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Transcript
How many light rays?? yRecall that only light rays which enter the core with an angle less than the acceptance angle will propagate yThere are an infinite number of possible ray angles, all less than acceptance angle Optical Communications Systems yIn theory then there are an infinite number of light rays? Range of angles over which light will not be transmitted Propagation in Fibre Range of angles over which light will be transmitted Electromagnetic Modes in Fibre Observing Modes Experimentally yVisible light is used as a source, typically HeNe laser (Red, 670 nm) yOutput from a fibre is projected onto a reflective surface, such as a white card in a darkened room yTo obtain an improved model for propagation in a fibre, EM wave theory must be used. yRay diagram or Geometric Optics approach remains useful as a way to visualise propagation in a fibre. yBasis of EM analysis is a solution to Maxwells equations for a fibre. yFor ease of analysis a fibre is frequently replaced by a planar optical waveguide, that is a slab of dielectric with a refractive index n1, sandwiched between two regions of lower refractive index n2. Output from singlemode fibre, HE11 mode n2 n1 Output from a fibre supporting two modes Output from a multimode fibre, a socalled speckle pattern n2 Planar waveguide Formation of Modes in a Fibre (I) Formation of Modes in a Fibre (II) B F B θ E F A d θ E A d C D yPropagation of an individual ray takes place in a zigzag pattern as shown yIn practice there is at the fibre input an infinite number of such rays, called more properly plane rays. yEach ray is in reality a line drawn normal to a wavefront, for example the wavefront shown by the dotted line FC above. yFor plane waves all points along the same wavefront must have identical phase. yThe wavefront intersects two of the upwardly travelling portions of the same ray at A and C. D C yUnless the phase at point C differs from that at point A by a multiple of 2π then destructive interference takes place and the ray does not propagate. yMoving along the ray path between A and C involves a phase change caused by the distance AB and BC and a phase change caused by reflection yCombining these two phase changes and setting the result equal to a multiple of 2π we get a condition for propagation of a "ray", more properly now called a mode. Types of Optical Fibre yThree distinct types of optical fibre have developed yThe reasons behind the development of different fibres are explored later yConcern here is to examine propagation in the different fibres Step Index Fibre The three fibre types are: • Step index fibre • Graded index fibre Multimode fibres • Singlemode fibre (also called monomode fibre) Step Index Fibre 0 N2 N1 Normalised Frequency for a Fibre yFor an optical fibre we can define the so-called normalised frequency "V" Cladding Diameter yConvenient dimensionless parameter that combines some key fibre variables Cladding yIt is defined thus: Core Diameter Core V= 2π πa λ 2 2 . n1 - n2 where a is the fibre radius and λ is the operating wavelength Refractive index profile for a step index optical fibre V is also very commonly defined using the numerical aperture NA thus: ySimplest and earliest form of fibre yThe larger the core diameter the more modes propagate Relative Refractive Index yNormally the symbol ∆ is used y∆ ∆ is defined thus: 2 ∆= 2 n1 - n2 2 2n1 if ∆ is << 1 then ∆ is given by: The normalised frequency V can be written in terms of ∆ : ∆= V= 2π π λ a.NA We will use this definition yWith a large core diameter many thousands of modes can exist yIt is also possible to define a so called relative refractive index for a fibre V= Modes in a MM Step Index Fibre yIn a multimode step index fibre, a finite number of guided modes propagate. Number of modes is dependent on: ƒ Wavelength λ, Core refractive index n1 ƒ Relative refractive index difference ∆, Core radius a yNumber of propagating modes (M) is normally expressed in terms of the normalised frequency V for the fibre: n1 - n2 n1 2π π λ a.n1 2∆ ∆ M= V 2 2 Problem: A step index fibre with a core diameter of 80 µm has a relative refractive index difference of 1.5%, a core refractive index of 1.48 and operates at 850 nm. Show (a) that the normalised frequency for the fibre is 75.8 and (b) that the number of modes is 2873 Influence of Core Size and Wavelength yAs the core diameter increases and with it the normalised frequency, the number of modes increases with a square law dependency on core size yAs the wavelength increases the number of modes decreases 850 nm 1320 nm Graded Index Fibre Cladding Diameter 0 Graded Index Fibre Propagation in a Graded Index Fibre N2 N1 Cladding Core Diameter Core Parabolic variation in refractive index yAn expanded ray diagram for a graded index fibre, showing a discrete number yTypical core diameter for this fibre type: 50 to 120 µm of refractive index changes n1 to n6 for the fibre axis to the cladding. yDifferent refractive index profiles have developed yResult is a gradual change in the direction of the ray, rather than the sharp change which occurs in a step index fibre Propagation in a Graded Index Fibre Graded Index Fibre Profiles The index variation n(r) in a graded index fibre may be expressed as a function of the distance (r) Cladding from the fibre axis Fibre Axis b a Core n(r) = ∆ (r/a)) n1 (1-2∆ α for r < a (core) Light ray (a) and (b) are refracted progressively within the fibre. Notice that light ray (a) follows a longer path within the fibre than light ray (b) n(r) = n1 (1-2∆ ∆) = n2 for r > a (cladding) yMeridional (axial) rays follow curved paths in the fibre as shown yBenefits of using graded index design are considered later Most common value of the profile parameter α is 2, a so called parabolic profile. An infinite profile Refractive index profiles for Graded Index fibres parameter implies a step index fibre Modes in a Graded Index Fibre Calculating the number of modes in a graded index fibre is very involved As an approximation it can be shown that the number of modes is dependent on the normalised frequency V and on the profile parameter α. That is M= where ∆, is again given by: α α+2 ∆= V 2 2 n1 - n2 n1 if ∆ is << 1 Exercise For the most common value of α show that for fibres with similar relative refractive indices, core radii and operating wavelengths, the number of modes propagating in a step index fibre is twice that in a graded index fibre Singlemode Fibre Refractive Index Profiles for SM Fibres Singlemode Optical Fibre Multimode graded index Multimode step index Cladding Small Core 0 N2 N1 Cladding Diameter Cladding Small Core Diameter Refractive index Core Conventional singlemode fibre (so called matched cladding) Depressed cladding singlemode fibre (less susceptible to bend loss) Up-and-down profile singlemode fibre (used in dispersion flattened fibre) also called multicladding fibre Triangular profile singlemode fibre (used in dispersion shifted fibre) profile Energy Distribution in a Singlemode Fibre Normalised Frequency for SM Fibres ySinglemode fibre exhibits a very large bandwidth and has thus become the fibre of choice in most high speed communications systems. yThe amplitude distribution of the optical energy in a singlemode fibre mode is not uniform, nor is it confined only to the core ySinglemode operation is best considered with the aid of the fibre normalised frequency V: yIn multimode fibres if we assume a mode model instead of ray diagram approach then some small percentage of the energy is contained within the cladding close to the core, but typically < 1% so the ray model is still a valid view V= 2π π a . NA λ yRay diagram model does not work for singlemode fibre 7-9 µm > 50 µm ySingle mode operation takes place where V is less than the so-called cutoff value of Vc = 2.405. yThe single mode is the lowest order mode that the waveguide will support, referred to as the HE11 mode. This mode cuts off at V=0. Core Core Cladding Cladding yAs will be explained practical V values are normally between about 2 to 2.4 ySinglemode operation is achieved by altering the fibre radius, NA or the wavelength in use so that V lies in the range above. Multimode energy distribution is confined to the core Singlemode energy distribution peaks in the centre of the core (Darker shading = higher energy) Mode Field Diameter and Spot Size (II) Mode Field Diameter and Spot Size (I) yMode field diameter (MFD) is an important property of SM fibres. yThe amplitude distribution of the HE11 mode in the transverse plane is not uniform, but is approximately gaussian in shape, as shown below Fibre centre The MFD is defined as the width of the amplitude distribution at a level 1/e (37%) from the peak or for power 13.5%from the peak - 3/2 = 0.65 + 1.619V yFor V < 2 the spot size is significantly larger than the core size. yFor V < 2 the beam is partially contained within the cladding and loss increases yFor this reason V should be between about 2 and 2.4 The spot size is the mode field radius w. Its value relative to core radius is given by the expression: w yAs the V value approaches 2.4 the spot size approaches the fibre radius. yMFD or spot size is frequently specified as well as core radius or diameter for the fibre Normalised spot size as a function of the fibre V value -6 + 2.879V a Cutoff Wavelength Singlemode operation only takes place above a theoretical cutoff wavelength λc where V < Vc = 2.405 λc = 2π π Vc a NA In practice the theoretical cutoff wavelength is difficult to measure. An alternative is EIA (Electronics Industry Association of America) cutoff wavelength, which states that the cutoff wavelength is: The wavelength at which the power in the HE21 mode is 0.1 dB of the power in the HE11 (fundamental mode) SM Fibre Summary and Problem yCore size is a useful parameter for multimode fibres, but is not so useful for SM fibres. yTelecommunications systems are normally designed to work close to the cutoff wavelength for good power confinement (small spot size), but not close enough to cutoff so that significant power is carried in higher modes. Exercise A singlemode fibre has a core refractive index of 1.465 and a cladding refractive index of 1.46. What is the maximum core size if the fibre is to support only one mode at 1300 nm? Answer: core radius 4.11 microns, 8.23 microns core diameter. If the wavelength is increased to 1550 nm what is the new fibre V value, the spot size and the MFD? Answer: V = 2.02, Spot size 5.18 microns, The EIA cutoff wavelength can be 100 nm less than the theoretical cutoff wavelength MFD 10.4 microns