Gouy phase shift
2024-4-14
Definition:
Additional phase shift produced during propagation of a focused Gaussian beam. (Often incorrectly written as "Guoy Phase Shift")
Gaussian beams produce an additional phase shift in the direction of propagation, which is different from the phase shift produced by plane waves of the same frequency. This different phase shift is called the Guyi phase shift:
where zR is the Rayleigh length, which corresponds to the position of the waistband. It causes the distance between wave fronts to be slightly larger than the distance between wave fronts for plane waves of the same frequency. This indicates that the phase wavefront propagates faster and therefore the local phase velocity is larger.
The total Goui phase shift produced by a Gaussian beam passing through the focus (from the far field at one end to the far field at the other end of the focus) is π.
Figure 1: When a beam with a wavelength of 1064nm and a beam waist radius of 100μm propagates in the air, the beam radius and Goui phase shift change in the propagation direction. The sign of the position is relative to the Rayleigh length.
It is normal for a Gaussian beam to have a different phase shift than a plane wave. A Gaussian beam can be viewed as a superposition of plane waves propagating in different directions. The phase shift of plane wave components that do not propagate in the direction of the optical axis is smaller than the phase shift of plane waves in the direction of the optical axis, and the overall phase shift comes from all the superimposed plane wave components.
The Guyi phase shift is larger for higher order transverse modes. For example, for the TEMnm mode, the enhancement factor is 1 + n + m. Therefore higher order modes in the optical resonator have higher resonant frequencies. The Goui phase shift will affect the beam quality of the laser resonator because it will relieve the frequency degeneracy of the resonator mode.
Additional phase shift produced during propagation of a focused Gaussian beam. (Often incorrectly written as "Guoy Phase Shift")
Gaussian beams produce an additional phase shift in the direction of propagation, which is different from the phase shift produced by plane waves of the same frequency. This different phase shift is called the Guyi phase shift:
where zR is the Rayleigh length, which corresponds to the position of the waistband. It causes the distance between wave fronts to be slightly larger than the distance between wave fronts for plane waves of the same frequency. This indicates that the phase wavefront propagates faster and therefore the local phase velocity is larger.
The total Goui phase shift produced by a Gaussian beam passing through the focus (from the far field at one end to the far field at the other end of the focus) is π.
Figure 1: When a beam with a wavelength of 1064nm and a beam waist radius of 100μm propagates in the air, the beam radius and Goui phase shift change in the propagation direction. The sign of the position is relative to the Rayleigh length.
It is normal for a Gaussian beam to have a different phase shift than a plane wave. A Gaussian beam can be viewed as a superposition of plane waves propagating in different directions. The phase shift of plane wave components that do not propagate in the direction of the optical axis is smaller than the phase shift of plane waves in the direction of the optical axis, and the overall phase shift comes from all the superimposed plane wave components.
The Guyi phase shift is larger for higher order transverse modes. For example, for the TEMnm mode, the enhancement factor is 1 + n + m. Therefore higher order modes in the optical resonator have higher resonant frequencies. The Goui phase shift will affect the beam quality of the laser resonator because it will relieve the frequency degeneracy of the resonator mode.
