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Journal of Physics B Atomic and Molecular Physics

Forward scattering (polarisation spectroscopy) of resonance radiation in partially coherent fields

Jakub Zakrzewski, T. Dohnalik

Published Jun 28, 1983• 13 citations
Publisher

Abstract

Previous theoretical treatments of polarisation spectroscopy (forward scattering) are generalised so as to include laser temporal coherence effects. It is shown that for the general case it is impossible to describe the signal obtained in terms of birefringence and dichroism. The generalisation of the concept of the polarisability tensor is given together with the approximate expression for the signal in terms of it. The simple example of the J g =0 to J e =1 transition in the forward scattering experiment is discussed in detail. Comparison is made between the signal lineshapes obtained for the phase diffusion model and the chaotic field model. The necessity of taking into account the statistical properties of the laser light in the forward scattering (polarisation spectroscopy) experiment is pointed out.

DOI
10.1088/0022-3700/16/12/009

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Previous theoretical treatments of polarisation spectroscopy (forward scattering) are generalised so as to include laser temporal coherence effects. It is shown that for the general case it is impossible to describe the signal obtained in terms of birefringence and dichroism. The generalisation of the concept of the polarisability tensor is given together with the approximate expression for the signal in terms of it. The simple example of the J g =0 to J e =1 transition in the forward scattering experiment is discussed in detail. Comparison is made between the signal lineshapes obtained for the phase diffusion model and the chaotic field model. The necessity of taking into account the statistical properties of the laser light in the forward scattering (polarisation spectroscopy) experiment is pointed out.
Abstract A theoretical and experimental study has been made of the intensity of forward scattered light in conditions of radio-frequency double resonance and level-crossing. The main conclusions are (i) that the magnetic resonance and level-crossing effects which are familiar in the laterally scattered light are to be found also in the forward scattered light, but (ii) that the resonance curves are Doppler-broadened, and the strength of the oscillatory field necessary to generate them is correspondingly increased, and (iii) that coherence narrowing is much more pronounced in forward than in lateral scattering. The differences derive from the coherence between the radiation from different atoms which is present in forward, but not in lateral scattering, and which is implicitly recognized in the classical theory of the propagation of light in polarizable media. The equations of electromagnetism form the basis of the present analysis. In the presence of the oscillatory magnetic field the polarization tensor is complex and time-dependent. The time dependence leads to the result that the number of eigenwaves necessary to describe propagated waves in the medium is four, as against the usual two. An arbitrary wave is resolved into a superposition of the four eigenwaves, all of which have different propagation constants. The analysis is very general, and is applicable to experiments with lasers. The components of the polarization tensor are derived by finding first the polarizability of individual atoms from a semi-classical theory of their interaction with light and magnetic fields. The macroscopic polarization, obtained by summing over individual atoms, is then given by folding the individual polarizabilities with the Doppler distribution of resonance frequencies. In the particular case studied in detail (the inter-combination resonance line, 2537 A, in mercury), the Doppler width is much greater than the radiation width, and the imaginary (absorptive) part of the polarizability is Gaussian. Expressions are derived in a ‘weak scattering’ approximation for the intensity of the forward scattered light. They are magnetic resonance functions which are found to be the Doppler-broadened equivalents of the familiar functions, based on Lorentzians, characteristic of scattering by a single atom. In the case of double resonance the forward scattered light is strongly modulated, as is the laterally scattered light. To investigate coherence narrowing, the zero-field level-crossing has been studied with the restriction of ‘weak scattering’ removed. The result is obtained that the width of levelcrossing curves is inversely proportional to the vapour density for magnetic fields such that the Zeeman splitting is small in relation to the Doppler width. This analytical result has been verified experimentally.
Quantum theoretical treatment of coherent forward scattering of light in a polarized atomic ensemble with an arbitrary angular momentum is developed. We consider coherent forward scattering of a weak radiation field interacting with a realistic multilevel atomic transition. Based on the concept of an effective Hamiltonian and on the Heisenberg formalism, we discuss the coupled dynamics of the quantum fluctuations of the polarization Stokes components of propagating light and of the collective spin fluctuations of the scattering atoms. We show that in the process of coherent forward scattering, this dynamics can be described in terms of a polariton-type spin wave created in the atomic sample. Our work presents a general example of an entangling process in the system of collective quantum states of light and atomic angular momenta, previously considered only for the case of spin-12\frac{1}{2}21​ atoms. We use the developed general formalism to test the applicability of the spin-12\frac{1}{2}21​ approximation for modeling the quantum nondemolishing measurement of atoms with a higher angular momentum.
The theoretical dependence of optical birefringence phenomena on the statistical nature of the light is investigated. Photon S-matrix calculations lead to expressions relating the change induced in the statistical nature of the beam to the molecular properties of the target sample. A hypothetical generalized optical birefringence experiment is analysed: in the experiment the coincidences of photons arriving at spatially separated detectors sensitive to different polarizations are observed with and without the sample in the beam, and the difference in the photon correlations depend on the initial statistical composition and polarization of the beam and the molecular properties of the sample. When the beam is generated by a thermal source the difference of the signals (with and without the sample) depends on the product of the polarizability and optical rotation tensors. When the light is generated by a single-mode coherent source the statistical properties of the light are such as to eliminate the second-order interaction terms, and so the experiment yields the hyperpolarizability and hyper-rotation tensors automatically and with the explicit exclusion of the polarization and rotation tensor contributions.
The polarisation properties of the single mode linearly polarised laser beam interaction with a Doppler broadened absorber has been investigated. The absorber is placed in a longitudinal tunable magnetic field. The laser beam is analysed with a polariser after it has traversed the absorber. With various analyser rotation angles the lineshapes of the nonlinear resonances known as the population effect and the Zeeman coherence effect have been studied near zero magnetic field tuning. Theoretical predictions derived from the semi-classical laser theory are compared with experimental results. The experiment has been carried out with a low power thermally stabilised 633 nm He-He laser. The measured lineshapes of the resonances of the 2 p 4 -3 s 2 transition in neon agree well with the theoretical predictions. By using an analyser in the beam an improved signal-to-noise ratio is shown to result.
Existing theories of level crossing and modulation effects in the light scattered from optically thin vapours are restricted to cases where the light from different atoms is either completely incoherent (lateral scattering) or completely coherent (forward scattering). In the latter case the resonances are Doppler broadened equivalents of the well known Lorentzian forms predicted for lateral scattering. The more general case of partial coherence of the scattered light, which might be expected at small scattering angles, has not previously been considered. In this paper the degree of coherence of the scattered light has been formulated in terms of an autocorrelation function. For scattering from an ideal gas the autocorrelation function may be split into two terms representing complete incoherence and complete coherence. The predicted resonances for scattering into an arbitrary direction are mixtures of the Lorentzian and Doppler broadened forms, but the latter have a strong angular dependence that effectively restricted their observation to the small angular range associated with diffraction from the active volume of the vapour.