10. Fiber Optics 10. Fiber Optics

10. Fiber Optics 10. Fiber Optics

This lecture

‹ Numerical aperture of optical fiber

‹ Allowed modes in fibers

‹ Attenuation

‹ Distortion

• Modal distortion

• Material dispersion

• Waveguide dispersion Last Lecture

• Fourier analysis

• Temporal coherence and line width

• Partial coherence

• Spatial coherence

Optical communication systems Optical communication systems

Optical-fiber cable

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

Light guides

Light guides

Optical fibers Optical fibers

Step-index fiber Graded-index fiber

10-4. Optics of propagation 10-4. 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) waveguides 10-5. 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 ϕ_m =ϕ_c

( ) ^{2 2}

max 1 1 1

2 2 2

cos _c 1 . . 1 1

d d d

m n ϕ N A n n

λ λ λ

= + = + = − +

(See p. 501) m=0; “straight-through mode” at ϕ = 90^o.

large m; “high-order mode” with ϕ near ϕ_c

Allowed modes : in fibers Allowed modes : in fibers

2 max

1 . .

2

m πd N A λ

⎛ ⎞

= ⎜ ⎟

⎝ ⎠

max

d 2

2

( . .) m ^{< →} λ π^< N A

Single-mode (mono-mode) fiber when :

For single-mode,

( )

max

2d . . 1

m N A

= λ + (for slabs)

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

Extrinsic losses : bending, defects, …

Intrinsic losses : absorption, Rayleigh scattering, …

Silica glass fiber

4

1 λ

⎛ ⎞

⎜ ⎟

⎝ ⎠

Attenuation (absorption) coefficient Attenuation (absorption) coefficient

[db/km]

10-7. Distortion 10-7. Distortion

Modal distortion

L’

L

Consider two extreme modes when m = 0 and m = m_max

[sec/km]

GRIN (graded index) fibers GRIN (graded index) fibers

Modal distortion

Material dispersion Material dispersion

Pulse broadening

Material dispersion Material dispersion

M : ps/nm^.km

: temporal pulse spread (psec) per unit spectral width (nm) per unit length (km)

Waveguide dispersion Waveguide dispersion

For a guided mode, the effective refractive-index of the mode is

1 sin n1 _eff 1sin 2

eff m c

g

c n

n n n n

v ϕ ϕ

≡ = → ≥ ≥ =

<

Waveguide

ϕ _m

For a certain guided mode, the dependence of ϕ_m = ϕ_m(λ) induces a pulse broadening.

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

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

Under-sea fiber networks Under-sea fiber networks

WDM and TDM WDM and TDM

WDM

(wavelength division multiplexing)

TDM

(time division multiplexing)

Optical MUX/DEMUX components Optical MUX/DEMUX components

AWG (arrayed waveguide grating)

Mach-Zehnder fiber interferometers Mach-Zehnder fiber interferometers