Definition: a range of phenomena associated with the superposition of waves
Categories: general optics, physical foundations
Author: Dr. Rüdiger Paschotta
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Interference in optics is an effect which can occur when two or more light beams are superimposed. More precisely, for interference to occur, several conditions have to be met:
- spatial and temporal overlap of the two light fields
- phase coherence of the two light fields
- non-orthogonal polarization states
If those conditions are all fulfilled, the resulting total light field does not have an optical intensity which equals the sum of the intensities of the superimposed beams. Instead, its complex amplitude is the sum of the amplitudes of the superimposed beams.
For example, the amplitudes of two equally intense light beams may have opposite signs at some location, so that they can cancel each other (destructive interference). On the other hand, with equal signs (equal phases) of both contributions (constructive interference), the total intensity can be four times (rather than only two times) that of the single beams.
Nevertheless, the total energy is conserved in any case. For example, if two light beams of equal intensity, frequency and polarization are superimposed on a screen with some angle between the beams, an interference pattern occurs which consists of bright and dark stripes (see Figure 1). It is called a standing wave pattern, since the minima and maxima of the total optical intensity can stay at their positions, although the optical waves are moving with high velocity.
Figure 2 illustrates the superposition of two circular waves with the same frequency but different source points. It shows a snapshot, i.e. the field distribution at one particular moment in time. As time progresses, the spatial patterns move away from the point sources.
By averaging the optical intensity corresponding to this pattern over one oscillating period, the interference pattern in Figure 3 is obtained. So this is also a standing-wave pattern.
Interference effects also occur in multimode fibers. Figure 4 shows the simulated output intensity profiles of a multimode fiber when a monochromatic input beam is scanned across its input face.
A Gaussian input beam is scanned through the horizontal line (slightly above the center of the fiber core). This model has been made with the RP Fiber Power software and is described in more detail on a separate page.
Interference effects are often (and most easily) observed for monochromatic light, but monochromaticity is not strictly a precondition. An interferometer with a close to zero arm length difference can show interference even for broadband light. An example for that is the famous Michselson–Morley experiment, which was carried out with broadband light.
Wave optics are generally needed to describe interference effects; geometrical optics or a simple picture of photons as particles of light are not suitable for that.
Importance of Interference Effects
The phenomenon of interference is of great importance in optics in general, and also in laser physics. Some examples:
- Interference governs the operation of interferometers, which are used in many variations for a wide range of applications, and is the basis of holography.
- Interference is essentially involved in the effect of spatial hole burning, e.g. in laser gain media.
- Interference is the basis of detecting beat notes in optical metrology.
See also: interferometers, optics, optical phase, coherence, holography, beat note, spotlight 2007-09-27, spotlight 2009-05-22
Questions and Comments from Users
Let us suppose that I have a broadband thermal light source which I pass through a hypothetical narrowband filter with a line width of a kilohertz. Further suppose that I have a truly single frequency laser. Can I produce an interference pattern if the two light sources have have frequencies close to each other?
The author's answer:
Yes, you can, although practically it would be difficult because you would get only very little thermal light through such a narrowband filter. Also, the interference pattern could be observed only with a fast camera, since it would fluctuate on a timescale of a millisecond.
Would spatial coherence be enough to satisfy the criterion for interference between two sources of light? Or would you need both spatial and temporal coherence?
The author's answer:
Basically, you only need a sufficiently high temporal coherence to observe coherence effects. However, if you want to have strong interference effects over the whole beam cross-section, you need high spatial coherence as well.
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What the difference between coherence and interference?
Does interference occur between two waves of different frequency?
The author's answer:
Coherence is a property of light, interference a phenomenon. Coherence is a prerequisite for observing interference.
If two light waves have quite similar frequencies, one may observe interference. Frequently, the optical frequency differences are so high that the correspondingly high beat frequencies prohibit the observation of interference.