DeepLightSeekdefinition:
The phase relationship of the electric field at different positions or times is determined.
Coherence is a very important concept in optics, directly related to the interference effect of light fields. When the phase difference of the electric field at different positions or times is determined, the optical field is called coherent.
Partial coherence indicates that there is a certain coherence in the phase difference. There are different methods to quantitatively represent coherence, which will be described below.
It is also commonly referred to as a process or technology that is coherent or incoherent. At this point, coherence refers to being phase dependent. For example, coherent beam synthesis refers to the mutual coherence between beams, while spatial beam synthesis is incoherent.
Figure 1: Inserting a prism into a spatially coherent laser beam produces an interference pattern on the screen.
catalogue
- Comparison of spatial coherence and temporal coherence
- Quantify coherence
- The importance of coherence in applications
- Coherence in Quantum Optics
Comparison of spatial coherence and temporal coherence
There are two different types of coherence:
- Spatial coherence represents the strong correlation (fixed phase relationship) of electric fields at different positions.
- For example, the electric field at different positions within the cross-section of the beam generated by lasers with different diffraction limit beam qualities oscillates completely coherently, although its time structure is complex and composed of components of different frequencies stacked together. Spatial coherence is a fundamental prerequisite for the strong directionality of laser beams.
- Time coherence refers to the strong correlation between electric fields at the same location but different times. For example, the output light of a single frequency laser has high temporal coherence because the time evolution of the electric field is determined and oscillates sinusoidally over a long period of time.
Figure 2-4 shows the difference in spatial and temporal coherence. Figure 2 shows a monochromatic Gaussian beam as a reference, which has both high spatial and temporal coherence.
Figure 2: Electric field distribution of Gaussian beam with high spatial and temporal coherence simultaneously.
The beam in Figure 3 has high spatial coherence, but poor temporal coherence. The wavefront is shown in the figure, and the beam quality is still relatively high, but the amplitude and phase of the beam change in the propagation direction. The local amplitude and wavefront spacing both vary. This beam can be generated by a supercontinuum light source.
Figure 3: A laser beam with good spatial coherence but poor temporal coherence.
The spatial coherence of the laser beam in Figure 4 is poor, but the temporal coherence is high. The wavefront has undergone deformation, resulting in a large beam divergence angle and poor beam quality.
However, the beam is monochromatic, so the distance between the deformed wavefronts is constant. This beam can be generated by a single frequency laser, and when the output light propagates in a non isotropic medium, the situation shown in the figure will be obtained.
Figure 4: A laser beam with poor spatial coherence and good temporal coherence.
Quantify coherence
There are several different methods to quantify coherence: - using coherence equations to represent coherence as a function of spatial or temporal distance. There are coherence functions of different orders. First order coherence is related to spectroscopy. The second-order coherence equation represents the intensity coherence, which is the photon focusing or anti focusing effect.
Higher order equations describe more details. Coherent time quantitatively describes first-order temporal coherence, which refers to the time required for coherence to disappear. The coherence length is the product of coherence time and the speed of vacuum light, and is therefore used to describe the temporal coherence characteristics, that is, the length of propagation before coherence disappears.
The linewidth of a single frequency laser is also related to temporal coherence, with narrow linewidth (high monochromaticity) corresponding to high temporal coherence. The visibility of stripes mainly characterizes the visibility of interference patterns formed by the superposition of electric fields.
The relationship between optical bandwidth and temporal coherence is quite important. For example, the pulse train generated by a mode-locked laser has a wide bandwidth, and its Fourier spectrum contains narrow discrete lines (see frequency comb).
Its temporal coherence is high because it still has strong coherence in the background for time delays that are integer multiples of long pulse periods. (Refer to the coherence of supercontinuum light and the coherence of ultrashort pulses.)
The importance of coherence in applications
Some applications require light to have high temporal and spatial coherence simultaneously. For example, in various interferometers, holography, and some optical sensors (such as fiber optic sensors). It is also very important in coherent beam synthesis technology.
Some applications require as little coherence of light as possible. For example, in coherence tomography, very low temporal coherence (while high spatial coherence) light is required, such as generated by interferometers, to achieve high spatial resolution, low temporal coherence is needed.
Some of these types of light sources, such as amplified spontaneous emission generated by laser amplifiers or supercontinuum generated in nonlinear media. Low temporal coherence light is also required in applications such as laser projection displays, imaging, and laser pens, as it reduces speckle and other similar interference effects.
Coherence in Quantum Optics
In quantum optics, coherence is commonly used to describe the atomic or ionic states of light radiation. At this point, coherence represents the phase relationship of the complex amplitude of the electronic state. This is very important in non inverted lasers. There is also the concept of coherent states in the optical field, which has other meanings.
