Table of contents

This special issue on Polarization Optics contains one review article and 23 research papers, many of which are based on presentations at the International Commission for Optics Topical Meeting on Polarization Optics, held in Polvijärvi, Finland, between 30 June and 3 July 2003. While this issue should not in any sense be considered as a `proceedings' of this meeting, the possibility of submitting papers to it was widely advertised during the meeting, which was attended by a large fraction of prominent scientists in the field of polarization optics. Thus the quality of papers in this special issue is high.

In announcing both the meeting and this special issue, we emphasized that the concept of `polarization optics' should be understood in a wide sense. In fact, all contributions dealing with the vectorial nature of light were welcome. As a result, the papers included here cover a wide range of different aspects of linear and nonlinear polarization optics. Both theoretical and experimental features are discussed. We are pleased to see that the conference and this special issue both reflect the wide diversity of important and novel polarization phenomena in optics.

The papers in this special issue, and other recently published works, demonstrate that even though polarization is a fundamental property of electromagnetic fields, interest in it is rapidly increasing. The fundamental relations between partial coherence and partial polarization are currently under vigorous research in electromagnetic coherence theory. In diffractive optics it has been found that the exploitation of the vectorial nature of light can be of great benefit. Fabrication of sophisticated, spatially variable polarization-control elements is becoming possible with the aid of nanolithography. Polarization singularities and the interplay of bulk properties and topology in nanoscale systems have created much enthusiasm. In nonlinear optics, the second harmonic waves generated on reflection and transmission of intense light enable research into the chirality of nanogratings. Pump-probe techniques allow one to visualize the effects of the nanostructure topology on the surface mode excitation. In quantum optics the coherent control of polarization may lead to new and fascinating applications.

Some authors of invited papers at the conference have written review-type introductory sections—they were encouraged to do so—but all contributions are genuine research papers with original results, and were judged according to the normal publication criteria of the journal. It is our pleasure to thank all authors for making this a splendid special issue of Journal of Optics A: Pure and Applied Optics.

We present a review of our studies of frequency conversion in various media using polarized radiation of different durations. We discuss our results on harmonic generation in fullerenes, ion beams, solid surfaces, colloidal metals, nonlinear crystals, dye vapours, metal-doped polymers, gases, and plasmas over a broad spectral range (from VUV to IR).

Polarization effects play an even more important role in nonlinear optics than in linear optics because of the richer set of phenomena describable by higher-order tensor relations. The present contribution surveys some recent research on polarization aspects of nonlinear optical interactions, paying special attention to nonlinear optical interactions in chiral isotropic optical materials. We especially address the question of the existence of a linear electro-optic effect in chiral isotropic materials and analyse some of the conflicting statements that have recently been made in the scientific literature.

In optical fields with sub-wavelength features the longitudinal field components become considerable. Therefore, the paraxial concept of 2D polarization has to be replaced by the description of the local behaviour of the 3D vector of the electric field. The heterodyne scanning probe optical microscope (heterodyne SPOM) allows one to measure the amplitude and phase of the optical field with sub-wavelength resolution. In this paper we will review some results of earlier work showing clearly the 3D aspect of the polarization in the diffracted field from a 1 µm pitch surface relief grating and present a new set-up for a polarization sensitive heterodyne SPOM. For the correct interpretation of SPOM images of optical fields with sub-wavelength features it is important to be aware of the field conversion by the fibre tip probe.

In the 2 × 2 matrices representing retarders and ideal polarizers, the eigenvectors are orthogonal. An example of the opposite case, where eigenvectors collapse onto one, is matrices M representing crystal plates sandwiched between a crossed polarizer and analyser. For these familiar combinations, M² = 0, so black sandwiches can be regarded as square roots of zero. Black sandwiches illustrate physics associated with degeneracies of non-Hermitian matrices.

The three-dimensional coherence matrix is interpreted by emphasizing its invariance with respect to spatial rotations. Under these transformations, it naturally decomposes into a real symmetric positive definite matrix, interpreted as the moment of inertia of the ensemble (and the corresponding ellipsoid), and a real axial vector, corresponding to the mean angular momentum of the ensemble. This vector and tensor are related by several inequalities, and the interpretation is compared to those in which unitary invariants of the coherence matrix are studied.

Performing three measurements (holograms) on the same sample with the same beam but different polarization, spurious spots can be reduced and the holographic image appears to be better. The change of polarization requires nothing more than a rotation of the sample around the beam's direction. For the reconstruction of the image one applies the standard Fourier transform (FT) techniques on a combination of the holograms obtained. The resulting image is better than that obtained with an unpolarized beam.

The connection between the degree of polarization and the effective degree of coherence is established. It is shown that from the formal point of view, the degree of polarization is a quantity analogous to the degree of coherence for scalar fields, provided that the coherence properties are examined as an average in some given domain. It is also demonstrated that the effective degree of coherence has a geometrical interpretation as the distance between the given mixed state and the incoherent state, normalized by the maximum distance in the geometry examined. The meaning of an analogous quantity in quantum optics is briefly discussed.

Short- and long-period fibre gratings with linear birefringence and/or rotational effects are studied by using a generalized coupled mode theory which, in a truncated form, is a very good approximation as long as the periodic perturbation is small. This generalized theory made possible the study of the contra-directional and co-directional couplings in an isotropic optical fibre with an isotropic periodic perturbation, in an anisotropic optical fibre with a periodic perturbation and in a fibre with an anisotropic periodic perturbation. That is to say, of short- and long-period fibre gratings with linear birefringence and rotational effects, also in the most general case in which the periodic perturbation is optically anisotropic.

In this paper we suggest a method of using optical wave polarization to carry information in optical fibre channels. The use of polarization increases the information capacity in the fibre. We show the effect of polarization mode dispersion on the method and the limitations it imposes. Concepts and considerations concerning implementation are also presented.

We analyse the changes in the partial polarization of random, stationary light fields in transmission through a near-field probe. The probe is modelled as a two-dimensional metal-coated optical fibre tip through which the field is propagated by applying the boundary-integral method. Both the magnitude of the opening angle and the aperture size of the probe are found to significantly influence the partial polarization of the field. We discuss the results in terms of both the conventional two-dimensional and the recent three-dimensional formalism for the degree of polarization.

The concept of the so-called closest field to a given vector function is extended to the non-polarized case. Attention is focused on transverse field solutions of the Maxwell equations whose transverse character is preserved under free propagation. The coherence matrix of the non-paraxial transverse field that is closest to a paraxial unpolarized transverse beam is given. It is shown that the intensity matrix of this closest field can be written as the sum of the intensity matrices of a non-polarized field and a totally polarized beam.

On the basis of the second-order intensity moments formalism, the relationship between the spatial structure and the overall polarization characteristics of partially polarized Gaussian Schell-model beams of a certain kind has been investigated. More specifically, attention has been focused on a type of source that cannot be distinguished from ordinary Gaussian Schell-model fields when polarization measurements are disregarded. For this class of beams several general properties have been obtained that enable us to link the beam coherence polarization matrix and the beam quality parameter with certain polarization degrees recently introduced in the literature.

For many practical applications, the polarization dependence of the Raman gain (Raman PDG) is considered as a drawback. Most approaches used to reduce the PDG are based on depolarization or scrambling of the pump source polarization. We report on an experimentally observed effect and describe a method for reducing the Raman PDG by means of polarization control with a fully polarized pump source. The method makes it possible to maintain high efficiency of the Raman gain. The absence of circular symmetry (on average) in non-polarization maintaining fibres allows one to find a certain polarization state of the pump to minimize the Raman PDG. The observed phenomenon is inherently related to polarization mode dispersion which always exists in optical fibres.

Blue phases (BPs) are cubic phases of cholesteric liquid crystals (CLC) with a sufficiently short pitch. They occur in three different phases (BPI, BPII, BPIII) in small temperature ranges between the cholesteric and the isotropic state. Light reflected by BP crystals is partially circularly polarized. Calculating the Müller matrices of the Bragg reflected light for different structural models makes it possible to compare the results with measurements and study other theoretical considerations. Specifically, Müller matrices for a polycrystalline specimen were analysed.

By nearly grazing waves we understand travelling waves having wavevectors forming an angle of nearly π/2 with respect to the normal of a planar surface. Multiple-beam superposition of nearly grazing waves has been recognized as giving rise to stepwise constant phase behaviour of the total field after reflections in dielectric gaps. This behaviour of the phase is polarization dependent. When two dielectric interfaces form a wedge with nearly grazing waves within, the formation of bright interference patterns can be easily achieved. One of the reasons for this is the above mentioned phase behaviour. An additional effect favouring pattern formation comes from the values of the Fresnel coefficients of reflection, which are close to unity for nearly grazing waves. Because both features have polarization dependence, a corresponding polarization dependence of the resulting interference patterns is also expected. Numerical results employing basic considerations of multiple-beam superposition of nearly grazing waves in dielectric wedges for s and p polarizations are presented under monochromatic and polychromatic illuminations. Experimental observations are also shown.

The polarization state of light double passing through the eye is mainly modified by the birefringent structures of the cornea and the retina. The effects of depolarization are often light in normal young eyes but these could change with age, ocular pathologies and refractive surgery. The influence of depolarization on the calculation of the ocular retardation has been studied. Results show that the larger the depolarization, the larger the error in the computed ocular retardation. Moreover, the influence of the corneal compensation on measurements of ocular polarimetry has also been explored. We found that an incomplete compensation of the retardation and/or corneal axis leads to both wrong estimation of the ocular retardation and an erroneous computation of the corneal axis.

To determine the polarization mode dispersion (PMD) in an optical device, a tunable light source and a polarimeter are used to measure the Jones or the Mueller matrix at different wavelengths. We show that a complete real-time PMD characterization can be performed using a broadband source and three polarization gratings. A polarization grating performs a periodic spatial change of the state of polarization of an incident beam. The diffraction pattern of these devices is composed of higher-order waves with a fixed polarization state that is independent of the incident one. Following a general mathematical model, we show that it is possible to design PGs to measure all the Stokes parameters. Since different wavelengths are diffracted under different angles, focusing the output of a PG on an array of photodetector, it is possible to measure simultaneously the Stokes parameters at different frequencies. Various fabrication techniques for continuous and pixillated PGs are described and the corresponding efficiencies and degrees of freedom outlined.

Results of numerical analysis of the variation of the spatio-temporal and polarization structure of pulses in the second harmonic generation and pulse amplification processes in the strong energy exchange regime are presented taking into account the diffraction, group velocity mismatch, temporal delay and the pulse shapes. It was demonstrated that as a result of the second order processes, the initially transversely homogeneous polarization structure of the fundamental harmonic beam undergoes significant changes in general. As a result, a transversely inhomogeneous distribution of the elliptical polarization is achieved in the fundamental harmonic beam that varies during the pulse propagation in a complex manner. The developed algorithm and program enable us to optimize the processes and to find the conditions where a high enough compression ratio of the second harmonic pulses or amplification efficiency of the fundamental harmonic pulses is achieved with a controlled polarization state, preserving sufficiently high beam quality.

A high-reflectivity coated mechanical silicon oscillator with high quality value of the mechanical resonance was employed as a planar rear mirror in a Fabry–Perot interferometer. Active stabilization of the interferometer improves the stability of the resonance and makes it possible to perform sensitive interferometric measurements. The frequency locking of lasers to optical cavities requires typically the generation of an error signal with a typical steep slope at resonance. The Hänsch–Couillaud locking method utilizes polarization spectroscopy by monitoring changes in the polarization of the light field reflected from the cavity. A polarization analyser detects dispersion shaped resonances which give the error signal for the electronic servo loop. The error signal contains information about the changes in the cavity length and thus the motion of the mechanical oscillator can be observed. The error signal was detected with the use of a spectrum analyser. The noise floor of the interferometer response indicates that the sensitivity of the optomechanical sensor or the minimum observable displacement in the mechanical oscillator position is Δx_min = 1.7 × 10⁻¹⁴ m. This gives high enough sensitivity to observe the Brownian motion of the oscillator at room temperature.

When a retroreflector has periodic structure, it also behaves as a diffraction grating. When its period becomes shorter, the effect of diffraction is more dominant than that of reflection. In particular, when the period steps into the resonance domain, the retroreflector no longer functions, because the number of diffraction orders decreases significantly and diffraction to the desired direction does not exist. Here, behaviours of micro-sized metallic and perfectly conducting retroreflectors of corner cube type over the period range of 1–100 wavelengths are analysed electromagnetically with the C method. Generally, metals and perfect conductors exhibit similar tendencies for TE polarization, but there are big differences in some cases for TM polarization, possibly owing to surface plasmon resonance. As an example application of periodic retroreflectors, object detection is considered and the required conditions for valid usage are provided.

Electromagnetic pulses are shown to have an intrinsic angular momentum along the direction of the net momentum of the pulse, unchanged by Lorentz boosts along this direction, and invariant to change of spatial origin. This intrinsic angular momentum is evaluated (together with the energy and momentum) for two types of pulses based on a localized oscillatory solution of the wave equation. The Lorentz boost required to bring each pulse to its zero-momentum frame is evaluated analytically.

Polarization hologram recording based on the effect of photoinduced anisotropy (PA) is reviewed, focusing on amorphous chalcogenides (ACh). Possible PA mechanisms in ACh are considered. Polarization holographic grating recording in amorphous As–S–Se (a-As–S–Se) films is experimentally studied and analysed in comparison with scalar recording. It is holographically established that linearly polarized 632.8 nm light produces photoinduced anisotropy and the chalcogen related D⁺, D⁻ centre reorientation and generation mechanism is proposed. It is used to explain the observed peculiarities of polarization (vector) recording in comparison with scalar recording based on photoinduced structural changes: much lower diffraction efficiency (4 × 10⁻³ % versus 4%), much larger specific recording energy (6400 J/(cm² %) versus 20 J/(cm² %)), difference in spatial frequency response, instability (vector hologram lifetime of about two days versus practically permanent scalar holograms), the absence of hologram self-enhancement (present in scalar recording), and near perfect reversibility. It is also experimentally found that light diffraction from the polarization holographic gratings in a-As–S–Se films is indeed anisotropic since the readout wave polarization diffracted in the minus first order is changed in such a way that the linear signal wave polarization orthogonal to the reference wave polarization is reconstructed. The results obtained are discussed.

We report the first sub-Doppler study of the magnetic field dependence of laser-induced fluorescence excitation spectra of alkali atoms making use of an extremely thin vapour cell (). This thin cell allows for sub-Doppler resolution without the complexity of atomic beam or laser cooling techniques. This technique is used to study the laser-induced fluorescence excitation spectra of Rb in a 50 G magnetic field. At this field strength the electronic angular momentum J and nuclear angular momentum I are only partially decoupled. As a result of the mixing of wavefunctions of different hyperfine states, we observe a nonlinear Zeeman effect for each sublevel, a substantial modification of the transition probabilities between different magnetic sublevels, and the appearance of transitions that are strictly forbidden in the absence of the magnetic field. For the case of right- and left-handed circularly polarized laser excitation, the fluorescence spectra differ qualitatively. Well pronounced magnetic field induced circular dichroism is observed. These observations are explained with a standard approach that describes the partial decoupling of I and J states.

Thin films of amorphous chalcogenide semiconductor As₂S₃ and As–S–Se systems were studied to record refractive-index and surface-relief modulated gratings with a period of 0.15–1 µm. The period and profile of the surface-relief modulated gratings were measured by AFM. The polarization properties of refractive-index modulated gratings are shown.