We consider reflection and transmission of polarized paraxial light beams at a plane dielectric interface. The field transformations taking into account a finite beam width are described based on the plane-wave representation and geometric rotations. Using geometrical-optics coordinate frames accompanying the beams, we construct an effective Jones matrix characterizing spatial-dispersion properties of the interface. This results in a unified self-consistent description of the Goos–Hanchen and Imbert–Fedorov shifts (the latter being also known as the spin Hall effect of light). Our description reveals the intimate relation of the transverse Imbert–Fedorov shift to the geometric phases between constituent waves in the beam spectrum and to the angular momentum conservation for the whole beam. Both spatial and angular shifts are considered as well as their analogues for higher-order vortex beams carrying intrinsic orbital angular momentum. We also give a brief overview of various extensions and generalizations of the basic beam-shift phenomena and related effects.

https://iopscience.iop.org/article/10.1088/2040-8978/15/1/014001/pdf

Goos-Hanchen and Imbert-Fedorov beam shifts: an overview

A birefringent interference polarizer which may be fabricated from readily available materials using established coextrusion techniques is provided. The polarizer has a level of light absorption near zero and can be fabricated to polarize and reflect light of specific wavelengths while transmitting light of other wavelengths. The polarizer includes multiple alternating oriented layers of at least first and second polymeric materials having respective nonzero stress optical coefficients which are sufficiently different to produce a refractive index mismatch between the first and second polymeric materials in a first plane which is different from the refractive index mismatch between the first and second polymeric materials in a second plane normal to the first plane. The refractive index mismatch in the first plane is preferably at least 0.03.

Birefringent interference polarizer

The scanning acoustic microscope in the reflection mode has proved to be a rather simple and direct means for monitoring the elastic properties of a solid surface. When smooth surfaces of crystalline material are examined in a liquid with a highly convergent sound beam they exhibit a distinct response. This characteristic response, which can be treated as a ’’signature’’, is obtained by recording the output of the microscope as the spacing between the acoustic lens and the object is varied. An angular‐spectrum approach is used to derive an expression for this output in terms of the reflectance function. This function has an angular dependence determined by the bulk constants of the material itself. The expression resulting from this treatment can be used to explain the source of contrast in acoustic images.

/pdf/an-angular-spectrum-approach-to-contrast-in-reflection-48dto03c67.pdf

An angular‐spectrum approach to contrast in reflection acoustic microscopy

The seven participating laboratories received films of two different thicknesses of Sc2O3 and Rh. All samples of each material were prepared in a single deposition run. Brief descriptions are given of the various methods used for determination of the optical constants of these coating materials. The measurement data are presented, and the results are compared. The mean of the variances of the Sc2O3 refractive-index determinations in the 0.40–0.75-nm spectral region was 0.03. The corresponding variances for the refractive index and absorption coefficient of Rh were 0.35 and 0.26, respectively.

/pdf/multiple-determination-of-the-optical-constants-of-thin-film-4qzn2lhdic.pdf

Multiple determination of the optical constants of thin-film coating materials

We report the first observation of the Goos-Hanchen shift of a light beam incident on a bare metal surface. This phenomenon is particularly interesting because the Goos-Hanchen shift for p polarized light in metals is negative and much bigger than the positive shift for s polarized light. The experimental result for the measured shifts as a function of the angle of incidence is in excellent agreement with theoretical predictions. In an energy-flux interpretation, our measurement shows the existence of a backward energy flow at the bare metal surface when this is excited by a p polarized beam of light.

Observation of Goos-Hänchen shifts in metallic reflection

The reflection of a beam of light at a plane interface is treated using the angular spectrum representation. The Goos-Hanchen shift is found to be proportional to the first derivative of the phase of the reflectance. The second derivative of the phase gives rise to a shift of the reflected beam along its direction of propagation. This new shift, called a focal shift, is different from the extra propagation distance of the beam predicted on the basis of a ray model for total internal reflection. Expressions are presented for the Goos-Hanchen and focal shifts for both s and p polarization.

An angular spectrum representation approach to the Goos-Hänchen shift

A high reflectance mirror utilizing a dielectric stack having multiple layers of low and high refractive index material, at least one of which is absorbing at the design wavelength. At least one pair of layers is formed on a substructure with the thickness of the individual layers being both different from a quarterwave optical thickness and preselected to maximize the reflectance of the mirror. Mirrors in which both dielectric materials in the stack have different absorptances at the design wavelength are disclosed with the layer thickness of one or more optimum pairs formed on a substructure being different from a quarterwave optical thickness such that the layers of higher absorptance material are less than a quarterwave optical thickness and the layers of lower absorptance material are more than a quarterwave optical thickness. The individual thicknesses of the layers are optimized to provide maximum reflectance, leading to a non-periodic stack when a substantial number of such optimum pairs of layers are utilized.

Multilayer mirror with maximum reflectance

The reflectance of a homogeneous amplifying layer between two transparent regions is determined theoretically with the help of the Fresnel formulas. The transparent region containing the incident beam has a higher refractive index, corresponding to an internal reflection configuration. In the limit of infinite layer thickness, the reflectance is a continuous monotonic function of incident angle, greater than unity for all angles. For certain finite values of layer thickness, the reflectance has a singular point. The results explain the reported observation of a reflectance of 1000 from an excited laser dye in contact with a quartz prism.

Internal reflection from an amplifying layer

The recently predicted focal shift associated with total internal reflection is shown to follow from the ray model of the Goos-Hanchen shift if the variation of the Goos-Hanchen shift with angle is taken into account.

Focal shift and ray model for total internal reflection

The reflectance from an amplifying region in which the gain decreases exponentially with distance from the surface is calculated as a function of incident angle. The results are similar in some respects to the reflectance from a uniform amplifying layer reported previously. In particular, a singular point occurs in the reflectance for certain values of the thickness of the amplifying region. However, the results for the exponential case do not explain the previously reported observation of large reflectance from a pumped laser dye. An asymptotic form of the reflectance for a thick amplifying region is presented. The results for asymptotic case are compared with various other theories of reflection from an amplifying region.

Charles K. Carniglia

Papers

An angular spectrum representation approach to the Goos-Hänchen shift

Multilayer mirror with maximum reflectance

Internal reflection from an amplifying layer

Focal shift and ray model for total internal reflection

Internal reflection from an exponential amplifying region