Imaging the local density of states of optical corrals

This paper reports the experimental observation, at optical frequencies, of the electromagnetic local density of states established by nanostructures corresponding to the recently introduced concept of optical corral [G. Colas des Francs et al., Phys. Rev. Lett. 86, 4950 (2001)]. The images obtained by a scanning near-field optical microscope under specific operational conditions are found in agreement with the theoretical maps of the optical local density of states. A clear functionality of detection by the scanning near-field optical microscope is thereby identified since the theoretical maps are computed without including any specific tip model.     

Dyadic Green's functions and electromagnetic local density of states

A formal proof to relate the concept of electromagnetic local density of states (LDOS) to the electric and magnetic dyadic Green's functions (DGF) is provided. The expression for LDOS is obtained by relating the electromagnetic energy density at any location in a medium at uniform temperature T to the electric and magnetic DGFs. The appropriate boundary conditions governing the DGFs are obtained and it is seen that the two types of DGFs are electromagnetic duals of each other. With this the concept of LDOS is also extended to material media. The LDOS is split into two terms—one that originates from the energy density in an infinite, homogeneous medium and the other that takes into account scattering from inhomogeneities. The second part can always be defined unambiguously, even in lossy materials. For lossy materials, the first part is finite only if spatial dispersion is taken into account.     

Mapping the local density of optical states of a photonic crystal with single quantum dots

We use single self-assembled InGaAs quantum dots as internal probes to map the local density of optical states of photonic crystal membranes. The employed technique separates contributions from nonradiative recombination and spin-flip processes by properly accounting for the role of the exciton fine structure. We observe inhibition factors as high as 70 and compare our results to local density of optical states calculations available from the literature, thereby establishing a quantitative understanding of photon emission in photonic crystal membranes.     

Signature of a Fano resonance in a plasmonic metamolecule's local density of optical states

We present measurements on plasmonic metamolecules under local excitation using cathodoluminescence which show a spatial redistribution of the local density of optical states at the same frequency where a sharp spectral Fano feature in extinction has been observed. Our analytical model shows that both near- and far-field effects arise due to interference of the same two eigenmodes of the system. We present quantitative insights both in a bare state, and in a dressed state picture that describe Fano interference either as near-field amplitude transfer between coupled bare states, or as interference of uncoupled eigenmodes in the far field. We identify the same eigenmode causing a dip in extinction to strongly enhance the radiative local density of optical states, making it a promising candidate for spontaneous emission control.     

Far-field approximation in electromagnetic scattering

The volume integral equation formalism is used to derive and analyze specific criteria of applicability of the far-field approximation in electromagnetic scattering by a finite three-dimensional object. In the case of wavelength-sized and larger objects, this analysis leads to a natural subdivision of the entire external space into a near-field zone, a transition zone, and a far-field zone. It is demonstrated that the general criteria of far-field scattering are consistent with the theory and practice of T-matrix computations.     

Single-atom density of states of an optical lattice

We consider a single atom in an optical lattice, subject to a harmonic trapping potential. The problem is treated in the tight-binding approximation, with an extra parameter kappa denoting the strength of the harmonic trap. It is shown that the kappa-->0 limit of this problem is singular, in the sense that the density of states for a very shallow trap (kappa-->0) is qualitatively different from that of a translationally invariant lattice (kappa=0). The physics of this difference is discussed, and densities of states and wave functions are exhibited and explained.     

Far-field properties of electromagnetic elliptical Gaussian vortex beams

The explicit far-field expressions for the TE and TM terms and energy flux distributions of electromagnetic elliptical Gaussian vortex beams are derived and their far-field properties including the phase singularities and energy flux distributions of the TE and TM terms and whole beam are studied in detail. It is shown that there exist two edge dislocations. The number and position of edge dislocations and energy flux distributions are dependent on the amplitude ratio and waist width ratio of electromagnetic elliptical Gaussian vortex beams. The analytical results are illustrated numerically.     

非傍轴双曲余弦-高斯脉冲电磁光束远场特性

利用矢量瑞利-索末菲衍射积分公式,推导出了非傍轴部分空间相干部分光谱相干双曲余弦-高斯(ChG)脉冲电磁光束在自由空间传输时交叉谱密度矩阵的远场解析公式,并用来表示脉冲电磁光束的光谱密度(光强)和偏振度。结果表明,对非傍轴远场部分空间相干部分光谱相干ChG脉冲电磁光束,其非傍轴性主要由参数f, f决定,而离心参数、脉冲宽度和时间相干长度影响其非傍轴行为。非傍轴部分空间相干部分光谱相干高斯-谢尔模型脉冲电磁光束的远场传输可作为特例处理。     

非傍轴双曲余弦-高斯脉冲电磁光束远场特性

利用矢量瑞利-索末菲衍射积分公式,推导出了非傍轴部分空间相干部分光谱相干双曲余弦-高斯(ChG)脉冲电磁光束在自由空间传输时交叉谱密度矩阵的远场解析公式,并用来表示脉冲电磁光束的光谱密度(光强)和偏振度。结果表明,对非傍轴远场部分空间相干部分光谱相干ChG脉冲电磁光束,其非傍轴性主要由参数f, f决定,而离心参数、脉冲宽度和时间相干长度影响其非傍轴行为。非傍轴部分空间相干部分光谱相干高斯-谢尔模型脉冲电磁光束的远场传输可作为特例处理。     

Staggered local density of states around the vortex in underdoped cuprates

We have studied a single vortex with the staggered flux (SF) core based on the SU(2) slave-boson theory of high T(c) superconductors. We find that, whereas the center in the vortex core is a SF state, as one moves away from the core center a correlated staggered modulation of the hopping amplitude chi and pairing amplitude Delta becomes predominant. We predict that in this region the local density of states exhibits staggered modulation when measured on the bonds, which may be directly detected by STM experiments.     

On the local quasiparticle density of states within the asymmetric Anderson model

We calculate the local density of states for the asymmetric Anderson model by applying a self-consistent perturbation approximation for the impurity electron's self-energy. The three-resonance structure obtained in the symmetric case at low temperatures, which features a narrow central peak at the Fermi level, is found to transform into a broad single resonance with increasing asymmetry. For any asymmetry the spectral density function approaches in the high temperature limit a broad two-resonance structure.     

Electrodynamic dip in the local density of states of a metallic wire

We have measured the differential conductance of a tunnel junction between a thin metallic wire and a thick ground plane, as a function of the applied voltage. We find that near zero voltage, the differential conductance exhibits a dip, which scales as 1/square root of [V] down to voltages V approximately 10k(B)T/e. The precise voltage and temperature dependence of the differential conductance is accounted for by the effect on the tunneling density of states of the macroscopic electrodynamics contribution to electron-electron interaction, and not by the short-ranged screened-Coulomb repulsion at microscopic scales.     

Mesoscopic fluctuations of the local density of states in interacting electron systems

We review our recent theoretical results for mesoscopic fluctuations of the local density of states in the presence of electron–electron interaction. We focus on the two specific cases: (i) a vicinity of interacting critical point corresponding to an Anderson–Mott transition, and (ii) a vicinity of non-interacting critical point in the presence of a weak electron–electron attraction. In both cases, strong mesoscopic fluctuations of the local density of states exist.     

Long-wavelength local density of states oscillations near graphene step edges

Using scanning tunneling microscopy and spectroscopy, we have studied the local density of states (LDOS) of graphene over step edges in boron nitride. Long-wavelength oscillations in the LDOS are observed with maxima parallel to the step edge. Their wavelength and amplitude are controlled by the energy of the quasiparticles allowing a direct probe of the graphene dispersion relation. We also observe a faster decay of the LDOS oscillations away from the step edge than in conventional metals. This is due to the chiral nature of the Dirac fermions in graphene.     

Probing the photonic local density of states with electron energy loss spectroscopy

Electron energy loss spectroscopy performed in transmission electron microscopes is shown to directly render the photonic local density of states with unprecedented spatial resolution, currently below the nanometer. Two special cases are discussed in detail: (i) 2D photonic structures with the electrons moving along the translational axis of symmetry and (ii) quasiplanar plasmonic structures under normal incidence. Nanophotonics in general and plasmonics, in particular, should benefit from these results connecting the unmatched spatial resolution of electron energy loss spectroscopy with its ability to probe basic optical properties such as the photonic local density of states.     

THz near-field optical imaging by a local source

A new THz imaging system based on a local illumination by a near-field source is presented. Model object is imaged, and sub-wavelength spatial resolution is demonstrated for the first time to our knowledge with this configuration. The contrast and the resolution are confirmed by a theoretical study based on the diffraction in near-field zone.     

Spontaneous-emission control by local density of states of photonic crystal cavity

The local density of states (LDOS) of two-dimensional square lattice photonic crystal (PhC) defect cavity is studied.The results show that the LDOS in the centre is greatly reduced,while the LDOS at the point off the centre (for example,at the point (0.3a,0.4a),where a is the lattice constant) is extremely enhanced.Further,the disordered radii are introduced to imitate the real devices fabricated in our experiment,and then we study the LDOS of PhC cavity with configurations of different disordered radii.The results show that in the disordered cavity,the LDOS in the centre is still greatly reduced,while the LDOS at the point (0.3a,0.4a) is still extremely enhanced.It shows that the LDOS analysis is useful.When a laser is designed on the basis of the square lattice PhC rod cavity,in order to enhance the spontaneous emission,the active materials should not be inserted in the centre of the cavity,but located at positions off the centre.So LDOS method gives a guide to design the positions of the active materials (quantum dots) in the lasers.