Extra Notes

• Introduction: Waves, Detection, Sources
  General Optical Communications Channel
  Basic Semiconductor Laser and Detector Principle


• Basic Comments Regarding Waves
  Wavelength, Frequency and Phase Velocity
  Three-D Image of Phase Velocity
  dB Loss, Dispersion and Acceptance Angle
  Acceptance and Mode Angles - Details
  Loss and Dispersion of Optical Fibers
  Dense Wave Wavelength Division Multiplexed Spectrum
  Diffraction, Focal Spot Diameter and Depth of Focus of a Lens


• Spectral Width, Linewidth
  General Concept of Spectral Width, Linewidth
  Representation of a Function of Time as a Sum of Cosines(Sines)
  Evaluation of the Cosine(Sine) Amplitudes at a Given Frequency from the f(t)
  The Delta Distribution and the Final Expression for the Amplitude; an Example!


• Channel Capacity
  Number of Quantization Levels
  Sampling, Quantization and Coding
  Limitation on M due to S/N Ratio - Heuristic Proof & Example
  Limitation on M due to S/N Ratio - Proof using Quantization
  Various Possible Coding Schemes
  Baud Versus Bit Rate, and Limitations for White Noise
  The Ideal Channel and The Shannon Limitation


• Shot, Thermal, Amplifier, and Relative Intensity Noise - Frequency Independent Signal to Noise Ratio Expressions
  Optical Signal Induced Shot Noise in a Simple p-i-n Dectector
  Shot Noise Limited SNR, Dark Current and Background Current
  Thermal Noise of a Resistor
  Signal to Noise Ratio Calculation when the Amplifier is Ideal
  Specification of Amplifier Noise - Noise Figure, Noise Temperature, Noise Current and Voltage
  Ideal Power-Out Versus Current Characteristic for a Laser Oscillator - Reflectivity and Internal Loss, External and Internal Quantum Efficiency, and Radiative Recombination


• Free-Space Communication Link - The Friis and Radar Formula
  Diffraction, Antenna Area, Solid Angle of the Main Antenna Lobe, and the Friis Formula for Free-Space Communication Link Sensitivity
  Relationships Among Directivity, Solid Angle of the Main Lobe, Antenna Gain, and Effective Area


• Basic Probability Concepts (CL Theorem)
  Binomial Distribution
  Binomial to Gaussian


• Low Pass Filter to Limit Bandwidth
  Bit Rate Equals Twice the Bandwidth


• PIN and APD Detectors
  Basic PIN Detector
  Basic Avalanche Photodiode


• Counting Modes and Noise Photons per Mode
  Modal Resonance Condition
  Longitudinal Mode Spectrum and Its Control
  Counting Modes per Unit Volume per Hz (Spectral Mode Density)
  Modes and Thermal Equilibrium at Temperature, T
  Noisy Photons - Proof that there is one per mode prior to amplification!


• The Optical Amplifier Principle and its Influence upon the Signal to Noise Ratio
  Fiber Optical Amplifier - Basic Principle
  In-Line Fiber Amplifier and its Influence on the SNR
  Derivation of the Power Gain and Amplified Spontaneous Emission
  Gain Saturation
  Simplified Derivation of Spontaneous-Signal Beat Noise
  Noise Figure of an Optical Amplifier


• Bit Error Rate and the SNR - the Eye Diagram and Pseudo-Random Sequences
  Formation of the Eye Diagram for Pseudo-Random Sequences
  Gaussian Probability of Error
  Complimentary Error Function and the Eye Diagram


• Receiver Specified by Input Noise Current and Voltage Sources - The Corresponding S/N Ration, K
  Basic Receiver Configuration
  Small Signal Analysis
  Noise Analysis
  Signal to Noise Ratio, K, as a Function of Photocurrent, I
  Photocurrent, I, as a Function of Signal to Noise Ratio, K


• The Transimpedance Amplifier
  Small Signal Analysis
  Spectral Noise Analysis
  Signal Noise Example


• Various Limits of the Signal to Noise Ratio
  High Resistance No Thermal - Amp or Shot Limited
  Delta f1 and Delta f2 Shot Noise Limits
  Low Resistance Thermal and Amp
  Low Resistance RC Bandwidth Limited


• Coherent Detection
  General Description of Coherent Detection
  Basic Detection Equations for Heterodyne and Homodyne Systems
  Bit Error Rates in terms of Photoelectron Number
  Homodyne ASK and Homodyne PSK Calculations
  The Balanced Heterodyne Detector usion a 3dB Coupler


• Couplers, Switches, Filters, and Multiplexers
  Electric Rield Equation: Amplitude and Phase
  Coupled Mode Equations
  3dB Coupler, Multiplexer, and Expression for the Coupling Coefficient


• Grating Subsystems
  Grating Equation Derivation
  Fundamental Spectral Resolution of a Grating
  Reflectivity of a Grating Mirror
  Passband Characteristics of a Grating Mirror
  Basic Cavity with a Grating Mirror


• Dispersion of Optical Pulses in Fibers
  Gaussian Pulse Spectrum
  Output Pulse
  Output Pulse Width
  Refractive Index Parameter


• Power and Rise Time Budgets
  Power Budget Example
  Rise Time Budget Example
  Star Network Power Budget Examples


• Basic Optical Waveguides - Fibers
  Slab Waveguide Modes - "Ray Picture"
  Graphical Solution for TE Modes
  The TE Mode Fields
  TM Modes and Cylindrical Geometry
  Common Applications of Bessel Functions
  Cylindrical Geometrical Functions (Bessel)
  Fiber Dispersion Relation - The Weak Guiding Limit
  The HE₁₁ Mode (Lowest Order-No Cutoff) and the HE_sp Modes (Generally)
  The EH_sp Modes and Mode Diagrams Analogous to the Slab Waveguide Diagrams
  Cylindrical Fiber Modes - HE₁₁ Mode