Phase velocity

Phase and group velocity

Group velocity

Fiber Attenuation

Variation N and n with wavelength

Dispersion Dispersion in optical fibers can be categorized into three different types, namely differential mode dispersion (DMD), group velocity dispersion (GVD) and polarization mode dispersion (PMD). They differ in what phenomenon causes them and in what properties they possess, which has to be taken into consideration when designing an equalizer. Because DMD is only of concern for multimode links and PMD can usually be neglected for 10 Gbps links, the focus in this report is on GVD compensation.

Main optical transmission impairments modal, Chromatic dispersion (CD) Polarization mode dispersion (PMD) - Both CD and PMD cause temporal spreading of the optical bits as they propagate along the fiber. Kerr effect ( non-linear effects) - Self phase modulation (SPM) - Cross phase modulation (XPM) - Four Wave Mixing (FWM) Amplified spontaneous emission (ASE) Attenuation - Intrinsic ( Material resonances and Rayleigh scattering) - Extrinsic ( Absorption and bending losses)

Bit rate versus distance limitation imposed by different types of dispersion

Introduction (contd…)

Modal dispersion DMD (also called multipath dispersion or intermodal dispersion) is present only in multimode fibers and is due to that different modes (which can be seen as different rays) travel at different speeds (take different paths) through the fiber, thus arriving at different times at the receiver.

Chromatic dispersion CD is a result of the wavelength-dependency of the refractive index of the fiber There is no source in nature that can radiate a single wavelength. The light is generally, composed of a sum or group of plane wave components and resulting in a packet of waves. This wave packet do not travel at the phase velocity of individual waves but observed at a group velocity Vg.

Effect of dispersion Inter-symbol interference (ISI) due to dispersion

Dispersion in fiber

Modal dispersion: multimode fiber

Variation of n with wavelength

Chromatic dispersion: Material dispersion

Chromatic dispersion: waveguide dispersion

The total dispersion in fused silica fibre

Fiber Bragg grating The term grating refers to a device whose operation involves interference among multiple optical signals originating from the same source, but with different phase shifts.

Fiber Bragg grating

Uniform and chirped grating

Chirped FBG

LCFBG: CD compensation

Energy of a wave

TYPES OF POLARIZATION LinearCircularElliptical

PMD: Without mode coupling

PMD effect Distance versus PMD coefficient limitations imposed by PMD

PMD effect Bit rate versus distance limitations imposed by PMD

Causes of PMD  Core diameter varies slightly in a random fashion during fiber-drawing process.  Internal forces induced by thermal expansion  External forces induced by the environment: (i) through handling, cabling such as bending and twisting. (ii) mechanical stress from nearby sources (railways and highways) of vibration. (iii) wind cause swaying stress of the aerially deployed fiber.  The birefringence is not constant along the length of the fiber but changes with distance in a a random way.  PMD is not fixed for a given fiber, it changes with wavelength as well as time, which makes it difficult to compensate for PMD.

Causes of PMD and DGD

Birefringence & PMD PMD results from the variation in the refractive index (birefringence) of the fiber with respect to the polarization of the light signal. The length over which the phase difference between x- and y- is 2π polarized waves is called beat length

 The effects of fiber birefringence on the polarization states of an optical signal are subject to pulse broadening.  A varying birefringence along the fiber length will cause each polarization mode to travel at a slightly different velocity and the polarization orientation will rotate with distance.  The delay time between the two orthogonal polarization mode during the propagation of pulse over a distance L is - L

PMD characterization PMD is characterized by differential group delay (DGD) in an optical link, which is the time delay between the two (orthogonal) principal state of polarization (PSPs). For long optical fibers, the PMD figure of merit typically specified by its mean DGD (ps) or its PMD co-efficient ( ps/km 1/2 ). The mean DGD for a fiber is a constant that represents both the average of DGD values at one time across a broad spectral bandwidth on the order of milliseconds. Changing environmental factors cause the instantaneous DGD at a given wavelength to vary randomly about the mean.