2One Dimensional EM Wave For most purposes, a travelling light wave can be presented as aone-dimensional, scalar wave provided it has a direction ofpropagation.Such a wave is usually described in terms of the electric field E.Wavelength EoPhasezA plane wave propagating in the direction of z is:The propagation constant (or wave number)Phase velocityn = Propagation medium refractive index
3Group VelocityAs monochromatic light wave propagates along a waveguide in thez direction, the points of constant phase travel at a phase velocity.Phase velocityHowever, non-monochromatic waves travellingtogether will have a velocity known as Group Velocity:1.441.461.4950017001900nng (nm)Ref. indexWhere the fibregroup index is:
4Classification of Polarization Light in the form of a plane wave in space is said to be linearly polarized.If light is composed of two plane waves of equal amplitude by differing in phase by 90°, then the light is said to be circularly polarized.If two plane waves of differing amplitude are related in phase by 90°, or if the relative phase is other than 90° then the light is said to be elliptically polarized.
5Linear PolarizationA plane electromagnetic wave is said to be linearly polarized.The transverse electric field wave is accompanied by a magnetic field wave as illustrated.
6Circular Polarization Circularly polarized light consists of two perpendicular electromagnetic plane waves of equal amplitude and 90° difference in phase.The light illustrated is right- circularly polarized.
7Elliptical Polarization Elliptically polarized light consists of two perpendicular waves of unequal amplitude which differ in phase by 90°.The illustration shows right- elliptically polarized light.
9Fibre DispersionData carried in an optical fibre consists of pulses of light energyconsists of a large number of frequencies travelling at a given rate.There is a limit to the highest data rate (frequency) that can besent down a fibre and be expected to emerge intact at the output.This is because of a phenomenon known as Dispersion (pulsespreading), which limits the "Bandwidth” of the fibre.si(t)Tso(t)OutputpulseLMany modesCause of Dispersion:Chromatic (Intramodal) DispersionModal (Intermodal) Dispersion
12Group and Phase Velocity The formation of a wave packet from the combination of two waveswith nearly equal frequencies. The envelope of the wave packageor group of waves travels at a group velocity vg.
13Chromatic/Intramodal Dispersion Intramodal dispersion arises due to the propagation delay differences betweenthe different spectral components of the transmitted signal.Further it increases with the increase in spectral width of the optical source.This spectral width is the range ofwavelengths emitted by the optical source.For example in the case of LED,it has a large spectral width about40 nm since it emits wavelengthsfrom 830–870 nm with the peak emission wavelength at 850 nm.In the case of laser diode which has a very narrow spectral width, the spectral widthis about 1 or 2 nm only.Thus the Intramodal dispersion can be reduced in an optical fiber using single modelaser diode as an optical source.Laser = 1-2 nm = R.M.S SpectralwidthLED(many modes) = 40 nmwavelength
14Chromatic/Intramodal Dispersion Main causes:Material dispersionWaveguide dispersion
15Material DispersionThis dispersion arises due to the different group velocities of the various spectralcomponents launched into the fiber.A material is said to exhibit material dispersion whenPulse spreading occurs even when different wavelengths follow the same path.Sometimes referred to as Chromatic dispersion ,since this is the same effect bywhich a prism spreads outa spectrum.In a prism, material dispersion (a wavelength-dependent refractive index)causes different colors to refract at different angles, splitting white light into a rainbow
17Material Dispersion RMS pulse broadening Refractive index of silica is frequency dependent. Thus differentfrequency (wavelength) components travel at different speedRMS pulse broadeningWhere material dispersion coefficient:-100100175Dmat2nd windowNote: Negative sign, indicates that lowwavelength components arrives beforehigher wavelength components.
18Waveguide DispersionThis results from variation of the group velocity with wavelength fora particular mode.Signal in the cladding travels with a different velocity than the signal in the coreThe amount of waveguide dispersion depends on the fiber design like core radius and the size of the fiber.This can usually be ignored in multimode fibres, since it is verysmall compared with material dispersion.However it is significant in monomode fibres.
19Waveguide DispersionIn the case of single mode fibers, waveguide dispersionarises when-100100175DmatWaveguide dispersionTotal dispersionMaterial dispersion
21Modal (Intermodal) Dispersion Result of different values of the group delay for each individual mode at a single frequency.This variation in the group velocities of the different modes results in a group delay spread of intermodal distortion.This distortion mechanism is eliminated by single-mode operation, but it is important in multimode fibers.
22Modal (Intermodal) Dispersion Lower order modes travel almost parallel to the centre line of the fibre cover the shortest distance, thus reaching the end of fibre sooner.The higher order modes (more zig-zag rays) take a longer routeas they pass along the fibre and so reach the end of the fibre later.Mainly in multimode fibers12Cladding n2Core n1c
23Modal Dispersion - SIMMF The time taken for ray 1 to propagate a length of fibre L gives the minimum delay time:The time taken for the ray to propagate a length of fibre L gives the maximum delay time:SinceThe delay differenceSince relative refractive index differenceThus
24Modal Dispersion - SIMMF For ,andThusFor a rectangular input pulse, the RMS pulse broadening due tomodal dispersion at the output of the fibre is:Total dispersion = chromatic dispersion + modal dispersion
25Modal Dispersion - GIMMF The delay differencethe RMS pulse broadening
26Modal Dispersion - GIMMF Intermodal dispersion in multimode fibers is minimized with the use of graded index fibers.Hence multimode graded index fibers show substantial bandwidth improvement over multimode step index fibers.The fiber has a parabolic index profile with a maximum at the core axis.
28Modal Dispersion - GIMMF It may be observed that apart from the axial ray the meridional rays follow sinusoidal trajectories of different path lengths which results from the index grading.The longer sinusoidal paths are compensated for by the higher speeds in the lower index medium away from the axis.The ray that travels along the axial ray is exclusively in the high index region at the core axis, and at the lowest speed.Thus there is an equalization of the transmission times of the various trajectories and the graded index profile reduces the disparity in the mode transit times.Thus the delay difference between the fastest and slowest modes are reduced for graded index fiber.
31Bandwidth Limitations Maximum channel bandwidth B:For non-return-to-zero (NRZ) data format: B = BT /2For return-to-zero (RZ) data format: B = BTWhere the maximum bit rate BT = 1/T, and T = bit duration.For zero pulse overlap at the output of the fibre BT <= 1/2where is the pulse width.For MMSF: BT (max) = 1/2TsFor a Gaussian shape pulse:BT 0.2/rmswhere rms is the RMS pulse width.For MMSF: BT (max) =0.2/ modalorBT (max) =0.2/ T Total dispersion
32Bandwidth Distance Product (BDP) The BDP is the bandwidth of a kilometer of fibre and is a constantfor any particular type of fibre.Bopt * L = BT * L (MHzkm)For example, A multimode fibre has a BDP of 20 MHz.km, then:-- 1 km of the fibre would have a bandwidth of 20 MHz- 2 km of the fibre would have a bandwidth of 10 MHzTypical B.D.P. for different types of fibres are:Multimode MHz.kmSingle Mode MHz.kmGraded Index MHZ.km
35Birefringence in single-mode fibers Because of asymmetries the refractive indices for the two degenerate modes (vertical & horizontal polarizations) are different. This difference is referred to as birefringence, :Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
36Birefringence in single-mode fibers The effects of fiber birefringence on the polarization states of an optical signal are another source of pulse broadening.Results from intrinsic factors such as geometric irregularities of the fiber core or internal stresses on it.External factors such as bending, twisting or pinching of the fiber can also lead to birefringence.All these mechanisms exist to some extent in the fiber, there will be a varying birefringence along its length.
39Fiber Beat LengthIn general, a linearly polarized mode is a combination of both of the degenerate modes. As the modal wave travels along the fiber, the difference in the refractive indices would change the phase difference between these two components & thereby the state of the polarization of the mode. However after certain length referred to as fiber beat length, the modal wave will produce its original state of polarization. This length is simply given by: