Total internal reflection

The total reflection is a phenomenon that is known primarily associated with electromagnetic waves ( such as visible light). They take place at the interface between two non-absorbing media of different sizes instead of propagation speed when the angle of incidence a certain value, the so-called critical angle for total reflection exceeds. A wave then no longer occurs predominantly in the second medium one, but is almost completely reflected or " thrown back " to the output medium. Below this critical angle is the reflectance at an interface is not zero, there is always a non-negligible part of the radiation is reflected at an interface.

The idea of ​​a total, ie complete reflection of a wave is an idealization, because even the fully reflected radiation is always lost in the practice part by absorption. For example, for visible light, the absorbed fraction can be neglected in highly transparent materials such as water and glass, however. Nevertheless, there may be the structure of the interface, even with highly transparent materials to reflection losses. One speaks in this case of frustrated total internal reflection.

The total reflection can be good visible light observed if this is true (see figure) in a transparent medium such as water or glass on the interface to air. In steep angle of incidence, the light enters from broken. Only a small part is reflected ( the case of glass about 4-5 %). The angle of incidence exceeds the critical angle, the reflectance rises suddenly to almost 100 %, which is higher than most mirrored surfaces.

• 3.1 Ultraviolet, visible and infrared radiation
• 3.2 X-ray radiation

Physical explanation

A beam of light (refractive index) comes from an optically denser medium and the interface to an optically thinner medium (refractive index) falls is broken off according to the Snell's law of refraction from the perpendicular of incidence - the angle of refraction is greater than the angle of incidence of the light. This case corresponds to the green beam path in the adjacent figure.

Is the angle of incidence increases, the refracted ray is parallel to the boundary surface (yellow optical path ) at a predetermined value. This angle is called the critical angle of total reflection, or a critical angle. The angle of total reflection can be calculated by means of the Snell's law of refraction:

For angles of incidence greater than the angle of refraction would, according to the Snell's law of refraction greater than 90 °. This is in contradiction to the assumption that the refracted ray passes into the optically thinner material. The electromagnetic wave (e.g., light) can not penetrate into the optically thinner medium and is totally reflected at the interface in place of the diffracted beam (only for completely transparent materials, that is, the extinction coefficient is equal to zero in the corresponding wavelength range ). The angle of reflection ( angle of reflection ) is as in the "normal " external reflection equals the angle of incidence (red beam path ). One therefore speaks of a total reflection.

Evanescent wave

The mechanism of total internal reflection are somewhat different than for example the reflection from metallic surfaces. From Maxwell's equations it follows that the electromagnetic wave at the interface of a sudden can not change their direction of propagation. Is formed of a standing wave on the surface, which also penetrates into the below optically thinner material. The field strength of this wave in the following material, decreasing in an exponential rate. The penetration depth (see also equation London ) designates the depth at which the amplitude of the decaying ( evanescent ) shaft only about 37% (more precisely, 1 / ) having the output amplitude.

Description of the evanescent wave:

Penetration depth:

Another special feature of the total reflection is observed in experiments rays offset the so-called Goos- Hänchen shift, that is the starting point of the reflected wave is not the point of incidence of the wave.

Attenuated total reflection and prevented

The physical description of the total reflection makes some simplifying assumptions. Thus, the reflection is viewed on two infinitely extended dielectric half-spaces ( transparent materials ), which of course does not correspond to the real processes. The approximations made ​​, however, are sufficiently accurate for most cases.

Some effects are not explained by these simplifications. For example, infrared light is totally reflected at the boundary surfaces of one ( infrared-transparent ) prism and the air, containing the spectrum of the totally reflected infrared radiation absorption lines of carbon dioxide and water vapor. The reason for this is the evanescent wave interacts with the optically thinner medium, that is, certain radiation components are absorbed by the optically thinner medium. This frequency-and material-dependent absorption components ( absorption centers of the second, optically thinner material ) are visible in the reflected beam. We therefore speak in this case of the attenuated total reflection (English attenuated total reflection, ATR). This effect is utilized, inter alia, in the ATR infrared spectroscopy.

Another effect occurs when behind the optically thinner material, an optically denser material (refractive index comparable to that of the first material ) is placed. As a function of distance from the interface at which total reflection takes place, parts of the evanescent wave in the third material may be transmitted. This leads in turn to an intensity attenuation of actually totally reflected wave, which is why one of the prevented or frustrated total reflection (English Frustrated total internal reflection, FTIR, not to be confused with Fourier transform infrared spectrometers and spectroscopy ) or by optical tunnel effect speaks. The effect is measured only when the distance between the first and third material corresponds only to a fraction of the wavelength of the incident wave.

Occurrence in nature

The sparkle of polished diamonds is essentially attributable to the total reflection. Despite the high refractive index of diamond light rays come into the gem into it, but only after a more or less large number of total reflections back from the stone out.

Technical Applications

Ultraviolet, visible, and infrared radiation

In the visible light region the refractive index of most materials is greater than a vacuum ( or air). This is in deviating prisms (and rarely in glass fibers) exploited. Here the total reflection at the transition from the optically denser medium ( prism, fiber core ) occurs for optically thinner ambient (air ), in the glass fiber, the thinner is " environment" A., a different type of glass. Light can be directed in such a manner with virtually no loss in a desired direction. Glass fiber cable can be as up to 20,000 meters carry information in the form of light without the need for amplification is necessary.

Another field of application is the use of total reflection on birefringence based polarizers. The property is exploited that birefringent materials polarization-dependent refractive indices, so that at a certain angle of incidence range transmits a polarization for the most part and the other is totally reflected. This behavior can also be used for polarization-dependent beam splitter.

Some other form of beam splitter can be realized by use of frustrated total reflection. Here, two prisms are placed in very short distance (in the range of a wavelength of the light ) from each other, while a part of the wave is reflected and another is transmitted into the second prism. About the distance can also adjust the ratio between the two components. Applies this principle, for example, in holography or as an optical switch at the transmission via fiber optic cables.

Also in the measurement technique, the effects mentioned numerous applications. Thus, the attenuated total reflection has been used since the late 1960s in the field of infrared spectroscopy ( ATR -IR spectroscopy in more detail ). Due to the low penetration depth can be as well thin and highly absorbent materials, such as aqueous solutions, study. Harmful interference, such as are observed in the transmission measurement of thin films, it does not occur. A similar advantage is obtained in the fluorescence microscopy, and specifically in the TIRF. There causes the small penetration depth, that is excited to fluoresce considerably less material, which results in a higher contrast. Furthermore, the most sensitive organic material is less rapidly destroyed.

The total reflection allows the construction of optical concentrators for concentrator cells designed to reduce the cost of photovoltaic systems. By total internal reflection, this is achieved with less effort than for example with Fresnel lenses. In prototypes so the irradiance is increased by factors of 1000 and above.

X-rays

The index of refraction of all materials in X-ray radiation is slightly less than 1 ( vacuum ), this in contrast to the visible region, where it is almost always significantly higher than 1. Since the values ​​usually differ only after the seventh decimal place (ie 0.999999 (x)) is often given in this area instead. Typical values ​​are in the range between 10-9 and 10-5, and are dependent on the quantum energy of the radiation, the atomic number and density of the material.

This makes it possible, in grazing incidence ( θ against 90 °) a total external reflection at the transition from vacuum to matter ( ie "optical" denser to " visually " dense medium ) to reach. Exploited the total reflection of X-rays in X-ray optics; For example, capillary optics based on this principle.

The refractive index of an absorption of the material can also be represented. In this case, the index of refraction is a complex number, the imaginary part represents the extinction coefficient. Thus, the representation of possibilities (that is ). Most materials are virtually transparent to X-rays, so that the extinction coefficient is generally smaller than 10-6 ( here, there are also differences between the materials by several orders of magnitude to 10-14). ( The purpose of the complex representation is that the amplitude of a wave can be used as formulated ).