Unit-7: Polarization Mode Dispersion https://sites.google.com/a/faculty.muet.edu.pk/abdullatif Department of Telecommunication, MUET UET Jamshoro 1
Goos Hänchen Shift The Goos-Hänchen effect is a phenomenon in which a light beam reflecting off a surface is spatially shifted as if it had briefly penetrated the surface before bouncing back. The explanation for the shifting is as under: Plane waves reflected by an interface, experience a phase shift which may depends on the angle of incidence. And the plane waves do not all have the same value of angle of incidence. So there is a range of angles of incidence producing a shift. Lateral shift is very small (d 0.06 to 0.10 μm for a silvered glass interface at a wavelength of 0.55 μm) Department of Telecommunication, MUET UET Jamshoro 2
Goos Haenchen Shift Department of Telecommunication, MUET UET Jamshoro 3
Mode Field Diameter (MFD) and Spot Size It is a measure of the distribution of optical power intensity across the end face of a single mode fiber. When light pulse is injected in the fiber, the largest percentage of light pulse travels in the core. Some light is distributed in the cladding. This wider distribution is known as mode field diameter. Department of Telecommunication, MUET UET Jamshoro 4
Mode Field Diameter (MFD) and Spot Size MFD is an important parameter for characterizing single-mode fiber properties It takes into account the wavelength-dependent field penetration into the fiber cladding. It is a better measure of the functional properties of singlemode fiber than the core diameter. For step index and graded (near parabolic profile) single-mode fibers operating near the cutoff wavelength λ c, the field is well approximated by a Gaussian distribution. MFD is generally taken as the distance between the opposite 1/e = 0.37 field amplitude points. Spot size (or mode-field radius) ω 0 is the nominal half width of the input excitation. Department of Telecommunication, MUET UET Jamshoro 5
Mode Field Diameter (MFD) and Spot Size Department of Telecommunication, MUET UET Jamshoro 6
Polarization As per Maxwell equations, E and H are both perpendicular to the direction of propagation. Department of Telecommunication, MUET UET Jamshoro 7
Polarization So electric field vector always points in the direction of x. This is termed as linearly polarized in x direction. Unpolarized light An ordinary lightwave consists of many transverse electromagnetic waves that vibrate in a variety of directions (i.e. in more than one plane) It is called unpolarized light (as shown in next slide) However any arbitrary direction of vibration can be represented as a combination of a parallel vibration and a perpendicular vibration. Therefore unpolarized light can be considered as composed of two orthogonal plane polarization components. Department of Telecommunication, MUET UET Jamshoro 8
Polarization Department of Telecommunication, MUET UET Jamshoro 9
Polarization Polarization is defined with respect to the orientation of Electric field. A linearly polarized wave travelling in k direction can be represented in the general form: A( x, t) ei A0 exp j t k. x with x=xe x +xe y +xe z representing a general position vector and k=k x e x +k y e y +k z e z representing the wave propagation vector. Here A 0 is the maximum amplitude of the wave and e i is a unit vector lying parallel to an axis designed by i. If k=k z e z and A denotes electric field E with coordinates e i =e x, then the real measurable electric field is given by: Department of Telecommunication, MUET UET Jamshoro 10
Polarization Ex( z, t) Re( E) exe0 x cos t kz It represents a plane wave in the z-direction. This wave is linearly polarized in x-direction. Consider another linearly polarized wave in y-direction: Ey( z, t) eye0 y cos t kz where δ is the relative phase difference between two waves. The resultant wave is: E( z, t) Ex( z, t) Ey( z, t) If δ is zero or an integer multiple of 2π, the waves are in phase. The resultant wave is also a linearly polarized wave (shown on next slide) with a polarization vector making an angle θ. Department of Telecommunication, MUET UET Jamshoro 11
Linear Polarization E0 y arctan E0 x with respect to e x and having a magnitude 2 2 1/2 0x 0y E E E Department of Telecommunication, MUET UET Jamshoro 12
Elliptical Polarization For general values of δ wave is elliptically polarized. Department of Telecommunication, MUET UET Jamshoro 13
Circular Polarization When E 0x =E 0y =E 0 and the relative phase difference / 2 2m where m 0, 1, 2,... then we have circularly polarized light. Department of Telecommunication, MUET UET Jamshoro 14
Polarization Mode Dispersion (PMD) Birefringence Mineral crystals e.g. calcite (calcium carbonate) have usually two distinct indices of refraction, and they are called birefringent materials. They are anisotropic material type. Isotropy is the uniformity of properties in all directions. Anisotropy measures the difference in properties along different axes. When light enters an anisotropic material, it is refracted into two rays, each polarized with the vibration directions oriented at right angles (mutually perpendicular) to one another and traveling at different velocities. This phenomenon is termed double refraction or birefringence. Department of Telecommunication, MUET UET Jamshoro 15
Polarization Mode Dispersion (PMD) Group delay Group delay per unit length was defined in unit 06 (slide no. 48) 2 g 1 1 d d L v c dk 2 c d Differential Group delay g In the time domain for a short section of fiber, the differential group delay (DGD) between slow and fast modes over the fiber length is defined as: L g Department of Telecommunication, MUET UET Jamshoro 16
Polarization Mode Dispersion (PMD) PMD results from fiber birefringence. It is a source of pulse broadening. Department of Telecommunication, MUET UET Jamshoro 17
Polarization Mode Dispersion (PMD) A short section of single mode fiber is shown in time domain. As shown in figure, fiber becomes bimodal. These two modes have different phase propagation constants β x and β y. They will have different group delays. The differential group delay (DGD) can be found from equation given on previous slide: d g ( x y ) L dω d n ( x n y ) dω c c Department of Telecommunication, MUET UET Jamshoro 18
Polarization Mode Dispersion (PMD) d n eff dω c neff d n c c dω where δτ g, the differential group delay per unit length, is called as the polarization mode dispersion (PMD) of the fiber and is usually expressed in units of picoseconds per kilometer of fiber eff Department of Telecommunication, MUET UET Jamshoro 19