Coupled Surface Modes Research Articles

Surface-mode enhanced photonic-crystal nano-imaging observed by a scanning near-field optical microscope

In this paper, we experimentally demonstrate the sub-wavelength loss-less nano-imaging effect achieved by the surface-mode coupling in a negative refraction silicon photonic crystal at a wavelength of 1100 nm. The surface mode and nano-imaging effect of the photonic crystal are experimentally studied with a scanning near-field optical microscope. The thickness and the wavelength dependence of the full width at half maximum of the focal spot reveal a direct evidence of the surface-mode enhanced nano-imaging effect, which is consistent with the simulation. As a consequence, a focal spot with a lateral resolution of λ/3 at the predicted wavelength has been achieved.

Plasmon resonance coupling in cold overdense dissipative plasma

Abstract It has been shown that the overdense plasma in the resonance conditions can be totally transparent to the incident electromagnetic waves, due to the excitation of the surface modes or plasmons. This scenario requires excitation of a single surface mode which is provided by placing a dielectric layer in front of the incident wave. Here, it is shown that this procedure would be complete and more efficient by arranging the conditions to excite coupled surface modes, namely by placing two dielectrics on both sides of the plasma layer. The results show that in this case, the overdense plasma slab could poses high transmittance in spite of the presence of the dissipative effects. In addition, in this case, the resonance conditions can be achieved more easily and efficiently, and can be used for wider range of the overdense plasma widths.

Dynamical quantum theory of heat transfer between plasmonic nanosystems

We develop a dynamical theory of heat transfer between two nano systems. In particular, we consider the resonant heat transfer between two nanoparticles due to the coupling of localized surface modes having a finite spectral width. We model the coupled nanosystem by two coupled quantum mechanical oscillators, each interacting with its own heat bath, and obtain a master equation for the dynamics of heat transfer. The damping rates in the master equation are related to the lifetimes of localized plasmons in the nanoparticles. We study the dynamics towards the steady state and establish connection with the standard theory of heat transfer in steady state. For strongly coupled nano particles we predict Rabi oscillations in the mean occupation number of surface plasmons in each nano particle.

Ultrafast modulation of near-field heat transfer with tunable metamaterials

We propose a mechanism of active near-field heat transfer modulation relying on externally tunable metamaterials. A large modulation effect is observed and can be explained by the coupling of surface modes, which is dramatically varied in the presence of controllable magnetoelectric coupling in metamaterials. We finally discuss how a practical picosecond-scale thermal modulator can be made. This modulator allows manipulating nanoscale heat flux in an ultrafast and noncontact (by optical means) manner.

Propagating Modes Generated by the Coupling of Evanescent Surface Modes in Metamaterial Slab Waveguides

Here, we report that evanescent surface modes at the interfaces between ε-negative and μ-negative metamaterials can be made into a propagating one via the introduction of symmetric slab structures. The slab induces strong coupling between double interfaces comprising the slab and also between two evanescent surface modes localized at each interface. The novel propagating mode has its origin in this strong coupling so that it becomes cut off when the core size (i.e., distance between double interfaces) becomes large enough to make the coupling effects negligible.

Semianalytical formulations for the surface modes of photonic woodpiles

We have developed semianalytical methods that allow us to perform a comprehensive analysis of the surface modes of photonic woodpiles. The surface modes of both finite and semi-infinite woodpiles are characterized using transfer matrix and plane-wave matrix formulations, and, in the case of finite structures, we give a general analytical description of the ``double-interface'' modes, which propagate simultaneously along the top and bottom surfaces. We show that if the number of layers is even, then such modes will only exist for specific directions of the Brillouin zone. However, if the number of layers is odd, then every surface mode is a double-interface mode, and, in this case, the direction of propagation plays an important role in determining the coupling strength between the two surfaces: for certain directions, the coupling is negligible even when the number of layers is small. The dispersion curves of two different double-interface modes can anticross or be interwoven, depending on the symmetry of the modes. We also describe the conditions under which coupled surface modes will exist when two woodpiles are used to create a Fabry-P\'erot cavity.

Cylindrical bubble dynamics

Bubbles generated between closely spaced parallel surfaces are approximately cylindrical. Here, cylindrical bubble dynamics are compared with those of spherical bubbles. In the linear approximation, the product of bubble radius and natural frequency of the monopole mode in water is ∼1m/s for a cylindrical bubble versus ∼3m/s for a spherical bubble. Radiation damping of a cylindrical bubble is an order of magnitude greater than for a spherical bubble, and for cylindrical bubbles larger than ∼1 μm it is the dominant loss mechanism, whereas spherical bubbles must be larger than ∼1 mm before radiation losses dominate. Also in contrast with spherical bubbles, the inertial load on a cylindrical bubble in an unbounded incompressible liquid is infinite and prohibits the existence of a monopole mode. Derivation of a dynamical equation for cylindrical bubbles in Rayleigh-Plesset form therefore requires the incompressible liquid to be of finite extent. The radial extent needed to impose the appropriate inertial load is found by comparison with results for a compressible liquid to be approximately 200 bubble radii. The resulting dynamical equation was further augmented to account for bubble deformation due to coupling of surface modes through nonlinearity. [Work supported by NIH DK070618 and EB011603.]

Multi-modal transmission of microwaves through hole arrays

The microwave transmission through hole arrays in thick metal plates for both large holes (cut-off below onset of diffraction) and small holes (cut-off above onset of diffraction) have been compared through both experiment and modelling. Enhanced transmission is in part mediated by the excitation of diffractively coupled surface waves. Large holes, with cut-off below the onset of diffraction (due to the hole periodicity), are able to support multiple modes in transmission when the depth of the holes is sufficient to support quantisation in the propagation direction. Small holes, with cut-off above the onset of diffraction however only support two coupled surface modes (symmetric and anti-symmetric) below diffraction.

Influence of roughness on near-field heat transfer between two plates

The surface roughness correction to the near-field heat transfer between two rough bulk materials is discussed by using second-order perturbation theory. The results allow for estimating the impact of surface roughness to the heat transfer in recent experiments between two plates and between a microsphere and a plate (using the Derjaguin approximation). Furthermore, we show that the proximity approximation for describing rough surfaces is valid for distances much smaller than the correlation length of the surface roughness even if the heat transfer is dominated by the coupling of surface modes.

Photonic-crystal surface modes found from impedances

We present a method for finding surface modes at interfaces between two-dimensional photonic crystals (PCs), in which the surface modes are represented as superpositions of the PCs' propagating and evanescent Bloch modes. We derive an existence condition for surface modes at an air-PC interface in terms of numerically calculated PC impedance matrices, and use the condition to find surface modes in the partial band gap of a PC. We also derive a condition for modes of a three-layer structure with two interfaces, and find both coupled surface modes and waveguide modes. We show that some waveguide modes cross the band edge and become coupled surface modes.

Controlled Plasmon Resonance Properties of Hollow Gold Nanosphere Aggregates

Hollow gold nanospheres (HGNs) ranging from 29.9 nm/8.5 nm (outer diameter/shell thickness) to 51.5 nm/4.5 nm and having aspect ratios spanning 3.5-11.7 were employed to investigate the ability to tailor charge oscillations of HGN aggregates by systematic variation of particle aspect ratio, interparticle gap, and nanosphere inner surface spatial separation. Altering these properties in aggregated HGNs led to control over the interparticle plasmon resonance. Thiol-mediated aggregation was accomplished using either ethanedithiol or cysteine, resulting in dimeric structures in which monomer subunits were spatially separated by <3 Å and 1.2 ± 0.7 nm, respectively. Particle dimensions and separation distances were confirmed by transmission electron microscopy. Experimental absorption spectra obtained for high-aspect ratio nanospheres dimerized using ethanedithiol exhibited an obvious blue shift of the surface plasmon resonance (SPR) relative to that observed for the native, monomeric HGN. This spectral difference likely results from a charge-transfer plasmon resonance at the dimer interface. The extent of the blue shift was dependent upon shell thickness. Dimers comprised of thin-shelled HGNs exhibited the largest shift; aggregates containing HGNs with thick shells (≥7 nm) did not display a significant SPR shift when the individual particles were in contact. By comparison, all cysteine-induced aggregates examined in this study displayed large interparticle gaps (>1 nm) and a red-shifted SPR, regardless of particle dimensions. This effect can be described fully by a surface mode coupling model. All experimental measurements were verified by finite difference time domain calculations. In addition, simulated electric field maps highlighted the importance of the inner HGN surface in the interparticle coupling mechanism. These findings, which describe structure-dependent SPR properties, may be significant for applications derived from the plasmonic nanostructure platform.

Radiative heat transfer at nanoscale: Closed-form expression for silicon at different doping levels

Radiative heat transfer at the nanoscale is becoming an important technological issue with the development of nano electromechanical systems (NEMS). In this article, we derive asymptotic expressions to compute near-field radiative heat transfer between two planes of silicon. We identify two physical mechanisms that give the dominant contribution at small gaps. For intrinsic and low-doped silicon, the main contribution is due to evanescent waves coming from propagating waves undergoing frustrated total internal reflections at the interfaces. For doping levels larger than N e =10 16 cm −3 surface mode coupling contributes to the heat transfer. Asymptotic expressions are also given in that case. In all cases, we compare analytical formulas with exact numerical calculations when varying the temperature and the doping concentration. We also give their range of validity.

The image performance of a negative index slab and a layered slab using coupled surface modes

This paper reviews the concept of high-resolution imaging of a negative index material (NIM) slab and compares its performance with the structure made based on the idea of coupled surface-modes layers. Fourier spectrum theoretical model and finite difference time domain numerical approach are applied to comprehensively characterize the structures and demonstrate the characteristics. It is highlighted that if the loss is small, a NIM slab can provide a better performance at a farther distance than the layered structure with the same thickness. However, considering a realistic design with relatively large loss, the later will offer a more promising performance to the loss and the image can be reconstructed in a farther distance from the object cascading more number of thin layers.

Radiative heat transfer at the nanoscale

We give a concise introduction into the radiative heat transfer at the nanoscale discussing the contribution of propagating, frustrated and coupled surface modes [1]. Especially, the latter contribution results in a heat flux, which can exceed the heat flux between two black bodies by several orders of magnitude for distances in the nanometer regime [1]. The prediction of such an enormous heat flux enhancement is usually based on Rytov's fluctuational electrodynamics [2] and has been verified in some very recent experiments [3,4,5]. Our aim is to show how the theoretical expression describing the nanoscale heat flux can be interpreted in terms of transmission coefficients and the universal quantum of thermal conductance by means of concepts of mesoscopic physics [6]. Such a formulation allows for studying the fundamental limits of radiative heat transfer [7,8] emphasizing the trade-off between the number of contributing modes and their transmission coefficient. [1] K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, Surface Science Reports 57, 59 (2005). [2] S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophyics (Springer, New York), Vol. 3. (1989). [3] S. Shen, A. Narayanaswamy, and G. Chen, Nano Lett. 9, 2909 (2009). [4] E. Rousseau, A. Siria, G. Jourdan, S. Volz, F. Comin, J. Chevrier, and J.-J. Greffet, Nature Photonics 3, 514 (2009). [5] R. Ottens, V. Quetschke, S. Wise, A. Alemi, R. Lundock, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Phys. Rev. Lett. 107, 014301 (2011). [6] S.-A. Biehs, E. Rousseau, and J.-J. Greffet, Phys. Rev. Lett. 105, 234301 (2010). [7] P. Ben-Abdallah and K. Joulain, Phys. Rev. B 82, 121419 (R) (2010). [8] S. Basu and Z. M. Zhang, J. Appl. Phys. 105, 093535 (2009).

Vertical surface emitting open coupled-cavities based on photonic crystal surface modes

Two types of vertical surface emitting photonic crystal cavities based on beaming mechanism and coupled surface modes are studied. It is shown that vertical emission with a zero divergence angle and a high quality factor can be easily achieved by the back-to-back cavity design. The periodic modulation to the cavity surface alters nonradiative surface modes into radiative surface modes, and the constructive interference of the radiative waves gives rise to vertical emission and improves the quality of the output beam. A high quality factor can be attributed to the nonradiative surface mode on the cavity back whose small part of energy can be transferred into the cavity surface by coupling. The resonant property and the coupling efficiency of the cavities are investigated and optimal cavity configurations are obtained. These open coupled-cavities are good candidates of highly directional light sources.

Control of surface modes in low loss hollow-core photonic bandgap fibers

We report on the fabrication and characterization of hollow-core photonic bandgap fibers that do not suffer from surface mode coupling within the photonic bandgap of the cladding. This enables low attenuation over the full spectral width of the bandgap--we measured a minimum loss of 15 dB/km and less than 50 dB/km over 300 nm for a fiber operating at 1550 nm. As a result of the increased bandwidth, the fiber has reduced dispersion and dispersion slope--by a factor of almost 2 compared to previous fibers. These features are important for several applications in high-power ultrashort pulse compression and delivery. Realizing these advances has been possible due to development of a modified fabrication process which makes the production of low-loss hollow-core fibers both simpler and quicker than previously.

Coupling of waveguide and surface modes in enhanced transmission through stacking gratings

The physics of enhanced transmission through two metallic gratings stacked one on top of another with a lateral shift is studied. Full electromagnetic calculations via the method of rigorous coupled-wave analysis show that enhanced transmission may result even when the slits in one grating are covered by the other. Despite the channel of waveguide mode is blocked, the coupling of strongly excited surface modes in one grating to the waveguide mode in another leads to an enhanced transmission which could even be larger than that in the case of two stacking gratings unshifted with respect to one another.

Near-field enhancement and imaging in double cylindrical polariton-resonant structures: Enlarging superlens

We experimentally demonstrate a prototype of a cylindrical enlarging lens capable of enhancing and restoring evanescent fields. The enabling phenomenon is the resonant excitation of coupled surface modes in a system of two cylindrical arrays of small resonant particles. As was shown in [S.I. Maslovski, S.A. Tretyakov, P. Alitalo, J. Appl. Phys. 96 (2004) 1293], this phenomenon in planar arrays can be used in electromagnetic near-field imaging. Here, we use a similar structure in a cylindrically symmetric configuration, which gives us a possibility to obtain an enlarged near-field image.

Gap modes of one-dimensional photonic crystal surface waves

The finite-difference time-domain method is employed for the analysis of coupling of the surface modes of two truncated one-dimensional photonic crystals separated by a gap. The wave vector, field distributions, and existence conditions of the coupled surface modes are investigated. The wave vector of symmetric gap modes increases with decreasing gap width, while that of antisymmetric modes decreases-exactly opposite of the situation for surface plasmons on metallic half-spaces separated by a dielectric gap. Photonic crystal gap modes could easily and effectively be used as nondissipating gap-mode waveguides.

Resonant optical transmission through a photonic crystal in the forbidden gap

We show that a slab of a photonic crystal whose thickness is $3.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ can transmit 100% of an incident beam whose frequency lies in the forbidden gap. This phenomenon is not linked to a volume defect but to the resonant coupling of leaky surface modes at both interfaces.