Abstract
Typically, the apertures of optical systems are large compared to their wavelength. In most cases, therefore, the ray optics concept represents a sufficiently accurate approximation to describe these optical systems.
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Notes
- 1.
x = r cos φ, y = r sin φ, z = z.
- 2.
A Gaussian or normal distribution f(x) is given by \( f\left( x \right) = 1/\left( {\sqrt {2\pi } b} \right)\exp \left\{ { - \left( {x - a} \right)^{2} /2b^{2} } \right\} \). a and b are the parameters of the distribution. The maximum and symmetry center lie at the position x = a. b is the distance of the inflection point from the symmetry center.
- 3.
The Guoy Shift arctan(z/z R ) of the phase exhibits different values for the higher-order modes. This leads to slightly different eigenfrequencies in spherical resonators (cf. Sect. 6.3.3).
- 4.
The Gaussian beam can also have different dimensions in both x- and y-directions, when w0 in the x- and y-directions takes on different values; it is then elliptically distorted.
- 5.
The solution structure given in Eq. 5.20 follows from this differential equation.
- 6.
Since the definition z R = πw 20 /λ also remains valid, unchanged, for the higher modes, modes with the same Rayleigh lengths are compared here.
- 7.
This is valid under the assumption of ideal lenses, transforming the beam without aberrations or optical disturbances. Any disturbance of the beam’s phase front leads to an increasing beam parameter product.
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© 2018 Springer-Verlag GmbH Germany, part of Springer Nature
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Poprawe, R., Boucke, K., Hoffman, D. (2018). Laser Beams. In: Tailored Light 1. RWTHedition. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01234-1_5
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DOI: https://doi.org/10.1007/978-3-642-01234-1_5
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