Beams Gaussian

A commercial fs-laser (CPA-10 Clark-MXR, MI, USA) was used for ablation. The parameters used for the laser output pulses were central wavelength 775 nm pulse energy -0.5 mj pulse duration 170-200 fs and repetition rate from single pulse operation up to 10 Hz. In these experiments the laser with Gaussian beam profile was used because of the lack of commercial beam homogenizers for femtosecond lasers. 

For the case of a laser pulse having a square time profile with width T and constant power F, at the center of the Gaussian beam, the above integral can be evaluated in closed form. For r = 0 (the center of the laser beam) the temperature increase is given by ... 

The electric field of a focused Gaussian beam in TEM00 at cylindrical coordinates z and r is given by [59],... 

As the disc spins, a protein edge passes through a focused Gaussian beam that has a beam radius p0. At the moment when the optic axis coincides with the protein edge in the near field, there is a quadrature condition in the far field set by... 

An MNF/microcylinder sensor exploits WGMs resonances in a cylinder (optical fiber), which are excited by an MNF. The arrangement of an MNF and a cylinder is shown in Fig. 13.li. As opposed to the WGM in a microsphere and microdisk considered in Sect. 13.3.1, the beam launched from the MNF into the cylinder spreads along the cylinder surface and eventually vanishes, even if there is no loss. The theory of resonant transmission of the MNF/microcylinder sensor was developed in Ref. 18. The resonant transmission power of this device can be modeled by a self-interference of a Gaussian beam that made n turns along the cylinder circumference ... 

Here, ry is the backscatter coefficient for the substrate and the line input dose which is equal to i /x. The Gaussian beam radius in the resist at penetration z is... 

By convolving the spreading Gaussian beam treatment with the experimentally determined relationship between resist thickness and input dose, Heidenreich was able to calculate line heights and profile widths at the substrate in good agreement with experiment. 

M.I. Angelova and B. Pouligny Trapping and Levitation of a Dielectric Sphere with off-Centered Gaussian Beams I Experimental. Pure Appl. Optics 2,261 (1993). 

The driving fields in nonlinear coherent microscopy can be dressed with alternative phase profiles. One of the simplest phase masks is a one-dimensional r-phase step across the transverse Gaussian beam profile. The resulting phase pattern resembles... 

Novotny, L., Sanchez, E. J., and Xie, X. S. 1998. Near-field optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams. Ultramicrosc. 71 21-29. 

Fig. 2 Relative excitation rates for the IPA and 2PA process along the beam propagation direction. (Solid line) On-axis intensity for a Gaussian beam with waist coq and wavelength k (dotted line) on-axis square of the intensity a Gaussian beam with waist coq and wavelength k (dashed line) on-axis square of the intensity a Gaussian beam with waist cjOq and wavelength 2k. In all cases, the ordinate is normalized to the value at the focus...

Although paraxial approximation becomes imsuitable for higher-WA optics and for non-Gaussian beams, the above insights should remain qualitatively valid in these cases as well. Since only the above-the-threshold intensity part of the spatio-temporal envelope of the beam is important for photomodification, usually this part can be reasonably well approximated by a Gaussian. 

Self-focusing occurs when power, Pq, exceeds the critical self-focusing power Per- A Gaussian beam experiences self-focusing after propagating distance, isf [46] ... 

E. Torrontegui, X. Chen, M. Modugno, A. Ruschhaupt, D. Guery-OdeUn, and I. G. Muga. Fast transitionless expansion of cold atoms in optical Gaussian-beam traps. Phys. Rev. A, 85(3) 033605-033613(2012). 

---