Rotational Doppler shift of a phase-conjugated photon

Abstract

The rotational Doppler shift of a photon with orbital angular momentum ±ℓ is shown to be an even multiple of the angular frequency Ω of the reference frame rotation when photon is reflected from the phase-conjugating mirror. The one-arm phase-conjugating interferometer is considered. It contains N Dove prisms or other angular momentum altering elements rotating in opposite directions. When such interferometer is placed in the rotating vehicle the δω = 4(N + 1/2)ℓ · Ω rotational Doppler shift appears and rotation of the helical interference pattern with angular frequency δω/2ℓ occurs. The accumulation of angular Doppler shift via successive passages through the N image-inverting prisms is due to the phase conjugation, for conventional parabolic retroreflector the accumulation is absent. The features of such a vortex phase conjugating interferometry at the single photon level are discussed. PACS numbers: 42.50.Tx 42.65.Hw 06.30.Gv 42.50.Dv

Optical angular momentum in a rotating frame

“…Frame rotation has also been employed when considering reflection and interference patterns [7][8][9]. However, the effect of frame rotation on the OAM of light itself has yet to be fully explored.…”

Mechanical Perspective on the Rotational Doppler Shift of a Single Photon

“…From equation (19), it can be concluded that change in frequency of one photon (or a gi for n photons) is directly proportional to the AM transferred by the relative rotational movement of the traversed object (Ω) with respect to the circularly polarized light beam traversing it (σ = ±1) [19,20]. Therefore, the interaction of light rays with the material implies that large energy exchanges in the form of AM would produce a strong rotational Doppler effect [19,21].…”

Configuration of vortex-antivortex lattices at output mirror of wide-area microchip laser

“…The synchronized modes of empty resonator form an almost perfect periodic lattice of dark spots [9]. Each dark spot is surrounded by a nearly circular flow resembling isolated optical vortex alike Laguerre-Gaussian beam [21,22]. The phase of optical field is a precise indicator of electromagnetic energy circulation [23].…”

“…A part of numerically obtained patterns is composed from zeros of amplitudes equispaced in a checkerboard geometry with alternating circulations as is shown in [8]. The macroscopic photons wavefunction Ψ ∼ E n ( r) [21] which is visualized by electric field amplitude E n ( r), demonstrates the regular lattices of field zeros with counter-rotating whirls around [ fig.6]. In contrast to optical speckle patterns [24] where vortex-antivortex pairs are distributed chaotically in space the lattice of whirls in wide-aperture lasers is periodic in space [ fig.5].…”