E&CE 477 Photonic Communications Systems & Devices

E&CE 477 Photonic Communications Systems & Devices
Winter 2006 Instructor: Hamed Majedi

Content 1- Overview of Photonic Communications
2- Optical Fiber: Waveguiding, Propagation Modes - Single Mode Fiber - Fiber Materials & Fabrication Procedures 3- Signal Degradation in Optical Fibers 4- Photonic Sources & Transmitters: LED & Laser Diodes - Single Mode Lasers, Modulation & Noise 5- Laser-Fiber Connections (Power Launching & Coupling) 6- Photodetectors 7- Digital Photonic Receivers & Digital Transmission systems 8- WDM & Photonic Networks

Lab & Computer Simulations
Lab sessions - Fiber Attenuation Measurement - Dispersion Measurement - Spectral Attenuation Measurements Computer Simulations using Photonic Transmission Design Suite 1.1 Lite 1- Bit error rate estimation of digital single channel fiber-optic link 2- Influence of fiber dispersion on the bit error rate 3- Fiber dispersion compensation by three different methods 4- Four channel WDM transmission by four wave mixing 5- Comparison of external vs. direct laser modulation for various bit rate 6- Two channel WDM add/drop multiplexer using fiber Bragg gratings & circulators.

Chapter 1 Overview of Photonic Communications

Optics Optics is an old subject involving the generation, propagation & detection of light. Three major developments are responsible for rejuvenation of optics & its application in modern technology: 1- Invention of Laser 2- Fabrication of low-loss optical Fiber 3- Development of Semiconductor Optical Device As a result, new disciplines have emerged & new terms describing them have come into use, such as: - Electro-Optics: is generally reserved for optical devices in which electrical effects play a role, such as lasers, electro-optic modulators & switches.

Photonics Optoelectronics: refers to devices & systems that are essentially electronics but involve lights, such as LED, liquid crystal displays & array photodetectors. Quantum Electronics: is used in connection with devices & systems that rely on the interaction of light with matter, such as lasers & nonlinear optical devices. Quantum Optics: Studies quantum & coherence properties of light. Lightwave Technology: describes systems & devices that are used in optical communication & signal processing. Photonics: in analogy with electronics, involves the control of photons in free space and matter.

Photonic Communications
Photonics reflects the importance of the photon nature of light. Photonics & electronics clearly overlap since electrons often control the flow of photons & conversely, photons control the flow of electrons. The scope of Photonics: 1- Generation of Light (coherent & incoherent) 2- Transmission of Light (through free space, fibers, imaging systems, waveguides, … ) 3- Processing of Light Signals (modulation, switching, amplification, frequency conversion, …) 4- Detection of Light (coherent & incoherent) Photonic Communications: describes the applications of photonic technology in communication devices & systems, such as transmitters, transmission media, receivers & signal processors.

Why Photonic Communications?
Extremely wide bandwidth: high carrier frequency ( a wavelength of nm corresponds to a center frequency of THz!) & consequently orders of magnitude increase in available transmission bandwidth & larger information capacity. Optical Fibers have small size & light weight. Optical Fibers are immune to electromagnetic interference (high voltage transmission lines, radar systems, power electronic systems, airborne systems, …) Lack of EMI cross talk between channels Availability of very low loss Fibers (0.25 to 0.3 dB/km), high performance active & passive photonic components such as tunable lasers, very sensitive photodetectors, couplers, filters, Low cost systems for data rates in excess of Gbit/s.

BW demands in communication systems
Type & applications Format Uncompressed Compressed Voice, digital telegraphy 4 kHz voice 64 kbps 16-32 kbps Audio 16-24 kHz kbps kbps (MPEG, MP3) Video conferencing or frames/s Mbps 64 kbps Mbps (H.261 coding) Data transfer, E-commerce,Video entertainment 1-10 Mbps Full-motion broadcast video frames/s 249 Mbps 2-6Mbps (MPEG-2) HDTV frames /s 1.6 Gbps 19-38 Mbps (MPEG-2)

Early application of fiber optic communication
Digital link consisting of time-division-multiplexing (TDM) of 64 kbps voice channels (early 1980). Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

SONET & SDH Standards SONET (Synchronous Optical NETwork) is the network standard used in north America & SDH (Synchronous Digital Hierarchy) is used in other parts of the world. These define a synchronous frame structure for sending multiplexed digital traffic over fiber optic trunk lines. The basic building block of SONET is called STS-1 (Synchronous Transport Signal) with Mbps data rate. Higher-rate SONET signals are obtained by byte-interleaving N STS-1 frames, which are scramble & converted to an Optical Carrier Level N (OC-N) signal. The basic building block of SDH is called STM-1 (Synchronous Transport Module) with Mbps data rate. Higher-rate SDH signals are achieved by synchronously multiplexing N different STM-1 to form STM-N signal.

SONET & SDH transmission rates
SONET level Electrical level Line rate (Mb/s) SDH equivalent OC-1 STS-1 51.84 - OC-3 STS-3 155.52 STM-1 OC-12 STS-12 622.08 STM-4 OC-24 STS-24 STM-8 OC-48 STS-48 STM-16 OC-96 STS-96 STM-32 OC-192 STS-192 STM-64 Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Evolution of fiber optic systems
1950s:Imaging applications in medicine & non-destructive testing, lighting 1960s:Research on lowering the fiber loss for telecom. applications. 1970s:Development of low loss fibers, semiconductor light sources & photodetectors 1980s:single mode fibers (OC-3 to OC-48) over repeater sapcings of 40 km. 1990s:Optical amplifiers (e.g. EDFA), WDM (wavelength division multiplexing) toward dense-WDM. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Operating range of 4 key components in the 3 different optical windows
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Major elements Of typical photonic comm link

Installation of Fiber optics

WDM Concept Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Chapter 2 Optical Fibers: Structures, Waveguiding & Fabrication

Theories of Optics Light is an electromagentic phenomenon described by the same theoretical principles that govern all forms of electromagnetic radiation. Maxwell’s equations are in the hurt of electromagnetic theory & is fully successful in providing treatment of light propagation. Electromagnetic optics provides the most complete treatment of light phenomena in the context of classical optics. Turning to phenomena involving the interaction of light & matter, such as emission & absorption of light, quantum theory provides the successful explanation for light-matter interaction. These phenomena are described by quantum electrodynamics which is the marriage of electromagnetic theory with quantum theory. For optical phenomena, this theory also referred to as quantum optics. This theory provides an explanation of virtually all optical phenomena.

In the context of classical optics, electromagentic radiation propagates in the form of two mutually coupled vector waves, an electric field-wave & magnetic field wave. It is possible to describe many optical phenomena such as diffraction, by scalar wave theory in which light is described by a single scalar wavefunction. This approximate theory is called scalar wave optics or simply wave optics. When light propagates through & around objects whose dimensions are much greater than the optical wavelength, the wave nature of light is not readily discerned, so that its behavior can be adequately described by rays obeying a set of geometrical rules. This theory is called ray optics. Ray optics is the limit of wave optics when the wavelength is very short. Quantum Optics Electromagnetic Optics Wave Optics Ray Optics

Engineering Model In engineering discipline, we should choose the appropriate & easiest physical theory that can handle our problems. Therefore, specially in this course we will use different optical theories to describe & analyze our problems. In this chapter we deal with optical transmission through fibers, and other optical waveguiding structures. Depending on the structure, we may use ray optics or electromagnetic optics, so we begin our discussion with a brief introduction to electromagnetic optics, ray optics & their fundamental connection, then having equipped with basic theories, we analyze the propagation of light in the optical fiber structures.

Electromagnetic Optics
Electromagnetic radiation propagates in the form of two mutually coupled vector waves, an electric field wave & a magnetic field wave. Both are vector functions of position & time. In a source-free, linear, homogeneous, isotropic & non-dispersive media, such as free space, these electric & magnetic fields satisfy the following partial differential equations, known as Maxwell’ equations: [2-1] [2-2] [2-3] [2-4]

In Maxwell’s equations, E is the electric field expressed in [V/m], H is the magnetic field expressed in [A/m]. The solution of Maxwell’s equations in free space, through the wave equation, can be easily obtained for monochromatic electromagnetic wave. All electric & magnetic fields are harmonic functions of time of the same frequency. Electric & magnetic fields are perpendicular to each other & both perpendicular to the direction of propagation, k, known as transverse wave (TEM). E, H & k form a set of orthogonal vectors.

Electromagnetic Plane wave in Free space
x z Direction of Propagation B y k An electromagnetic wave is a travelling wave which has time varying electric and magnetic fields which are perpendicular to each other and the direction of propagation, z. S.O.Kasap, optoelectronics and Photonics Principles and Practices, prentice hall, 2001

Linearly Polarized Electromagnetic Plane wave
[2-5] [2-6] Angular frequency [rad/m] [2-7] Wavenumber or wave propagation constant [1/m] Wavelength [m] intrinsic (wave) impedance [2-8] velocity of wave propagation [2-9]

A plane EM wave travelling along , has the same (or
z E x = o sin( w t–kz ) Propagation B k and have constant phase in this xy plane; a wavefront A plane EM wave travelling along , has the same (or y ) at any point in a given plane. All electric field vectors in a given plane are therefore in phase. The planes are of infinite extent in the directions. S.O.Kasap, optoelectronics and Photonics Principles and Practices, prentice hall, 2001

Wavelength & free space
Wavelength is the distance over which the phase changes by In vacuum (free space): [2-10] [2-11]

EM wave in Media Refractive index of a medium is defined as:
For non-magnetic media : [2-12] Relative magnetic permeability Relative electric permittivity [2-13]

Intensity & power flow of TEM wave
The poynting vector for TEM wave is parallel to the wavevector k so that the power flows along in a direction normal to the wavefront or parallel to k. The magnitude of the poynting vector is the intensity of TEM wave as follows: [2-14]

Connection between EM wave optics & Ray optics
According to wave or physical optics viewpoint, the EM waves radiated by a small optical source can be represented by a train of spherical wavefronts with the source at the center. A wavefront is defined a s the locus of all points in the wave train which exhibit the same phase. Far from source wavefronts tend to be in a plane form. Next page you will see different possible phase fronts for EM waves. When the wavelength of light is much smaller than the object, the wavefronts appear as straight lines to this object. In this case the light wave can be indicated by a light ray, which is drawn perpendicular to the phase front and parallel to the Poynting vector, which indicates the flow of energy. Thus, large scale optical effects such as reflection & refraction can be analyzed by simple geometrical process called ray tracing. This view of optics is referred to as ray optics or geometrical optics.

rays k Wave fronts r E (constant phase surfaces) z l P O
A perfect spherical wave A perfect plane wave A divergent beam (a) (b) (c) Examples of possible EM waves rays S.O.Kasap, optoelectronics and Photonics Principles and Practices, prentice hall, 2001

General form of linearly polarized plane waves
Any two orthogonal plane waves Can be combined into a linearly Polarized wave. Conversely, any arbitrary linearly polarized wave can be resolved into two independent Orthogonal plane waves that are in phase. [2-15] Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Elliptically Polarized plane waves
[2-16] Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Circularly polarized waves

Laws of Reflection & Refraction
Reflection law: angle of incidence=angle of reflection Snell’s law of refraction: [2-18] Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Total internal reflection, Critical angle
2 1 > Incident light Transmitted (refracted) light Reflected k t TIR Evanescent wave i r ( a ) b c Light wave travelling in a more dense medium strikes a less dense medium. Depending on the incidence angle with respect to , which is determined by the ratio of the refractive indices, the wave may be transmitted (refracted) or reflected. (a) (b) (c) and total internal reflection (TIR). Critical angle [2-19]

Phase shift due to TIR The totally reflected wave experiences a phase shift however which is given by: Where (p,N) refer to the electric field components parallel or normal to the plane of incidence respectively. [2-20]

Optical waveguiding by TIR: Dielectric Slab Waveguide
Propagation mechanism in an ideal step-index optical waveguide. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Launching optical rays to slab waveguide
[2-21] Maximum entrance angle, is found from the Snell’s relation written at the fiber end face. [2-22] Numerical aperture: [2-23] [2-24]

Optical rays transmission through dielectric slab waveguide
For TE-case, when electric waves are normal to the plane of incidence must be satisfied with following relationship: [2-25] Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Note Home work 2-1) Find an expression for ,considering that the electric field component of optical wave is parallel to the plane of incidence (TM-case). As you have seen, the polarization of light wave down the slab waveguide changes the condition of light transmission. Hence we should also consider the EM wave analysis of EM wave propagation through the dielectric slab waveguide. In the next slides, we will introduce the fundamental concepts of such a treatment, without going into mathematical detail. Basically we will show the result of solution to the Maxwell’s equations in different regions of slab waveguide & applying the boundary conditions for electric & magnetic fields at the surface of each slab. We will try to show the connection between EM wave and ray optics analyses.

EM analysis of Slab waveguide
For each particular angle, in which light ray can be faithfully transmitted along slab waveguide, we can obtain one possible propagating wave solution from a Maxwell’s equations or mode. The modes with electric field perpendicular to the plane of incidence (page) are called TE (Transverse Electric) and numbered as: Electric field distribution of these modes for 2D slab waveguide can be expressed as: wave transmission along slab waveguides, fibers & other type of optical waveguides can be fully described by time & z dependency of the mode: [2-26]

TE modes in slab waveguide
z y Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Modes in slab waveguide
The order of the mode is equal to the # of field zeros across the guide. The order of the mode is also related to the angle in which the ray congruence corresponding to this mode makes with the plane of the waveguide (or axis of the fiber). The steeper the angle, the higher the order of the mode. For higher order modes the fields are distributed more toward the edges of the guide and penetrate further into the cladding region. Radiation modes in fibers are not trapped in the core & guided by the fiber but they are still solutions of the Maxwell’ eqs. with the same boundary conditions. These infinite continuum of the modes results from the optical power that is outside the fiber acceptance angle being refracted out of the core. In addition to bound & refracted (radiation) modes, there are leaky modes in optical fiber. They are partially confined to the core & attenuated by continuously radiating this power out of the core as they traverse along the fiber (results from Tunneling effect which is quantum mechanical phenomenon.) A mode remains guided as long as

Optical Fibers: Modal Theory (Guided or Propagating modes) & Ray Optics Theory
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000 Step Index Fiber

Modal Theory of Step Index fiber
General expression of EM-wave in the circular fiber can be written as: Each of the characteristic solutions is called mth mode of the optical fiber. It is often sufficient to give the E-field of the mode. [2-27]

The modal field distribution, , and the mode propagation constant, are obtained from solving the Maxwell’s equations subject to the boundary conditions given by the cross sectional dimensions and the dielectric constants of the fiber. Most important characteristics of the EM transmission along the fiber are determined by the mode propagation constant, , which depends on the mode & in general varies with frequency or wavelength. This quantity is always between the plane propagation constant (wave number) of the core & the cladding media . [2-28]

At each frequency or wavelength, there exists only a finite number of guided or propagating modes that can carry light energy over a long distance along the fiber. Each of these modes can propagate in the fiber only if the frequency is above the cut-off frequency, , (or the source wavelength is smaller than the cut-off wavelength) obtained from cut-off condition that is: To minimize the signal distortion, the fiber is often operated in a single mode regime. In this regime only the lowest order mode (fundamental mode) can propagate in the fiber and all higher order modes are under cut-off condition (non-propagating). Multi-mode fibers are also extensively used for many applications. In these fibers many modes carry the optical signal collectively & simultaneously. [2-29]

Fundamental Mode Field Distribution
Mode field diameter Polarizations of fundamental mode Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Ray Optics Theory (Step-Index Fiber)
Skew rays Each particular guided mode in a fiber can be represented by a group of rays which Make the same angle with the axis of the fiber. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Different Structures of Optical Fiber

Mode designation in circular cylindrical waveguide (Optical Fiber)
The electric field vector lies in transverse plane. The magnetic field vector lies in transverse plane. TE component is larger than TM component. TM component is larger than TE component. y l= # of variation cycles or zeros in direction. m= # of variation cycles or zeros in r direction. r x z Linearly Polarized (LP) modes in weakly-guided fibers ( ) Fundamental Mode:

Two degenerate fundamental modes in Fibers (Horizontal & Vertical Modes)

Mode propagation constant as a function of frequency
Mode propagation constant, , is the most important transmission characteristic of an optical fiber, because the field distribution can be easily written in the form of eq. [2-27]. In order to find a mode propagation constant and cut-off frequencies of various modes of the optical fiber, first we have to calculate the normalized frequency, V, defined by: [2-30] a: radius of the core, is the optical free space wavelength, are the refractive indices of the core & cladding.

Plots of the propagation constant as a function of normalized frequency for a few of the lowest-order modes

Single mode Operation The cut-off wavelength or frequency for each mode is obtained from: Single mode operation is possible (Single mode fiber) when: [2-31] [2-32]

Single-Mode Fibers Example: A fiber with a radius of 4 micrometer and
has a normalized frequency of V=2.38 at a wavelength 1 micrometer. The fiber is single-mode for all wavelengths greater and equal to 1 micrometer. MFD (Mode Field Diameter): The electric field of the first fundamental mode can be written as: [2-33]

Birefringence in single-mode fibers
Because of asymmetries the refractive indices for the two degenerate modes (vertical & horizontal polarizations) are different. This difference is referred to as birefringence, : [2-34] Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Fiber Beat Length In general, a linearly polarized mode is a combination of both of the degenerate modes. As the modal wave travels along the fiber, the difference in the refractive indices would change the phase difference between these two components & thereby the state of the polarization of the mode. However after certain length referred to as fiber beat length, the modal wave will produce its original state of polarization. This length is simply given by: [2-35]

Multi-Mode Operation Total number of modes, M, supported by a multi-mode fiber is approximately (When V is large) given by: Power distribution in the core & the cladding: Another quantity of interest is the ratio of the mode power in the cladding, to the total optical power in the fiber, P, which at the wavelengths (or frequencies) far from the cut-off is given by: [2-36] [2-37]

Chapter 3 Signal Degradation in Optical Fibers

Signal Attenuation & Distortion in Optical Fibers
What are the loss or signal attenuation mechanism in a fiber? Why & to what degree do optical signals get distorted as they propagate down a fiber? Signal attenuation (fiber loss) largely determines the maximum repeaterless separation between optical transmitter & receiver. Signal distortion cause that optical pulses to broaden as they travel along a fiber, the overlap between neighboring pulses, creating errors in the receiver output, resulting in the limitation of information-carrying capacity of a fiber.

Attenuation (fiber loss)
Power loss along a fiber: The parameter is called fiber attenuation coefficient in a units of for example [1/km] or [nepers/km]. A more common unit is [dB/km] that is defined by: Z= l Z=0 P(0) mW mw [3-1] [3-2]

Fiber loss in dB/km Where [dBm] or dB milliwat is 10log(P [mW]). [3-3]
z=0 Z=l [3-3]

Optical fiber attenuation vs. wavelength

Absorption Absorption is caused by three different mechanisms:
1- Impurities in fiber material: from transition metal ions (must be in order of ppb) & particularly from OH ions with absorption peaks at wavelengths 2700 nm, 400 nm, 950 nm & 725nm. 2- Intrinsic absorption (fundamental lower limit): electronic absorption band (UV region) & atomic bond vibration band (IR region) in basic SiO2. 3- Radiation defects

Scattering Loss Small (compared to wavelength) variation in material density, chemical composition, and structural inhomogeneity scatter light in other directions and absorb energy from guided optical wave. The essential mechanism is the Rayleigh scattering. Since the black body radiation classically is proportional to (this is true for wavelength typically greater than 5 micrometer), the attenuation coefficient due to Rayleigh scattering is approximately proportional to This seems to me not precise, where the attenuation of fibers at 1.3 & 1.55 micrometer can be exactly predicted with Planck’s formula & can not be described with Rayleigh-Jeans law. Therefore I believe that the more accurate formula for scattering loss is

Absorption & scattering losses in fibers

Typical spectral absorption & scattering attenuations for a single mode-fiber

Bending Loss (Macrobending & Microbending)
Macrobending Loss: The curvature of the bend is much larger than fiber diameter. Lightwave suffers sever loss due to radiation of the evanescent field in the cladding region. As the radius of the curvature decreases, the loss increases exponentially until it reaches at a certain critical radius. For any radius a bit smaller than this point, the losses suddenly becomes extremely large. Higher order modes radiate away faster than lower order modes. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Microbending Loss Microbending Loss: microscopic bends of the fiber axis that can arise when the fibers are incorporated into cables. The power is dissipated through the microbended fiber, because of the repetitive coupling of energy between guided modes & the leaky or radiation modes in the fiber. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Dispersion in Optical Fibers
Dispersion: Any phenomenon in which the velocity of propagation of any electromagnetic wave is wavelength dependent. In communication, dispersion is used to describe any process by which any electromagnetic signal propagating in a physical medium is degraded because the various wave characteristics (i.e., frequencies) of the signal have different propagation velocities within the physical medium. There are 3 dispersion types in the optical fibers, in general: 1- Material Dispersion 2- Waveguide Dispersion 3- Polarization-Mode Dispersion Material & waveguide dispersions are main causes of Intramodal Dispersion.

Group Velocity Wave Velocities:
1- Plane wave velocity: For a plane wave propagating along z-axis in an unbounded homogeneous region of refractive index , which is represented by , the velocity of constant phase plane is: 2- Modal wave phase velocity: For a modal wave propagating along z-axis represented by , the velocity of constant phase plane is: 3- For transmission system operation the most important & useful type of velocity is the group velocity, This is the actual velocity which the signal information & energy is traveling down the fiber. It is always less than the speed of light in the medium. The observable delay experiences by the optical signal waveform & energy, when traveling a length of l along the fiber is commonly referred to as group delay. [3-4] [3-5]

Group Velocity & Group Delay
The group velocity is given by: The group delay is given by: It is important to note that all above quantities depend both on frequency & the propagation mode. In order to see the effect of these parameters on group velocity and delay, the following analysis would be helpful. [3-6] [3-7]

Input/Output signals in Fiber Transmission System
The optical signal (complex) waveform at the input of fiber of length l is f(t). The propagation constant of a particular modal wave carrying the signal is Let us find the output signal waveform g(t). z-=0 Z=l [3-8] [3-9]

[3-10] [3-11] [3-14]

Intramodal Dispersion
As we have seen from Input/output signal relationship in optical fiber, the output is proportional to the delayed version of the input signal, and the delay is inversely proportional to the group velocity of the wave. Since the propagation constant, , is frequency dependent over band width sitting at the center frequency , at each frequency, we have one propagation constant resulting in a specific delay time. As the output signal is collectively represented by group velocity & group delay this phenomenon is called intramodal dispersion or Group Velocity Dispersion (GVD). This phenomenon arises due to a finite bandwidth of the optical source, dependency of refractive index on the wavelength and the modal dependency of the group velocity. In the case of optical pulse propagation down the fiber, GVD causes pulse broadening, leading to Inter Symbol Interference (ISI).

Dispersion & ISI A measure of information capacity of an optical fiber for digital transmission is usually specified by the bandwidth distance product in GHz.km. For multi-mode step index fiber this quantity is about 20 MHz.km, for graded index fiber is about 2.5 GHz.km & for single mode fibers are higher than 10 GHz.km. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

How to characterize dispersion?
Group delay per unit length can be defined as: If the spectral width of the optical source is not too wide, then the delay difference per unit wavelength along the propagation path is approximately For spectral components which are apart, symmetrical around center wavelength, the total delay difference over a distance L is: [3-15] [3-16]

D has a typical unit of [ps/(nm.km)].
is called GVD parameter, and shows how much a light pulse broadens as it travels along an optical fiber. The more common parameter is called Dispersion, and can be defined as the delay difference per unit length per unit wavelength as follows: In the case of optical pulse, if the spectral width of the optical source is characterized by its rms value of the Gaussian pulse , the pulse spreading over the length of L, can be well approximated by: D has a typical unit of [ps/(nm.km)]. [3-17] [3-18]

Material Dispersion

Material Dispersion The refractive index of the material varies as a function of wavelength, Material-induced dispersion for a plane wave propagation in homogeneous medium of refractive index n: The pulse spread due to material dispersion is therefore: [3-19] [3-20] is material dispersion

Material Dispersion Diagrams

Waveguide Dispersion Waveguide dispersion is due to the dependency of the group velocity of the fundamental mode as well as other modes on the V number, (see Fig 2-18 of the textbook). In order to calculate waveguide dispersion, we consider that n is not dependent on wavelength. Defining the normalized propagation constant b as: solving for propagation constant: Using V number: [3-21] [3-22] [3-23]

Waveguide Dispersion Delay time due to waveguide dispersion can then be expressed as: [3-24] Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Waveguide dispersion in single mode fibers
For single mode fibers, waveguide dispersion is in the same order of material dispersion. The pulse spread can be well approximated as: [3-25] Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Polarization Mode dispersion

Polarization Mode dispersion
The effects of fiber-birefringence on the polarization states of an optical are another source of pulse broadening. Polarization mode dispersion (PMD) is due to slightly different velocity for each polarization mode because of the lack of perfectly symmetric & anisotropicity of the fiber. If the group velocities of two orthogonal polarization modes are then the differential time delay between these two polarization over a distance L is The rms value of the differential group delay can be approximated as: [3-26] [3-27]

Chromatic & Total Dispersion
Chromatic dispersion includes the material & waveguide dispersions. Total dispersion is the sum of chromatic , polarization dispersion and other dispersion types and the total rms pulse spreading can be approximately written as: [3-28] [3-29]

Total Dispersion, zero Dispersion
Fact 1) Minimum distortion at wavelength about 1300 nm for single mode silica fiber. Fact 2) Minimum attenuation is at 1550 nm for sinlge mode silica fiber. Strategy: shifting the zero-dispersion to longer wavelength for minimum attenuation and dispersion. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Optimum single mode fiber & distortion/attenuation characteristics
Fact 1) Minimum distortion at wavelength about 1300 nm for single mode silica fiber. Fact 2) Minimum attenuation is at 1550 nm for sinlge mode silica fiber. Strategy: shifting the zero-dispersion to longer wavelength for minimum attenuation and dispersion by Modifying waveguide dispersion by changing from a simple step-index core profile to more complicated profiles. There are four major categories to do that: nm optimized single mode step-fibers: matched cladding (mode diameter 9.6 micrometer) and depressed-cladding (mode diameter about 9 micrometer) 2- Dispersion shifted fibers. 3- Dispersion-flattened fibers. 4- Large-effective area (LEA) fibers (less nonlinearities for fiber optical amplifier applications, effective cross section areas are typically greater than ).

Single mode fiber dispersion

Single mode Cut-off wavelength & Dispersion
Fundamental mode is with V=2.405 and Dispersion: For non-dispersion-shifted fibers (1270 nm – 1340 nm) For dispersion shifted fibers (1500 nm nm) [3-30] [3-31] [3-32]

Dispersion for non-dispersion-shifted fibers (1270 nm – 1340 nm)
is relative delay minimum at the zero-dispersion wavelength , and is the value of the dispersion slope in [3-33] [3-34] [3-35]

Dispersion for dispersion shifted fibers (1500 nm- 1600 nm)
[3-36] [3-37]

Example of dispersion Performance curve for Set of SM-fiber

Example of BW vs wavelength for various optical sources for SM-fiber.

MFD Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Bending Loss Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Bending effects on loss vs MFD

Bend loss versus bend radius

Temporal changes in a medium with Kerr nonlinearity and negative GVD
Temporal changes in a medium with Kerr nonlinearity and negative GVD. Since dispersion tends to broaden the pulse, Kerr Nonlinearity tends to squeeze the pulse, resulting in a formation of optical soliton.

Chapter 4 Photonic Sources

Contents Review of Semiconductor Physics Light Emitting Diode (LED)
- Structure, Material,Quantum efficiency, LED Power, Modulation Laser Diodes - structure, Modes, Rate Equation,Quantum efficiency, Resonant frequencies, Radiation pattern Single-Mode Lasers - DFB (Distributed-FeedBack) laser, Distributed-Bragg Reflector, Modulation Light-source Linearity Noise in Lasers

Review of Semiconductor Physics
a) Energy level diagrams showing the excitation of an electron from the valence band to the conduction band. The resultant free electron can freely move under the application of electric field. b) Equal electron & hole concentrations in an intrinsic semiconductor created by the thermal excitation of electrons across the band gap Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

n-Type Semiconductor Donor level in an n-type semiconductor.
The ionization of donor impurities creates an increased electron concentration distribution. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

p-Type Semiconductor Acceptor level in an p-type semiconductor.
The ionization of acceptor impurities creates an increased hole concentration distribution Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Intrinsic & Extrinsic Materials
Intrinsic material: A perfect material with no impurities. Extrinsic material: donor or acceptor type semiconductors. Majority carriers: electrons in n-type or holes in p-type. Minority carriers: holes in n-type or electrons in p-type. The operation of semiconductor devices is essentially based on the injection and extraction of minority carriers. [4-1] [4-2]

The pn Junction Electron diffusion across a pn junction
creates a barrier potential (electric field) in the depletion region. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Reverse-biased pn Junction
A reverse bias widens the depletion region, but allows minority carriers to move freely with the applied field. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Forward-biased pn Junction
Lowering the barrier potential with a forward bias allows majority carriers to diffuse across the junction. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Direct Band Gap Semiconductors

Indirect Band Gap Semiconductors

Light-Emitting Diodes (LEDs)
For photonic communications requiring data rate Mb/s with multimode fiber with tens of microwatts, LEDs are usually the best choice. LED configurations being used in photonic communications: 1- Surface Emitters (Front Emitters) 2- Edge Emitters

Cross-section drawing of a typical GaAlAs double heterostructure light
emitter. In this structure, x>y to provide for both carrier confinement and optical guiding. b) Energy-band diagram showing the active region, the electron & hole barriers which confine the charge carriers to the active layer. c) Variations in the refractive index; the lower refractive index of the material in regions 1 and 5 creates an optical barrier around the waveguide because of the higher band-gap energy of this material. [4-3] Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Surface-Emitting LED Schematic of high-radiance surface-emitting LED. The active region is limitted to a circular cross section that has an area compatible with the fiber-core end face. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Edge-Emitting LED Schematic of an edge-emitting double heterojunction LED. The output beam is lambertian in the plane of junction and highly directional perpendicular to pn junction. They have high quantum efficiency & fast response. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Light Source Material Most of the light sources contain III-V ternary & quaternary compounds. by varying x it is possible to control the band-gap energy and thereby the emission wavelength over the range of 800 nm to 900 nm. The spectral width is around 20 to 40 nm. By changing 0<x<0.47; y is approximately 2.2x, the emission wavelength can be controlled over the range of 920 nm to 1600 nm. The spectral width varies from 70 nm to 180 nm when the wavelength changes from 1300 nm to 1600 nm. These materials are lattice matched.

Spectral width of LED types

Rate equations, Quantum Efficiency & Power of LEDs
When there is no external carrier injection, the excess density decays exponentially due to electron-hole recombination. n is the excess carrier density, Bulk recombination rate R: Bulk recombination rate (R)=Radiative recombination rate + nonradiative recombination rate [4-4] [4-5]

In equilibrium condition: dn/dt=0
With an external supplied current density of J the rate equation for the electron-hole recombination is: [4-6] In equilibrium condition: dn/dt=0 [4-7]

Internal Quantum Efficiency & Optical Power
[4-8] Optical power generated internally in the active region in the LED is: [4-9]

External Quantum Eficiency
In order to calculate the external quantum efficiency, we need to consider the reflection effects at the surface of the LED. If we consider the LED structure as a simple 2D slab waveguide, only light falling within a cone defined by critical angle will be emitted from an LED. [4-10]

[4-11] [4-12] [4-13] [4-14]

Modulation of LED The frequency response of an LED depends on:
1- Doping level in the active region 2- Injected carrier lifetime in the recombination region, . 3- Parasitic capacitance of the LED If the drive current of an LED is modulated at a frequency of the output optical power of the device will vary as: Electrical current is directly proportional to the optical power, thus we can define electrical bandwidth and optical bandwidth, separately. [4-15] [4-16]

LASER (Light Amplification by the Stimulated Emission of Radiation)
Laser is an optical oscillator. It comprises a resonant optical amplifier whose output is fed back into its input with matching phase. Any oscillator contains: 1- An amplifier with a gain-saturated mechanism 2- A feedback system 3- A frequency selection mechanism 4- An output coupling scheme In laser the amplifier is the pumped active medium, such as biased semiconductor region, feedback can be obtained by placing active medium in an optical resonator, such as Fabry-Perot structure, two mirrors separated by a prescribed distance. Frequency selection is achieved by resonant amplifier and by the resonators, which admits certain modes. Output coupling is accomplished by making one of the resonator mirrors partially transmitting.

Pumped active medium Three main process for laser action:
1- Photon absorption 2- Spontaneous emission 3- Stimulated emission Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Lasing in a pumped active medium
In thermal equilibrium the stimulated emission is essentially negligible, since the density of electrons in the excited state is very small, and optical emission is mainly because of the spontaneous emission. Stimulated emission will exceed absorption only if the population of the excited states is greater than that of the ground state. This condition is known as Population Inversion. Population inversion is achieved by various pumping techniques. In a semiconductor laser, population inversion is accomplished by injecting electrons into the material to fill the lower energy states of the conduction band.

Fabry-Perot Resonator
[4-18] R: reflectance of the optical intensity, k: optical wavenumber

Laser Diode Laser diode is an improved LED, in the sense that uses stimulated emission in semiconductor from optical transitions between distribution energy states of the valence and conduction bands with optical resonator structure such as Fabry-Perot resonator with both optical and carrier confinements. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Laser Diode Characteristics
Nanosecond & even picosecond response time (GHz BW) Spectral width of the order of nm or less High output power (tens of mW) Narrow beam (good coupling to single mode fibers) Laser diodes have three distinct radiation modes namely, longitudinal, lateral and transverse modes. In laser diodes, end mirrors provide strong optical feedback in longitudinal direction, so by roughening the edges and cleaving the facets, the radiation can be achieved in longitudinal direction rather than lateral direction.

DFB(Distributed FeedBack) Lasers
In DFB lasers, the optical resonator structure is due to the incorporation of Bragg grating or periodic variations of the refractive index into multilayer structure along the length of the diode. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000

Laser Operation & Lasing Condition
To determine the lasing condition and resonant frequencies, we should focus on the optical wave propagation along the longitudinal direction, z-axis. The optical field intensity, I, can be written as: Lasing is the condition at which light amplification becomes possible by virtue of population inversion. Then, stimulated emission rate into a given EM mode is proportional to the intensity of the optical radiation in that mode. In this case, the loss and gain of the optical field in the optical path determine the lasing condition. The radiation intensity of a photon at energy varies exponentially with a distance z amplified by factor g, and attenuated by factor according to the following relationship: [4-19]

[4-20] Z=0 Z=L [4-21] Lasing Conditions: [4-22]

Threshold gain & current density
[4-23] For laser structure with strong carrier confinement, the threshold current Density for stimulated emission can be well approximated by: [4-24]

Optical output vs. drive current

Semiconductor laser rate equations
Rate equations relate the optical output power, or # of photons per unit volume, , to the diode drive current or # of injected electrons per unit volume, n. For active (carrier confinement) region of depth d, the rate equations are: [4-25]

Threshold current Density & excess electron density
At the threshold of lasing: The threshold current needed to maintain a steady state threshold concentration of the excess electron, is found from electron rate equation under steady state condition dn/dt=0 when the laser is just about to lase: [4-26] [4-27]

Laser operation beyond the threshold
The solution of the rate equations [4-25] gives the steady state photon density, resulting from stimulated emission and spontaneous emission as follows: [4-28]

External quantum efficiency
Number of photons emitted per radiative electron-hole pair recombination above threshold, gives us the external quantum efficiency. Note that: [4-29]

Laser Resonant Frequencies
Lasing condition, namely eq. [4-22]: Assuming the resonant frequency of the mth mode is: [4-30] [4-31]

Spectrum from a laser Diode
[4-32]

Laser Diode Structure & Radiation Pattern
Efficient operation of a laser diode requires reducing the # of lateral modes, stabilizing the gain for lateral modes as well as lowering the threshold current. These are met by structures that confine the optical wave, carrier concentration and current flow in the lateral direction. The important types of laser diodes are: gain-induced, positive index guided, and negative index guided.

(a) gain-induced guide (b)positive-index waveguide (c)negative-index waveguide

Laser Diode with buried heterostructure (BH)

Single Mode Laser Single mode laser is mostly based on the index-guided structure that supports only the fundamental transverse mode and the fundamental longitudinal mode. In order to make single mode laser we have four options: 1- Reducing the length of the cavity to the point where the frequency separation given in eq[4-31] of the adjacent modes is larger than the laser transition line width. This is hard to handle for fabrication and results in low output power. 2- Vertical-Cavity Surface Emitting laser (VCSEL) 3- Structures with built-in frequency selective grating 4- tunable laser diodes .

Frequency-Selective laser Diodes: Distributed Feedback (DFB) laser
[4-33]

Frequency-Selective laser Diodes: Distributed Feedback Reflector (DBR) laser

[4-35] Output spectrum symmetrically distributed around Bragg wavelength in an idealized DFB laser diode

Frequency-Selective laser Diodes: Distributed Reflector (DR) laser

Modulation of Laser Diodes
Internal Modulation: Simple but suffers from non-linear effects. External Modulation: for rates greater than 2 Gb/s, more complex, higher performance. Most fundamental limit for the modulation rate is set by the photon life time in the laser cavity: Another fundamental limit on modulation frequency is the relaxation oscillation frequency given by: [4-36] [4-37]

Relaxation oscillation peak

Pulse Modulated laser In a pulse modulated laser, if the laser is completely turned off after each pulse, after onset of the current pulse, a time delay, given by: [4-38]

Temperature variation of the threshold current

Linearity of Laser Information carrying electrical signal s(t)
LED or Laser diode modulator Optical putput power: P(t)=P[1+ms(t)]

Nonlinearity x(t) Nonlinear function y=f(x) y(t)
Nth order harmonic distortion:

Intermodulation Distortion
Harmonics: Intermodulated Terms:

Laser Noise Modal (speckel) Noise: Fluctuations in the distribution of energy among various modes. Mode partition Noise: Intensity fluctuations in the longitudinal modes of a laser diode, main source of noise in single mode fiber systems. Reflection Noise: Light output gets reflected back from the fiber joints into the laser, couples with lasing modes, changing their phase, and generate noise peaks. Isolators & index matching fluids can eliminate these reflections.