Download e-book for kindle: Laser Resonators and Beam Propagation by N. Hodgson, H. Weber

By N. Hodgson, H. Weber

ISBN-10: 0199256047

ISBN-13: 9780199256044

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Example: At which distance L are all parallel incoming rays focused by a lens with focal lengthf? In this case a parallel beam (see Fig. 9a), hitting the lens at an angle aIwill be focused into the point x,=faI. This means that we obtain information on the angular ray distribution by looking at the intensity pattern in the focal plane of a focusing lens. We actually see the Fourier transform of the incoming beam (see Sec. 4). 30) a2 = C xI + D a1 All rays starting at point x , under arbitrary angles will be reunified in point x,.

In the thin lens approximation,any change in ray position or angle inside the medium is neglected which means that we do not propagate the ray between the two surfaces. 16). 19) Note that the curvature pis positive for convex surfaces (center of curvature to the right of the interface) and negative for concave surfaces. For a glass plate in air, for instance, this effective distance is smaller than the actual physical thickness L of the plate. This means that objects will appear closer to the eye if we look through the plate (this is, of course, only true for near objects which are viewed under an angle).

In plane 1, the beam is characterized by a rectangle in phase space with area dda. In the focal plane only rays with an angle a smaller than d 2 f can be detected (we assume that the beam diameter on the lens is also 4. 41) the area in phase space remains constant. 42) Let us also look at the depth of field zoin the focal plane. 43) Fig. 12 Focusing of a beam with angular divergence Aa by a lens. The right hand graph shows the effect of the propagation from plane 1 to plane 2 in phase space. 44) Since the beam parameter product dAd4 is constant, the depth of field decreases quadratically with the spot size.

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Laser Resonators and Beam Propagation by N. Hodgson, H. Weber


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