DeepLightSeekdefinition:
An optical element that contains periodic structures that cause diffraction of light beams.
A diffraction grating is an optical device that diffracts light. It contains a periodic structure that causes spatial amplitude or phase changes. A common type is a reflective grating, where the reflective surface has a periodic structure and the phase change produced is position dependent. There is still a transmission grating, and the phase change of the transmission grating is related to its position, also due to the periodic structure of the surface.
Figure 1: The white light emitted by a high-power supercontinuum light source is dispersed in space after diffraction to display its spectral content. By using a smoke machine, the path of the light beam can be seen.
catalogue
- Detail description of diffraction grating
- Littrow structure
- Spectral resolution and beam radius
- Distribution of output power in various levels of diffracted beams
- Preparation method of grating
- Application of Diffraction Grating
Detail description of diffraction grating
Sometimes it is necessary to consider the spatial frequency of phase changes related to position caused by gratings. For the simplest sine phase change, there are only two spatial frequency components of ± 2 π/d, where d is the period of the grating structure.
The wave vector component of light with an incident angle θ in the grating plane is k • sin θ, where k=2 π/λ, where λ is the wavelength of the light. Normal reflection will result in a wave vector component of - k • sin θ for the reflected light.
Due to the phase modulation of the grating, the reflected light also contains another plane wave vector component of - k • sin θ ± 2 π/d. It corresponds to a diffraction order of ± 1. Therefore, the angle between the emitted light and the normal can be obtained to satisfy:
Figure 2: Diffraction beams at all levels of the grating.
If the phase change of the grating is not sinusoidal, there is multi-level diffraction, and the exit angle can be calculated by the following more general formula:
Different symbol rules can be used for diffraction orders, so some terms may have negative signs in front of them.
From the above equation, it may be concluded that the sin θ out value is greater than 1, and the corresponding diffraction order does not exist. Figure 2 shows an example where only diffraction orders -1~+3 exist.
Figure 3: The relationship between the output angle and wavelength of the reflected beam. The incident beam has a fixed incident angle of 25 °.
The grating period in Figure 3 is 800 per millimeter, and the curve describes the variation of the emission angle with wavelength. For zero order diffraction (pure reflection, m=0), the angle is constant, while the angles of other orders vary with wavelength. For example, second-order diffraction with m=2 only occurs when the wavelength is less than 560 nm.
Figure 4 shows the relationship between the number of diffraction orders and the ratio of wavelength to diffraction grating period, as well as the relationship with the incident angle. The shorter the wavelength, the larger the grating period, and the corresponding number of diffraction orders.
Figure 4: The relationship between the color encoding number and wavelength of a non-zero order diffraction grating divided by the grating period.
Littrow structure
In the reflective grating of Littrow structure, the diffraction grating (usually a first-order beam) returns along the direction of the incident beam. Therefore, the following conditions are met:
This structure is commonly used, for example, as an end reflector for laser resonators. A given grating direction can determine a certain wavelength within the gain bandwidth of the laser medium, at which the resonant cavity beam path is closed, that is, laser generation can be achieved. This technology can be used in wavelength tunable lasers, such as external cavity diode lasers.
Spectral resolution and beam radius
In a grating spectrometer, the property that the direction of the beam obtained from the diffraction grating is wavelength dependent is utilized. At this point, the wavelength resolution is not only related to the angular dispersion (measured in micro radians per nanometer), but also depends on the beam divergence angle: the smaller the divergence angle, the more accurate the angle change can be obtained.
Therefore, high wavelength resolution requires a large illumination spot on the grating. The relative wavelength resolution Δ λ/λ is on the order of 1/(mN), where m is the diffraction order and N is the number of grating grooves illuminated.
Distribution of output power in various levels of diffracted beams
It is very important to understand the distribution of output power in the diffracted beams at all levels. In other words, it is necessary to determine the diffraction efficiency of a certain level of beam. This depends on the shape of the phase change related to wavelength. Usually, different diffraction theories can be used to calculate diffraction efficiency.
It is possible to optimize the diffraction grating so that almost all optical power is distributed on a certain order of diffraction beam, resulting in high diffraction efficiency at that order.
This is called a blazed grating (small step grating), and the phase change can be represented by a sawtooth wave function. Under the given incident angle and wavelength conditions, it is necessary to adjust the slope of the grating surface to optimize the grating. In the Littrow structure described above, the linear part of the structure is parallel to the wavefront of the incident light.
Preparation method of grating
The following methods can be used to prepare gratings:
- The traditional method is to use a cutting machine to carve the required surface concave convex structure (groove structure) on the metal surface. Although it is difficult to achieve very small intervals with engraved gratings, they can serve as robust metal glitter gratings with high barrier lake efficiency. The significant disadvantage of their use in grating spectrometers is the generation of some stray light due to surface irregularities.
- Holographic surface gratings are prepared using photolithography technology, which can achieve finer grating structures. Simple holographic gratings have a sinusoidal phase change, resulting in lower diffraction efficiency. However, due to their very regular surface, they do not produce stray light.
- They can be prepared from many hard materials, such as silicon dioxide and semiconductor materials, and advanced preparation techniques can achieve precisely controlled structures, such as blazed gratings.
- Volume holographic grating is a periodic refractive index structure in transparent media. They have high diffraction efficiency and produce very little stray light, but are very sensitive to temperature and humidity changes. Wrap it with a suitable coating on the surface to reduce the impact of humidity.
Diffraction gratings can also be prepared on prisms, and the structure combining prisms and gratings is called a grating. Suitable parameters can be selected, such as light with a specific wavelength, to ensure its unbiased transmission through the grating.
In addition, grating structures can be prepared on the surface of the dielectric mirror to obtain reflective gratings with high reflectivity.
Application of Diffraction Grating
Diffraction gratings have many applications. Here are some main examples:
- Used as a grating spectrometer, it utilizes the property of diffraction angle and wavelength dependence. Figure 5 shows a typical device diagram. The obtained spectrum contains multi-level diffraction, especially when the recorded wavelength range is large.
Figure 5: Design diagram of Czerny Turner monochromator.
- A pair of diffraction gratings can also be used as dispersion elements, where the angular variation of the output is wavelength independent. The schematic diagram in Figure 6 contains four gratings, and all wavelength components finally converge together.
- By using a pair of gratings and reflecting light back from a plane mirror, the same result as above can be obtained. (Note that the mirror may need to be slightly tilted at this time, so that the reflected light will be offset relative to the vertical direction and can be separated from the incident light.) This grating device can be used as a dispersion pulse extender or compressor, which will be used in chirped pulse amplifiers. Compared to prisms, they can generate greater dispersion.
Figure 6: Device diagram of four gratings, that is, two grating pairs. Grating 1 separates the incident light beams based on their wavelengths (the path of two beams with different wavelengths is shown in the figure), and after passing through Grating 2, the two beams become parallel. Grating 3 and 4 recombine the light beams together. The total path length is wavelength dependent, therefore this grating device generates significant dispersion.
- As mentioned above, diffraction gratings (Littrow structure) can be used for wavelength tuning of lasers.
- In spectral beamforming, diffraction gratings can be used to combine light of slightly different wavelengths emitted by different emitters into one beam.
