Optical Fibres - Dispersion Part 1

Transcription

1 ECE 455 Lecture 05 1 Otical Fibres - Disersion Part 1 Stavros Iezekiel Deartment of Electrical and Comuter Engineering University of Cyrus HMY 445 Lecture 05 Fall Semester 016

2 ECE 455 Lecture 05 Otical ulse This is distorted as it roagates along a fibre Disersive medium, e.g. otical fibre z Direction of roagation DISPERSION WHAT WE KNOW SO FAR

3 ECE 455 Lecture 05 3 From Lecture 0: The signal travelling through an otical fibre can be degraded due to: Attenuation (leads to loss of ower) Nonlinearity (we have not discussed this yet) and Disersion leads to ulse sreading. Pulses become wider as they cover more distance in the fibre, for examle: Pulses overla to cause a bit error Bit stream at fibre Bit stream inut at fibre outut T b t t Rule of thumb B T L L 4σ L σ rms ulse sread er distance Units: ns/km

4 ECE 455 Lecture 05 4 From Lecture 04: Main tyes of fibre and refractive index rofile Note: Standard single mode fibre is ste-index

5 ECE 455 Lecture 05 5 Silica fibres Single-mode (Ste index) Multimode (Ste index) Do not have modal disersion (because they are single mode) Exhibit modal disersion (also called intermodal disersion) This does not mean that they have no disersion at all. From Lecture 04: Main tyes of fibre and modal disersion Multimode (Graded index) Minimises modal disersion

6 ECE 455 Lecture 05 6 htt://fobasics.blogsot.com.cy/?viewclassic Ste-index multimode fibres suffer from modal disersion because the different modes (rays of light) travel different distances in covering the length of the fibre. Note: the different colours are used simly to show different ray aths. A urely monochromatic source will still lead to modal disersion. δτ L n c 1 n1 n n ( NA) c n From Question Sheet 3: Modal disersion (ns/km) considering simle ray analysis and looking at difference between shortest and longest (meridional) ray aths.

7 ECE 455 Lecture 05 7 In this lecture we will start to consider other tyes of disersion: Disersion Modal Disersion Also called: Intermodal Disersion Multimode Disersion Occurs in: Multimode fibres NOT in single-mode Chromatic Disersion Also called: Intramodal Disersion Occurs in: single-mode and multimode fibres Polarization-mode Disersion (PMD) Mostly a roblem for single-mode fibres that are comensated for chromatic disersion, and at long distances Material Disersion Due to nonlinear wavelength deendence of refractive index with wavelength Waveguide Disersion Due to light roagating in cladding of fibre, can be engineered with different refractive index rofiles

8 ECE 455 Lecture 05 8 PHYSICAL CAUSES OF DISPERSION

9 ECE 455 Lecture 05 9 Modal disersion in a few words There must be more than one mode for this tye of disersion Inut light is launched into a multimode fibre, exciting multile modes of roagation. Because the core diameter is sufficiently large, we can use ray otics to model the roagation. Different modes have the same seed (strictly seaking the same grou velocity), but they travel different distances relative to fibre length. This leads to different arrival times at the outut and thus ulse sreading. A graded index rofile hels to reduce modal disersion.

10 ECE 455 Lecture Chromatic disersion in a few words Also called intramodal within a mode. Essentially occurs due to the light being launched into the fibre being having a sread of wavelengths (i.e. colours, hence the name chromatic disersion). Has two comonents: Material disersion (due to refractive index deendency on wavelength) Waveguide disersion Occurs in both multimode and single-mode fibres, but we neglect it in multimode fibres because their intermodal disersion is larger. But we cannot neglect it in single-mode fibres.

11 ECE 455 Lecture Chromatic disersion in a few words material disersion Otical sources (even lasers) are not urely monochromatic, but instead they have a sectral width if we look at their otical sectrum Hence different wavelengths (or different colours, hence the name chromatic) will be resent in the inut ulse. IN t Silica has a nonlinear variation of refractive index with wavelength v g ( λ ) ( λ ) v ( ) v < g 1 g λ Hence different wavelengths travel at different grou velocities OUT Leading to ulse sreading t

12 ECE 455 Lecture 05 1 Chromatic disersion in a few words waveguide disersion Because of the small core diameter (tyically 8 μm) relative to the wavelength of the light, light launched into a single-mode fibre actually travels with a mode field diameter that is larger than the core diameter. Hence art of the otical ower is couled into the cladding, which has a lower refractive index than the core, leading to a higher velocity. The mode field diameter increases with wavelength, leading to more ower being couled into the cladding and thus a higher overall grou velocity. Material and waveguide disersion combine to give overall chromatic disersion

13 ECE 455 Lecture Polarisation mode disersion (PMD) in a few words Light can travel in two orthogonal states of olarisation; if these see different values of refractive index (due to birefringence), then ulse sreading occurs: Birefringence can be caused either by material or waveguide effects. Waveguide PMD is essentially due to manufacturing variations leading to nonconcentric cores, ellitical cores or ellitical fibre:

14 ECE 455 Lecture Comaring chromatic & modal disersion, single and multimode fibres Chromatic (intramodal) disersion also exists in multimode fibres, but for this tye of fibre the biggest cause of disersion is modal disersion. - For multimode fibres, we usually ignore chromatic disersion when we calculate the total disersion. For chromatic disersion - Material disersion makes a larger contribution comared to waveguide disersion. Multimode fibres Modal disersion Chromatic (intramodal) Caused by: Material disersion Waveguide disersion Single-mode fibres Multimode fibres have worse disersion erformance comared to single mode.

15 ECE 455 Lecture Otical fibre U. of Washington z If we have a ulse of light which is not monochromatic (it contains a grou of wavelengths), then we will have disersion: CHROMATIC DISPERSION

16 ECE 455 Lecture n n 1 O 1 n In single-mode fibres, there is no intermodal disersion (because there is only one mode of roagation). However, we have chromatic (intramodal) disersion n Material disersion Waveguide disersion Due to nonlinear relationshi between n andλ Chromatic disersion Disersion due to fact that grou velocity changes with wavelength Due to refractive index rofile of the fibre. Changes with λ.

17 ECE 455 Lecture Disersion for a standard single mode fibre (silica) Disersion is minimised at 1310 nm. Note: unit is s/(nm.km) But disersion is non-zero at 1550 nm, which is the wavelength of minimum attenuation.

18 ECE 455 Lecture We begin by looking at the contribution of material disersion. This is caused because of the finite sectral width of otical sources and the nonlinear deendence of refractive index with wavelength. This results in grou velocity disersion, so we need to know something about grou velocity.

19 ECE 455 Lecture PHASE VELOCITY/GROUP VELOCITY

20 ECE 455 Lecture 05 0 Grou and hase velocity All otical sources (including lasers) have a finite sectral width: Intensity (arbitrary units) λ: sectral width, FWHM Peak wavelength λ 0 Each wavelength will see a different value of refractive index, and so travel at different seeds: n λ The refractive index varies nonlinearly with wavelength λ

21 ECE 455 Lecture 05 1 Although we mainly secify wavelength rather than frequency, it will be more convenient to use frequency for this discussion. We will also consider just two, very closely saced frequencies within the grou: Intensity (arbitrary units) ω 0 ω ω 1 ω δω ω -ω 1

22 ECE 455 Lecture 05 At any given wavelength, we can consider the light to be an electromagnetic wave whose electric field is a sinusoidal travelling wave (in the + z direction): E( z, t) E0 cos ( kz ωt) (1) k π λ ω ω π v ( fλ) T k () (3) (4) hase constant angular frequency hase velocity π π π k n λ λ / n λ 0 0 nk 0 k ω v ω c / n nk 0 k free 0 sace hase constant

23 ECE 455 Lecture 05 3 Transverse electromagnetic wave x z

24 ECE 455 Lecture 05 4 Hence if we take the simlified icture of assuming that our otical source emits two closely saced frequencies ω 1 andω, the corresonding waves are: E 1 E0 t cos ( k1z ω1 ) E E0 cos ( kz ωt) The suerosition (addition) of these two waves gives the total waveform as: E T [ ( k z ω t) + cos ( k z ω )] E0 cos 1 1 t (5) Total waveform Suerosition of two waves

25 ECE 455 Lecture 05 5 Destructive Interference Constructive interference z E E cos ( k1z ω1 ) 0 t cos ( k1z ω1 ) 0 t

26 ECE 455 Lecture cosα + cosβ cos ( α β ) cos ( α + 1 β ) E T cos ( k k ) z ( ω ω ) t ( k + k ) z ( ω ω ) 1 1+ cos 1 1 E0 t (6) ~ E0 k g ω g E T E 0 cos cos [ 1( ) 1( ) ] k1 k z ω1 ω t [ 1( k k ) 1 + z ( ω + ω ) t] 1 1 k ω

27 ECE 455 Lecture 05 7 E T [ k z ω t] [ k z ω t] ~ E cos cos 0 g g (7) If the frequencies are closely saced, then: 1 ω 1 ω ω ω ( ω ω ) 1+ ω ( ω ω ) ω 1 ω << g 1 ω >> ω g

28 ECE 455 Lecture 05 8 We can think of the resultant electric field E T as an amlitude-modulated wave: E T [ k z ω t] [ k z ω t] ~ E cos cos 0 g g ENVELOPE Modulation frequency ω g CARRIER Carrier frequency ω E T Normalised field t Suerosition of the two waves is equivalent to amlitude modulation (DSB-Suressed carrier) -1 Time

29 ECE 455 Lecture 05 9 [ ] [ ] t z k t z k E E g g T ω ω cos cos ~ 0 ENVELOPE CARRIER Velocity of carrier is: k k k k v ω ω ω ω Phase velocity (8)

30 ECE 455 Lecture E T [ k z ω t] [ k z ω t] ~ E cos cos 0 g g ENVELOPE CARRIER Velocity of enveloe is: v g ω k g g ω1 ω k k 1 dω dk Grou velocity (9)

31 ECE 455 Lecture The signal roagates at the grou velocity v g. N.B. The enveloe does not exist as a hysical artefact; it reresents the maximum excursion of the wave amlitude. 1 v g Normalised field v -1 Time

32 ECE 455 Lecture 05 3 From (8): ω kv and substituting into (9): d vg ω v + dk k dv dk (10) v v g + k dλ dv dk dλ Now, k π/λ, hence: dk dλ π λ k λ v g v λ d dv λ (11)

33 ECE 455 Lecture If the hase and grou velocities are equal, then the enveloe will travel at the same seed as the carrier wave, and there will be no disersion. From equation (11), this imlies that the hase velocity should not deend on wavelength if we are to achieve disersion-less transmission. v g v no disersion v g v disersion

34 ECE 455 Lecture The lot between ω and k is known as the disersion relation. From (9), the gradient of this curve will yield the grou velocity: ω ω x v ω x k x v g d ω dk k k x k k x

35 ECE 455 Lecture ω v g v In normal disersion, the grou velocity is less than the hase velocity. v g < v k normal disersion In anomalous disersion, the grou velocity exceeds the hase velocity. ω v g > v anomalous v g v disersion htt:// k

36 ECE 455 Lecture Animation 01