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Question 1:
(a) A manufacturer wishes to make a silica-core, step-index fiber with 𝑉 = 20 and
numerical aperture 𝑁𝐴 = 0.3 to be used at 1.55 µm. If 𝑛1 = 1.458, calculate the
approximate number of modes, the core radius, and the cladding index.
(b) If the fiber in part (a) is to be used in single-mode regime, what would be the
wavelength of the optical source? What are the reasons that make the operation at
this wavelength impractical?
Same problem in Midterm 2008 but added to it this question (What are the reasons
that make the operation at this wavelength impractical?)
From the problem we get 𝑙𝑎𝑚𝑑𝑎0′ = 12.8898 µm
Think for the reasons !
Question 2:
(a) Obtain an estimate for the maximum number of modes that can propagate at 800
nm in a step-index optical fiber of core diameter 40 µm and indices of refraction
of 1.5 and 1.479.
For cylindrical optical fiber:
Givens: lamda0=800nm ,a=20 µm ,n1=1.5 ,n2=1.479
From NA relation in in Slides 2 - P.51 we can get NA.
From V relation in P.51 and we know (ko=2*pi/lamda0) we can get V.
Maximum number of modes = V2/2
Question 3:
1) A step-index multimode fiber with a numerical aperture of 0.20 supports
approximately 1000 modes at an 850-nm wavelength.
(a) What is the diameter of its core?
(b) How many modes does the fiber support at 1320 nm?
(c) How any modes does the fiber support at 1550 nm?
Givens: NA=0.20 ,lamda0=850 nm ,Number of modes=1000 modes
(a) Number of modes = V2/2
Get V
From V relation in Slides 2 - P.51 and we know (ko=2*pi/lamda0) we can get a.
(b)-(c) For same NA & a and given lamda0' we can get V then number of modes.
Question 4:
3) Consider a fiber with a 25-µm core radius, a core index 𝑛1 = 1.48, and Δ= 0.01.
(a) If λ= 1320 nm, what is the value of V and how many modes propagate in the fiber?
(b) What percent of the optical power flows in the cladding?
(c) If the core-cladding difference is reduced to Δ = 0.003, how many modes does the fiber support and
what fraction of the optical power flows in the cladding?
Givens: a=25 µm ,n1=1.48 , Δ = 0.01
(a) lamda0=1320 nm
From NA relation in Slides 1 - p.28 we can get NA
From V relation in Slides 2 - P.51 and we know (ko=2*pi/lamda0) we can get V.
Number of modes = V2/2
(c) Δ’ = 0.003
For same n1 we can get NA’ and for same lamda0 & a we can get number of modes ‘ .
Question 5:
Find the core radius necessary for single-mode operation at 1320 nm of a step-index fiber
with 𝑛1 = 1.480 and 𝑛2 = 1.478. What are the numerical aperture and maximum
acceptance angle of this fiber
Givens: lamda0=1320 nm ,n1=1.480 ,n2=1.478
From NA relation in in Slides 1 - P.28 we can get NA.
From NA relation in same page NA= no sin(θomax) we can get θomax where no =1
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