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Spectrum

spectrum

Light source spectrum defines the relative quantity of light emitted per wavelength ( or per frequency ). It is illustrated by a curve giving the relative intensity ( ordinate ) emitted per wavelength or frequency ( axis ). Several definitions are used to quantify the spectral width. In most cases, spectral width is given by the full width at half maximum (FWHM) which is the distance on the axis between wavelengths ( or frequencies ) with relative intensity equal to half of maximum value.



Light sources

There are essentially two kinds of light sources ( laser non included ). Thermal light sources transform part of their thermal energy into light. They have a continuous spectrum and can generally be modelized with black body theory. Spectrum and emitted power depend on light source temperature. Emitted power grows with temperature as maximum of the spectrum curve shifts to short wavelengths. Examples include sunlight and tungsten light sources.

For luminescent light sources, a photon is emitted by an atom when collapsing from a "high energy" state ( excited state ) to a "low energy" state. Energy gap ( between low and high energy states ) defines the emitted light energy and consequently its wavelength. As atoms have discrete energy gaps, a luminescent light source produces a discontinuous spectrum made of emission lines. Naturally, atoms are mostly in "low energy" states. Light is emitted only if atoms have been excited first. Excitation can be electrical, optical, acoustical, mechanical,…, depending on the light source. Examples include Mercury-vapor lamps and sodium lamps. For luminescent light sources, FWHM on the global spectrum doesn't make sens but can be defined for each particular emission line. For emission line, spectrum width is also called linewidth.

Relation between spectrum and pulse duration

For luminescent light sources and also lasers ( and without considering any spectrum broadening effects ) there is a relation between the minimum linewidth possible and the natural lifetime of atoms in the excited state. It is given by the Heisenberg uncertainty principle. The larger the lifetime, the smaller the minimum linewidth. As well, knowing spectrum of an emission line allows to calculate the minimum duration possible of a light pulse. This applies mainly for short pulse lasers ( mode locked lasers ) approaching this limit.

Doppler effect

Doppler Fizeau effect

Applied to light, Doppler effect is the change in frequency ( fe and fr being the frequency respectively in the light source and observer referentials ) of a light wave for an observer moving relatively to the light source. This change depends on relative speed ( v ) between observer and light source but also on wave direction compared to relative speed direction. This effect is mainly observed for light source made with gaz. Because of thermal excitation, atoms have different relative speeds with the observer. Consequently, the observed spectrum is broadened. This spectrum broadening occurs on gaz luminescent sources but also on gaz lasers like HeNe lasers, ion lasers, etc…

References

"Optique Fondements et applications" - 2004 - author : José-Philippe Perez.

"Cours d'optique physique" - Institut d'optique théorique et appliquée - 1985 - author : Christian Imbert.

"Cours d'optique ondulatoire" - Université Denis Diderot Paris 7 - 2006 - author : G.Rebmann.

"Études graphiques des propriétés optiques des lames minces" - Journal de physique - 1950 - author : D. Malé.



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