arXiv subjects

Chun-Fang Li

Publications and source records attributed to Chun-Fang Li.

At least 19 recordsLinked to original sources

arXiv2025

Revisiting optical rotation in helically-coiled fibers

The interpretation of optical rotation in optically active media as circular birefringence has persisted for over two centuries, yet the inherent fallacy in this phenomenological theory remains unnoticed. Recently, we employed logical reasoning to demonstrate that isotropic chiral media, a kind of optically active media, do not exhibit circular birefringence. This finding implies that the Jones vector is not able to completely describe the polarization state of a plane light wave. To further explore the reason, here we revisit the phenomenon of optical rotation in helically-coiled optical fibers. Firstly, we use similar logical reasoning to prove that helically coiled fibers do not exhibit circular birefringence, either. Secondly, based on the experimental observations of Papp and Harms, we argue that the Jones vector is mathematically an entity in the local reference frame associated with the propagation direction. It cannot completely describe the state of polarization relative to the laboratory reference frame. Meanwhile, we also demonstrate that the rotation observed by Papp and Harms reflects the rotation of the Tang frame relative to the Serret-Frenet frame.

physics.optics↗

arXiv2025

Tunable lateral displacement and spin beam splitter for ballistic electrons in two-dimensional magnetic-electric nanostructures

We investigate the lateral displacements for ballistic electron beams in a two-dimensional electron gas modulated by metallic ferromagnetic (FM) stripes with parallel and antiparallel (AP) magnetization configurations. It is shown that the displacements are negative as well as positive, which can be controlled by adjusting the electric potential induced by the applied voltage and the magnetic field strength of FM stripes. Based on these phenomena, we propose an efficient way to realize a spin beam splitter, which can completely separate spin-up and spin-down electron beams in the AP configuration by their corresponding spatial positions.

cond-mat.mes-hall↗

arXiv2023

Stokes parameters alone cannot completely characterize the polarization of plane light waves

It was generally assumed that the Stokes parameters are complete characterization for the state of polarization of a plane light wave so that their counterparts in quantum optics, called the Stokes operators, represent the polarization of photons. Here we show, through analyzing the properties of polarized plane waves in an optically active medium, that the Stokes parameters are not able to completely characterize the state of polarization of a plane wave. The key point is that only when a plane wave is expanded in terms of the orthogonal base modes, which are physically meaningful, can the two expansion coefficients make up the Jones vector. Taking this into consideration, we demonstrate that the Stokes parameters of any elliptically polarized wave in an isotropic chiral medium, determined solely by its Jones vector, are transmitted unchanged. They are not able to reflect the rotation of its polarization ellipse along with the propagation. The relationship of the Stokes parameters with the polarization of light needs further investigation.

physics.optics↗

arXiv2022

On a heuristic point of view concerning the optical activity

Motivated by a recent finding that Fresnel's phenomenological description of the optical activity in the chiral medium is not self-consistent, we conduct a thorough investigation into the nature of the polarization of a plane light wave. We demonstrate that the polarization of light is the reflection of one of its quantum-mechanical properties, called the quasi-spin. Unexpectedly, the quasi-spin is not an observable with respect to the laboratory coordinate system. Instead, it is with respect to the momentum-dependent local coordinate system. The representative operators for the quasi-spin are the Pauli matrices. The wavefunction is the Jones vector. In order to completely determine a state of polarization, two different kinds of degrees of freedom are needed. One is the degrees of freedom to characterize the state of quasi-spin. They are the Stokes parameters, the expectation values of the Pauli matrices in the state described by the Jones vector. The other is the degrees of freedom to specify the local coordinate system, including the propagation direction and an angle of rotation about it. Accordingly, there are two independent mechanisms to change the state of polarization. One is to change the state of quasi-spin in a fixed local coordinate system. This is the traditional mechanism that can be expressed as an SU(2) rotation of the Jones vector. The other is to change the local coordinate system with the state of quasi-spin remaining fixed in it. At last, we show that it is the newly-identified mechanism that accounts for the optical activity.

physics.optics↗

arXiv2022

No circular birefringence in a chiral medium: an analysis of single-mode refraction

It is generally believed that the right-handed circularly polarized (RCP) and left-handed circularly polarized (LCP) waves in an isotropic chiral medium propagate at different velocities, known as circular birefringence. Here we show that this is not the case. After obtaining the refraction and reflection coefficients of any elliptically polarized wave at the surface of a chiral medium, we derive the conditions for single-mode refraction. By means of the process of single-mode refraction, we demonstrate that both the refracted RCP and the refracted LCP waves at normal incidence can be expressed as a coherent superposition of a pair of orthogonal linearly polarized waves that are rotated simultaneously. As a result, they must propagate at the same velocity as the linearly polarized waves. A physical interpretation is also given in detail. In particular, we show that the state of polarization of any elliptically polarized wave in a chiral medium is rotated with propagation. Such a rotation amounts to the rotation of polarization bases without involving the change of the Jones vector. The rotation of the RCP and LCP waves, as special cases of elliptically polarized waves, results in two opposite phases as if they propagated at different phase velocities with their polarization states transmitted unchanged.

physics.optics↗

arXiv2021

From Poynting vector to new degree of freedom of polarization

Up till now, the Jones vector is, strictly speaking, only a notion about the state of polarization of plane electromagnetic waves though it is generally applied to paraxial fields approximately. Here we generalize it to non-paraxial fields. The same as the Jones vector for plane waves, the generalized Jones vector for non-paraxial fields is global in the sense that it does not depend on the field position. This is achieved by investigating the effect of the polarization on the Poynting vector in the non-paraxial superposition of four plane waves. Even more importantly, by doing so we find that in addition to the Jones vector, another degree of freedom, called the Stratton vector, is also needed to completely describe the state of polarization of non-paraxial fields. It is shown that the polarization described by the global Jones vector is dependent on the position. The position dependence of the polarization originates in the position dependence of the polarization bases. The Stratton vector specifies the way in which the polarization bases depend on the position. A general expression for the dependence of the Poynting vector on the Stratton and Jones vectors is also given.

physics.optics↗

arXiv2020

Spinor wave equation, relativistic condition, and nonlocality of photon spin

The purpose of this paper is to derive the photon spin and to deduce its properties from a pair of quantum equations for the photon. To this end, Darwin's equations are reinterpreted so as to meet the need of the quantum mechanics of the photon. It is found that the photon wavefunction transforms under Lorentz transformation as a spinor. The relativistic nature of the photon is expressed through a constraint equation on the wavefunction in such a way that the wave equation, which takes on the form of the Schrödinger equation, is not Lorentz covariant unless the constraint equation is taken into account. The wave equation predicts the existence of a kind of spin, an intrinsic degree of freedom. But the constraint equation makes the spin nonlocal in the sense that no unique local density exists for the spin in position space. The nonlocality of the photon spin is a reflection of the nonlocality of the photon itself.

quant-ph↗

arXiv2020

New mechanism for polarization singularity of vector vortex beams

It was recently realized that the polarization bases of the plane-wave modes in the integral representation of a light beam need to be determined by a degree of freedom arising from the divergence-free Maxwell's equation. This is a frequently introduced real unit vector in the literature, called Stratton vector. The polarization bases so determined are singular at the momentum that is parallel to the Stratton vector. Here we show that the polarization singularity of vector vortex beams given by the integral representation comes from the singularity of the polarization bases in association with the Stratton vector. The consistency of the polarization structure of the vector vortex beams with their polarization bases is also discussed.

physics.optics↗

arXiv2020

Deriving photon spin from relativistic quantum equations: Nonlocality of photon spin and relativistic quantum constraint

The difficulties encountered up till now in the theory of identifying the spin and orbital angular momentum of the photon stem from the approach of dividing the angular momentum of the photon into spin and orbital parts. Here we derive the spin of the photon from a set of two relativistic quantum equations that was first cast from the free-space Maxwell equations by Darwin in 1932. Much attention is focused on the nonlocal properties of the photon spin that are determined by the relativistic quantum constraint, one of the so-called Darwin equations. Meanwhile, we point out that for the Darwin equations to describe the quantum motion of the photon, the upper and lower parts of the wavefunction cannot be the electric and magnetic fields as Darwin prescribed. Their nonlocal relations are investigated. The Lorentz covariance of the Darwin equations is also proven, to the best of our knowledge, for the first time.

quant-ph↗

arXiv2020

Are vector vortex beams endowed with any entanglement?

Polarization of light beams is one of the most important physical phenomena. But up till now it was only described in the paraxial approximation in which it is considered to be a single degree of freedom that is characterized by the local Stokes parameters over the transverse plane. Based on such a description, vector vortex beams are considered to be entangled in polarization and spatial mode. Here we show that there is not any entanglement in a large class of representative vector vortex beams, including the well-known cylindrical-vector beams. This is achieved by developing an approach to exactly characterize the polarization of a general beam. It is found that the Stokes parameters, when generalized rigorously to a general beam in momentum space, are physical quantities with respect to a natural coordinate system. The so-called Stratton vector determining the natural coordinate system fixes a natural representation for the polarization in which the Pauli matrices represent the intrinsic degree of freedom of the polarization with respect to the natural coordinate system. As a result, the Stratton vector itself shows up as another degree of freedom of the polarization. From this point of view, the light beams specified by a Stratton vector parallel to the propagation axis as well as by the eigenvalues of the Pauli matrix $\hatσ_1$ are precisely vector vortex beams. They are not endowed with any entanglement.

physics.optics↗

arXiv2019

A full characterization of the polarization of vector light beams

We present an approach to fully characterize the polarization of general vector light beams. When attempting to generalize the notion of Stokes parameters to nonparaxial light beams in momentum space, we find that the Jones function that determines the Stokes parameters through the Pauli matrices is defined over a natural coordinate system that is fixed by a constant unit vector, called the Stratton vector. We further show that the Pauli matrices represent the intrinsic degree of freedom of the polarization with respect to the natural coordinate system so that the Stratton vector acts as an additional degree of freedom that complements the intrinsic degree of freedom to fully characterize the polarization. As a consequence of the new degree of freedom, the Stratton vector, in helicity states, a phase factor that has observable physical effects is identified. Examples of its application to characterizing the state of polarization are also given.

physics.optics↗

arXiv2018

From nonholonomic quantum constraint to canonical variables of photons I: true intrinsic degree of freedom

We report that the true intrinsic degree of freedom of the photon is neither the polarization nor the spin. It describes a local property in momentum space and is represented in the local representation by the Pauli matrices. This result is achieved by treating the transversality condition on the vector wavefunction as a nonholonomic quantum constraint. We find that the quantum constraint makes it possible to generalize the Stokes parameters to characterize the polarization of a general state. Unexpectedly, the generalized Stokes parameters are specified in a momentum-space local reference system that is fixed by another degree of freedom, called Stratton vector. Only constant Stokes parameters in one particular local reference system can convey the intrinsic degree of freedom of the photon. We show that the optical rotation is one of such processes that change the Stratton vector with the intrinsic quantum number remaining fixed. Changing the Stratton vector of the eigenstate of the helicity will give rise to a Berry's phase.

quant-ph↗

arXiv2017

On polarization of vector light beams: origin of Berry phase

When generalized from plane waves to general vector beams, the notion of polarization described by the Stokes parameters turns out to be defined in a momentum-associated system that is fixed by the so-called Stratton vector. As the true intrinsic degree of freedom in the language of quantum mechanics, the polarization of light beams in any fixed momentum-associated system is able to characterize their vectorial feature in the laboratory reference system. The Stratton vector is therefore the degree of freedom to distinguish the vectorial feature of light beams that have the same "polarization". Such an observable effect of the Stratton vector helps to understand why plane waves of the same helicity and the same momentum can be different by a Berry phase. This might be the first time to reveal the physical origin of the Berry phase.

physics.optics↗

arXiv2017

A key role of transversality condition in quantization of photon orbital angular momentum

The effect of the transversality condition on the quantization of the photon orbital angular momentum is studied. The quantum gauge that is deduced from the transversality condition is shown to be a Berry gauge. It determines a helicity-dependent reference point relative to which the position is canonically conjugate to the momentum. As a result, the photon orbital angular momentum about the origin of the laboratory reference system split into two parts. One is the orbital angular momentum of the photon about the reference point, which is canonical. The other is the orbital angular momentum of the photon concentrated at the reference point, which is dependent on the helicity. Only when the Berry-gauge degree of freedom of a paraxial beam is perpendicular to the propagation direction, does the total orbital angular momentum reduce to its canonical part. One of the observable effects of the Berry-gauge degree of freedom is also clarified.

quant-ph↗

arXiv2017

Quantum-mechanical description of entanglement between photon's polarization and momentum

It has been accepted that the polarization of the photon in vector beams is entangled with its momentum. Here a quantum description is advanced for the polarization that shows entanglement with the momentum. This is done by showing that the Jones vector at each value of the momentum plays the role of the polarization wavefunction in the sense that the Pauli matrices represent the Cartesian components of the polarization in the local reference system with respect to which the Jones vector is defined. The unit vector that the constraint of transversality condition requires to specify the local reference system turns out to be a gauge degree of freedom that determines the entanglement of the polarization with the momentum and has observable effects.

quant-ph↗

arXiv2016

Orbital angular momentum is dependent 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 originates from the former part is spin, and the angular momentum that originates from 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 effect 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 part of 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↗

arXiv2016

Representation theory for vector electromagnetic beams

A representation theory of finite electromagnetic beams in free space is formulated by factorizing the field vector of the plane-wave component into a $3 \times 2$ mapping matrix and a 2-component Jones-like vector. The mapping matrix has one degree of freedom that can be described by the azimuthal angle of a fixed unit vector with respect to the wave vector. This degree of freedom allows us to find out such a beam solution in which every plane-wave component is specified by the same fixed unit vector $\mathbf{I}$ and has the same normalized Jones-like vector. The angle $θ_I$ between the fixed unit vector and the propagation axis acts as a parameter that describes the vectorial property of the beam. The impact of $θ_I$ is investigated on a beam of angular-spectrum field scalar that is independent of the azimuthal angle. The field vector in position space is calculated in the first-order approximation under the paraxial condition. A transverse effect is found that a beam of elliptically-polarized angular spectrum is displaced from the center in the direction that is perpendicular to the plane formed by the fixed unit vector and the propagation axis. The expression of the transverse displacement is obtained. Its paraxial approximation is also given.

physics.optics↗

arXiv2016

Degree of diffraction for monochromatic light beams

A parameter, called the degree of diffraction, is defined to describe the diffractive spreading of a monochromatic light beam. The same as the degree of paraxiality that was introduced by Gawhary and Severini in Opt. Lett. 33, 1360 (2008), the degree of diffraction depends only on beam's angular spectrum. With this definition, it is possible to quantitatively compare the diffractive spreading of different light beams.

physics.optics↗