10. fiber optics10. fiber opticsoptics.hanyang.ac.kr/~shsong/10-fiber optics.pdf · 2016-08-31 ·...
TRANSCRIPT
10. Fiber Optics10. Fiber Optics
This lecture Numerical aperture of optical fiberAllowed modes in fibersAttenuationDistortion
• Modal distortion• Material dispersion• Waveguide dispersion
Last Lecture• Fourier analysis• Temporal coherence and line width• Partial coherence• Spatial coherence
10-4. Optics of propagation10-4. Optics of propagation
Cladding (n2)
Core (n1)
Air (n0)
Numerical aperture (N.A.)
Step index fiber
10-5. Allowed modes : in slab (planar) waveguides10-5. Allowed modes : in slab (planar) waveguides
Modes (self-sustaining waves) must satisfy the condition.
Total number of propagating modes is the value of m when m cϕ ϕ=
( ) 2 2max 1 1 1
2 2 2cos 1 . . 1 1cd d dm n N A n nϕ
λ λ λ= + = + = − +
(See p. 501)
m=0; “straight-through mode” at ϕ = 90o.
large m; “high-order mode” with ϕ near ϕc
Allowed modes : in fibersAllowed modes : in fibers
2
max1 . .2
dm N Aπλ
⎛ ⎞= ⎜ ⎟⎝ ⎠
maxd 22
( . .)m
N Aλ π< → <Single-mode (mono-mode) fiber when :
For single-mode,
( )max2 . . 1dm N Aλ
= + (for slabs)
10-7. Distortion10-7. Distortion
Modal distortion
L’
L
Consider two extreme modeswhen m = 0 and m = mmax
[sec/km]
Material dispersionMaterial dispersion
M : ps/nm.km: temporal pulse spread (psec)
per unit spectral width (nm)per unit length (km)
Waveguide dispersionWaveguide dispersion
For a guided mode, the effective refractive-index of the mode is
1 1 1 2sin n sineffeff m cg
ncn n n nv
ϕ ϕ≡ = → ≥ ≥ =
<
Waveguide
ϕ m
For a certain guided mode, the dependence of ϕm = ϕm(λ) induces a pulse broadening.