Two-photon-absorption magneto-optic dispersion spectrometer   

FIELD OF THE INVENTION

This invention relates to optical spectrometers utilizing circular birefringence to rotate the linear polarization of light, and more particularly to deducing the photon wavelength based on an analysis of light polarization after propagating light through the circularly birefringent medium.

BACKGROUND OF THE INVENTION

High resolution measurement of light frequency from incoherent sources typically makes use of cavity interference such as Fabry Perot interferometers and gratings, or absorption lines from some medium. Interferometers such as a Fabry Perot or gratings are expensive and have low acceptance angles, meaning the deviation from the desired angle at which the light enters the interferometer has very little tolerance. Moreover, for such interferometers increasing the spectral resolution lowers the transmission of the signal (reduces the number of photons included in the signal). Absorption line mediums (e.g., iodine, potassium and sodium) require some atomic or molecular transition in the medium, and they only occur at discrete and fixed frequency locations. Additionally, since absorption lines absorb light, they deplete the strength of the signal being measured.

Magneto-optic spectrophotometers can be used to measure frequency, but they only distinguish light near a particular absorption line from light that is not near a particular absorption line, which provides very low frequency resolution in comparison to the current invention.

FIG. 1 is a diagram of rubidium spectra, in accordance with one embodiment of the present invention.

FIG. 2 shows the basic configuration of a two-photon-absorption magneto-optic dispersion spectrometer in accordance with one embodiment of the present invention.

FIG. 3 shows the real (X′) and imaginary (X″) portions of the electric susceptibility near a split absorption line caused by a magnetic field. The figure also shows the difference in susceptibility between each circularly polarized component of a test beam for test beam paths propagating with and against a magnetic field shifted susceptibility in accordance with one embodiment of the present invention.

FIG. 4 is a plot of transmission spectra into two separate channels, a first output and second output, in accordance with one embodiment of the present invention.

DETAILED DESCRIPTION

Several drawings illustrate physical the attributes of a magneto optic dispersion spectrometer, and quantities that may be manifested with its construction, in accordance with embodiments of the present invention. Examples are described that have particular gaseous mediums, transitions, wavelengths of complimentary light pairs, etc. for purposes of illustration. However, it should be noted that the choices of particular gaseous medium and particular transitions are abundant. Also, while concomitant to the chosen transitions, the wavelengths of the light pairs, test beam and reference beam, have wide latitude of choice upon a continuum. Thus it is recognized that the apparatus and means described herein may vary without departing from the basic underlying concepts of the invention.

The current invention is an optical spectrometer based on dispersion from two-photon-absorption. An optical spectrometer measures some property of light, typically intensity as a function of wavelength. A dispersion spectrometer utilizes a rapidly changing electric susceptibility to demarcate intensity at a particular wavelength. Embodiments of the current invention are based the creation of a medium where in selected frequency regions the dispersion changes rapidly but absorption is mostly absent. The frequency region between two absorption lines has these properties and is exploited herein. One way to create two absorption lines is to apply a magnetic field to an atomic vapor and split a single absorption line into two absorption lines.

Light that propagates through a gaseous medium is preferentially absorbed when its energy corresponds to a particular atomic transition. This preferential absorption (otherwise known as resonance absorption) also affects light phase, or dispersion. The electric susceptibility is used to describe both the absorption and dispersion effects. Whenever the real portion of the electric susceptibility, for each circular polarization state of light are different, then the medium becomes circularly birefringent. A linear polarized beam will undergo polarization rotation to another linear polarized state while traveling through a circular birefringent medium. It will be shown that the electric susceptibilities for the test beam that manifest from two-photon-absorption in an gaseous medium can be manipulated to bring about circular birefringence that changes rapidly enough to make an ultra high resolution spectrometer.

A circular birefringent medium in the present invention accomplishes circular birefringence based on a physical phenomena called two-photon-absorption. Consider an atomic transition from a ground state (lowest allowed energy state of an atom) to an intermediate excited state, which can occur with the absorption of a single photon. A single photon resonance is a photon frequency bandwidth where the energy of the photon matches an allowed atomic transition. Furthermore, consider another transition from the intermediate excited state to another still higher energy state, a final excited state that can occur with the absorption of a single photon. Two-photon-absorption is the direct transition from the ground state to the final excited state, avoiding the intermediate state, by the simultaneous absorption of two photons. A two-photon-transition identifies the states of the substance involved in two-photon-absorption. A two-photon-absorption line is a frequency bandwidth of light that can be absorbed by the process of two-photon-absorption. FIG. 1 is a diagram illustrating the process of two-photon-absorption, in accordance with one embodiment of the present invention.

In the case of two-photon-absorption, the only restriction upon the energy of the photons is that the sum of their energies match the total energy of the atomic transition:

E excited - E ground = hc λ 1 + hc λ 2 Equation   1

Equation (1) demonstrates that there is some freedom of choice of wavelengths λ1 & α2. Conservation of energy requires only that the sum of the two photon energies match the two photon transition, which is a considerably relaxed condition compared to a sequential transition, where each photon energy individually matches the transition energy. This enables tuning of the spectrometer to different wavelengths. In this manner, the two-photon-absorption line frequency location is tunable simply by tuning the reference light frequency. Single photon resonance is not required, nor excluded in the two-photon-absorption process.

Practical two-photon-absorption involves the rigid application of angular momentum selection rules. Because conservation of angular momentum is never violated, selection rules place restrictions upon the interaction of light with matter, and are exploited to produce circular birefringence. In units of h, all photons have an angular momentum. Since angular momentum is a vector, it has magnitude and direction. A photon with right-handed circular polarization has an angular momentum direction opposite to the propagation direction, and a magnitude of one. A photon with left-handed circular polarization has an angular momentum direction in the same direction as the propagation direction, and a magnitude of one. Circularly polarized light is in a stationary or eigen state. Linearly polarized light on the other hand has angular momentum of one, but the direction is in a super position of eigen states. Upon absorption of a photon the angular momentum vector is transferred into the system that absorbs it. But in the case of linearly polarized light, the direction of the transferred angular momentum vector is equally likely to be in the forward direction as the backwards direction.

For atomic dipole transitions, or allowed transitions, there is a change in magnitude of angular momentum between the initial state and final state of one, with the emission or absorption of a single photon. Consider a sequence of two dipole transitions of an atom. Beginning with lowest energy state of the atom, the ground state, a transition can occur to an excited state, denoted here as an intermediate excited state, with absorption of a photon. Then another transition can occur from the intermediate excited state to a final excited state with another photon absorption. By vector addition, angular momentum that the ground state and the final excited state have may differ by zero or two (e.g., 1-1=0; 1+1=2). Now consider the same situation except that instead of sequential absorption of two photons there is simultaneous absorption of two photons, denoted two-photon-absorption. If the angular momentum of the atom\'s ground state and final excited state are identical, then two-photon-absorption can occur only with a photon pair that have angular momentum vectors aligned in opposite directions. Similarly, if the angular momentum of the atom\'s ground state and the final excited state differ by two, then two-photon-absorption can occur only with a photon pair that have angular momentum that is aligned in the same direction. Extrapolating from single photons to beams, all the photons of a circularly polarized beam of light have their angular momentum vectors aligned in the same direction.

Applying the above concepts we can begin to explain the present invention. FIG. 2 illustrates the major components that operate as an optical spectrometer, in accordance with one embodiment of the present invention. A gaseous substance involved in the two-photon-absorption process is contained in cell 06. For example cell 06 may be a transparent vessel that contains rubidium, some of which will be in a vapor state. A heater and a temperature controller may be implemented to control the temperature of the vapor. An example set of states and corresponding transition energy wavelengths for the Rubidium are: 5S1/2→5P1/2→4D3/2 with 794 nm and 1475 nm respectively. Thus a reference laser may have a wavelength near 794 nm that provides a circularly polarized reference beam propagating through cell 06. There will then be a two-photon-absorption line for a test beam 03 line near 1475 nm. Since the reference beam 04 is circularly polarized, the selection rules dictate there will be a two-photon-absorption line for only one circularly polarized component of test beam 03. Thus a two-photon-absorption line influences one circular component of the test beam 03, and the other circular component is unaffected making the medium circularly birefringent.

An absorption line affects light not only by absorption, but affects light phase as well. The electric susceptibility is used to describe both effects. To quantify the birefringence, the electric susceptibility can be used and is defined here in terms of dielectric polarization density:

P=εo{right arrow over (E)}  Equation 2

is dimensionless and also a complex quantity, and is expressed in component form as:

′Equation 3

The polarization of test beam 03 may be linear, but if not a linear polarizer 08 may be implemented to produce linear polarization. Using a circular polarization basis to express the linear polarized test beam 03, with some minor approximations and removing time dependence, the electric field of the test beam 03 after traveling a distance l within the birefingent medium inside cell 6 is:

E →  ( l ) = - E o 2  exp [   { ω c  ( 1 + + ′ 2 +   + ′′ 2 )  l } ]  + ^  + E o 2  exp [   { ω c  ( 1 + - ′ 2 +   - ′′ 2 )  l } ]  - ^

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