OPTI510R: Photonics. Khanh Kieu College of Optical Sciences, University of Arizona Meinel building R.626

Transcription

1 OPTI510R: Photonics Khanh Kieu College of Optical Sciences, University of Arizona Meinel building R.626

2 Announcements Homework #4 is assigned, due March 25 th Start discussion on optical fibers

3 Optical fibers Outline: Introduction Fiber dispersion and compensation techniques Fiber fabrication Nonlinear optical effects in fibers Fiber amplifiers Passive fiber components

4 Introduction to optical fibers Outline: Brief history Geometrical optics description Wave optics description Fiber modes Fiber loss, fiber dispersion

5 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

6 Geometrical description = NA

7 Geometrical description

8 Guided-wave analysis n 2 core for < a a n 1 cladding for > a

9 Guided-wave analysis

10 Guided-wave analysis (credit: G. Agrawal)

11 Guided-wave analysis (credit: G. Agrawal)

12 Bessel function basics Bessel functions of the first kind Modified Bessel functions of the second kind u( r) J ( k r) l (core) T u(r) = K l (gr) (cladding)

13 Zeroth and higher order modes 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.

14 Eigen-value equation

15 Eigen-value equation

16 Classification of modes (credit: G. Agrawal)

17 Eigen-value equation (credit: G. Agrawal)

18 Linearly polarized modes

19 Linearly polarized modes (credit: G. Agrawal)

20 Fundamental modes (credit: G. Agrawal)

21 Fundamental modes

22 Fundamental modes

23 Fundamental modes (credit: G. Agrawal)

24 Modes profile 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 LP 01 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.

25 Attenuation in optical fiber Attenuation coefficient (db/km) a = 1 L 10log 10 1 T with T = P(L) P(0) Power transmission ratio as a function of distance z P( z) P(0) e - z for in km -1 Calculate (db) through (km -1 ) (db) = 4.343* (km -1 )

26 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

27 Propagation loss in optical fiber Current loss is < 0.2dB/km for single mode fiber working around 1550nm

28 Propagation loss in optical fiber Predicted the loss in optical fiber could be < 20dB/km Loss was ~1000dB/km at that time

29 Propagation loss in optical fiber Internet enablers: 1. Low loss optical fiber based on fused silica 2. Compact, low-cost diode lasers

30 Communication window Water absorption Loss performance in fused silica fiber

31 Communication window <1dB/mile of loss over >10 THz of bandwidth! Loss performance in fused silica fiber

32 Compared to coaxial

33 Scattering loss Light, Object D D << : Rayleigh scattering D ~ : Mie scattering D >> : Geometrical scattering Rayleigh scattering is one of the dominant sources of loss in optical fibers Inelastic scattering: Brillouin, Raman

34 Rayleigh scattering I ( ) ~ D 6 (1 + cos 2 ( ))/ 4 (source: Wikipedia)

35 Infrared absorption Strategy is to use heavier atoms to lower vibrational energies Transmission window Vibrational phonon absorption edge (source: Wikipedia)

36 Bending loss

37 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

38 Bending loss In Corning Clearcurve fiber Progress in bendable fiber

39 Progress in bendable fiber

40 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