Coherence of Planar Wavefronts - Spatial & Temporal

In summary, the conversation discusses the coherence of planar wavefronts, specifically whether they are both spatially and temporally coherent or only spatially coherent. It is noted that the function E(r) = E0exp(±ik·r) does not satisfy the wave equation and therefore, may not be considered a true wave equation. The question of the time dependence of planar wavefronts is also brought up, with the conclusion that while they are considered spatially coherent by definition, they do not necessarily need to be equidistant in space to be temporally coherent.
  • #1
Navid
2
0
Homework Statement
Planar wave coherence
Relevant Equations
Plane wave equation: E(r) = E0exp(±ik·r)
Hi, are planar wavefronts both spatially and temporally coherent? Or, they are only spatially coherent and need not be temopral?
 
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  • #2
Hello Navid, :welcome: !

E(r) = E0exp(±ik·r) is more a wave function than a wave equation (that would look like ##u_{xx}=u_{tt}##). As you can see, your function does not satisfy the wave equation.

You first have to say something about the time dependence...
 
  • #3
The main thing I want to get clear is a planar wavefront by definition should be spatially coherent. But, do they need to be equidistant in space as well, meaning do they, by definition, need to be temporally coherent?
 
  • #4
##\exp\bigl (ik(t)\cdot r\bigr)## is still planar but not necessarily temporally coherent. But now I've said something about the time dependence.
 

1. What is coherence in terms of planar wavefronts?

Coherence refers to the degree of similarity between two or more wavefronts. In the context of planar wavefronts, coherence describes the extent to which the waves maintain a constant phase relationship as they propagate through space and time.

2. How is coherence measured for planar wavefronts?

Coherence can be measured using various techniques, such as interferometry or spectral analysis. These methods involve comparing the phases and amplitudes of the wavefronts at different points in space or time, and calculating a coherence function or correlation coefficient.

3. What is the difference between spatial coherence and temporal coherence?

Spatial coherence refers to the similarity of two wavefronts at different points in space, while temporal coherence describes the similarity of two wavefronts at different points in time. In other words, spatial coherence is concerned with the spatial distribution of the wavefronts, while temporal coherence is concerned with the time evolution of the wavefronts.

4. Why is coherence important in applications involving planar wavefronts?

Coherence is important because it affects the interference and diffraction patterns of light waves. In applications such as imaging, holography, and optical communications, the coherence of the wavefronts determines the quality of the resulting image or signal.

5. How can coherence be controlled for planar wavefronts?

Coherence can be controlled by manipulating the sources of the wavefronts, such as using lasers or spatial filters. Additionally, techniques such as phase shifting or filtering can be used to improve the coherence of the wavefronts. However, achieving perfect coherence is difficult in practice due to various factors such as environmental disturbances and imperfections in the optical system.

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