Physical optics

As a wave optics or physical optics, is called in physics the portion of the optics, which treats light as electromagnetic wave. Using the wave optics properties such as color, interference ability, diffraction and polarization of light can be explained, can not be explained by geometrical optics.

History

In the 17th century it was recognized that the classical interpretation of light must be incomplete as a bundle of straight beams. Diffraction and interference can not be explained in this way. Christiaan Huygens noticed in 1650 that light propagation would explain analogous to water waves phenomena. He formulated his Huygens' principle, which states that any point on a diffractive surface assume spherical elementary waves that overlap and thus cause the observed diffraction effects. First, Huygens was not taken seriously, as it favored the corpuscular theory of Isaac Newton. Only in the 19th century, the wave theory (also called wave theory ) confirmed by the double -slit experiment of Thomas Young. The works of Joseph von Fraunhofer and Fresnel Augustin Jean built the theory further. Friedrich Magnus fword turned the wave theory to explain its comprehensive diffraction experiments.

Basics

When considering the interactions of light with matter different effects were observed, which can no longer be explained by geometrical optics. To form behind openings - as well as behind edges generally - when passing parallel light rays ( or sufficiently distant point light source) in the shadow region bright stripes with decreasing intensity. The light is diffracted. In case of multiple columns of gap distances in the order of the wavelength of the light used to enter superposition of the diffraction at the individual edges. The light is interfering. In the case of very short wavelengths or very large objects the diffraction of light is not annoying and it is expected with the laws of geometrical optics ( = geometrical optics ). In light of wave optics is described by a transverse wave with wavelength, amplitude and phase. Each wave is represented mathematically as the solution of a wave equation:

This is the Laplace operator, c is the speed of light and u the place and time t abhängende wave function. The wave function can be either scalar or vector. The vector description of the light is necessary when the polarization plays a part, otherwise the scalar description easier.

Transition to Geometrical Optics

The wave equation is equivalent to the Helmholtz equation, since both are related via the Fourier transformation in the time or frequency:

This is the Fourier transform of. Performs to the wave number a, we obtain the Helmholtz equation

A solution of this equation is derived from the approach

Under the approximation that the amplitude is slowly varying, ie can be considered to be constant over a distance in the order of the wavelength.

The surfaces determine the surfaces of equal phase ( = wave fronts ). For example, would a plane wave result. The gradient indicates the direction of propagation of the different points of the wave front. In the example, the gradient of the plane wave and the wave fronts propagate in the x direction. In the vicinity of a point, any, described by the above solution wave as a plane wave with wave number ( refractive index at this point) and propagation direction are considered. called eikonal and is an important function in geometrical optics, because it determines the local wave vectors of the wave ( direction of propagation times wave number ). The beam paths in geometrical optics are identical to the local wave vectors. Under the given approximation, by employing the approach to the Helmholtz equation, the eikonal equation are obtained:

This equation states that the refractive index determines the phase of the wave and forms the formal basis of geometrical optics:

• The approximation that the amplitude of the wave does not vary in the order of the wavelength corresponding to the usual statement that the geometrical optics is valid as long as the scattering properties are very much larger than the wavelength of light.
• The local refractive index determines the gradient of the phase, and thus the local propagation direction and wave number of the wave.

Paraxial rays

A large field of application of wave optics deals with lasers. Laser light is almost monochromatic one hand and on the other hand so tightly collimated, the light beam for long distances remains close to the axis ( = does not diverge ). Such waves are solutions of the Helmholtz equation under the paraxial approximation. This states that the amplitude may not greatly change in the propagation direction. Mathematically this means that the second derivative of the amplitude with respect to z can be neglected.

An important solution that results from this approximation, the Gaussian solution. The picture to the Gaussian distributed intensity distribution of light of a laser pointer is visible.

Color and intensity

The color of the light corresponds to the wavelength thereof. Monochromatic light has only one wavelength while white light is a superposition of many waves with different wavelengths. Actually, the frequency of the light wave crucial for the color; The wavelength depends on the propagation velocity and thus the medium in which the light propagates. In conventional statements about the color of light in relation to its wavelength, the dispersion in a vacuum is required. In air, the propagation velocity is slightly less than the vacuum speed of light, so that the wavelength of a certain frequency in air only slightly deviates from the in vacuo. The intensity of light is proportional to the square of the amplitude of this wave, averaged over time.

Coherence and interference

In addition to the amplitude can be seen, the phase of the wave. If several waves in a constant phase relationship, it is called coherence. Coherent waves have the characteristic that they can interfere with each other. Different waves are superimposed in such a way that it ( true wave crest to wave crest - constructive interference ) for amplification or attenuation ( wave crest meets trough - destructive interference ) occurs.

Polarization

Although a transverse wave oscillates always perpendicular to the direction of light propagation, but still has two degrees of freedom. Find the vibration only in one plane instead or does it change regularly, so it is called polarized light. The polarization can be explained only by the vectorial representation as an electromagnetic wave.

Wavefronts

Instead of light rays we consider the generalized concept of the wavefront in the wave optics. A wave front is a surface that combines the different points of the same phase the waves. Light rays are always perpendicular to the wavefront.

Limits of wave optics

There are phenomena that can not be explained by the wave theory. These include the Wilhelm Hall wax in 1887 and discovered by Albert Einstein in 1905 declared outer photoelectric effect (Nobel Prize 1921). Einstein explained the interaction between light and matter with the light quantum hypothesis. We then spoke of wave -particle duality. The apparent contradiction that light both as waves and as particles behave is dissolved by the modern quantum physics.