OPTI510R: Photonics

Khanh Kieu

College of Optical Sciences,

University of Arizona

kkieu@optics.arizona.edu

Meinel building R.626

mailto:kkieu@optics.arizona.edu

Announcements

Homework #4 is assigned, due March 25th

Start discussion on optical fibers

Optical fibers

Outline:

• Introduction

• Fiber dispersion and compensation techniques

• Fiber fabrication

• Nonlinear optical effects in fibers

• Fiber amplifiers

• Passive fiber components

Introduction to optical fibers

Outline:

• Brief history

• Geometrical optics description

• Wave optics description

• Fiber modes

• Fiber loss, fiber dispersion

Geometrical description

Contain a central core surrounded

by a lower-index cladding

Two-dimensional waveguides with

cylindrical symmetry

Step-index fiber: refractive index of

the core is uniform

Graded-index fibers: refractive index

varies inside the core

Geometrical description

= NA

Geometrical description

Guided-wave analysis

acore

cladding

for < a

for > a

n1

n2

Guided-wave analysis

Guided-wave analysis

(credit: G. Agrawal)

Guided-wave analysis

(credit: G. Agrawal)

Bessel function basics

)()( rkJru Tl

u(r) =Kl (gr)

(core) (cladding)

Bessel functions of the first kind Modified Bessel functions of

the second kind

Examples of radial distribution u(r) for l=0 and l=3. The proportionality constants

are determined by continuous u(r) and du/dr at r = a.

Zeroth and higher order modes

Eigen-value equation

Eigen-value equation

Classification of modes

(credit: G. Agrawal)

Eigen-value equation

(credit: G. Agrawal)

Linearly polarized modes

Linearly polarized modes

(credit: G. Agrawal)

Fundamental modes

(credit: G. Agrawal)

Fundamental modes

Fundamental modes

Fundamental modes

(credit: G. Agrawal)

Modes profile

http://www.rp-photonics.com

Electric field amplitude profiles

for all the guided modes of

a fiber with a top-hat refractive

index profile (→ step index fiber).

The two colors indicate different

signs of electric field values. The

lowest-order mode (m = 0, n = 1,

called LP01 mode) has an

intensity profile which is similar to

that of a Gaussian beam. In

general, light launched into

a multimode fiber will excite a

superposition of different modes,

which can have a complicated

shape.

Attenuation in optical fiber

Attenuation coefficient (dB/km)

Power transmission ratio as a function of distance z

a =1

L10log10

1

T with T =

P(L)

P(0)

1-z- kmin for )0(

)(e

P

zP

Calculate (dB) through (km-1)

(dB) = 4.343* (km-1)

Sources of attenuation in silica fiber

Absorption

• Vibrational transitions in the IR

• Electronic and molecular transitions in the UV

• Extrinsic absorption from adsorbed water and other impurities

Scattering

• Rayleigh scattering

• Extrinsic scattering from defects due to manufacturing errors

• Raman, Brillouin scattering

Propagation loss in optical fiber

Current loss is < 0.2dB/km for single mode fiberworking around 1550nm

Propagation loss in optical fiber

Predicted the loss in optical fiber could be < 20dB/km

Loss was ~1000dB/km at that time

Propagation loss in optical fiber

1. Low loss optical fiber based

on fused silica

2. Compact, low-cost diode lasers

Internet enablers:

Communication window

Loss performance in fused silica fiber

Water absorption

Communication window

Loss performance in fused silica fiber

10 THz of

bandwidth!

Compared to coaxial

Scattering loss

Light,

D

ObjectD > : Geometrical scattering

Rayleigh scattering is one of the dominant sources of loss in optical fibers

Inelastic scattering: Brillouin, Raman

Rayleigh scattering

I () ~ D6(1 + cos2())/4

(source: Wikipedia)

http://upload.wikimedia.org/wikipedia/commons/5/5e/SDIM0241b.jpghttp://upload.wikimedia.org/wikipedia/commons/5/5e/SDIM0241b.jpg

Infrared absorption

(source: Wikipedia)

Strategy is to use heavier atoms

to lower vibrational energies

Vibrational phonon absorption edgeTransmission window

Bending loss

Bending loss

• Loss mechanism: coupling to non-propagating modes

• Larger loss for longer wavelength (at a given bending radius)

• Smaller loss for higher NA

• Critical bending radius

Bending loss calculation:

• D. Marcuse, QE 2007

Progress in bendable fiber

Bending loss

In Corning Clearcurve

fiber

Progress in bendable fiber

Sources of dispersion in optical fiber

Modal dispersion• Occurs in multimode fibers coming from differences in group velocity for

different modes

Material dispersion• Results from the wavelength dependence of the bulk refractive index

Waveguide dispersion• Results from the wavelength dependence of the effective index in a

waveguide

• Material + waveguide dispersion is termed chromatic dispersion

Polarization mode dispersion• Results from the fact that different polarizations travel at different speeds

due to small birefringence that is present

Nonlinear dispersion – example is self-phase modulation