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Lecture 4: Signal Propagation in Fiber 朱祖勍1

Optical Communications and Networking

朱祖勍

Sept. 25, 2017


Nonlinear Effects

The assumption of linearity may not always be valid.

Nonlinear effects are all related to the power ofoptical signals (EM waves).

Nonlinear interaction depends on the interactionlength and the cross-sectional area of the fiber.

Longer interaction length => larger nonlinear effect

Smaller cross-sectional area => higher light intensity => largernonlinear effect


Nonlinear Effects

As the optical signal propagates along the fiber, itspower decreases due to fiber loss.

Most of the nonlinear effects occur early in the fiberand diminish as the signal propagates.

Two categories of nonlinear effectsDue to the interaction of light waves with phonons (molecularvibrations) in silica.

Due to the dependence of the refractive index on the intensity of theoptical signal.


Nonlinear Scattering Effects

Interactions of light waves with phonons (molecularvibrations) in the silica medium, i.e., scattering

Energy transfer from photons (光子) to phonons (声子)

In scattering, energy gets transferred from one lightwave to another at a longer wavelength, and the lostenergy 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.

Pump

Stokes

Stokes

molecular


Nonlinear Scattering Effects

Stimulated Brillouin Scattering (SBS)Stokes and pump waves propagate in opposite directions

Cause distortion within a single wavelength channel (~20 MHz linewidth)

Stimulated Raman Scattering (SRS)Energy transfer from shorter-wavelength signals to a longer-wavelength signals

Cause distortion in multiple wavelength channels, broadband effect

Bi-directional distortions.


Nonlinear Effects

Fiber refractive index n is a function of the intensityI of the optical signal, i.e., n(ω, I).In the presence of nonlinearities, the dielectricpolarization in the fiber: P(r, t) = PL(r, t) + PNL(r, t).

PL(r, t) is the linear dielectric polarization.PNL(r, t) is the nonlinear dielectric polarization.

PNL(r, t) = ε0χ(3)E3(r, t), χ(3) is the third-ordernonlinear susceptibility and is a constant.The nonlinear dielectric polarization causes therefractive index to become intensity dependent.


Self-Phase Modulation

Generally, nonlinear dielectric polarization generates newfrequency component.Chromatic dispersion leads to “phase mismatch” between thenew frequency component generated at location z and thosegenerated at other locations.Therefore, the new frequency component is negligible.

New Frequency Component


Phase-Mismatching

Fiber nonlinear effects get reduced when there is phase mismatch.The pulses, which were temporally coincident, cease to be so afterpropagating for some distance and cannot interact further.Chromatic dispersion is not a bad thing in this case! (~2 ps/nm/kmcan be helpful)


Self-Phase ModulationBy neglecting the new frequency component, we have

From the wave equations, we can solve and obtain β0

Because of SPM, the phase of the electric field contains aterm that is proportional to the intensity of the electric field.Because of the pulse’ temporal shape, it does not have aconstant intensity. Thus, the phase shifts on different parts ofthe pulse are different.Thus, SPM causes chirping of the pulses.


Cross-Phase Modulation

In WDM systems, the intensity-dependent nonlinear effectsare enhanced since the combined signal from all thechannels can be quite intense.

The intensity-dependent phase shift induced by SPM alone isenhanced because of the intensities of the signals in theother channels. This effect is Cross-Phase Modulation (CPM).

Consider a WDM system with two channels with fields E1 andE2:

SPM CPM



In WDM systems, the intensity-dependent nonlinear effectsare enhanced since the combined signal from all thechannels can be quite intense.

The intensity-dependent phase shift induced by SPM alone isenhanced because of the intensities of the signals in theother channels. This effect is Cross-Phase Modulation (CPM).

Consider a WDM system with two channels with fields E1 andE2:

SPM CPM



In practice, the effect of CPM can be significantly reduced byincreasing the wavelength spacing to 100 GHz.

Because of chromatic dispersion, the propagation constantsof the channels would then be sufficiently different such thatthe phase-matching condition is eliminated.

In general, nonlinear effects are weak and depend on longinteraction lengths to build up to significant levels, so creatingphase-mismatching is an effective method to over comenonlinearities.


Four-Wave Mixing

New Waves

Three adjacent wavelength channels, fi, fj and fk, interact to produce afourth frequency, fFWM, where fFWM = fi + fj - fk, known as four-wave mixing.

Lecture 5: Passive Components 朱祖勍1

Optical Communications and Networking

朱祖勍

Sept. 25, 2017


Optical Components

Optical components are fundamental buildingblocks for the engineering of optical communicationsystems.

Understanding their operational principles isessential to understand the operation of opticalnetworks.

Two categories of optical componentsPassive: components that are incapable of providing power gain.

Active: components that are capable of providing power gain.


Passive Components

Optical passive components: components thatcannot generate photons (optical power gain).

Couplers

Isolators and Circulators

Filters

Wavelength Multiplexers

…


Optical Coupler

An optical coupler is used to combine and splitsignals in an optical network.

A 2 x 2 coupler consists of two input ports and twooutput ports.

The most commonly used couplers are made byfusing two fiber together in the middle.

A coupler can be designed to be either wavelengthselective or wavelength independent.


Optical Fiber Coupler



l = Coupling Length

κ = Coupling Coefficient

Input Ports Output Ports



l = Coupling Length

Power Transfer Function:

Light Splitting



l = Coupling Length

Light Combining

Conservation of energy: the total energy of input light wavesequals to that of the output waves, if we assume that thecoupler is lossless.

Lossless combining is impossible, and we cannot design afiber coupler with three ports where the power input at two ofthe ports is completely delivered to the third port.


3-dB Optical Fiber Coupler

Bi-directional device1:2 Splitter2:1 Combiner, 3 dB

Loss in Theory


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 waveguideUseful for Optical Integration


Multimode Interface (MMI) Coupler


Optical Isolator

Reciprocal devices: the devices work exactly the same wayif their inputs and outputs are reversed.

Non-reciprocal device: the devices that are directional.

Isolators: allow signal transmission in one direction but blockall 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:


Optical Isolator

An isolator has two key parameters, insertion loss andisolation.

Insertion loss: loss in the allowed direction, should be assmall as possible, i.e., 1 dB.

Isolation: loss in the non-allowed direction, should be aslarge 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


Review of Polarization

The state of polarization (SOP) of light propagating in anSMF refers to the orientation of its electric field vector.

At any time, the electric field vector can be expressed as alinear combination of two orthogonal linear SOPs.


Polarizer and Faraday Rotator

Polarizer: passes only light in a linear SOP and blocks lightin the orthogonal SOP.

Faraday rotator (quarter wave plate): rotates the light’s SOPclockwise, by π/4, regardless of the propagation direction.

PolarizerFaraday Rotator


Operational Principle of Optical Isolators

Light from left to right can pass through, since its SOP alignswith the SOP permitted by the right polarizer.

Light from right to left is blocked, since its SOP is orthogonalto the SOP permitted by the left polarizer.


Polarization-Independent Isolator

Birefringent beam displacer (spatial walk-off polarizer): splits lightinto two orthogonal SOP components.Half-wave plate: rotates the SOP by π/4 clockwise for signalsfrom left to right, and by π/4 counter-clockwise for signals fromright to left.


Optical Circulator

A circulator is similar to an isolator, except that it has more thantwo ports.A circulator can be built with multiple isolators.


Optical Circulator

1

2

3

An optical circulator can be used to distinguish the lightpropagating in different directions.


Wavelength Selection Technologies

Optical filters: select wavelength channels to pass throughand reject the rest. The rejected wavelengths may also beobtained.

Wavelength multiplexer: combines signals at differentwavelengths on its input ports onto a common output port.

Wavelength de-multiplexer: performs the opposite functionof multiplexer.

Wavelength multiplexers and de-multiplexers are used inWDM terminals, wavelength crossconnects, and wavelengthadd/drop multiplexers.


Multiplexers and Filters

Wavelength Filter

Wavelength Multiplexer


Wavelength Cross-Connect

Wavelength Cross-Connect (WXC): routes signals from aninput port to an output port based on the wavelength.

A static WXC can be realized with wavelength multiplexerand de-multiplexers. Its cross-connect pattern is fixed at thetime of the device is made.


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 frequencydomain should be sharp to reduce the crosstalk fromadjacent wavelength channels.

The filters should be low-costFabricate them using integrated-optic waveguide technology.

Realize them with all-fiber devices.


Cascade Filters in WDM System

Pass-band becomes narrower

Misalignment in the frequency domaincan kill signal.

Cascade 4 Times

Original Filter’s Frequency Response

OverallFrequency Response


Gratings

Device whose operation involves interferenceamong optical signals originating from the samesource but with different phase shifts.

Reflection Grating Transmission Grating


Diffraction Gratings

Multiple narrow slits (缝) are spaced equally apart on thegrating plane.

Light transmitted through each slits spreads out in all directionsdue to diffraction.

The constructive interference at a wavelength occurs amongthe light beams whose incidence angle and diffraction anglefollows the grating equation: d[sin(θ)-sin(ϕ)] = mλ.


Bragg Gratings

Bragg grating: periodic perturbation in the propagatingmedium.

The perturbation is usually a periodic variation of therefractive index of the medium.

Bragg grating is widely used in optical communications.

Bragg grating causes the reflection of the signal light due torefractive index difference, i.e., light energy is coupled fromone direction to another.


Bragg Gratings

For two waves propagating in opposite directions withpropagation constants β0 and β1, energy is coupled from oneto another if the Bragg phase-matching condition is satisfied:| β0 - β1| = 2π/Λ, where Λ is the period of the grating.

Since β0 = 2πneff/λ0, the optical signal is reflected if itswavelength satisfies λ0 = 2neff Λ, and the others pass through.


Fiber Bragg Grating

Fiber Bragg gratings (FBGs) are attractive devices due tolow-loss, ease of coupling with other fibers, polarization-insensitive …

FBGs can be made by using the photosensitivity of opticalfibers.


Wavelength Add/Drop with Fiber Bragg Gratings

Single-channel add/drop

Multiple-channel add/drop


Fabry Perot Filter

A Fabry-Perot filter consists of the cavity formed by two highlyreflective mirrors placed parallel to each other.

For an optical signal at λ, if the cavity length is l = mλ/2, all thelight waves transmitted through the right mirror add in phase.

If a wavelength λ can satisfy l = mλ/2, it is a resonantwavelength.


Fabry-Perot Filter

A is the absorption loss of each mirror, R is the reflectivity ofeach mirror, n is the refractive index of the cavity, and l is thecavity length.

The power transfer function of the Fabry-Perot filter:


Fabry Perot Filter

Free spectral range (FSR): the spectral range between twosuccessive passbands of the filter.

Full-width at half of maximum (FWHM): 3-dB bandwidth.


All-Optical Clock Recovery

Optical RZ FPF Optical clockF{

·}

T0

f0f0

F-1{·

}

SOA

All-Optical Clock Recovery

FPF output (200 ps/div)

FPF+SOA output (200 ps/div)

RF spectra of the recovered clocks

7 dB


Mach-Zehnder Interferometer

A Mach-Zehnder interferometer (MZI) is an interferometricdevice that makes use of two interfering paths of differentlengths.

Mach-Zehnder interferometers are typically constructed withtwo 3-dB couplers interconnected through two paths ofdifferent lengths.


Multi-Stage Mach-ZehnderInterferometer

MZI(ΔL)

MZI(2ΔL)

MZI(4ΔL)

MZI(8ΔL)

Stage 1

Stage 2

Stage 3

Stage 4

Overall

Frequency Response


Wavelength Multiplexer/De-Multiplexer with MZI

An MZI can be used as a 1 x 2 de-multiplexer.

Provide two wavelength channels λ1 and λ2 to makeT11(λ1) = 1 and T12(λ2) = 1, then for WDM signalwith λ1 and λ2 going into input 1, λ1 will be deliver tooutput 1, and λ2 will be deliver to output 2.

The 1 x 2 de-multiplexer is a fundamental buildingblock of More complicated de-multiplexers.


Mach-Zehnder Interferometer for O/E Modulation

Broadband Electrode

Broadband Electrode

Optical Waveguide

Data Input Termination

Light Input Light Output


Mach-Zehnder Interferometer for O/E Modulation


Arrayed Waveguide Grating

An Arrayed Waveguide Grating (AWG) is a generalizationof the Mach-Zehnder Interferometer.

It consists of two multiport couplers interconnected by anarray of waveguides.

The AWG is a device where several copies of the samesignal, 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.


Arrayed Waveguide Grating


Wavelength Cross-Connect with AWG

8 x 8 Arrayed Waveguide Grating

λ1λ2λ3λ4λ5λ6λ7λ8

12345

678

12345

678


Wavelength Cross-Connect with AWG



WN X WNWavelength

Router(AWGR)

T_WC

T_WC

T_WC

T_WC

1

W

2

…

T_WC

T_WC

T_WC

T_WC

1

W

2

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T_WC

T_WC

T_WC

1

W

2

…

1

2

…

N

F_WC & LR

F_WC & LR

F_WC & LR

F_WC & LR

12

…W

F_WC & LR

F_WC & LR

F_WC & LR

F_WC & LR

12

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W

F_WC & LR

F_WC & LR

F_WC & LR

F_WC & LR

12

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1

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N

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