Exercise 5 We want to couple the energy of an argon-ion laser beam of wavelength
ID: 3163783 • Letter: E
Question
Exercise 5 We want to couple the energy of an argon-ion laser beam of wavelength A-488 nm into a fiber optic cable. Refractive indices of the fiber optic cable are 1.62 for the core and 1.50 for the cladding. The beam of the laser has a cross sectional area of 10 mm with negligible divergence and the entire beam has to be coupled into a diameter of 50 um (fiber core). A lens is used to couple the laser beam into the fiber. a) Calculate the acceptance angle of the fiber b) What should the focal length of the lens be to couple the beam into such a small fiber core section (take Ds 0.7 Dc)Explanation / Answer
Answer:
(a) Acceptance angle a = Sin-1{ [(n12 - n22)1/2 ] / na }
where n1 = refractive index of core = 1.62, n2 = refractive index of cladding = 1.50, na = refractive index of air (1.00)
Therefore, a = Sin -1 { [(1.622 - 1.502 )1/2 ] / 1.00 } = Sin -1 (2.6244 - 2.25)1/2 = 37.720.
(b) In order to couple light of wavelength from a collimated laser beam of diameter D into a fiber of mode field diameter , choose a lens with a focal length f = D (/4)
where, D is the diameter of the laser beam, is the dimeter of the fiber core = 50 x 10-6 m
Given that, the wavelength of the laser = 488 nm, cross-sectional area of the laser beam 10 mm2, from this area we can calculate the diameter of the beam.
Diameter = 2 (radius) and radius = (area / 3.14 )1/2 = (10 mm2/ 3.14)1/2 = 1.784 mm
Then, diameter of the laser beam D = 2 (1.784 mm) = 3.569 mm.
Therefore, focal length of the lens f = D (/4) = (3.569 mm) ( 3.14 x 50 x 10-6 m / 4 x 488 nm) = 0.319 m
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.