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Register a new userProperties of Spin and Orbital Angular Momenta of Light
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This paper analyzes the algebraic and physical properties of the spin and orbital angular momenta of light in the quantum mechanical framework. The consequences of the fact that these are not angular momenta in the quantum mechanical sense are worked out in mathematical detail. It turns out that the spin part of the angular momentum has continuous eigenvalues. Particular attention is given to the paraxial limit, and to the definition of Laguerre--Gaussian modes for photons as well as classical light fields taking full account of the polarization degree of freedom.
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We report the experimental preparation of optical superpositions of high orbital angular momenta(OAM). Our method is based on the use of spatial light modulator to modify the standard Laguerre-Gaussian beams to bear excessive phase helices. We demonstrate the surprising performance of a traditional Mach-Zehnder interferometer with one inserted Dove prism to identify these superposed twisted lights, where the high OAM numbers as well as their possible superpositions can be inferred directly from the interfered bright multiring lattices. The possibility of present scheme working at photon-count level is also shown using an electron multiplier CCD camera. Our results hold promise in high-dimensional quantum information applications when high quanta are beneficial.
There is an interesting but not so popular quantity called pseudo orbital angular momentum (OAM) in the Landau-level system, besides the well-known canonical and mechanical OAMs. The pseudo OAM can be regarded as a gauge-invariant extension of the canonical OAM, which is formally gauge invariant and reduces to the canonical OAM in a certain gauge. Since both of the pseudo OAM and the mechanical OAM are gauge invariant, it is impossible to judge which of those is superior to the other solely from the gauge principle. However, these two OAMs have totally different physical meanings. The mechanical OAM shows manifest observability and clear correspondence with the classical OAM of the cyclotron motion. On the other hand, we demonstrate that the standard canonical OAM as well as the pseudo OAM in the Landau problem are the concepts which crucially depend on the choice of the origin of the coordinate system. We try to reveal the relation between the pseudo OAM and the mechanical OAM as well as their observability by paying special attention to the role of guiding-center operator in the Landau problem.
We give an exact self-consistent operator description of the spin and orbital angular momenta, position, and spin-orbit interactions of nonparaxial light in free space. Both quantum-operator formalism and classical energy-flow approach are presented. We apply the general theory to symmetric and asymmetric Bessel beams exhibiting spin- and orbital-dependent intensity profiles. The exact wave solutions are clearly interpreted in terms of the Berry phases, quantization of caustics, and Hall effects of light, which can be readily observed experimentally.
We present an optomechanical device designed to allow optical transduction of orbital angular momentum of light. An optically induced twist imparted on the device by light is detected using an integrated cavity optomechanical system based on a nanobeam slot-mode photonic crystal cavity. This device could allow measurement of the orbital angular momentum of light when photons are absorbed by the mechanical element, or detection of the presence of photons when they are scattered into new orbital angular momentum states by a sub-wavelength grating patterned on the device. Such a system allows detection of a $l = 1$ orbital angular momentum field with an average power of $3.9times10^3$ photons modulated at the mechanical resonance frequency of the device and can be extended to higher order orbital angular momentum states.
We develop a general framework to analyze the two important and much discussed questions concerning (a) `orbital and `spin angular momentum carried by light and (b) the paraxial approximation of the free Maxwell system both in the classical as well as quantum domains. After formulating the classical free Maxwell system in the transverse gauge in terms of complex analytical signals we derive expressions for the constants of motion associated with its Poincar{e} symmetry. In particular, we show that the constant of motion corresponding to the total angular momentum ${bf J}$ naturally splits into an `orbital part ${bf L}$ and a `spin part ${bf S}$ each of which is a constant of motion in its own right. We then proceed to discuss quantization of the free Maxwell system and construct the operators generating the Poincar{e} group in the quantum context and analyze their algebraic properties and find that while the quantum counterparts $hat{{bf L}}$ and $hat{{bf S}}$ of ${bf L}$ and ${bf S}$ go over into bona fide observables, they fail to satisfy the angular momentum algebra precluding the possibility of their interpretation as `orbital and `spin operators at the classical level. On the other hand $hat{{bf J}}=hat{{bf L}}+ hat{{bf S}}$ does satisfy the angular momentum algebra and together with $hat{{bf S}}$ generates the group $E(3)$. We then present an analysis of single photon states, paraxial quantization both in the scalar as well as vector cases, single photon states in the paraxial regime. All along a close connection is maintained with the Hilbert space $mathcal{M}$ that arises in the classical context thereby providing a bridge between classical and quantum descriptions of radiation fields.
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