interference (original) (raw)

Definition: a range of phenomena associated with the superposition of waves

Categories: general optics, physical foundations

• optical effects
  • absorption
  • birefringence
  • diffraction
  • dispersion
  • dispersive waves
  • evanescent waves
  • Faraday effect
  • focusing
  • imaging
  • interference
  • optical aberrations
  • optical phase shifts
  • phase matching
  • photodarkening
  • polarization changes
  • propagation losses
  • reflection
  • refraction
  • scattering
  • spatial walk-off
  • superluminal transmission
  • temporal walk-off
  • thermal blooming
  • thermal radiation
  • total internal reflection
  • wavefront distortions
  • nonlinear optical effects
  • electro-optic effect
  • (more topics)

Related: interferometersopticsoptical phasecoherenceholographybeat noteLight Plus Light = Darkness: No Energy Problem, but Quantum WeirdnessInterference Effects with Imbalanced Intensity Levels

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Contents

What is Interference?

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

Figure 1: Standing wave interference pattern (showing the optical intensity) from the superposition of two elliptical Gaussian beams under some angle.

If those conditions are all fulfilled, the resulting total light field does not have an optical intensity which simply equals the sum of the intensities of the superimposed beams. Instead, its complex amplitude is the sum of the amplitudes of the superimposed beams, and that kind of superposition can lead to strong intensity modulations. 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.

Interference between Plane Waves

A particularly simple case is interference between monochromatic plane waves of equal optical frequency, which leads to a simple standing (not moving) interference pattern. Its spatial period and orientation is determined by the difference in ($\vec{k}$) vectors. The larger the difference in propagation direction is, the larger is the magnitude of the difference in ($\vec{k}$) vectors, and the faster is the spatial variation. Consider the extreme cases:

• For counterpropagating waves, the standing-wave pattern has a period which is half the optical wavelength.
• For nearly copropagating waves, the period can be far longer (many wavelengths), and the intensity variation is in a direction which is approximately perpendicular to the propagation direction.

Other Example Cases

Figure 2: Snapshot of the superposition of two circular waves.

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.

Figure 3: Time-averaged intensity 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.

Figure 4: Intensity profiles at the end of a multimode fiber, shown as animated graphics.

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 an arm length difference close to zero can show interference even for broadband polychromatic light. A historic example is the Michelson–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.

Moving Interference Patterns

When light components with equal optical frequency are superimposed, a standing-wave pattern can result. If the optical frequencies differ, this can result in a moving interference pattern.

For example, consider two plane waves with very narrow linewidth and optical frequencies differing by the small amount of 1 kHz. The relative optical phase of the two waves at any location continuously changes by ($2\pi$) per millisecond. This leads to an interference pattern which is moving by one spatial period per millisecond. The magnitude of the spatial period is determined by the difference in ($\vec{k}$) vectors. If the two plane waves are propagating in the same direction, there is only a very small difference in ($\vec{k}$) vectors, leading to a long period of the interference pattern. The velocity of its movement is essentially the group velocity of that light. For counterpropagating waves, the difference in ($\vec{k}$) vectors would be far larger, leading to a very rapid spatial oscillations and a far lower velocity of movement of the interference pattern.

Interference Effects on the Photon Level

Interference effects are also observed in quantum optics, and can lead to remarkable observations. Some examples:

• Single photons, as obtained from very faint light sources or from single-photon sources, exhibit interference effects just like classical light regarding the probabilities — although detection forces a photon to appear e.g. at one of two output ports of an interferometer. This has been extensively studied e.g. for the classical double-slit experiment: Each photon probes the paths through both slits, and one cannot tell which route it took; any attempt to obtain which-path information would involve an interaction which destroys the normal interference properties.
• The very remarkable Hong–Ou–Mandel effect (HOM effect) occurs when two indistinguishable photons simultaneously enter a 50:50 beam splitter from different input ports: In the ideal case, they always exit the same output port, i.e., it is impossible for one photon to exit one port while the other photon exits the other port. That quantum interference process cannot be explained by classical wave theory. A core element is indistinguishability of the photons: There are two amplitude contributions for one photon going each way, which cancel out (destructive interference). Incomplete cancellation occurs when the photons differ in arrival time, optical spectrum or other properties. In fact, the interference contrast can be used as a measure of the degree of indistinguishability, e.g. for subsequently emitted photons from single-photon sources.

Importance of Interference Effects

The phenomenon of interference is of great importance in optics in general, and also in laser physics and quantum photonics. 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. It is also widely used in quantum information processing.
• 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.
• Moving interference patterns occur in some cases, e.g. in stimulated Brillouin scattering, where narrowband light is reflected at a moving high-frequency sound wave generating a refractive index pattern, and the superimposed light waves can in turn maintain that sound wave.

Frequently Asked Questions

What is optical interference?

Interference is an effect where the superposition of two or more light beams results in a total optical intensity that is not simply the sum of the individual intensities, but instead shows a pattern of high and low intensity.

What conditions are necessary for interference to occur?

For interference to occur, the light beams must have spatial and temporal overlap, they must be phase-coherent, and their polarization states must not be orthogonal to each other.

What is the difference between constructive and destructive interference?

Constructive interference occurs when light waves are in phase, combining to produce a higher total intensity. Destructive interference happens when they are out of phase, which can lead to them canceling each other out.

What is a standing wave pattern?

A standing wave pattern is a stationary interference pattern with fixed locations of minimum and maximum intensity. It can be formed by superimposing light waves that have the same optical frequency.

What happens when light beams with different frequencies interfere?

When light beams with different optical frequencies are superimposed, they create a moving interference pattern. The pattern's velocity depends on the frequency difference and the angle between the beams.

Can interference occur with single photons?

Yes, single photons also exhibit interference. In a double-slit experiment, for example, each photon behaves as if it passes through both slits, and the probability of its detection on a screen forms an interference pattern.

Is interference possible with broadband light?

Yes, interference can be observed with broadband polychromatic light. For instance, an interferometer with a path length difference between its arms that is close to zero can show interference effects even with a broadband source.

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