Lyubomir Stoyanov

Lyubomir Stoyanov is an optical researcher associated with the Department of Quantum Electronics at Sofia University. His author-hosted profile and publication list identify work on structured laser fields and their propagation.^[ref] His coauthored work includes measurements of the Gouy phase of Bessel-Gaussian beams and higher-order Hermite-Gaussian optical modes.

A 2024 experiment used spatial light modulator preparation of higher-order Hermite-Gaussian optical modes and interferometry to compare their Gouy phase with the familiar mode-order prediction.^[ref] Measuring the phase supplies information that a beam's spot pattern alone cannot provide.

For an original ideal-mode example, define the positive Gouy-phase function bywhere $z_R>0$ is the Rayleigh range. In a field convention containing $e^{i(kz-\omega t)}$, this factor contributes $e^{-i{\psi }_{mn}}$. Thus the $(m,n)=(2,0)$ mode at $z=z_R$ has ${\psi }_{20}=3\pi /4$, three times the fundamental mode's $\pi /4$. The formula states a convention explicitly so that the sign of the additional field phase is not confused with the sign of the named positive function.

Comparing modes at matched $z/z_R$ is important. A change of focusing geometry can change the Rayleigh range, while the mode-order factor changes the phase at a fixed normalized distance. An interferometric comparison therefore needs both mode identification and calibrated propagation position. These ideal numbers illustrate the model; they are not fitted results from the paper.