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

Optical communication systemsOptical communication systems

Optical-fiber cable

AM, FM, and Digital AM, FM, and Digital

Light guides Light guides

Optical fibersOptical fibers

Step-index fiber Graded-index fiber

10-4. Optics of propagation10-4. Optics of propagation

Cladding (n2)

Core (n1)

Air (n0)

Numerical aperture (N.A.)

Step index fiber

Skip distance :

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)

10-6. Attenuation (loss)10-6. Attenuation (loss)

Extrinsic losses : bending, defects, …

Intrinsic losses : absorption, Rayleigh scattering, …

Silica glass fiber

4

1λ

⎛ ⎞⎜ ⎟⎝ ⎠

Attenuation (absorption) coefficientAttenuation (absorption) coefficient

[db/km]

10-7. Distortion10-7. Distortion

Modal distortion

L’

L

Consider two extreme modeswhen m = 0 and m = mmax

[sec/km]

GRIN (graded index) fibersGRIN (graded index) fibers

Modal distortion

Material dispersionMaterial dispersion

Pulse broadening

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.

10-8. High-bit-rate optical fiber commun.10-8. High-bit-rate optical fiber commun.

Under-sea fiber networksUnder-sea fiber networks

WDM and TDMWDM and TDM

WDM(wavelength division multiplexing)

TDM(time division multiplexing)

Optical MUX/DEMUX componentsOptical MUX/DEMUX components

AWG (arrayed waveguide grating)

Mach-Zehnder fiber interferometersMach-Zehnder fiber interferometers