G. Nienhuis

Commutation rules and eigenvalues of spin and orbital angular momentum of radiation fields

Abstract We investigate the separation of the total angular momentum J of the electromagnetic field into a ‘spin’ part S and an ‘orbital’ part L. We show that both ‘spin’ and ‘orbital’ angular momentum are observables. However, the transversality of the radiation field affects the commutation relations for the associated quantum operators. This implies that neither S nor L are angular momentum operators. Moreover their eigenvalues are not discrete. We construct field modes such that each mode excitation (photon) is in a simultaneous eigenstate of S z and L z. We consider the interaction of such a photon with an atom and the resulting effect on the internal and external part of the atomic angular momentum.

Eigenfunction description of laser beams and orbital angular momentum of light

Abstract The propagation of light beams through astigmatic lens systems is accompanied by a transfer of orbital angular momentum. We develop a method to describe propagating light beams by operators of which the field is an eigenfunction. This method is applied to determine when an astigmatic lens system transforms gaussian beams into other gaussian beams and where in the system angular momentum is transferred. We show that the Gouy phase is equal to the dynamical phase of a quantummechanical harmonic oscillator with time-dependent energy.

Doppler effect induced by rotating lenses

The orbital angular momentum inherent to light beams with a helical wavefront can be transferred to non-isotropic lenses. A system of three cylindrical lenses suffices to transform an arbitrary paraxial input beam by inverting one transverse direction of the mode function. This also inverts the orbital angular momentum of a Laguerre-Gaussian beam with mode index m. The corresponding transfer of angular momentum shows up directly as a frequency shift 2mΩ when the lens system is set in rotation at frequency Ω around the axis.

Intrinsic orbital angular momentum of paraxial beams with off-axis imprinted vortices.

We investigate the orbital angular momentum (OAM) of paraxial beams containing off-axis phase dislocations and put forward a simple method to calculate the intrinsic orbital angular momentum of an arbitrary paraxial beam. Using this approach we find that the intrinsic OAM of a fundamental Gaussian beam with a vortex imprinted off axis has a Gaussian dependence on the vortex displacement, implying that the expectation value of the intrinsic OAM of a photon can take on a continuous range of values (i.e., integer and noninteger values in units of h). Finally, we investigate, both numerically and experimentally, the far-field profiles of beams carrying half-integer OAM per photon, these beams having been created by the method of imprinting off-axis vortices.

Polychromatic and rotating beams of light

Beams of light with rotating polarization or mode patterns can be viewed as superpositions of components with a well-defined angular momentum hm per photon, each having a frequency shift m times the rotation frequency. Such beams can also be created after passing a monochromatic beam through rotating optical elements. We discuss the properties of the angular momentum of such beams, both for a rotating polarization and a rotating amplitude pattern. We also consider beams where the polarization is not uniform.

Steady state of atoms in a resonant field with elliptical polarization

We present a complete set of analytical and invariant expressions for the steady-state density matrix of atoms in a resonant radiation field with arbitrary intensity and polarization. The field drives the closed dipole transition with arbitrary values of the angular momenta J{sub g} and J{sub e} of the ground and excited state. The steady-state density matrix is expressed in terms of spherical harmonics of a complex direction given by the field polarization vector. The generalization to the case of broadband radiation is given. We indicate various applications of these results.

Photons in polychromatic rotating modes

We propose a quantum theory of rotating light beams and study some of its properties. Such beams are polychromatic and have either a slowly rotating polarization or a slowly rotating transverse mode pattern. We show that there are, for both cases, three different natural types of modes that qualify as rotating, one of which is a type not previously considered. We discuss differences between these three types of rotating modes on the one hand and nonrotating modes as viewed from a rotating frame of reference on the other. We present various examples illustrating the possible use of rotating photons, mostly for quantum information processing purposes. We introduce in this context a rotating version of the two-photon singlet state.

Geometric phases in astigmatic optical modes of arbitrary order

The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different orders, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of nonastigmatic optical modes with orbital angular momentum in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov–Bohm effect, which provides some complementary insights into the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical desc...

Angular momentum and vortices in paraxial beams

The free propagation of a paraxial light beam can be exactly mapped on the free evolution of a 2D harmonic oscillator over half an oscillation period. We apply this mapping to give an analytical description of the dynamics of vortices and their relation to the orbital angular momentum of light.

Angular momentum in evanescent waves

Abstract We quantize the angular momentum of the electromagnetic field in a linear medium. We consider the interaction of an atom with an evanescent wave. We discuss the transfer of angular momentum in such a wave in relation to some recent experiments.