Mapping the plasmon resonances of metallic nanoantennas

We study the light scattering and surface plasmon resonances of Au nanorods that are commonly used as optical nanoantennas in analogy to dipole radio antennas for chemical and biodetection field-enhanced spectroscopies and scanned-probe microscopies. With the use of the boundary element method, we calculate the nanorod near-field and far-field response to show how the nanorod shape and dimensions determine its optical response. A full mapping of the size (length and radius) dependence for Au nanorods is obtained. The dipolar plasmon resonance wavelength lambda shows a nearly linear dependence on total rod length L out to the largest lengths that we study. However, L is always substantially less than lambda/2, indicating the difference between optical nanoantennas and long-wavelength traditional lambda/2 antennas. Although it is often assumed that the plasmon wavelength scales with the nanorod aspect ratio, we find that this scaling does not apply except in the extreme limit of very small, spherical nanoparticles. The plasmon response depends critically on both the rod length and radius. Large (500 nm) differences in resonance wavelength are found for structures with different sizes but with the same aspect ratio. In addition, the plasmon resonance deduced from the near-field enhancement can be significantly red-shifted due to retardation from the resonance in far-field scattering. Large differences in near-field and far-field response, together with the breakdown of the simple scaling law must be accounted for in the choice and design of metallic lambda/2 nanoantennas. We provide a general, practical map of the resonances for use in locating the desired response for gold nanoantennas.     

Properties of TM resonances on metallic slit gratings

Electromagnetic resonances on metallic slit gratings induced by TM polarized incident light have been investigated and physically interpreted. We have developed an electromagnetic model imposing surface impedance boundary conditions on the metallic grating surface from which we derive simple formulas explaining all physical properties of these resonances. It is demonstrated that Fabry-Perot (or cavity) resonances are generated by the zeroth slit mode yielding extraordinary transmission. For very narrow slits, the resonant H-field is squeezed to the slit walls and causes enhanced power losses. The excitation of surface plasmon polaritons (SPPs), however, is generated by two mode coupling. SPPs are linked to sharp absorption peaks and dips in transmittance. It is shown that these phenomena are primarily caused by the interaction of the electromagnetic fields with the finite conducting slit walls. These findings have been confirmed by measured transmittance data of gold gratings with periods of 0.5 μm, 1 μm, and 2 μm.     

Phase constraint for the waves diffracted by lossless symmetrical gratings at Littrow mount

The energy conservation of grating diffraction is analyzed in a particular condition of incidence in which two incident waves reach a symmetrical grating from the two sides of the grating normal at the first-order Littrow mounting. In such a situation the incident waves generate an interference pattern with the same period as the grating. Thus in each direction of diffraction, interference occurs between two consecutive diffractive orders of the symmetrical incident waves. By applying only energy conservation and the geometrical symmetry of the grating profile to this problem it is possible to establish a general constraint for the phases and amplitudes of the diffracted orders of the same incident wave. Experimental and theoretical results are presented confirming the obtained relations.     

The influence of grating profile on surface plasmon polariton resonances recorded in different diffracted orders

Abstract

Nonlinear processes involved in the manufacture of nominally sinusoidal surface relief diffraction gratings can introduce distortions into the profile of these surfaces. Such distortions may dramatically affect both the specular reflectivity and diffracted efficiencies from such a surface, particularly if it is metallic. To illustrate this a comprehensive numerical modelling study of the optical coupling to surface plasmon polaritons on silver gratings has been undertaken. The grating surface profile is represented in terms of a truncated Fourier series, the effect of varying the amplitude, and then the phase, of each Fourier component in turn, is explored. This illustrates the sensitivity of individual features to specific harmonic components of the surface, for surface plasmon resonances recorded in both the zeroth and higher diffracted orders.     

Interferometric measurement of phase change on reflection

We show an interferometric method for measuring phase change with known uncertainty. Because this measurement uses the backreflection from a sample, the height is intrinsically removed, and only the phase change is measured. The uncertainty in the phase change measurement is +/-3.8 degrees and is dominated by the background subtraction method. We also investigate the effect of the phase change on the interferometric radius measurement. The theoretical worst-case error in the interferometric radius measurement due to the phase change is 30 nm.     

Grating-coupled transmission-type surface plasmon resonance sensors based on dielectric and metallic gratings

We investigated grating-coupled transmission-type surface plasmon resonance (SPR) for sensing applications. In the transmission-type SPR structure, propagating surface plasmons are outcoupled to radiation modes by dielectric and metallic gratings on a metal film. The results calculated in air and water suggest that the proposed structures present extremely linear sensing characteristics. In terms of a figure of merit, a metallic grating-based structure performs 5.4 and 3.7 times better than that of a dielectric grating in air and water, respectively.     

Interferometric characterization of subwavelength lamellar gratings

We propose a new, to our knowledge, method for determining the two main critical parameters of periodic one-dimensional lamellar structures, namely, linewidths and etched depths. The method is simple and requires only two measurements for the phase of the zero-transmitted order under two orthogonal polarizations. It is inspired by the analogy between subwavelength gratings and anisotropic homogeneous thin films. The method is tested with experimental data obtained with a Mach-Zehnder interferometer. Etched depths and linewidths derived from the interferograms and electromagnetic theory are compared with scanning-electron-microscope observations.     

Generation of infrared surface plasmon resonances with high refractive index sensitivity utilizing tilted fiber Bragg gratings

We demonstrate the use of tilted fiber gratings to assist the generation of localized infrared surface plasmons with short propagation lengths and a sensitivity of dlambda/dn = 3,365 nm in the aqueous index regime. It was also found that the resonances could be spectrally tuned over 1,000 nm at the same spatial region with high coupling efficiency (in excess of 25 dB) by altering the polarization of the light illuminating the device.     

Interferometric phase and frequency measurements of the propagation speed of acoustic waves

It is shown that direct measurements of the phase and frequency of the electrical signal at the interferometer output yield an increase in the sensitivity and accuracy with which the propagation speed of acoustic waves in a medium can be determined.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 49, No. 4, pp. 654–658, October, 1985.     

Regularities of nanofocusing of a surface plasmon wave near the nanoapex of a metallic microtip

Nanofocusing of the electromagnetic energy of the optical frequency range into a nanosized spatial area in the vicinity of the nanoapex of a metallic microtip with a radius of curvature of the apex on the order of a few nanometers, which occurs when the surface plasmon wave converges to the tip, is studied. The metal boundary near the apex is considered approximately as the surface of the paraboloid of revolution. It is shown that, in the approximation of the absence of losses in the metal, the electric field distribution near the nanoapex is determined only by its radius of curvature and the frequency of the plasmon wave normalized to the plasma frequency of the metal. The impact of absorption in the metal on this distribution is considered. For microtips made of highly conductive materials, the absorption in the metal in the optical frequency range is shown to have almost no influence on the size of the focal nanoregion.     

Angular responses of the first diffracted order in over-modulated volume diffraction gratings

Abstract

Kogelnik's coupled-wave (CW) theory has been used for decades to predict the diffraction efficiency of volume diffraction gratings. Although this theory has been applied with success to volume diffraction gratings recorded under a great variety of experimental conditions, its predictions deviate from the actual behaviour whenever the hologram is thin or the refractive index is high. In these cases, it is necessary to use a more general CW theory or the rigorous coupled-wave (RCW) theory. Both of these theories allow for more than two orders to propagate inside the hologram. The difference between them is that in the CW theory the second derivatives that appear in the coupled equations are disregarded. The RCW theory does not incorporate any approximation and thus, since it is rigorous, permits judging the accuracy of the approximations included in Kogelnik's CW theory and the more general CW theory. In this article a comparison between the predictions of the three theories for phase transmission diffraction gratings is carried out. Over-modulated diffraction gratings are also recorded in photographic emulsions in order to study the applicability of Kogelnik's theory in this case. Good agreement between theory and experiment is found for both Kogelnik's theory and the RCW theory formulations in the particular experimental cases studied.     

Interferometric sensor based on coherent imaging of gratings

A sensitive interferometric sensor scheme that is based on coherent imaging of a first phase grating onto a second phase grating, their periods accurately matched, is suggested. Experimental data, obtained with a setup based on the suggested scheme, are presented. The sensor was found capable of measuring an angular tilt of a mirror less than 0.5 microrad. Compared with a previously suggested measuring scheme, the novelty of the one presented here is the inclusion of a second set of gratings, which eliminates measurement ambiguity. Some characteristics of the sensor scheme are discussed.     

Aberrations of diffracted wave fields. II. Diffraction gratings

The Rayleigh-Sommerfeld theory is applied to diffraction of a spherical wave by a grating. The grating equation is obtained from the aberration-free diffraction pattern, and its aberrations are shown to be the same as the conventional aberrations obtained by using Fermat's principle. These aberrations are shown to be not associated with the diffraction process. Moreover, it is shown that the irradiance distribution of a certain diffraction order is the Fraunhofer diffraction pattern of the grating aperture as a whole aberrated by the aberration of that order.     

Interferometric fabrication of modulated submicrometer gratings in photoresist

Interferometric recording is applied to the fabrication of modulated submicrometer gratings in photoresist.High diffraction efficiency requires optimized recording conditions, which are obtained by the use of an on-axis continuous surface-relief grating for the generation of the object beam. The optimized phase function is copied into the resist layer by means of a self-aligned two-step recording process with an intermediate copy in a volume photopolymer hologram. As a result, we demonstrate high carrier frequency surface-relief off-axis fan-out gratings for illumination in transmission with visible light.     

Design and applications of lattice plasmon resonances

With their unique optical properties associated with the excitation of surface plasmons, metal nanoparticles (NPs) have been used in optical sensors and devices. The organization of these NPs into arrays can induce coupling effects to engineer new optical responses. In particular, lattice plasmon resonances (LPRs), which arise from coherent interactions and coupling among NPs in periodic arrays, have shown great promise for realizing narrow linewidths, angle-dependent dispersions, and high wavelength tunability of optical spectra. By engineering the materials, shapes, sizes, and spatial arrangements of NPs within arrays, one can tune the LPR-based spectral responses and electromagnetic field distributions to deliver a multitude of improvements, including a high figure-of-merit, superior light–matter interaction, and multiband operation. In this review, we discuss recent progress in designing and applying new metal nanostructures for LPR-based applications. We conclude this review with our perspective on the future opportunities and challenges of LPR-based devices.

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Phase effects in guided mode resonances II: measuring the angular phase of a surface plasmon polariton

We show how the phase of a resonant interaction between a focused beam and a guided mode can be directly observed in a pupil imaging experiment, in which the irradiance leaving the pupil of a standard microscope is relayed to an image sensor through a combination Wollaston prism, calcite beam splitter and polarizer. We apply the method to the observation of a surface plasmon polariton resonance excited in a corrugated silver film fabricated using electron beam lithography. We discuss how this particular imaging configuration could be adapted for applications in plasmonic optical sensing.     

Error analysis of digital phase measurement of distorted waves

An analysis of errors associated with the digital measurement of phase angle between two signals, one of which may be distorted by a harmonic, is presented. All the results were found by running a simulation program on a VAX 11/780 computer. The results are very useful for the users of the phase meters. This technique may introduce large errors for some particular types of input waves. The main purpose of this work is to explain how large the error could be under certain conditions on the input waves     

Interferometric characterization of phase masks

We demonstrate a novel interferometric technique for highly accurate characterization of phase masks used in optical fiber grating fabrication. The principle of the measurement scheme is based on the analysis of the interference pattern formed between the first- and zero-order beams transmitted through or reflected from the grating under test. For spatial resolution of a few millimeters, our methods allow the determination of local variations of the order of 1-microm grating period with an accuracy of a few picometers. These methods are applicable to a broad class of diffractive grating structures.     

Using surface plasmon resonances to test the durability of silver-copper films

Silver has high reflectivity in the visible and infrared but cannot be used fully because of its distressing lack of durability. A technique that uses the surface plasmon resonance phenomenon offers a sensitive method for studying the corrosion of silver and assessing improvements. It has been used in the investigation of the effects of flashing a thin layer, approximately 1 nm thick, of copper over silver in an attempt at cathodic protection. Tests include exposing silver and silver-copper films to air, 94% relative humidity, water, and hydrogen sulfide.