arXiv subjects

Chun-Fang Li

Publications and source records attributed to Chun-Fang Li.

At least 37 records · Page 2Linked to original sources

arXiv2016

On angular momentum of photons: the role of transversality condition in quantum mechanics

Whether the total angular momentum of the photon can be separated into spin and orbital parts has been a long-standing problem due to the constraint of transversality condition on its vector wavefunction. A careful analysis shows that the situation arises from a misuse of the constraint in quantum mechanics. To use the constraint properly, we convert the vector representation into a two-component representation in which the wavefunction is not constrained by any conditions. Upon doing so, we not only separate the spin conceptually from the orbital angular momentum but also identify the Berry gauge in which the two-component wavefunction can be canonically quantized. A corollary is that only in one particular Berry gauge can a radiation field be canonically quantized in terms of the plane waves. The degree of freedom to fix the Berry gauge, which reflects a symmetry of the constraint, turns out to have observable quantum effects.

quant-ph↗

arXiv2015

On photon angular momentum: transversality condition, Berry degree of freedom, and non-commutativity of photon position

Different from the usual conclusion that the separation of the photon angular momentum into orbital and spin parts is physically meaningless, the orbital and spin angular momenta are demonstrated in the first-quantization framework not to satisfy the standard commutation relation. It is shown on the basis of the transversality condition that the spin is aligned with the propagation direction so that only the helicity can be the intrinsic degree of freedom. It is also shown on the same basis that only in the so-called intrinsic reference system does the helicity behave intrinsic. The intrinsic reference system of the photon is determined by the "action" of a gauge potential, the Berry potential, on the helicity of the photon. The Berry potential is fixed by a vector-valued degree of freedom, called the Berry degree of freedom. Because only the position of the photon in its intrinsic reference system is canonically conjugate to the momentum, the intrinsic reference system itself is endowed with quantum effects that depend on the Berry degree of freedom as well as the helicity. This not only explains the so-called spin Hall effect of light but also helps to understand why the total angular momentum cannot be generally split into helicity-independent orbital and helicity-dependent spin parts.

quant-ph↗

arXiv2013

On the angular momentum of photons: effects of transversality condition on the quantization of radiation fields

The notion of intrinsic system of coordinates is introduced for the photon from the constraint of transversality condition. The degree of freedom to specify the intrinsic system is extracted from the same constraint, which turns out to be responsible for the spin Hall effect of light. It is shown that the fundamental quantization conditions that break down in the laboratory system of coordinates restore in the intrinsic system, which make it realizable to canonically quantize the radiation field. It is also shown that the dependence of the intrinsic system on the momentum underlies the noncommutativity of photon position in the laboratory system. The commutation relations of the spin and orbital angular momentum that were found by van Enk and Nienhuis [J. Mod. Opt. \textbf{41}, 963 (1994)] in a second quantized theory are re-derived in the present first quantized theory.

physics.optics↗

arXiv2013

Electronic analogy of Goos-Hänchen effect: a review

The analogies between optical and electronic Goos-Hänchen effects are established based on electron wave optics in semiconductor or graphene-based nanostructures. In this paper, we give a brief overview of the progress achieved so far in the field of electronic Goos-Hänchen shifts, and show the relevant optical analogies. In particular, we present several theoretical results on the giant positive and negative Goos-Hänchen shifts in various semiconductor or graphen-based nanostructures, their controllability, and potential applications in electronic devices, e.g. spin (or valley) beam splitters.

physics.optics↗

arXiv2011

Characterization of vector diffraction-free beams

It is observed that a constant unit vector denoted by $\mathbf I$ is needed to characterize a complete orthonormal set of vector diffraction-free beams. The previously found diffraction-free beams are shown to be included as special cases. The $\mathbf I$-dependence of the longitudinal component of diffraction-free beams is also discussed.

physics.optics↗

arXiv2011

Electron beams of cylindrically symmetric spin polarization

Cylindrically symmetric electron beams in spin polarization are reported for the first time. They are shown to be the eigen states of total angular momentum in the $z$ direction. But they are neither the eigen states of spin nor the eigen states of orbital angular momentum in that direction.

quant-ph↗

arXiv2011

Controllable Goos-Hänchen shifts and spin beam splitter for ballistic electrons in a parabolic quantum well under a uniform magnetic field

The quantum Goos-Hänchen shift for ballistic electrons is investigated in a parabolic potential well under a uniform vertical magnetic field. It is found that the Goos-Hänchen shift can be negative as well as positive, and becomes zero at transmission resonances. The beam shift depends not only on the incident energy and incidence angle, but also on the magnetic field and Landau quantum number. Based on these phenomena, we propose an alternative way to realize the spin beam splitter in the proposed spintronic device, which can completely separate spin-up and spin-down electron beams by negative and positive Goos-Hänchen shifts.

cond-mat.mes-hall↗

arXiv2010

Photon spin operator and Pauli matrix

Any polarization vector of a plane wave can be decomposed into a pair of mutually orthogonal base vectors, known as a polarization basis. Regarding this decomposition as a quasi-unitary transformation from a three-component vector to a corresponding two-component spinor, one is led to a representation formalism for the photon spin. The spin operator $\hat{\boldsymbol γ}$ defined on the space of unit spinors, referred to as the Jones space, has only component along the wave vector and is represented by one of the Pauli matrices in the commonly used polarization basis. It is deformed by the quasi-unitary transformation from the spin operator that is defined on the space of unit polarization vectors, referred to as the Pancharatnam space. On the basis of this theory, it is shown that the Cartesian components of spin operator $\hat{\boldsymbol γ}$ are mutually commutative and the spin angular momentum in units of $\hbar$ is exactly the component of the Stokes vector along the wave vector.

physics.optics↗

arXiv2010

A unit vector for characterizing the spin polarization of free electron

New degrees of freedom having the form of a unit vector are identified for characterizing the spin polarization of free electron. It is shown that when only the spin is considered, the non-commutativity of the Cartesian components of the Pauli vector allows us to use the azimuthal angle of a second direction, denoted by unit vector $\mathbf I$, with respect to the quantization direction to characterize the spin polarization. The rotation of $\mathbf I$ through an angle about the quantization axis leads to a rotation of the spin polarization vector through twice the angle about the same axis. Discussions are also made in Heisenberg picture as well. Upon utilizing this approach to a free electron and letting the quantization direction for each plane wave be the wave vector, we arrive at a representation in which the unit vector $\mathbf I$ functions as an independent index to characterize the spin polarization.

quant-ph↗

arXiv2009

Angular momentum of non-paraxial light beam: Dependence of orbital angular momentum on polarization

It is shown that the momentum density of free electromagnetic field splits into two parts. One has no contribution to the net momentum due to the transversality condition. The other yields all the momentum. The angular momentum that is associated with the former part is spin, and the angular momentum that is associated with the latter part is orbital angular momentum. Expressions for the spin and orbital angular momentum are given in terms of the electric vector in reciprocal space. The spin and orbital angular momentum defined this way are used to investigate the angular momentum of nonparaxial beams that are described in a recently published paper [Phys. Rev. A 78, 063831 (2008)]. It is found that the orbital angular momentum depends, apart from an $l$-dependent term, on two global quantities, the polarization represented by a generalized Jones vector and a new characteristic represented by a unit vector $\mathbf{I}$, though the spin depends only on the polarization. The polarization dependence of orbital angular momentum through the impact of $\mathbf{I}$ is obtained and discussed. Some applications of the result obtained here are also made. The fact that the spin originates from the momentum density that has no contribution to the net momentum is used to show that there does not exist the paradox on the spin of circularly polarized plane wave. The polarization dependence of both spin and orbital angular momentum is shown to be the origin of conversion from the spin of a paraxial Laguerre-Gaussian beam into the orbital angular momentum of the focused beam through a high numerical aperture.

physics.optics↗

arXiv2009

Transmission gap, Bragg-like reflection, and Goos-Hänchen shifts near the Dirac point inside a negative-zero-positive index metamaterial slab

Motivated by the realization of the Dirac point (DP) with a double-cone structure for optical field in the negative-zero-positive index metamaterial (NZPIM), the reflection, transmission, and Goos-Hänchen (GH) shifts inside the NZPIM slab are investigated. Due to the linear Dirac dispersion, the transmission as the function of the frequency has a gap, thus the correspond reflection has a frequency or wavelength window for the perfect reflection, which is similar to the Bragg reflection in the one-dimensional photonic crystals. Near the DP, the associated GH shifts in the transmission and reflection can be changed from positive to negative with increasing the wavelength. These negative and positive shifts can also be enhanced by transmission resonances, when the frequency is far from that at the DP. All these phenomena will lead to some potential applications in the integrated optics and optical devices.

physics.optics↗

arXiv2009

Goos-Hänchen shifts in frustrated total internal reflection studied with wave packet propagation

We have investigated that the Goos-Hänchen (GH) shifts in frustrated total internal reflection (FTIR) studied with wave packet propagation. In the first-order approximation of the transmission coefficient, the GH shift is exactly the expression given by stationary phase method, thus saturates an asymptotic constant in two different ways depending on the angle of incidence. Taking account into the second-order approximation, the GH shift always depends on the width of the air gap due to the modification of the beam width. It is further shown that the GH shift with second-order correction increases with decreasing the beam width at the small incidence angles, while for the large incidence angles it reveals a strong decrease with decreasing the beam width. These phenomena offers the better understanding of the tunneling delay time in FTIR.

physics.optics↗

arXiv2009

Tunable Goos-Hänchen shift and polarization beam splitter in electro-optic crystals

We have investigated the tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals, based on the Pockels effect. The positive and negative lateral shifts could be easily controlled by adjusting the permittivity tensor, which is modulated by the external applied electric field. An alternative way to realize the polarization beam splitter was also proposed by the polarization-dependent lateral shifts. Numerical simulations for Gaussian-shaped incident beam have demonstrated the above theoretical results obtained by stationary phase method. All these phenomena have potential applications in optical devices.

physics.optics↗

arXiv2009

Voltage-tunable lateral shifts of ballistic electrons in semiconductor quantum slabs

It is investigated that the lateral shifts of the ballistic electrons transmitted through a semiconductor quantum slabs can be negative as well as positive, which are analogous to the anomalous lateral shifts of the transmitted light beam through a dielectric slab. The necessary condition for the shift to be negative is advanced. It is shown that the lateral shifts depend not only on the structure parameters of semiconductor quantum slab, but also on the incidence angle and the incident energy. Numerical calculations further indicate that the lateral shifts can be tuned from negative to positive by the external applied electric field. The voltage-tunable lateral shifts may lead to potential applications in quantum electronic devices.

cond-mat.mes-hall↗

arXiv2009

Experimental evidence for new symmetry axis of electromagnetic beams

The new symmetry axis of a well-behaved electromagnetic beam advanced in paper Physical Review A 78, 063831 (2008) is not purely a mathematical concept. The experimental result reported by Hosten and Kwiat in paper Science 319, 787 (2008) is shown to demonstrate the existence of this symmetry axis that is neither perpendicular nor parallel to the propagation axis.

physics.optics↗

arXiv2007

Integral transformation solution of free-space cylindrical vector beams and prediction of modified-Bessel-Gaussian vector beams

A unified description of the free-space cylindrical vector beams is presented, which is an integral transformation solution to the vector Helmholtz equation and the transversality condition. The amplitude 2-form of the angular spectrum involved in this solution can be arbitrarily chosen. When one of the two elements is zero, we arrive at either transverse-electric or transverse-magnetic beam mode. In the paraxial condition, this solution not only includes the known $J_1$ Bessel-Gaussian vector beam and the axisymmetric Laguerre-Gaussian vector beam that were obtained by solving the paraxial wave equations, but also predicts two new kinds of vector beam, called the modified-Bessel-Gaussian vector beam.

physics.optics↗

arXiv2007

Unified theory for Goos-Hänchen and Imbert-Fedorov effects

A unified theory is advanced to describe both the lateral Goos-Hänchen (GH) effect and the transverse Imbert-Fedorov (IF) effect, through representing the vector angular spectrum of a 3-dimensional light beam in terms of a 2-form angular spectrum consisting of its 2 orthogonal polarized components. From this theory, the quantization characteristics of the GH and IF displacements are obtained, and the Artmann formula for the GH displacement is derived. It is found that the eigenstates of the GH displacement are the 2 orthogonal linear polarizations in this 2-form representation, and the eigenstates of the IF displacement are the 2 orthogonal circular polarizations. The theoretical predictions are found to be in agreement with recent experimental results.

physics.optics↗

arXiv2006

Physical mechanism of superluminal traversal time: interference between multiple finite wave packets

The mechanism of superluminal traversal time through a potential well or potential barrier is investigated from the viewpoint of interference between multiple finite wave packets, due to the multiple reflections inside the well or barrier. In the case of potential-well traveling that is classically allowed, each of the successively transmitted constituents is delayed by a subluminal time. When the thickness of the well is much smaller in comparision with a characteristic length of the incident wave packet, the reshaped wave packet in transmission maintains the profile of the incident wave packet. In the case of potential-barrier tunneling that is classically forbidden, though each of the successively transmitted constituents is delayed by a time that is independent of the barrier thickness, the interference between multiple transmitted constituents explains the barrier-thickness dependence of the traversal time for thin barriers and its barrier-thickness independence for thick barriers. This manifests the nature of Hartman effect.

quant-ph↗