Gouy Gaussian-Beam Phase
See focused light acquire an extra phase shift as its wavefronts pass the waist.
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Gouy Gaussian-Beam Phase
This module explores the Gouy phase shift in paraxial Hermite-Gaussian beams. The Gouy phase is given by psi = (N+1)atan(xi), where xi=z/zR and N is the total transverse mode order. The reduced curvature is xi/(1+xi^2).
Worked Example
Below is a step-by-step calculation for mode order 0 and reduced position 1:
- Parameters: Mode order N = 0, reduced position xi = 1.
- Gouy phase: psi = (0 + 1) * atan(1) = 1 * 0.7853981633974483 = 0.7853981633974483 radians.
- Reduced wavefront curvature: zR/R = 1 / (1 + 1^2) = 1 / 2 = 0.5.
- Phase slope: d(psi)/d(xi) = (0 + 1) / (1 + 1^2) = 0.5.
Experiment
Use the interactive tool to explore phase shifts:
- Navigate to the Gouy Gaussian-Beam Phase interactive module.
- Set Mode order to 1 and Reduced position to 1.
- Note the Gouy phase radians becomes 1.5707963267948966 radians, doubling the fundamental mode phase shift.
Limitations
This model evaluates phase in the paraxial approximation. It does not calculate exact non-paraxial spherical waves.
References
The following references provide further details:
Experience it interactively
Adjust parameters, observe in real time, and build deep intuition with Riano’s interactive Gouy Gaussian-Beam Phase module.
Try Gouy Gaussian-Beam Phase on Riano →