Optical Communications and Networking Sept. 25, 2017 Lecture 4: Signal Propagation in Fiber 1
Nonlinear Effects The assumption of linearity may not always be valid. Nonlinear effects are all related to the power of optical signals (EM waves). Nonlinear interaction depends on the interaction length and the cross-sectional area of the fiber. Longer interaction length => larger nonlinear effect Smaller cross-sectional area => higher light intensity => larger nonlinear effect Lecture 4: Signal Propagation in Fiber 2
Nonlinear Effects As the optical signal propagates along the fiber, its power decreases due to fiber loss. Most of the nonlinear effects occur early in the fiber and diminish as the signal propagates. Two categories of nonlinear effects Due to the interaction of light waves with phonons (molecular vibrations) in silica. Due to the dependence of the refractive index on the intensity of the optical signal. Lecture 4: Signal Propagation in Fiber 3
Nonlinear Scattering Effects Interactions of light waves with phonons (molecular vibrations) in the silica medium, i.e., scattering Energy transfer from photons ( 光子 ) to phonons ( 声子 ) In scattering, energy gets transferred from one light wave to another at a longer wavelength, and the lost energy is absorbed by the phonons in the fiber. Pump wave: the first light wave at shorter wavelength. Stokes wave: the second light wave at longer wavelength. Stokes Pump molecular Lecture 4: Signal Propagation in Fiber Stokes 4
Nonlinear Scattering Effects Stimulated Brillouin Scattering (SBS) Stokes and pump waves propagate in opposite directions Cause distortion within a single wavelength channel (~20 MHz line width) Stimulated Raman Scattering (SRS) Energy transfer from shorter-wavelength signals to a longerwavelength signals Cause distortion in multiple wavelength channels, broadband effect Bi-directional distortions. Lecture 4: Signal Propagation in Fiber 5
Nonlinear Effects Fiber refractive index n is a function of the intensity I of the optical signal, i.e., n(ω, I). In the presence of nonlinearities, the dielectric polarization in the fiber: P(r, t) = P L (r, t) + P NL (r, t). P L (r, t) is the linear dielectric polarization. P NL (r, t) is the nonlinear dielectric polarization. P NL (r, t) = ε 0 χ (3) E 3 (r, t), χ (3) is the third-order nonlinear susceptibility and is a constant. The nonlinear dielectric polarization causes the refractive index to become intensity dependent. Lecture 4: Signal Propagation in Fiber 6
Self-Phase Modulation New Frequency Component Generally, nonlinear dielectric polarization generates new frequency component. Chromatic dispersion leads to phase mismatch between the new frequency component generated at location z and those generated at other locations. Therefore, the new frequency component is negligible. Lecture 4: Signal Propagation in Fiber 7
Phase-Mismatching Fiber nonlinear effects get reduced when there is phase mismatch. The pulses, which were temporally coincident, cease to be so after propagating for some distance and cannot interact further. Chromatic dispersion is not a bad thing in this case! (~2 ps/nm/km can be helpful) Lecture 4: Signal Propagation in Fiber 8
Self-Phase Modulation By neglecting the new frequency component, we have From the wave equations, we can solve and obtain β 0 Because of SPM, the phase of the electric field contains a term that is proportional to the intensity of the electric field. Because of the pulse temporal shape, it does not have a constant intensity. Thus, the phase shifts on different parts of the pulse are different. Thus, SPM causes chirping of the pulses. Lecture 4: Signal Propagation in Fiber 9
Cross-Phase Modulation In WDM systems, the intensity-dependent nonlinear effects are enhanced since the combined signal from all the channels can be quite intense. The intensity-dependent phase shift induced by SPM alone is enhanced because of the intensities of the signals in the other channels. This effect is Cross-Phase Modulation (CPM). Consider a WDM system with two channels with fields E 1 and E 2 : Lecture 4: Signal Propagation in Fiber SPM CPM 10
Cross-Phase Modulation In WDM systems, the intensity-dependent nonlinear effects are enhanced since the combined signal from all the channels can be quite intense. The intensity-dependent phase shift induced by SPM alone is enhanced because of the intensities of the signals in the other channels. This effect is Cross-Phase Modulation (CPM). Consider a WDM system with two channels with fields E 1 and E 2 : Lecture 4: Signal Propagation in Fiber SPM CPM 11
Cross-Phase Modulation In practice, the effect of CPM can be significantly reduced by increasing the wavelength spacing to 100 GHz. Because of chromatic dispersion, the propagation constants of the channels would then be sufficiently different such that the phase-matching condition is eliminated. In general, nonlinear effects are weak and depend on long interaction lengths to build up to significant levels, so creating phase-mismatching is an effective method to over come nonlinearities. Lecture 4: Signal Propagation in Fiber 12
Four-Wave Mixing New Waves Three adjacent wavelength channels, f i, f j and f k, interact to produce a fourth frequency, f FWM, where f FWM = f i + f j - f k, known as four-wave mixing. Lecture 4: Signal Propagation in Fiber 13
Optical Communications and Networking Sept. 25, 2017 1
Optical Components Optical components are fundamental building blocks for the engineering of optical communication systems. Understanding their operational principles is essential to understand the operation of optical networks. Two categories of optical components Passive: components that are incapable of providing power gain. Active: components that are capable of providing power gain. 2
Passive Components Optical passive components: components that cannot generate photons (optical power gain). Couplers Isolators and Circulators Filters Wavelength Multiplexers 3
Optical Coupler An optical coupler is used to combine and split signals in an optical network. A 2 x 2 coupler consists of two input ports and two output ports. The most commonly used couplers are made by fusing two fiber together in the middle. A coupler can be designed to be either wavelength selective or wavelength independent. 4
Optical Fiber Coupler 5
Optical Fiber Coupler Input Ports Output Ports l = Coupling Length κ = Coupling Coefficient 6
Optical Fiber Coupler Light Splitting l = Coupling Length Power Transfer Function: 7
Optical Fiber Coupler Light Combining l = Coupling Length Conservation of energy: the total energy of input light waves equals to that of the output waves, if we assume that the coupler is lossless. Lossless combining is impossible, and we cannot design a fiber coupler with three ports where the power input at two of the ports is completely delivered to the third port. 8
3-dB Optical Fiber Coupler Bi-directional device 1:2 Splitter 2:1 Combiner, 3 db Loss in Theory 9
Multimode Interface (MMI) Coupler Single-Mode Region Multi-Mode Region Single-Mode Region Bi-directional device, based on substrate waveguides. Utilize mode splitting in Multi-Mode waveguide Useful for Optical Integration 10
Multimode Interface (MMI) Coupler 11
Optical Isolator Reciprocal devices: the devices work exactly the same way if their inputs and outputs are reversed. Non-reciprocal device: the devices that are directional. Isolators: allow signal transmission in one direction but block all transmission in the reversed direction, i.e., non-reciprocal. Isolators are used to prevent reflections. A B From A to B: From B to A: 12
Optical Isolator An isolator has two key parameters, insertion loss and isolation. Insertion loss: loss in the allowed direction, should be as small as possible, i.e., 1 db. Isolation: loss in the non-allowed direction, should be as large as possible, i.e., 40 ~ 50 db. Isolators operate with the assistance of polarization. A B From A to B: insertion loss From B to A: isolation 13
Review of Polarization The state of polarization (SOP) of light propagating in an SMF refers to the orientation of its electric field vector. At any time, the electric field vector can be expressed as a linear combination of two orthogonal linear SOPs. 14
Polarizer and Faraday Rotator Polarizer Faraday Rotator Polarizer: passes only light in a linear SOP and blocks light in the orthogonal SOP. Faraday rotator (quarter wave plate): rotates the light s SOP clockwise, by π/4, regardless of the propagation direction. 15
Operational Principle of Optical Isolators Light from left to right can pass through, since its SOP aligns with the SOP permitted by the right polarizer. Light from right to left is blocked, since its SOP is orthogonal to the SOP permitted by the left polarizer. 16
Polarization-Independent Isolator Birefringent beam displacer (spatial walk-off polarizer): splits light into two orthogonal SOP components. Half-wave plate: rotates the SOP by π/4 clockwise for signals from left to right, and by π/4 counter-clockwise for signals from right to left. 17
Optical Circulator A circulator is similar to an isolator, except that it has more than two ports. A circulator can be built with multiple isolators. 18
Optical Circulator 2 1 3 An optical circulator can be used to distinguish the light propagating in different directions. 19
Wavelength Selection Technologies Optical filters: select wavelength channels to pass through and reject the rest. The rejected wavelengths may also be obtained. Wavelength multiplexer: combines signals at different wavelengths on its input ports onto a common output port. Wavelength de-multiplexer: performs the opposite function of multiplexer. Wavelength multiplexers and de-multiplexers are used in WDM terminals, wavelength crossconnects, and wavelength add/drop multiplexers. 20
Multiplexers and Filters Wavelength Filter Wavelength Multiplexer 21
Wavelength Cross-Connect Wavelength Cross-Connect (WXC): routes signals from an input port to an output port based on the wavelength. A static WXC can be realized with wavelength multiplexer and de-multiplexers. Its cross-connect pattern is fixed at the time of the device is made. 22
Design Requirements on Optical Filters Good optical filters should have low insertion loss. The insertion loss should be independent of the SOP. The filters operation should be temperature insensitive. The filters should have very flat passbands. The passband s rising and falling edges in the frequency domain should be sharp to reduce the crosstalk from adjacent wavelength channels. The filters should be low-cost Fabricate them using integrated-optic waveguide technology. Realize them with all-fiber devices. 23
Cascade Filters in WDM System Pass-band becomes narrower Misalignment in the frequency domain can kill signal. Cascade 4 Times Original Filter s Frequency Response Overall Frequency Response 24
Gratings Device whose operation involves interference among optical signals originating from the same source but with different phase shifts. Reflection Grating Transmission Grating 25
Diffraction Gratings Multiple narrow slits ( 缝 ) are spaced equally apart on the grating plane. Light transmitted through each slits spreads out in all directions due to diffraction. The constructive interference at a wavelength occurs among the light beams whose incidence angle and diffraction angle follows the grating equation: d[sin(θ)-sin(ϕ)] = mλ. 26
Bragg Gratings Bragg grating: periodic perturbation in the propagating medium. The perturbation is usually a periodic variation of the refractive index of the medium. Bragg grating is widely used in optical communications. Bragg grating causes the reflection of the signal light due to refractive index difference, i.e., light energy is coupled from one direction to another. 27
Bragg Gratings For two waves propagating in opposite directions with propagation constants β 0 and β 1, energy is coupled from one to another if the Bragg phase-matching condition is satisfied: β 0 - β 1 = 2π/Λ, where Λ is the period of the grating. Since β 0 = 2πn eff /λ 0, the optical signal is reflected if its wavelength satisfies λ 0 = 2n eff Λ, and the others pass through. 28
Fiber Bragg Grating Fiber Bragg gratings (FBGs) are attractive devices due to low-loss, ease of coupling with other fibers, polarizationinsensitive FBGs can be made by using the photosensitivity of optical fibers. 29
Wavelength Add/Drop with Fiber Bragg Gratings Single-channel add/drop Multiple-channel add/drop 30
Fabry Perot Filter A Fabry-Perot filter consists of the cavity formed by two highly reflective mirrors placed parallel to each other. For an optical signal at λ, if the cavity length is l = mλ/2, all the light waves transmitted through the right mirror add in phase. If a wavelength λ can satisfy l = mλ/2, it is a resonant wavelength. 31
Fabry-Perot Filter A is the absorption loss of each mirror, R is the reflectivity of each mirror, n is the refractive index of the cavity, and l is the cavity length. The power transfer function of the Fabry-Perot filter: 32
Fabry Perot Filter Free spectral range (FSR): the spectral range between two successive passbands of the filter. Full-width at half of maximum (FWHM): 3-dB bandwidth. 33
All-Optical Clock Recovery T 0 SOA Optical RZ FPF Optical clock All-Optical Clock Recovery F{ } f 0 f 0 F -1 { } 7 db FPF output (200 ps/div) FPF+SOA output (200 ps/div) RF spectra of the recovered clocks 34
Mach-Zehnder Interferometer A Mach-Zehnder interferometer (MZI) is an interferometric device that makes use of two interfering paths of different lengths. Mach-Zehnder interferometers are typically constructed with two 3-dB couplers interconnected through two paths of different lengths. 35
Multi-Stage Mach-Zehnder Interferometer MZI (ΔL) MZI (2ΔL) MZI (4ΔL) MZI (8ΔL) Stage 1 Stage 2 Frequency Response Stage 3 Stage 4 Overall 36
Wavelength Multiplexer/De-Multiplexer with MZI An MZI can be used as a 1 x 2 de-multiplexer. Provide two wavelength channels λ 1 and λ 2 to make T 11 (λ 1 ) = 1 and T 12 (λ 2 ) = 1, then for WDM signal with λ 1 and λ 2 going into input 1, λ 1 will be deliver to output 1, and λ 2 will be deliver to output 2. The 1 x 2 de-multiplexer is a fundamental building block of More complicated de-multiplexers. 37
Mach-Zehnder Interferometer for O/E Modulation Optical Waveguide Broadband Electrode Light Input Broadband Electrode Light Output Data Input Termination 38
Mach-Zehnder Interferometer for O/E Modulation 39
Arrayed Waveguide Grating An Arrayed Waveguide Grating (AWG) is a generalization of the Mach-Zehnder Interferometer. It consists of two multiport couplers interconnected by an array of waveguides. The AWG is a device where several copies of the same signal, but shifted in different phases, are added together. Compared with an MZI chain, an AWG has lower loss, flatter passband, and is easier to fabricate. 40
Arrayed Waveguide Grating 41
Wavelength Cross-Connect with AWG 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 λ1 λ2 λ3 λ4 λ5 λ6 λ7 λ8 8 x 8 Arrayed Waveguide Grating 42
Wavelength Cross-Connect with AWG 43
Wavelength Cross-Connect 1 1 1 2 2 W 1 2 W 1 WN X WN Wavelength Router (AWGR) 2 W 1 2 W 1 1 2 N 2 W 2 W N 44
Wavelength Cross-Connect 1 1 1 2 2 W 1 2 W 1 WN X WN Wavelength Router (AWGR) 2 W 1 2 W 1 1 2 N 2 W 2 W N 45
Wavelength Cross-Connect 1 1 1 2 2 W 1 2 W 1 WN X WN Wavelength Router (AWGR) 2 W 1 2 W 1 1 2 N 2 W 2 W N 46