled configuration allows for excitation of SPP waves in a practical manner without using a prism.
Let us consider the boundary-value problem for the grating-coupled configuration  shown schematically in Fig. 3. The half-spaces and are vacuous. The region is occupied by the chiral STF with relative permittivity dyadic (1). The region is occupied by a metal with a uniform relative permittivity . The region contains a surface-relief grating of period , the interface of the metal and the chiral STF being specified by the function . Therefore, the relative permittivity dyadic in the region can be specified as
The face of the structure is illuminated by a plane wave propagating in the plane and making an angle with the axis. The incident electromagnetic field phasors may be written in terms of Floquet harmonics as [2,27,28]
In Eqs. (18), (21), and (23), the unit vectors represent the -polarization state and the unit vectors represent the -polarization state. The amplitudes , and at least one of the amplitudes and is nonzero. All reflection amplitudes and transmission amplitudes , , are unknown and have to be determined.
The unknown amplitudes can be obtained using the rigorous coupled-wave approach (RCWA) [2,28]. In the region , both and are expanded in terms of Floquet harmonics with respect to ; likewise, the relative permittivity dyadic is expanded in terms of a Fourier series with respect to . For implementation on a digital computer, the numbers of terms in the expansions are restricted to such that . The region is divided into electrically thin slices parallel to the plane , and the material in each slice is taken to be homogeneous with respect to . The region is divided into electrically thin homogeneous slices. Thus, the total number of slices in the region equals . A stable algorithm is used to determine the unknown reflection and transmission amplitudes [2,29–31].
For planewave illumination, . The elements of the matrices in the relations
D. Numerical Results and Discussion
Calculations of , , and were made for . For realistic numerical results, a single-resonance Lorentz model  was used for each of the relative permittivity scalars as follows:32], we used , , , , , , and . Choosing gold as the metal, we used measured values of for a thermally evaporated gold film .
In order to calculate and , we set , , and . Although the RCWA can be used for high values of the grating depth , the choice of 20 nm is close to the planar interface treated in the canonical boundary-value problem but will still excite Floquet harmonics of order [34,35]. Furthermore, we chose the grating function
Equation (15) was solved for several values of numerically using a combination of search and Newton–Raphson methods . For each solution that represents an SPP wave propagating parallel to , there is a solution representing an SPP wave propagating parallel to . As an example, plots of the real and the imaginary parts of the relative wavenumbers of SPP waves in Fig. 4 for and clearly show that multiple SPP waves with differences in phase speed and propagation length can be excited at a fixed value of to propagate in a specific direction in the plane. Parenthetically, any procedure to search for solutions of implicit equations, such as Eq. (15), can miss some solutions.
An SPP wave predicted by the solution of the canonical boundary-value problem can be excited as a Floquet harmonic of order in the grating-coupled configuration by a plane wave, if the relation5. The figure shows that the excitation of SPP waves is possible at multiple angles of incidence of monochromatic light for . A map such as the one in Fig. 5 is very helpful in choosing the period of the grating to excite multiple SPP waves at a fixed frequency in the grating-coupled configuration.
The excitation of SPP waves in the grating-coupled configuration is indicated by the presence of high-magnitude bands in the absorptance spectrum that do not change when the thickness of the dielectric material (chiral STF in the present case) on top of the metallic grating is changed beyond a sufficiently large value . Confidence in the identification increases when the thickness-independent high-absorptance bands in the plane also match the predictions of the canonical boundary-value problem.
We computed the absorptances and for chiral STFs of thickness and gratings of depth . The results for and are presented in Fig. 6 with and without being overlaid by Fig. 5. The plots of and show that the predictions of the canonical boundary-value problem agree with some high-absorptance bands. These bands were also found not to change significantly when was used for calculations. Therefore, these SPP waves are excited by -polarized incident plane waves. Some of the predicted SPP waves are also excited by -polarized incident plane waves, as can be seen from the plots of . However, experience indicates that not every SPP wave predicted by the solution of the canonical boundary-value problem is strongly excited in the grating-coupled configuration, because the partnering dielectric material is of finite thickness in the grating-coupled configuration but not in the canonical problem [37,38].
Figure 7 is analogous to Fig. 6, except that the grating depth was increased to 120 nm. Fewer predictions from Fig. 5 can be found to hold in Fig. 7, because grating troughs shift and split absorptance peaks on the axis. The deeper the troughs, the more is their effect, as has been established theoretically as well as experimentally [39,40].
3. EXPERIMENTAL WORK
Experimental work on the grating-coupled configuration was undertaken in order to validate the theoretical understanding. The validation could only be qualitative because all parameters appearing in the relative permittivity dyadic of any chiral STF have never been completely determined, although chiral STFs have been routinely deposited on planar substrates for over two decades now [2,18]. After fabricating metallic gratings, we deposited chiral STFs thereon and then measured the specular reflectances and transmittances for illumination by linearly polarized plane waves.
A. Fabrication of Metallic Grating
A gold grating was fabricated on a silicon wafer using electron-beam lithography  as follows. A 15-nm-thick adhesive layer of titanium was deposited on a silicon wafer using electron-beam evaporation [18,42] on a LAB 18 modular thin-film deposition system (LAB 18, Kurt J. Lesker, Jefferson Hills, Pennsylvania, USA). A layer of photoresist diluted with anisole was spin-coated on the titanium layer. A pattern comprising 150-nm-thick parallel lines spaced 150 nm apart was exposed using a 12 nA 200 μm electron beam with 20 nm beam step size and dose. The sample was immersed first in n-amyl acetate for 3 min and then in 2-propanol for 1 min. The top surface was blow dried with nitrogen and the pattern was developed with developer for 45 s, then rinsed with deionized water, and finally dried by blowing nitrogen. Residual photoresist was removed in a descumming process in the M4L150 Plasma System (MetroLine, Corona, California, USA) with the radiofrequency power set at 100 W; oxygen flowing at 150 sccm and helium flowing at 50 sccm were applied for flushing for 60 s at a working pressure of 550 mTorr. A refurbished e-gun/thermal evaporator (Semicore, Livermore, California, USA) was then used to deposit 15-nm-thick titanium and 75-nm-thick gold layers in succession.
For the lift-off process, the sample was first rinsed with acetone and 2-propanol for 15 min and 2 min, respectively. Then the PRS-3000 photoresist stripper was used at 80°C for 15 min, followed by rinsing with 2-propanol for 3 min. Subsequent rinsing in deionized water and drying with nitrogen was followed by the descumming process for 90 s in the M4L150 Plasma System with the radiofrequency power set at 200 W, oxygen flowing at 150 sccm, helium flowing at 50 sccm, and 550 mTorr pressure. The last step was to deposit a 30-nm-thick layer of gold on the top of the sample using the LAB 18 system.
The top-view image of a gold grating on a silicon wafer acquired on a scanning electron microscope (SEM) (FEI Nova NanoSEM 630, Hillsboro, Oregon, USA) is shown in Fig. 8. The gold ridges are in width and the spacing between adjacent ridges is ; thus, and .
B. Deposition of Chiral STF
A structurally right-handed () 5-period-thick chiral STF was deposited on the gold grating in a custom-made low-pressure chamber by the resistive-heating thermal evaporation technique [18–20] as follows.
2 g zinc selenide (ZnSe) powder (Alfa Aesar, Ward Hill, Massachusetts, USA) was placed in a tungsten boat (S6-.005W, R. D. Mathis, Long Beach, California, USA) that was secured as a heating element in an electrical heater located inside the low-pressure chamber. About 15 cm above the boat, the gold grating was affixed to a planar platform using Kapton tape (E. I. du Pont de Nemours, Wilmington, Delaware, USA). The grating was positioned so that the grating lines were oriented parallel to the axis. The platform can rotate about a central normal axis (the axis) passing through it and rock about the axis, with motors for both motions controlled externally using a desktop computer. A quartz crystal monitor (QCM) was mounted close to the gold grating in order to monitor the deposition rate. A shutter was rotated into position between the boat and the grating. The chamber was closed and pumped down to a base pressure of 0.6 μTorr. Then a 101 A current was passed through the boat, and the rocking motor was used to orient the grating so that the collimated ZnSe vapor flux would be directed at an angle with respect to the plane.
A computer-controlled rotating motor was then turned on to implement the serial bideposition technique . The deposition of one period of the chiral STF was set to occur in 120 cycles. At the beginning of each cycle, deposition would occur for . Then the platform would be rotated about the axis by 180° in , further deposition would then occur for , and the platform would be then rotated by 183° about the axis in as the last step of the cycle. Thus, the duration of the deposition of one period was 750 s. The QCM readings were used to maintain the deposition rate at , which would yield . After the shutter was rotated to allow the collimated vapor flux to reach the slide, five periods of the chiral STF were deposited. The motors were then paused, the slide was shuttered off, inlet valves were opened to bring the chamber back to 1 atm, and the chamber was opened.
In order to deposit a 7-period-thick chiral STF, the foregoing process was implemented first to deposit the first five periods. Then the boat was reloaded with ZnSe and two more periods were deposited.
The cross-sectional SEM images of the two samples are shown in Fig. 9. In the sample with the 5-period chiral STF [Fig. 9(a)], a -nm-thick layer of gold lies on top of the silicon wafer. On top of this gold layer is the gold grating with an average depth . Together, the five periods of the chiral STF have an average height of 1.75 μm, so that . Because of the fluctuations in the deposition rate and the inertia of the rotating motor, this value is different from the targeted value of 150 nm. Another reason for the difference is that the sample did not cleave vertically but with a tilt, leading to an overestimation of heights from the cross-sectional SEM image. From the SEM image of the sample with the 7-period chiral STF [Fig. 9(b)], the estimates are as follows: , , and . The cleavage plane for the second sample is very likely more tilted than for the first sample.
C. Optical Characterization
The optical-characterization procedure described in detail elsewhere  to explore the circular Bragg phenomenon was adapted to measure the spectra of the eight specular remittances (, etc., and , etc.) of a chiral STF deposited on top of the gold grating. In a custom-made variable-angle spectroscopic system, a halogen light source (HL-2000, Ocean Optics, Dunedin, Florida, USA) was used. The light from that source traveled through a Glan-Taylor linear polarizer (GT10, ThorLabs, Newton, New Jersey, USA) located inside a lens tube mount (SM1PM10, ThorLabs) before illuminating the sample at an angle in the plane. Then either the specularly transmitted or reflected light went through a second linear polarizer (GT5, ThorLabs) before getting detected by a CCD spectrometer (HRS-BD1-025, Mightex Systems, Pleasanton, California, USA). The intensity of light detected by the spectrometer when the sample is absent was used for normalization for all measurements. The first and the second polarizers were adjusted for , , , and combinations. The angle varied from 10° to 70° for reflectance measurements, but from 0° to 70° for transmittance measurements. The wavelength varied from 600 to 900 nm.
All specular transmittances were found to be infinitesimal at most. No nonspecular transmittance was detected either. This was not surprising because of the 30-nm-thick gold layer and the silicon wafer in the sample. No nonspecular reflectances could also be detected. Given that and , all nonspecular reflectances must theoretically be null valued. Therefore,
Plots of the measured values of and in the plane of both samples are presented in Fig. 10. One sample comprises a 5-period-thick chiral STF, the other a 7-period-thick chiral STF. The high-absorptance bands in all of these plots are very similar to those in their theoretical analogs presented in Figs. 6 and 7: the bands that tilt leftward and the bands that curve rightward, as increases. Similar features can be seen as the predictions for SPP-wave excitation in Fig. 5 emerging from the SPP wavenumbers presented in Fig. 4.
Several high-absorptance bands in Fig. 10 for the sample with the 5-period-thick chiral STF appear similar to some high-absorptance bands for the sample with the 7-period-thick chiral STF. In Fig. 11(a), several high-absorptance bands for the sample with the 5-period-thick chiral STF are identified by black dashed lines. The same lines are overlaid in Fig. 11(b) for the sample with the 7-period-thick chiral STF in order to identify those features that are either not affected at all or are affected slightly by the increase in the number of periods. The bands that are not highly affected by the number of periods (beyond a threshold value  not investigated here) in the chiral STF must represent the excitation of the phenomena whose electromagnetic fields are localized to the metal/chiral-STF interface within a distance less than 5 periods normally on the chiral-STF side of the interface. These phenomena are SPP waves [2,44].
Thus, we have experimentally shown that SPP waves guided together by a metal and a chiral STF can be excited in the grating-coupled configuration. Furthermore, as many as three distinct SPP waves can be guided along the axis in several spectral regimes, and these SPP waves can be excited by - as well as -polarized incident light.
4. CONCLUDING REMARKS
Excitation of multiple SPP waves due to the interface of a metallic grating and a chiral sculptured thin film was investigated and confirmed both theoretically and experimentally.
In the theoretical part of our investigation, the rigorous coupled-wave approach was used to calculate the absorptance of a structure comprising a chiral STF atop a rectangular metallic grating when that structure is illuminated by a linearly polarized plane wave whose wavevector lies wholly in the corrugation plane. The incidence direction could be either normal or oblique with respect to the thickness direction of the structure, and the polarization state of the incident plane wave could be either or . High-absorptance bands in the plane were correlated with the SPP wavenumbers calculated from the solution of the underlying canonical boundary-value problem. Our results indicated that multiple distinct SPP waves can be excited at a specific frequency by varying the incidence direction in the grating-coupled configuration.
In the experimental part of our investigation, first the resistive-heating thermal evaporation technique was used to deposit chiral STFs of zinc selenide on gold gratings made by electron-beam lithography. Then the transmittance and reflectance spectra of the fabricated structures were measured using a custom-made variable-angle spectroscopic system in order to qualitatively validate the theoretical results. Nonspecular reflectances and specular as well as nonspecular transmittances were found to be absent, as expected from theory. Several high-absorptance bands in the plane were found to be virtually unaffected by whether the number of periods of the chiral STF was five or seven. These bands therefore indicated the excitation of SPP waves guided by the metal/chiral-STF interface. As many as three distinct SPP waves were found to be excitable by - and/or -polarized light at a specific frequency simply by choosing the appropriate angle of incidence.
Compared to the prism-coupled configuration, the grating-coupled configuration is advantageous in that a high-refractive-index prism is unnecessary and free-space excitation of SPP waves is possible. Although the guiding interface has to be periodically corrugated instead of planar, lithography and lift-off techniques are commonplace nowadays. The multiplicity of SPP waves at a specific frequency when the nonmetallic partnering material is periodically nonhomogenous offers obvious advantages for optical sensing of analytes and on-chip communication.
Turkish Ministry of National Education.
S. E. thanks the Turkish Ministry of National Education for partial financial support of her graduate studies. A. L. is grateful to the Charles Godfrey Binder Endowment at Penn State for ongoing support of his research activities.
1. A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, 1982).
2. J. A. Polo Jr., T. G. Mackay, and A. Lakhtakia, Electromagnetic Surface Waves: A Modern Perspective (Elsevier, 2013).
3. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999). [CrossRef]
4. K. Usui-Aoki, K. Shimada, M. Nagano, M. Kawai, and H. Koga, “A novel approach to protein expression profiling using antibody microarrays combined with surface plasmon resonance technology,” Proteomics 5, 2396–2401 (2005). [CrossRef]
5. V. Kanda, P. Kitov, D. R. Bundle, and M. T. McDermott, “Surface plasmon resonance imaging measurements of the inhibition of Shiga-like toxin by synthetic multivalent inhibitors,” Anal. Chem. 77, 7497–7504 (2005). [CrossRef]
6. I. Abdulhalim, M. Zourob, and A. Lakhtakia, “Surface plasmon resonance for biosensing: a mini-review,” Electromagnetics 28, 214–242 (2008). [CrossRef]
7. G. Stabler, M. G. Somekh, and C. W. See, “High-resolution wide-field surface plasmon microscopy,” J. Microsc. 214, 328–333 (2004). [CrossRef]
8. L. Berguiga, T. Roland, K. Monier, J. Elezgaray, and F. Argoul, “Amplitude and phase images of cellular structures with a scanning surface plasmon microscope,” Opt. Express 19, 6571–6586 (2011). [CrossRef]
9. L. Grave de Peralta, C. J. Regan, and A. A. Bernussi, “SPP tomography: a simple wide-field nanoscope,” Scanning 35, 246–252 (2013). [CrossRef]
10. J. S. Sekhon and S. S. Verma, “Plasmonics: the future wave of communication,” Curr. Sci. India 101, 484–488 (2011).
11. J. T. Kim, J. J. Ju, S. Park, M.-S. Kim, S. K. Park, and M.-H. Lee, “Chip-to-chip optical interconnect using gold long-range surface plasmon polariton waveguides,” Opt. Express 16, 13133–13138 (2008). [CrossRef]
12. A. V. Krasavin and A. V. Zayats, “Silicon-based plasmonic waveguides,” Opt. Express 18, 11791–11799 (2010). [CrossRef]
13. A. Emboras, C. Hoessbacher, C. Haffner, W. Heni, U. Koch, P. Ma, Y. Fedoryshyn, J. Niegemann, C. Hafner, and J. Leuthold, “Electrically controlled plasmonic switches and modulators,” IEEE J. Sel. Top. Quantum Electron. 21, 4600408 (2015). [CrossRef]
14. A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: experimental evidence,” J. Nanophoton. 3, 033506 (2009). [CrossRef]
15. S. E. Swiontek, D. P. Pulsifer, and A. Lakhtakia, “Optical sensing of analytes in aqueous solutions with a multiple surface-plasmon-polariton-wave platform,” Sci. Rep. 3, 1409 (2013). [CrossRef]
16. L. Liu, M. Faryad, A. S. Hall, G. D. Barber, S. Erten, T. E. Mallouk, A. Lakhtakia, and T. S. Mayer, “Experimental excitation of multiple surface-plasmon-polariton waves and waveguide modes in a one-dimensional photonic crystal atop a two-dimensional metal grating,” J. Nanophoton. 9, 093593 (2015). [CrossRef]
17. N. O. Young and J. Kowal, “Optically active fluorite films,” Nature 183, 104–105 (1959). [CrossRef]
18. A. Lakhtakia and R. Messier, Sculptured Thin Films: Nanoengineered Morphology and Optics (SPIE, 2005).
19. D. M. Mattox, The Foundations of Vacuum Coating Technology (Noyes, 2003).
20. I. J. Hodgkinson and Q. h. Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, 1997).
21. J. A. Polo Jr. and A. Lakhtakia, “On the surface plasmon polariton wave at the planar interface of a metal and a chiral sculptured thin film,” Proc. R. Soc. London A 465, 87–107 (2009). [CrossRef]
22. Devender, D. P. Pulsifer, and A. Lakhtakia, “Multiple surface plasmon polariton waves,” Electron. Lett. 45, 1137–1138 (2009). [CrossRef]
23. S. Erten and A. Lakhtakia, “Excitation of multiple surface-plasmon-polariton waves at metal/chiral-sculptured-thin-film interfaces,” Proc. SPIE 8465, 846513 (2012). [CrossRef]
24. S. E. Swiontek and A. Lakhtakia, “Influence of silver-nanoparticle layer in a chiral sculptured thin film for surface-multiplasmonic sensing of analytes in aqueous solution,” J. Nanophoton. 10, 033008 (2016). [CrossRef]
25. H. J. Simon, D. E. Mitchell, and J. G. Watson, “Surface plasmons in silver films—a novel undergraduate experiment,” Am. J. Phys. 43, 630–636 (1975). [CrossRef]
26. V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients (Wiley, 1975).
27. K. Rokushima, R. Antoš, J. Mistrík, Š. Višňovský, and T. Yamaguchi, “Optics of anisotropic nanostructures,” Czech. J. Phys. 56, 665–764 (2006). [CrossRef]
28. M. Onishi, K. Crabtree, and R. A. Chipman, “Formulation of rigorous coupled-wave theory for gratings in bianisotropic media,” J. Opt. Soc. Am. A 28, 1747–1758 (2011). [CrossRef]
29. L. Li, “Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity,” J. Opt. Soc. Am. A 10, 2581–2591 (1993). [CrossRef]
30. N. Chateau and J.-P. Hugonin, “Algorithm for the rigorous coupled-wave analysis of grating diffraction,” J. Opt. Soc. Am. A 11, 1321–1331 (1994). [CrossRef]
31. M. G. Moharam, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995). [CrossRef]
32. S. Erten, A. Lakhtakia, and G. D. Barber, “Experimental investigation of circular Bragg phenomenon for oblique incidence,” J. Opt. Soc. Am. A 32, 764–770 (2015). [CrossRef]
33. K. M. McPeak, S. V. Jayanti, S. J. P. Kress, S. Meyer, S. Iotti, A. Rossinelli, and D. J. Norris, “Plasmonic films can easily be better: rules and recipes,” ACS Photon. 2, 326–333 (2015). [CrossRef]
34. D. P. Nicholls, S.-H. Oh, T. W. Johnson, and F. Reitich, “Launching surface plasmon waves via vanishingly small periodic gratings,” J. Opt. Soc. Am. A 33, 276–285 (2016). [CrossRef]
35. C. Rivas, M. E. Solano, R. Rodríguez, P. B. Monk, and A. Lakhtakia, “Asymptotic model for finite-element calculations of diffraction by shallow metallic surface-relief gratings,” J. Opt. Soc. Am. A 34, 68–79 (2017). [CrossRef]
36. Y. Jaluria, Computer Methods for Engineering (Taylor & Francis, 1996).
37. G. Lévêcque and O. J. F. Martin, “Optimization of finite diffraction gratings for the excitation of surface plasmons,” J. Appl. Phys. 100, 124301 (2006). [CrossRef]
38. J. Dutta, S. A. Ramakrishna, and A. Lakhtakia, “Characteristics of surface plasmon-polariton waves excited on 2D periodically patterned columnar thin films of silver,” J. Opt. Soc. Am. A 33, 1697–1704 (2016). [CrossRef]
39. S. H. Zaidi, M. Yousaf, and S. R. J. Brueck, “Grating coupling to surface plasma waves. I. First-order coupling,” J. Opt. Soc. Am. A 8, 770–779 (1991). [CrossRef]
40. M. V. Shuba and A. Lakhtakia, “Splitting of absorptance peaks in absorbing multilayer backed by a periodically corrugated metallic reflector,” J. Opt. Soc. Am. A 33, 779–784 (2016). [CrossRef]
41. S. Thoms, “Electron beam lithography,” in Nanofabrication Handbook, S. Cabrini and S. Kawata, eds. (CRC Press, 2012).
42. R. F. Bunshah, ed., Handbook of Deposition Technologies for Films and Coatings: Science, Technology and Applications, 2nd ed. (Noyes, 1994).
43. I. Hodgkinson, Q. h. Wu, B. Knight, A. Lakhtakia, and K. Robbie, “Vacuum deposition of chiral sculptured thin films with high optical activity,” Appl. Opt. 39, 642–649 (2000). [CrossRef]
44. M. A. Motyka and A. Lakhtakia, “Multiple trains of same-color surface plasmon polaritons guided by the planar interface of a metal and a sculptured nematic thin film,” J. Nanophoton. 2, 021910 (2008). [CrossRef]