Chiral Light and the Stokes Parameters

Light is electromagnetic radiation which can be interpreted as wave of an electrical field vector E and a magnetic field vector B, each of them oscillating and perpendicular to the axis of translation and E.LB. For unpolarized light, the electrical field vector has an infinite number of orientations. If one restricts its oscillations to one plane, for example by a linearly polarizing filter, we speak of linearly polarized light. Also here, E L B is valid. This light is used in a polarimeter for the measurement of the optical rotation of a chiral molecule in solution.

Electromagnetic radiation can moreover consist of asymmetric light, called circularly polarized light. The photons then have angular momentum, called helicity, spinning either to the left or the right.

If one assumes that light can be described as an electromagnetic wave that oscillates in all planes, then circular polarized light only oscillates in one plane which rotates around the direction of propagation of the light. A more precise definition of circularly polarized light can be found in Barron (2004) saying that in a circularly polarized light beam, the tip of the electric field vector in a fixed plane perpendicular to the direction of propagation traces out a circle with time. Light is addressed right-circularly polarized light if the tip of the E vector rotates clockwise when viewed from the observer towards the light source. In circularly polarized light the electric field vector remains constant magnitude in time but proceeds in form of a helix in the propagation direction. Also here, at each point in space and time, the magnetic field is perpendicular to the electric field and to the direction of propagation.

Unpolarized light, linearly polarized light, and circularly polarized light including their wavelength X are schematically illustrated in Fig. 2.11.

Circularly polarized electromagnetic radiation can be produced in a laboratory using a light source and a X/4-plate. If tunable energy and a higher photon's energy of up to 12 eV are required, vacuum ultraviolet CPL can be produced artificially in a modern synchrotron.

More difficult is the detection of CPL at various energies. Here, polarimeters, such as the Onuki-type polarimeter can be applied. In Fig. 2.12 different polarizations of light, which were created at 7 eV at the synchrotron center LURE, Paris-Orsay, are given. The images clearly allow distinguishing between linearly, ellipti-cally, and circularly polarized light.

But how can we experimentally specify the three parameters of electromagnetic radiation namely intensity, phase, and polarization? Four Stokes Parameters, I, Q, U, and V (or in an alternative classification So, Si, S2, and S3 as described by Barron (2004)) can do so and are to be determined. In a right-handed orthogonal coordinate system formed by r and 1 (see Fig. 2.13) the propagation direction is described by s. The total intensity I of electromagnetic radiation is given by Eq. 2.19.

For monochromatic light, IL and IR are uniquely specified if the degree of linear polarization (Eq. 2.20)

is known. By a = a' sin^ and b = a' cosfi the equation a/b = tan^ is given, where a and b are the semimajor axes of the elliptically polarized light, a' is the hypotenuse, and Yis the angle between l and the major axis (Fig. 2.13). The definitions given in Eqs. 2.21 and 2.22

are given for the Stokes parameters describing the elliptical polarization. In this notation, circular polarization is to be regarded as a particular case of elliptical polarization.

The four Stokes parameters are connected via Eq. 2.23

For unpolarized light, Eq. 2.24 indicates

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