Gaussian beams
2024-1-28
Definition:
The electric field of a beam on a plane perpendicular to the optical axis can be expressed by the Gaussian equation, sometimes with an additional parabolic phase curve.
Gaussian beams and resonator modes
If the resonator is stable, the optical medium in the resonator is isotropic, and the medium surface is either flat or parabolic, then the lowest-order mode (TEM00 or transverse fundamental mode) in the transverse direction of the optical resonator is the Gaussian mode. . Therefore, a laser that radiates only the transverse fundamental mode radiates a beam that is close to a Gaussian shape. Any deviation from the previously described conditions, such as the presence of thermal lensing in the gain medium, will make the beam non-Gaussian and will also excite multiple longitudinal modes. Higher order longitudinal modes can be described by the Hermite-Gauss equation or the Laguerre-Gauss equation. In any case, the deviation from the Gaussian spectral pattern can be quantitatively expressed by the M2 factor. Gaussian beam has the highest beam quality, the corresponding beam parameter product is the smallest, and the corresponding M2 = 1.
The fundamental mode of optical fiber is not strictly Gaussian, but the shape is not very different from Gaussian. Therefore, with appropriate optics, a Gaussian beam can be efficiently entered into a single-mode fiber (80% or greater).
Importance of Gaussian Beam
The importance of Gaussian beam is reflected in the following important characteristics:
The intensity cross-sectional curve of a Gaussian beam at any position along the optical axis is Gaussian, but the beam radius changes.
After passing some simple optical elements (e.g., aberration-free lenses).
When there is no beam distortion in the cavity, the Gaussian beam is the lowest order mode (resonator mode) of the optical resonator. Therefore the output of many lasers is a Gaussian beam.
The mode shape in single-mode fiber is close to Gaussian. Often a Gaussian approximation is used in calculations because it is relatively simple to calculate beam propagation.
Higher order modes correspond to the Hermitian-Gaussian type. The field distribution is more complex and the beam parameter product is larger.
Gaussian mode analysis can be extended to beams with poor beam quality, requiring the M2 factor.
The electric field of a beam on a plane perpendicular to the optical axis can be expressed by the Gaussian equation, sometimes with an additional parabolic phase curve.
Gaussian beams and resonator modes
If the resonator is stable, the optical medium in the resonator is isotropic, and the medium surface is either flat or parabolic, then the lowest-order mode (TEM00 or transverse fundamental mode) in the transverse direction of the optical resonator is the Gaussian mode. . Therefore, a laser that radiates only the transverse fundamental mode radiates a beam that is close to a Gaussian shape. Any deviation from the previously described conditions, such as the presence of thermal lensing in the gain medium, will make the beam non-Gaussian and will also excite multiple longitudinal modes. Higher order longitudinal modes can be described by the Hermite-Gauss equation or the Laguerre-Gauss equation. In any case, the deviation from the Gaussian spectral pattern can be quantitatively expressed by the M2 factor. Gaussian beam has the highest beam quality, the corresponding beam parameter product is the smallest, and the corresponding M2 = 1.
The fundamental mode of optical fiber is not strictly Gaussian, but the shape is not very different from Gaussian. Therefore, with appropriate optics, a Gaussian beam can be efficiently entered into a single-mode fiber (80% or greater).
Importance of Gaussian Beam
The importance of Gaussian beam is reflected in the following important characteristics:
The intensity cross-sectional curve of a Gaussian beam at any position along the optical axis is Gaussian, but the beam radius changes.
After passing some simple optical elements (e.g., aberration-free lenses).
When there is no beam distortion in the cavity, the Gaussian beam is the lowest order mode (resonator mode) of the optical resonator. Therefore the output of many lasers is a Gaussian beam.
The mode shape in single-mode fiber is close to Gaussian. Often a Gaussian approximation is used in calculations because it is relatively simple to calculate beam propagation.
Higher order modes correspond to the Hermitian-Gaussian type. The field distribution is more complex and the beam parameter product is larger.
Gaussian mode analysis can be extended to beams with poor beam quality, requiring the M2 factor.
