3 :6 Consider a fiber with a 25-μm core radius, a core index n 1 = 1.48, and
Δ= 0.01.
(a) Show that the value of V is 25 at 1320 nm and that 312 modes propagate
in thefiber.
(b) Show that 7.5 % of the optical powerflows in the cladding.
(c) If the core-cladding difference is reduced toΔ= 0.003, show that the
fiber supports 94 modes and that now 13.7 % of the optical powerflows
in the cladding.
3 :7 Consider a step-indexfiber that has a 5-μm core radius, an index difference
Δ= 0.002, and a core index n 1 = 1.480.
(a) By calculating the V number, verify that at 1310 nm this is a
single-modefiber.
(b) Verify that at 820 nm thefiber is not single-mode because V = 3.514.
3 :8 Consider a 62.5-μm core diameter graded-indexfiber that has a parabolic
index profile (α= 2). Suppose the fiber has a numerical aperture
NA = 0.275.
(a) Show that the V number for thisfiber at 850 nm is 63.5.
(b) Show that the number of guided modes is 1008 at 850 nm.
3 :9 A graded-indexfiber with a parabolic index profile (α= 2) has a core index
n 1 = 1.480 and an index differenceΔ= 0.010.
(a) Using Eqs. (3.4) and (3.15) show that the maximum value of the core
radius for single-mode operation at 1310 nm is 3.39μm.
(b) Show that the maximum value of the core radius for single-mode
operation at 1550 nm is 4.01μm.3 :10 Calculate the numerical apertures of (a) a plastic step-indexfiber having a
core refractive index of n 1 = 1.60 and a cladding index of n 2 = 1.49, (b) a
step-indexfiber having a silica core (n 1 = 1.458) and a silicone resin clad-
ding (n 2 = 1.405). (Answer: 0.58; 0.39).
3 :11 Consider a FBG that has the following parameter values: neff= 1.48 and
Λ= 532 nm at 20 °C.
(a) Show that this FBG will reflect a wavelengthλB= 1547 nm at 20 °C.
(b) Suppose that the Bragg wavelength changes linearly with temperature
with an incremental wavelength changeΔλB= 23.4 pm/°C per incre-
mental temperature change ΔT. Show that the Bragg wavelength is
1547.351 nm when T = 35 °C.
(c) Show that the Bragg wavelength is 1546.766 nm when T = 10 °C?
3 :12 Consider an optoelectronic device page that has a 30-cm length offiber
coiled up inside. Show that the volume saved by using a reduced-cladding
fiber with a cladding diameter of 80μm is 2.2 mm^3 smaller compared to a
fiber with a 125-μm outer cladding diameter.
86 3 Optical Fibers for Biophotonics Applications