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Physical Review A

Forward-scattering ring structure and the spectra dependence on laser frequency

Anne Lindberg, Birger Stahlberg, Kalle‐Antti Suominen

Published Aug 1, 1994• 3 citations
Publisher

Abstract

We present analytical predictions based on a semiclassical theory concerning a single-mode cw laser interaction with longitudinally Zeeman tuned J=1--J=0 atomic systems. In the theoretical model, the laser frequency detuning from the inhomogeneously broadened absorber line center is considered. Equation for the interaction signal are derived for all rotations of a polarizating analyzer transmisson axis with respect to an original laser beam linear polarization. Results are presented for the forward-scattering case when the analyzer transmission axis is orthogonal to the beam polarization. Calculated results on bright and dark ring-shaped light structures are compared with experimental ones originating from a Gaussian beam interaction with a neon 1${\mathit{s}}_{4}$(J=1, g=1.464)--2${\mathit{p}}_{3}$(J=0) transition. Calculated results on forward-scattering spectra are presented, i.e., the forward-scattering light intensity as a function of the longitudinal magnetic tuning when the laser frequency is fixed to selected detunings from the absorber line center. Spectra are presented both for the case when the inhomogeneously broadened line originates from a single absorbing isotope and for the case when it originates from overlapping contributions of two isotopes. The results show that laser frequency detunings of tens of megahertz from the absorber line center(s) show up in the forward-scattering spectra. The conclusion is that reliable data on atomic parameters of a nonlinearly absorbing sample can be extracted from experimental spectra only when the sample is monoisotopic and when the laser frequency detuning from the absorber line center is known.

DOI
10.1103/physreva.50.1531

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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.

Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Jul 5, 1966•87 citations
We present analytical predictions based on a semiclassical theory concerning a single-mode cw laser interaction with longitudinally Zeeman tuned J=1--J=0 atomic systems. In the theoretical model, the laser frequency detuning from the inhomogeneously broadened absorber line center is considered. Equation for the interaction signal are derived for all rotations of a polarizating analyzer transmisson axis with respect to an original laser beam linear polarization. Results are presented for the forward-scattering case when the analyzer transmission axis is orthogonal to the beam polarization. Calculated results on bright and dark ring-shaped light structures are compared with experimental ones originating from a Gaussian beam interaction with a neon 1s4{\mathit{s}}_{4}s4​(J=1, g=1.464)--2p3{\mathit{p}}_{3}p3​(J=0) transition. Calculated results on forward-scattering spectra are presented, i.e., the forward-scattering light intensity as a function of the longitudinal magnetic tuning when the laser frequency is fixed to selected detunings from the absorber line center. Spectra are presented both for the case when the inhomogeneously broadened line originates from a single absorbing isotope and for the case when it originates from overlapping contributions of two isotopes. The results show that laser frequency detunings of tens of megahertz from the absorber line center(s) show up in the forward-scattering spectra. The conclusion is that reliable data on atomic parameters of a nonlinearly absorbing sample can be extracted from experimental spectra only when the sample is monoisotopic and when the laser frequency detuning from the absorber line center is known.
We present experimental and theoretical investigations of a Gaussian laser beam interacting with Zeeman-tuned J=1\ensuremath{\rightarrow}J=0 atomic systems. In our experiment a single-mode cw dye-laser beam traverses a neon discharge in a longitudinal magnetic field. The excited neon transitions used for these studies are 1s4{\mathit{s}}_{4}s4​(J=1,g=1.464)\ensuremath{\rightarrow}2p3{\mathit{p}}_{3}p3​(J=0) and 1s2{\mathit{s}}_{2}s2​(J=1,g=1.034)\ensuremath{\rightarrow}2p1{\mathit{p}}_{1}p1​(J=0). In the laser-induced forward-scattered light, dark and bright ring-shaped structures are observed. The ring structures are investigated as a function of the magnetic detuning of the m=\ifmmode\pm\else\textpm\fi{}1 sublevels and as a function of the laser-beam power. We find that the line shapes of the spectra, i.e., the forward-scattered light intensities as a function of the magnetic detuning, are sensitive to the transverse intensity distribution of the laser beam. Analytical expressions based on a semiclassical theory are derived and the calculated results on the ring structures and the spectra are compared with the experimental results. Good agreement between the calculated and the experimental results are obtained only when the transverse effects are taken into account.
The forward-scattered light observed when a single-mode dye laser interacts with the three neon transitions 1 s 5 ( J = 2)-2 p s ( J = 2), 1s 3 ( J = 0)-2 p 5 ( J = 1), and 1 s 4 ( J = 1)-2 p 7 ( J = 1) has been investigated as an applied longitudinal magnetic field is varied. The 1 s 5 and the 1 s 3 states are metastable. This condition allows a comparison of the spectra for the cases 1 s 5 ( J = 2)-2 p 8 ( J = 2) and 1 s 3 ( J = 0)-2 p 5 ( J = 1) in order to discuss whether the complex line shapes obtained for the J = 2 to J = 2 atomic system are due to higher-order coherences or whether they originate from coherences between m = ±1 states. Experimental and calculated line shapes are presented. The calculations have been performed with the use of a semiclassical model for the light/matter interaction. A J = 0 to J = 1 (or a J = 1 to J = 1) model reproduces the overall shapes of the recorded spectra for all three transitions. The results show that, even when laser beam spatial effects and the sample isotopic effects are taken into account, interpretations of forward-scattering spectra in order to determine atomic parameters can reliably be done for simple J = 0 to J = 1 systems only.
An important effect to be considered in forward-scattering experiments is demonstrated. Ring-shaped structures are observed in the transverse intensity distribution of the forward-scattered light induced by an intense CW single-mode dye laser in an excited neon system. These structures depend upon the laser detuning from the absorber line centre, the magnetic field strength and the neon gas pressure. A preliminary interpretation of the phenomenon is given and its consequences for the interpretation of forward-scattering spectra are pointed out.
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.
This paper presents new results for the steady states of a detuned ring laser with a saturable absorber. We employ a semiclassical model which assumes homogeneously broadened two-level atoms. We proceed by solving the Maxwell-Bloch equations for the longitudinal dependence of the steady states of this system, and then simplify our solution by use of the uniform-field approximation. We present uniform-field results for squared electric field versus operating frequency, and for each of these versus cavity tuning and laser excitation. Various cavity linewidths and both resonant and nonresonant amplifier and absorber line-center frequencies are considered. The most notable finding is that cavity detuning breaks the degeneracies found in the steady-state solutions of the fully tuned case. This leads to the prediction that an actual system will bifurcate from the zero-intensity solution to a steady-state solution as laser excitation increases from zero, rather than to the small-amplitude pulsations found for the model with exactly resonant tuning of the cavity and the media line centers. Other phenomena suggested by the steady-state results include tuning-dependent hysteresis and bistability, and instability in both intensity and frequency due to the appearance of one or more new steady-state solutions as tuning is varied. These effects of detuning are being tested by a linearized stability analysis whose results will be reported separately.
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.