Multiple plasmonic modes with sculptured thin films

Surface-plasmon-polariton (SPP) waves are electromagnetic waves that propagate along the planar interface of a metal and a homogeneous dielectric (nonconducting) material. They have become a popular topic in contemporary research. Proposed uses include plasmonic circuits to make ultrafast computers, plasmonics-based invisibility cloaks, and highly efficient light-emitting diodes.¹ Extremely sensitive chemical and biochemical detection systems^{2, 3} and imaging systems^4,5 have already been demonstrated.

Research on SPP-wave-based chemical and biochemical detection systems in particular have flourished for over two decades. Species such as pesticides, explosives, environmental pollutants, bacteria, viruses, toxins, allergens, and biomedical analytes have been detected. Researchers remain focused on various means of exciting and detecting the SPP wave,⁶ binding of recognition molecules to the interface for detecting biomaterials,³ and incorporating surrounding structures to modify the SPP wave.^{7, 8} Our own approach has been to modify the dielectric material by making it unidirectionally periodically nonhomogeneous. The chosen dielectric materials are sculptured thin films (STFs).

An STF may be formed when a chemical vapor is directed at some angle relative to the surface of a planar substrate in a vacuum chamber. Under suitable conditions, the vapor particles spontaneously coalesce into parallel nanocolumns (∼100nm cross-sectional diameter) projecting at an angle to the substrate plane, that angle being determined by the vapor deposition angle, the vapor species, and the deposition conditions. If the substrate is rotated or rocked, the nanocolumns can form various shapes. Such ‘sculptured thin films’ can be classified as nanoengineered metamaterials.⁹

Figure 1. Schematic of the Kretschmann configuration.

We examined two types of STFs for exciting SPP waves: sculptured nematic thin films (SNTFs) and chiral STFs. SNTFs are produced by rocking the substrate to produce slanted wavy nanocolumns with essentially 2D morphology,¹⁰ while chiral STFs are produced by rotating the substrate about its normal to produce helical nanocolumns^{11, 12} with 3D morphology. In addition to functioning simply as the dielectric side of the interface along which the SPP travels, an STF may have an advantage over dense dielectric materials in certain applications because of its tailorable porosity.^{9, 13} In detector applications, STFs may allow analytes to infiltrate very close to the interface for very sensitive detection and, at the same time, filter out larger undesirable particles.

An STF is an electromagnetically complex medium because it is nonhomogeneous along the direction normal to the planar interface, and it is optically biaxial since, in general, the cross-sections of the nanocolumns are elliptical. To our knowledge, this is the first time that the properties of SPP waves have been examined at an interface involving such a complex medium. In the process of solving relevant boundary-value problems, we discovered that a metal/STF interface can simultaneously support multiple modes of SPP-wave propagation, each mode with a different set of characteristics. Some of the differing characteristics, which may be of technological use, are the phase speed, the polarization states on the two sides of the interface, and the degree of localization to the interface.

The propagation of SPP waves along a planar interface cannot be excited simply by shining light on it. Many methods have been developed to couple an incident light wave to an SPP wave. One popular method uses the Kretschmann configuration.^{14, 15} In this configuration, a very thin metallic film is impressed on the planar face of a dielectric block, and a coupling slab (often, a prism) with a sufficiently high index of refraction is placed in contact with the other side of the metal film, as shown in Figure 1. As the angle of incidence of light is changed in small steps, a sudden large drop in intensity of the reflected light indicates the excitation of an SPP wave. We chose to calculate absorbance for a more definite indication of SPP wave excitation. Conventional wisdom is that SPP waves can only be excited with incident p-polarized light (which has its electric field in the same plane as the incident ray and the normal to the substrate). Indeed, our calculations show that some SPP-wave modes at a metal/STF interface in the Kretschmann configuration may be excited by p-polarized light. Surprisingly, however, we found that other SPP-wave modes at metal/STF interfaces may be excited by s-polarized light (which has its electric field perpendicular to the plane of the incident ray and the normal to the substrate). Furthermore, conversion between the two linear polarization states can occur in STFs.

Calculations were performed for SNTFs made of titanium oxide. We considered a class of SNTFs for which the vapor deposition angle is made to vary sinusoidally as the film is grown. Such SNTFs are periodically nonhomogeneous in the thickness direction. Published empirical characterizations¹⁶ of related columnar thin films enabled us to estimate the permittivity tensors of the titanium-oxide SNTFs. The calculations were performed for an interface in the Kretschmann configuration with an aluminum film of thickness 15nm and the coupling high-index material being zinc selenide. The free-space wavelength of the incident light was fixed at 633nm. Figure 2 shows the absorbance for an SNTF consisting of two periods with a total thickness of 800nm. The average vapor deposition angle and the modulation amplitude are assumed to be 50^° and 30^°, respectively. The solid curve shows the absorbance of incident p-polarized light as a function of the angle of incidence. Sharp peaks at angles of incidence of 49.91^° and 75.73^° indicate the excitation of two different SPP-wave modes. The dashed curve shows the absorbance of s-polarized light as a function of the angle of incidence. The sharp peak at 53.32^° indicates the excitation of an SPP wave by incident s-polarized light.

Figure 2. Absorbance as a function of the angle of incidence for a titanium-dioxide-SNTF/aluminum interface in the Kretschmann configuration. The solid line is for the absorbance of p-polarized incident light, and the dashed line for the absorbance of s-polarized light. The two sharp peaks in the solid line at 49.91^°and 75.73^° indicate the excitation of SPP-wave modes by incident p-polarized light, and the sharp peak in the dashed line at 55.32^°indicates the excitation of an SPP wave by incident s-polarized light.

While growing a chiral STF, the vapor deposition angle is held fixed as the substrate is rotated about an axis passing normally through it. As the rotation speed is also fixed, helical nanocolumns grow with a certain pitch. We looked for SPP waves over a range of values of the pitch.¹⁷ Figure 3 shows the phase speed of the SPP wave modes, relative to the speed of light in free space, as a function of the reciprocal of the pitch. The metal film is, again, aluminum with a thickness of 15nm, and the chiral STF is made of titanium oxide grown with a vapor deposition angle of 20^°. We found five different modes of SPP-wave propagation, with two to four modes present for each value of the pitch investigated. In most cases we found SPP-wave propagation possible for a chiral STF that is only two pitches thick, but some modes at some values of the pitch required more pitches in order to efficiently support propagation. Each mode, except mode 5, has a lower bound of the pitch beyond which the mode ceases to exist. It was not possible to discern an upper bound of the pitch for the existence of each SPP wave mode, as serious computational difficulties were encountered at large pitch values.

Figure 3. Relative phase speed of SPP-wave modes for a chiral-STF/aluminum interface in the Kretschmann configuration. The horizontal axis is the reciprocal of the pitch multiplied by 394nm.

We have theoretically demonstrated the existence of multiple SPP-wave modes at the planar boundary of a nonhomogeneous material of a certain type (STF) and a metal. The differences in phase speed and polarization states among the modes will allow selective excitation and detection, enabling new applications of SPP waves. Other novel SPP wave behavior may yet be discovered with consideration of other forms of STF periodicity, different STF materials, and various metals. The demonstrated ability to pattern STFs using standard photolithography¹⁸ promises to open up additional applications in chemical detection and plasmonic circuits.¹⁹ We plan to intensively study the role of STF morphology in the multiplicity of modes of SPP wave propagation, with an eye toward practical feasibility. Simultaneously, we will experimentally establish that the periodic nonhomogeneity of many STFs does indeed engender that multiplicity.