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Unformatted text preview: Focusing and Collimation 1 It is desired to use commercially available optical lens systems to perform laser beam focusing and laser beam collimation. A microscope objective is to be used to focus a collimated laser beam of freespace
wavelength 600nm to a spot size of 0.75 um. The lens has a focal length of 4mm. The
numerical aperture, NA, is deﬁned as the product of the refractive index of the focusing region and the sine of the half apex angle of the cone of focused light (a). That is,
NA : n sin a. ‘If the focusing is in air (as in this case), then the cone of focused light is in air and n =
1. Calculate, showing all work, the minimum numerical aperture to focus the beam to a
0.75 pm spot size. Express your answer accurately to four signiﬁcant ﬁgures and put it in the space provided. It is desired to build a line-of-sight laser optical communications system connect—
ing the Van Leer Electrical Engineering building and the new Klaus Advanced Com-
puting building. The distance between the laser and the receiver is 100 m. For safety
reasons, a visible wavelength is needed. Therefore, it is decided to use a semiconduc—
tor diode laser of wavelength 600nm. Also, for safety reasons, the diameter of the laser
beam at the Klaus building receiver needs to be no more than 50 mm (about 2 A
beam-expanding collimator is to be used with the diode laser in the Van Leer building.
Calculate, showing all work, the output diameter of the beam from the collimator at the
Van Leer building in order to produce a beam of 50 mm diameter at the Klaus building. Express your answer in millimeters accurately to four signiﬁcant ﬁgures. Put your ﬁnal answer in the space provided.
Minimum numerical aperture of focusing lens 2 Laser beam diameter at collimator output 2 mm. Focusing and Collimation 1 Focusing
D = 0.750 um Converging angle 0 due to focusing by lens 4A 9:;5 The angle 0 corresponds to the full apex angle of the cone. The half apex angle a is 2 A 2 0.600nm 0‘ = $5 = ;O.750,um = 0.509296'rad = 29.1805deg and so the minimum numerical aperture is NAmin = 0.487563 Collimation Far-ﬁeld angle measured to the Klaus building 0.050 m 0 = 100m = 0.00050md = 0.0286479deg Far—ﬁeld angle due to diffraction by a laser beam of diameter D 4A
0=—— 7rD 4A 4 0600/1771
D=——=—-———=1.2 7r 0 7r 0.0005rad 5 789mm The collimator output diameter must be larger than the output beam diameter. ...
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- Spring '08