= Francesco D'Angelo
{c}
\b[Francesco D'Angelo] is an optical specialist associated with Edmund Optics, whose own laser-optics staff directory identifies him as a Senior Solutions Engineer.<Laser Optics Expertise staff directory at Edmund Optics>[Meet the Team, labeled Francesco D'Angelo entry]{ref} He is the named author of the technical note <Propagation of a Gaussian Beam Through a Thin Lens by Francesco D'Angelo>, which explains <Gaussian beam> propagation and transformation by a <thin lens>.
The note relates <beam waist>, <beam divergence> and <Rayleigh range>, then uses the complex beam parameter to calculate how a <thin lens> changes the beam. This connects an optical component specification to the actual position and size of a focused beam, instead of treating every incident beam as a perfectly parallel bundle of rays.<Propagation of a Gaussian Beam Through a Thin Lens by Francesco D'Angelo>[Equations (2)–(5), propagation parameters; later thin-lens transformation]{ref}
An illustrative consequence of the note's ideal <Gaussian beam> relation $w_0\theta=\lambda/\pi$ is easy to check. At a fixed <wavelength> $\lambda=1\,\mu\mathrm{m}$, a <beam waist> radius of $0.5\,\mathrm{mm}$ gives a far-field <beam divergence> half-angle of approximately $0.637\,\mathrm{mrad}$. Halving the <beam waist> radius doubles that half-angle. Focusing to a smaller spot and obtaining lower <beam divergence> cannot be chosen independently within this model.<Propagation of a Gaussian Beam Through a Thin Lens by Francesco D'Angelo>[Equations (3)–(5), ideal Gaussian waist-divergence relation]{ref}
The employer's https://www.edmundoptics.eu/capabilities/laser-optics/expertise/[laser-optics staff directory] includes a labeled portrait.
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