Dielectric or plasmonic Mie object at air–liquid interface: The transferred and the traveling momenta of photon

Considering the inhomogeneous or heterogeneous background, we have demonstrated that if the background and the half-immersed object are both non-absorbing, the transferred photon momentum to the pulled object can be considered as the one of Minkowski exactly at the interface. In contrast, the presence of loss inside matter, either in the half-immersed object or in the background, causes optical pushing of the object. Our analysis suggests that for half-immersed plasmonic or lossy dielectric, the transferred momentum of photon can mathematically be modeled as the type of Minkowski and also of Abraham. However, according to a final critical analysis, the idea of Abraham momentum transfer has been rejected. Hence,an obvious question arises: whence the Abraham momentum? It is demonstrated that though the transferred momentum to a half-immersed Mie object(lossy or lossless) can better be considered as the Minkowski momentum, Lorentz force analysis suggests that the momentum of a photon traveling through the continuous background, however, can be modeled as the type of Abraham. Finally, as an interesting sidewalk, a machine learning based system has been developed to predict the time-averaged force within a very short time avoiding time-consuming full wave simulation.     

Electromagnetic momenta and forces in dispersive dielectric media

When the effects of dispersion are included, neither the Abraham nor the Minkowski expression for electromagnetic momentum in a dielectric medium gives the correct recoil momentum for absorbers or emitters of radiation. The total momentum density associated with a field in a dielectric medium has three contributions: (i) the Abraham momentum density of the field, (ii) the momentum density associated with the Abraham force, and (iii) a momentum density arising from the dispersive part of the response of the medium to the field, the latter having a form evidently first derived by Nelson (1991) [8]. All three contributions are required for momentum conservation in the recoil of an absorber or emitter in a dielectric medium. We consider the momentum exchanged and the force on a polarizable particle (e.g., an atom or a small dielectric sphere) in a host dielectric when a pulse of light is incident upon it, including the dispersion of the dielectric medium as well as a dispersive component in the response of the particle to the field. The force can be greatly increased in slow-light dielectric media.     

Decomposition of the total momentum in a linear dielectric into field and matter components

The long-standing resolution of the Abraham–Minkowski electromagnetic momentum controversy is predicated on a decomposition of the total momentum of a closed continuum electrodynamic system into separate field and matter components. Using a microscopic model of a simple linear dielectric, we derive Lagrangian equations of motion for the electric dipoles and show that the dielectric can be treated as a collection of stationary simple harmonic oscillators that are driven by the electric field and produce a polarization field in response. The macroscopic energy and momentum are defined in terms of the electric, magnetic, and polarization fields that travel through the dielectric together as a pulse of electromagnetic radiation. We conclude that both the macroscopic total energy and the macroscopic total momentum are entirely electromagnetic in nature for a simple linear dielectric in the absence of significant reflections.     

Electromagnetic momentum conservation in media

That static electric and magnetic fields can store momentum may be perplexing, but is necessary to ensure total conservation of momentum. Simple situations in which such field momentum is transferred to nearby bodies and point charges have often been considered for pedagogical purposes, normally assuming vacuum surroundings. If dielectric media are involved, however, the analysis becomes more delicate, not least since one encounters the electromagnetic energy–momentum problem in matter, the ‘Abraham–Minkowski enigma’, of what the momentum is of a photon in matter. We analyze the momentum balance in three nontrivial examples obeying azimuthal symmetry, showing how the momentum conservation is satisfied as the magnetic field decays and momentum is transferred to bodies present. In the last of the examples, that of point charge outside a dielectric sphere in an infinite magnetic field, we find that not all of the field momentum is transferred to the nearby bodies; a part of the momentum appears to vanish as momentum flux towards infinity. We discuss this and other surprising observations which can be attributed to the assumption of magnetic fields of infinite extent. We emphasize how formal arguments of conserved quantities cannot determine which energy–momentum tensor is more “correct”, and each of our conservation checks may be performed equally well in the Minkowski or Abraham framework.     

Optical filter based on omnidirectional reflectors

Optical filters based on dielectric omnidirectional reflectors are theoretically analyzed both in the frequency domain and in time domain. It is shown that an optical filter can be made by drilling periodic air holes in a dielectric omnidirectional reflector. The filter’s optical properties can be controlled by varying the lattice constant and the radius of air holes without changing the reflector’s thickness. Thus different filters can be easily integrated in one reflector. This kind of filter is expected to be used in optical communication devices and vertical cavity surface emitting lasers. PACS 42.70.Qs; 42.79.Ci; 78.20.Bh     

Optical and sound helical structures in a Mandelstam-Brillouin mirror

It is shown theoretically that the phase conjugation of a speckle optical field in a Mandelstam-Brillouin mirror is accompanied by the excitation of helical hypersonic waves with a step equal to one-half of the optical wavelength. The excitation of these waves violates the initial isotropy of the dielectric medium. The predicted effect admits clear physical interpretation based on the angular momentum conservation. The angular momentum transfer from the light to the medium occurs in the vicinity of an optical singularity (optical vortex line) due to reversal of the light orbital angular momentum by the phase-conjugation mirror. The excitation of hypersonic waves transferring the angular momentum is the necessary condition for the reversal of the angular momentum of the reflected light.     

平板式螺旋相位板的设计与应用

传统的螺旋相位板是一种利用沿方位角方向介质材料高度递增实现对光束相位调控产生涡旋光束的光学器件,由于这种特殊的几何结构特征使其不能通过相位板的叠加而调控出射光束所携带的角量子数.本文基于坐标变换方法将介质材料沿方位角方向折射率不变而高度递增的传统螺旋相位板变换为一种介质材料沿方位角方向高度不变而折射率递增的平板式螺旋相位板.通过理论分析与数值模拟,发现本文所设计的平板式螺旋相位板不仅与传统螺旋相位板一样能够产生高质量的涡旋光束,而且平板式螺旋相位板的高度和涡旋光束携带的角量子数可以根据介质材料的折射率选取而任意调节.为了实际应用的需要,可以通过叠加多层平板式螺旋相位板以获得不同角量子数的涡旋光束.这种平板式螺旋相位板在光传输、光通信等领域具有广阔的潜在应用价值.     

Energy–momentum tensor for the electromagnetic field in a dielectric

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy–momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Rather than construct a total momentum from the Abraham momentum or the Minkowski momentum, we define a thermodynamically closed system consisting of a propagating electromagnetic field and a negligibly reflecting dielectric and we identify the Gordon momentum as the conserved total momentum by the fact that it is invariant in time. In the formalism of classical continuum electrodynamics, the Gordon momentum is therefore the unique representation of the total momentum in terms of the macroscopic electromagnetic fields and the macroscopic refractive index that characterizes the material. We also construct continuity equations for the energy and the Gordon momentum, noting that a time variable transformation is necessary to write the continuity equations in terms of the densities of conserved quantities. Finally, we use the continuity equations and the time–coordinate transformation to construct an array that has the properties of a traceless, symmetric energy–momentum tensor.     

Whence the Minkowski momentum?

Electromagnetic waves carry the Abraham momentum, whose density is given by p_EM = S(r,t) / c². Here S(r,t) = E(r,t) × H(r,t) is the Poynting vector at point r in space and instant t in time, E and H are the local electromagnetic fields, and c is the speed of light in vacuum. The above statement is true irrespective of whether the waves reside in vacuum or within a ponderable medium, which medium may or may not be homogeneous, isotropic, transparent, linear, magnetic, etc. When a light pulse enters an absorbing medium, the force experienced by the medium is only partly due to the absorbed Abraham momentum. This absorbed momentum, of course, is manifested as Lorentz force (while the pulse is being extinguished within the absorber), but not all the Lorentz force experienced by the medium is attributable to the absorbed Abraham momentum. We consider an absorptive/reflective medium having the complex refractive index n₂ + iκ₂, submerged in a transparent dielectric of refractive index n₁, through which light must travel to reach the absorber/reflector. Depending on the impedance-mismatch between the two media, which mismatch is dependent on n₁, n₂, κ₂, either more or less light will be coupled into the absorber/reflector. The dependence of this impedance-mismatch on n₁ is entirely responsible for the appearance of the Minkowski momentum in certain radiation pressure experiments that involve submerged objects.     

Equivalence of the Abraham momentum and the Minkowski momentum of photons in media

The century-long debate on the momentum of light in a medium involves two rival forms of momentum, namely those of Abraham and Minkowksi. In this Letter, we analyze this dilemma from the view of the quantum theory of light, the result of which can be easily extended to the classical level. It is found that the Abraham momentum of one polariton mode in linear and dispersive dielectrics differs from its Minkowski momentum, by a considerable factor. However, after taking all branches into consideration, we find the two lead to the same end, which unifies the two rival forms of momentum. The sum rule is traditional, but our conclusion provides a new perspective on the Abraham-Minkowski dilemma, and is consistent with existing experiments including a recent measurement of recoil momentum of atoms using an atom interferometer with Bose-Einstein Condensates [G. K. Campbell et al. Phys. Rev. Lett. 94, 170403 (2005).], the Cerenkov effect, the Doppler effect and the phase matching conditions in nonlinear optical processes.     

Fiber-to-waveguide coupler based on the parabolic reflector

We present a fiber-to-waveguide coupling structure, the so-called vertical J coupler, based on the parabolic reflector. The device addresses the multiple objectives of high coupling efficiency, large bandwidth operation, polarization insensitivity, and compact footprint. The optical mode emanating from a fiber arranged normal to the plane of the substrate is incident underneath the parabolic reflector, turned through 90 degrees and focused into a dielectric waveguide. The viability of the coupler is demonstrated by finite-difference time-domain electromagnetic simulation as well as preliminary fabrication and optical testing of the device.     

Division of the energy and of the momentum of electromagnetic waves in linear media into electromagnetic and material parts

We defend a natural division of the energy density, energy flux and momentum density of electromagnetic waves in linear media in electromagnetic and material parts. In this division, the electromagnetic part of these quantities have the same form as in vacuum when written in terms of the macroscopic electric and magnetic fields, the material momentum is calculated directly from the Lorentz force that acts on the charges of the medium, the material energy is the sum of the kinetic and potential energies of the charges of the medium and the material energy flux results from the interaction of the electric field with the magnetized medium. We present reasonable models for linear dispersive non-absorptive dielectric and magnetic media that agree with this division. We also argue that the electromagnetic momentum of our division can be associated with the electromagnetic relativistic momentum, inspired on the recent work of Barnett [Phys. Rev. Lett. 104 (2010) 070401] that showed that the Abraham momentum is associated with the kinetic momentum and the Minkowski momentum is associated with the canonical momentum.     

微光机电系统滤波器可调谐特性分析

分析了基于法布里-珀罗腔的微光机电系统可调谐滤波器中,空气腔厚度与峰值波长间的关系。微光机电系统中,空气腔的厚度一般在一个波长附近,因此腔的干涉级数较小,两边反射镜的反射相位对峰值波长的影响比较大。从反射相位出发,推导出了基于这种结构的可调谐滤波器中空气腔厚度和谐振波长之间的线性关系,并通过数值计算进行了验证。分析了影响滤波器调谐灵敏度的因素,构成介质反射镜的薄膜材料的高低折射值以及薄膜堆的层数都能改变线性系数的值。最后估算了一定波长范围内这种线性关系的误差。     

Study of detached back reflector designs for thin‐film silicon solar cells

We present a precise and flexible method to investigate the impact of diverse detached reflector designs on the optical response of p–i–n thin‐film silicon solar cells. In this study, the term detached reflectors refers to back reflectors that are separated from the silicon layers by an intermediate rear dielectric of several micrometers. Based on the utilization of a highly conductive n‐doped layer and a local electrical contact scheme, the method allows the use of non‐conductive rear dielectrics such as air or transparent liquids. With this approach, diverse combinations of back reflector and rear dielectric can be placed behind the same solar cell, providing a direct evaluation of their impact on the device performance. We demonstrate the positive effect of a rear dielectric of low refractive index on the light trapping and compare the performance of solar cells with an air/Ag and a standard ZnO/Ag back reflector design. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transmission characteristics of optical waveguide corners

Two-dimensional dielectric waveguide corners with air reflector or metal reflector have been investigated by means of the method of plane-wave expansion, which has the advantage of being compact for optical integrated circuit applications. The operating principle of these waveguide corners is based on the total internal reflection or large partial reflection. The corner losses and field profiles are presented for various waveguide parameters. It is found that the corner loss can be small if the waveguide corner is properly fabricated.     

Very slow surface plasmons: Theory and practice (Review)

The theory and practical applications of very slow (antisymmetric) optical plasmons are described. These plasmons can exist on thin metal films and filaments and (as standing waves) on metal spheres and ellipsoids. The material presented here extends the conventional concepts of electromagnetic modes of spaces, probability of spontaneous emission, construction of optical images, optical focusing, and the photon momentum. The reviewed achievements in this field have been obtained in the last years. The problem of the photon momentum in a medium has been a subject of irreconcilable disputes for nearly 100 years, beginning with Minkowski and Abraham’s famous papers. Various practical applications are considered, including experiments with the significant enhancement of atom spontaneous emission into a plasmon field mode of a nanoparticle; experiments on focusing optical radiation into a spot much smaller than the diffraction-limited one (the so-called almost ideal Pendry lens, which produces an image with details much smaller than the light wavelength); and, finally, a greatly increased (by factors of 10, 100, or more) photon momentum in plasmon.     

Comparative study of Mo_2Ga_2C with superconducting MAX phase Mo_2GaC: First-principles calculations

The structural, electronic, optical and thermodynamic properties of Mo_2Ga_2C are investigated using density functional theory(DFT) within the generalized gradient approximation(GGA). The optimized crystal structure is obtained and the lattice parameters are compared with available experimental data. The electronic density of states(DOS) is calculated and analyzed. The metallic behavior for the compound is confirmed and the value of DOS at Fermi level is 4.2 states per unit cell per e V. Technologically important optical parameters(e.g., dielectric function, refractive index, absorption coefficient, photo conductivity, reflectivity, and loss function) are calculated for the first time. The study of dielectric constant(ε1) indicates the Drude-like behavior. The absorption and conductivity spectra suggest that the compound is metallic.The reflectance spectrum shows that this compound has the potential to be used as a solar reflector. The thermodynamic properties such as the temperature and pressure dependent bulk modulus, Debye temperature, specific heats, and thermal expansion coefficient of Mo_2Ga_2C MAX phase are derived from the quasi-harmonic Debye model with phononic effect also for the first time. Analysis of T c expression using available parameter values(DOS, Debye temperature, atomic mass,etc.) suggests that the compound is less likely to be superconductor.     

Scaling of optical forces in dielectric waveguides: rigorous connection between radiation pressure and dispersion

We show that eigenmodes of dielectric optical waveguides exert surface dilation forces on waveguide boundaries owing to radiation pressure, and we develop an exact scaling law relating modal dispersion of an arbitrary dielectric waveguide to the magnitude of optical forces generated by radiation pressure. This result points to highly dispersive waveguides as an optimal choice for the generation of large optical forces in nano-optomechanical systems. Exact agreement with ab initio calculations is demonstrated.     

Surface plasmon-assisted optical switching/bistability at telecommunication wavelengths in nonlinear dielectric gratings

In this paper, we numerically investigate nonlinear optical responses in dielectric gratings coated by flat metallic surface, where the structural parameters are chosen for wavelengths of operation at the telecom regime. The presented designs show the output light reflection with respect to the incident intensity of increasing, decreasing, and non-monotonic belt-shape functions. Nonlinear optical responses including switching and bistability appeared in the telecom region owing to assistance of surface plasmon resonance excited at the metal/dielectric interface, which enhances the diffraction efficiency and induces the momentum matching for the leaky modes of the dielectric grating. This results in electric intensity-effective refractive index dependence enhancement in the Kerr nonlinear media. Our design and investigation of the linear and nonlinear optical responses will provide a general guideline for a hybrid metallic-dielectric structure-based optical switching/bistability device design.     

The momentum of an electromagnetic wave inside a dielectric derived from the Snell refraction law

Author of the paper [M. Testa, Ann. Physics 336 (2013) 1] has derived a conclusion that there is a connection between the Snell refraction law and the Abraham form of the momentum of light in matter. In other words, author derived the Snell law on assumption that the momentum of light in matter decreases by n$n$ times as compared with that in free space. The conclusion is derived under assumption that the forces exerted on an optical medium by an electromagnetic field do not distinguish between polarization and free charges. We show that, on the contrary, the Minkowski form of the momentum of light in matter directly follows from the Snell law. No previous assumption is required for this purpose.