Course 4. Optics and Optical Components

Module 1. Reflection: Plane and Spherical Mirrors

    1.1 Basics
        1.1.1 Light as a ray
            1.1.1.1 Definition of a ray - direction of propagation of a wave
            1.1.1.2 In a homogeneous medium, light travels in a straight line
                        (rectilinear propagation)
        1.1.2 Two cases of rays
            1.1.2.1 From a point sources, rays point away from the source
            1.1.2.2 From a very distant point, rays are parallel
        1.1.3 Geometric Optics
            1.1.3.1 Treats light as a ray
            1.1.3.2 Useful for understanding operation of many components,
                        like lenses and prisms
    1.2 Reflection
        1.2.1 Types of reflection
            1.2.1.1 Specular reflection
            1.2.1.2 Diffuse reflection
            1.2.1.3 Reflection from metallic surfaces
            1.2.1.4 Reflection from dielectric surfaces
            1.2.1.5 Definition of reflectivity
        1.2.2 The law of reflection
            1.2.2.1 Angle of incidence equals angle of reflection
            1.2.2.2 Incident ray, reflected ray and surface normal; in same plane
    1.3 Reflection from a plane surface: plane mirrors
        1.3.1 Types of plane mirrors
            1.3.1.1 Metallic
            1.3.1.2 Front surface
            1.3.1.3 Back surface
        1.3.2 Image formation in a plane mirror
            1.3.2.1 Real image
            1.3.2.2 Virtual image
    1.4 Reflection from a curved surface: spherical mirrors
        1.4.1 Types of spherical mirrors
            1.4.1.1 Concave
            1.4.1.2 Convex
        1.4.2 Image formation with spherical mirrors
            1.4.2.1 Focal length
            1.4.2.2 Magnification
            1.4.2.3 Aberrations
        1.4.3 Special types
            1.4.3.1 Mangin
            1.4.3.2 Schmidt


Module 2. Refraction: Prisms and Lenses

    2.1 Basics of refraction
        2.1.1 Snell's Law—Review from Module 1-3 and expand
        2.1.2 Refraction at a plane surface
            2.1.2.1 Plane of incidence: the incident, reflected and refracted
                        ray all lie in the plane of incidence
            2.1.2.2 Critical angle
            2.1.2.3 Total internal reflection
        2.1.3 Refraction at a spherical surface
            2.1.3.1 Convex spherical surface
            2.1.3.2 Concave spherical surface
            2.1.3.3 Image point
            2.1.3.4 Paraxial rays
            2.1.3.5 Real images
            2.1.3.6 Virtual images
            2.1.3.7 Refraction equation for a spherical surface
                        (n1/s1 + n2/s2 = (n2 - n1)/R )
                        Review from Module 1-3 and expand on it
    2.2 Lenses
        2.2.1 Thick lens
            2.2.1.1 Refraction at two spherical surfaces
            2.2.1.2 Focal points
            2.2.1.3 Principal points
            2.2.1.4 Conjugate relations
            2.2.1.5 Image forming capabilities of a thick lens
        2.2.2 Thin lens
            2.2.2.1 Types of lenses
                - positive (convex)
                - negative (concave)
                - plano-convex
                - plano-concave
            2.2.2.2 Concept of focal length
            2.2.2.3 Magnification
            2.2.2.4 Power of a lens
            2.2.2.5 Conjugate points
            2.2.2.6 Lensmaker's equation
                        (1/f = (n-1)(1/R1 - 1/R2))
                        Review from Module 1-3 and expand on it
            2.2.2.7 Image formation with a thin lens
            2.2.2.8 Thin lens imaging equation (1/f = 1/o + 1/i)
                        Review from Module 1-3 and expand on it
        2.2.3 Combination of lenses
            2.2.3.1 Imaging with multiple lenses
            2.2.3.2 f-stop
            2.2.3.3 Numerical aperture
            2.2.3.4 Aperture stop
            2.2.3.5 Field stop
        2.2.4 Simple optical Systems
            2.2.4.1 Simple magnifier
            2.2.4.2 Microscope
            2.2.4.3 Telescopes
            2.2.4.4 Laser collimator
            2.2.4.5 Camera
        2.2.5 Ray tracing
            2.2.5.1 Chief ray
            2.2.5.2 Marginal ray
            2.2.5.3 Graphical procedures
            2.2.5.4 Introduction to computer codes
        2.2.6 Aberrations
            2.2.6.1 Primary (Seidel) Aberrations
                - Spherical
                - Coma
                - Astigmatism
                - Field curvature
                - Distortion
            2.2.6.2 Chromatic Aberrations
    2.3 Prisms
        2.3.1 Simple prisms
            2.3.1.1 Apex angle
            2.3.1.2 Deviation angle
            2.3.1.3 Color dispersion
            2.3.1.4 Minimum deviation angle
        2.3.2 Porro prism
            2.3.2.1 Right angle prism
            2.3.2.2 Reverses an image
        2.3.3 Dove prism
            2.3.3.1 Structure
            2.3.3.2 Interchanges two light rays
        2.3.4 Pentaprism
            2.3.4.1 Structure
            2.3.4.2 Accurate deviation of light ray by 90 deg
        2.3.5 Cube corner prism
            2.3.5.1 Shape
            2.3.5.2 Accurately redirects a beam of light on itself
        2.3.6 Applications of prisms
            2.3.6.1 Dispersing light into its component wavelengths
            2.3.6.2 Deviate the path of a beam of light
            2.3.6.3 Bend a light beam at a right angle
            2.3.6.4 Separate polarization components of a light beam


Module 3. Imaging in Optical Systems

    3.1 Imaging with a single lens
        3.1.1 Determination of focal points and focal lengths
            3.1.1.1 Primary focal points
            3.1.1.2 Secondary focal points
        3.1.2 Focal plane
            3.1.2.1 Definition
            3.1.2.2 Significance: all rays parallel before entering the lens
                        are focused at same point on focal plane
        3.1.3 Graphical location of image
            3.1.3.1 Ray tracing technique for locating image
                       formed by converging thin lens
            3.1.3.2 Ray tracing technique for locating image
                       formed by diverging thin lens
            3.1.3.3 Real and virtual images
        3.1.4 Use of lens equation
            3.1.4.1 Sign convention
            3.1.4.2 1/f = 1/s + 1/s"
            3.1.4.3 Calculate distance of image from lens
        3.1.5 Magnification
            3.1.5.1 Definition of magnification
            3.1.5.2 Equation for lateral magnification
            3.1.5.3 Sign convention
    3.2 Imaging with multiple lenses
        3.2.1 Ray tracing techniques for two lenses
            3.2.1.1 First determine image produced by first lens
            3.2.1.2 Treat this image as a virtual object for second lens
            3.2.1.3 A ray from this source is drawn thru the center of the
                        second lens and a ray parallel to the axis before the second lens
                        is drawn thru the secondary focal point of the second lens
            3.2.1.4 These rays intersect at the final image
        3.2.2 Analytical approach to imaging with two lenses
            3.2.2.1 Apply this lens formula to each lens successively to locate final image
            3.2.2.2 Overall magnification is product of magnification of individual lenses
        3.2.3 Imaging with more than two lenses: continue to apply above
                 techniques successively to the lenses
    3.3 Stops
        3.3.1 Basic definitions
            3.3.1.1 Aperture stop
            3.3.1.2 Field stop
            3.3.1.3 Entrance pupil and exit pupil
        3.3.2 Aperture stop
            3.3.2.1 Always a real stop
            3.3.2.2 Identification of the aperture stop
            3.3.2.3 Location of aperture stop, entrance pupil and exit pupil
                        for two lenses separated by a stop
        3.3.3 Passage of light from object point to image point thru optical system
            3.3.3.1 Chief ray
            3.3.3.2 Marginal ray
            3.3.3.3 Identification of entrance and exit pupils
        3.3.4 Field stop
            3.3.4.1 Procedure for locating field stop
            3.3.4.2 Definitions of entrance and exit windows
    3.4 Image forming optical systems
        3.4.1 Binoculars
            3.4.1.1 Design of typical binoculars-use of Porro prisms
            3.4.1.2 Image formation
            3.4.1.3 Optical performance
        3.4.2 Astronomical telescope
            3.4.2.1 Design
            3.4.2.2 Angular magnification
        3.4.3 Camera
            3.4.3.1 Design of simple camera
            3.4.3.2 Image formation in the camera
            3.4.3.3 Control of aperture and shutter speed allows great flexibility


Module 4. Interference: Coatings and Filters

    4.1 Fundamentals of interference phenomena
        4.1.1.Manifestation of the wave nature of light
            4.1.1.1 The principle of superposition of waves
            4.1.1.2 Huygen's principle
        4.1.2 Interference of two waves
            4.1.2.1 Patterns that are formed
            4.1.2.2 Analogy to water waves
            4.1.2.3 Constructive and destructive interference
    4.2 Examples of interference phenomena
        4.2.1 Young's two-slit experiment
            4.2.1.1 Experimental method
            4.2.1.2 Two slit interference pattern
            4.2.1.3 Interpretation of the pattern
            4.2.1.4 Locations of bright and dark fringes
        4.2.2 Interference involving multiple reflections
            4.2.2.1 Reflection from a plane parallel film
            4.2.2.2 Origin of the interference
            4.2.2.3 Intensity contours
            4.2.2.4 Sharpness of the fringes
            4.2.2.5 Definition of visibility
    4.3. Applications of interference
        4.3.1 Natural interference
        4.3.1.1 The air wedge
            4.3.1.2 Newton's rings
            4.3.1.3 Soap bubbles, oil slicks
        4.3.2 Thin film coatings
            4.3.2.1 Antireflection coatings
                - Principles
                - Performance
            4.3.2.2 High reflection coatings
                - Principles
                - Performance
            4.3.2.3 Narrow-band filters
                - Principles
                - Performance
            4.3.2.4 Bandpass filters
                - Principles
                - Performance
        4.3.3 The Michelson interferometer
            4.3.3.1 Optical design
            4.3.3.2 Principles of operation
            4.3.3.3 Formation of fringes


Module 5. Diffraction: Gratings and Lasers

    5.1 Fundamentals of diffraction
        5.1.1 Bending of light around the edges of an object
            5.1.1.1 Manifestation of wave nature of light
            5.1.1.2 Light appears in what would be a shadow in geometric optics
        5.1.2 Huygens-Fresnel diffraction theory
            5.1.2.1 Huygen's principle
            5.1.2.2 Superposition of many waves
            5.1.2.3 Leads to beam spread
    5.2 Commom diffraction patterns
        5.2.1 Diffraction from a single slit
            5.2.1.1 Light spreads mostly in direction perpendicular to slit
            5.2.1.2 Half angle divergence of central fringe
            5.2.1.3 Positions of first minima
            5.2.1.4 Higher order fringes
        5.2.2 Near field versus far field diffraction
            5.2.2.1 Fraunhofer diffraction
            5.2.2.2 Fresnel diffraction
            5.2.2.3.Rayleigh range
        5.2.3 Diffraction from a square aperture
            5.2.3.1 Half angles of central spot
            5.2.3.2 Higher order spots in two dimensions
        5.2.4 Diffraction from a circular aperture
            5.4.4.1 Airy pattern
            5.4.4.2 Airy disc
            3.4.4.3 Rayleigh criterion (resolution)
        5.2.5 Diffraction around a thin one dimensional object (like a wire)
            5.2.5.1 Light spreads mostly in the direction perpendicular to the object
            5.2.5.2 Central spot
            5.2.5.3 Higher order spots - positions
    5.5 Diffraction gratings
        5.5.1 Transmissi0n gratings
            5.5.1.1 Aperture with thousands of parallel narrow slits
            5.5.1.2 The diffraction pattern fron a transmission grating
            5.5.1.3 The grating equation
        5.5.2 Reflection gratings
            5.5.2.1 Line rulings on a flat mirror
            5.5.2.2 The diffraction pattern from a reflection grating
            5.5.2.3 Blaze
            5.5.2.4 Effect of blaze on the diffraction pattern
        5.5.3 Fabrication of gratings
            5.5.3.1 Master gratings made with a ruling engine
            5.5.3.2 Less expensive replica gratings
            5.5.3.3 Holographic gratings
        5.5.4 Important properties of diffraction gratings
            5.5.4.1 Number of grooves per mm
            5.5.4.2 Spectral range
            5.5.4.3 Free spectra; ramge
            5.5.4.4 Blaze wavelength
            5.5.4.5 Efficiency
            5.5.4.6 Ghost and stray light
            5.5.4.7 Resolution
        5.5.5 Care and cleaning of diffraction gratings
    5.6 Diffraction of laser beams
        5.6.1 Diffraction effects on laser beam divergence
            5.6.1.1 Fresnel number for a laser
            5.6.1.2 Diffraction limited beam divergence angle
            5.6.1.3 How divergence angle varies with number of transverse modes
            5.6.1.4 Only Gaussian beams are truly diffraction-limited
            5.6.1.5 Beam quality (M2)
        5.6.2 Effect of diffraction on focusing of laser beams
            5.6.2.1 Diffraction limited focal spot size
            5.6.2.2 Depth of focus


Module 6. Polarization: Linear and Elliptical

    6.1 Nature of polarization
        6.1.1 Light as a transverse wave
            6.1.1.1 Difference from longitudinal waves
            6.1.1.2 Orientation of electric field in a light wave
        6.1.2 Polarization involves oscillation of electric field in only one direction
            6.1.2.1 Perpendicular to direction of propagation
            6.1.2.2 Oscillates at the frequency of the light wave
            6.1.2.1 Diagram illustrating the oscillation
    8.2 Types of polarization
        6.2.1 Unpolarized (natural) light
            6.2.1.1 Mixture of oscillations
            6.2.1.2 Oriented in all possible directions
        6.2.2.Linear
            6.2.2.1 Electric field vector vibrates in one direction perpendicular to
                        direction of propagation
            6.2.2.2 May be separated into components along two orthogonal axex
            6.2.2.3 These components vibrate in phase
            6.2.2.4 Also called plane polarized
        6.2.3.Circular
            6.2.3.1 Electric field vector rotates around the direction of propagation
            6.2.3.2 Frequency of rotation equals light frequency
            6.2.3.3 Magnitude of electric field stays the same during rotation
            6.2.3.4 Projection of electric field vector on transverse plane is a circle
        6.2.4. Elliptical
            6.2.4.1 Electric field vector rotates around the direction of propagation
            6.2.4.2 Frequency of rotation equals light frequency
            6.2.4.3 Magnitude of electric field changes during rotation
            6.2.4.4 Projection of electric field vector on transverse plane is an ellipse
            6.2.4.5 Elliptical polarization is the general case
        6.2.5 Conversion of one form to another
            6.2.5.1 Retarders
            6.2.5.2 Quarter wave plates
            6.2.5.3 Half wave plates
    6.3 Sources of polarization
        6.3.1.Direct generation
            6.3.1.1 Lasers
            6.3.1.2 The electron synchrotron
        6.3.2.Selective absorption
            6.3.2.1 Dichroic crystals
            6.3.2.2 Polaroid sheet
        6.3.3 Polarization by reflection (to be discussed in section 6.4)
        6.3.4 Polarizing prisms
            6.3.4.1 Double refraction
            6.3.4.2 How polarizing prisms work
            6.3.4.3 Nicol prism
            6.3.4.4 Wollaston prism
            6.3.4.5 Glan-Thompson prism
        6.3.5 Polarization by refraction
            6.3.5.1 Refracted light is partially polarized
            6.3.5.2 A stack of plates will provide a high degree of polarization
        6.3.6 Polarization by scattering
            6.3.6.1 Light scattered by particles is partially polarized
            6.3.6.2 Light from sky is partially polarized
    8.4 Fresnel's equations
        6.4.1 Describe reflection at a dielectric surface
            6.4.1.1 Value of reflection at normal incidence
            6.4.1.2 Definition of s and p components
            6.4.1.3 Behavior of s component vs angle
            6.4.1.4 Behavior of p component vs angle
        6.4.2 Brewster's angle
            6.4.2.1 Position of the minimum reflection of the p component
            6.4.2.2 Equation for Brewster's angle in terms of the index of refraction
            6.4.2.3 Use to reduce reflection losses
            6.4.3.4 Use to produce polarized light
    6.5 Analysis of polarized light
        6.5.1 Law of Malus
            6.5.1.1 Definition of an analyzer
            6.5.1.1 Equation for law of Malus
            6.5.1.2 Behavior with linearly polarized light
        6.5.2 Analysis procedures
            6.5.2.1 No intensity variation with analyzer alone
                - No intensity variation with analyzer plus quarter wave plate means unpolarized
                   light
                - Intensity variation with analyzer plus quarter wave plate means circularly     
                   polarized light or mixture of circularly polarized and unpolarized light
                - Procedures for distinguishing these two cases
            6.5.2.2 Intensity variation with analyzer alone
                - If one position of analyzer gives zero intensity, one has linearly polarized light
                - If no position gives zero, but there is a zero when a quarter wave plate is added,
                  one has elliptically polarized light
                - If there is no zero when quarter wave plate one has mixture of unpolarized and
                  linearly polarized light, or a mixture of elliptically polarized and linearly polarized light
                - Procedures for distinguishing these two cases


Module 7. Fiber Optical Properties, Couplers,
Receivers and Transmitters

This module builds on and expands modules 1-5 and 1-6
    7.1 Properties of optical fibers
        7.1.1 Losses
            7.1.1.1 Absorption
            7.1.1.2 Scattering
            7.1.1.3 Inhomogeneities
            7.1.1.4 Microbending and macrobending
        7.1.2 Dispersion
            7.1.2.1 Masterial dispersion
            7.1.2.2 Waveguide dispersion
            7.1.2.3 Modal dispersion
        7.1.3 Numerical aperture of fibers
            7.1.3.1 Definition
            7.1.3.2 Relation to maximum acceptance angle
        7.1.4 Fiber strength
            7.1.4.1 Fiber breaking strength
            7.1.4.2 Time-dependent strength
    7.2 Couplers
        7.2.1 Methods of coupling of source to fibers
            7.2.1.1 Lenses
            7.2.1.2 Fibers with tapered ends
            7.2.1.3 Integral LED/lens
            7.2.1.4 Graden index lenses for lasers
        7.2.2 Performance of couplers
            7.2.2.1 Losses
            7.2.2.2 Power delivered to fiber
    7.3 Transmitters
        7.3.1 Sources
            7.3.1.1 LEDs
            7.3.1.2 Laser diodes
            7.3.1.3 Wavelength choices
            7.3.1.4 Source noise
        7.3.2 Driving circuits
            7.3.2.1 LED circuits
            7.3.2.2 Laser driving circuits
        7.3.3 Transmitter performance
            7.3.3.1 Bandwidth
            7.3.3.2 Power delivered to fiber
    7.4 Receivers
        7.4.1 Detectors    
            7.4.1.1 Photodiodes
            7.4.1.2 Avalanche photodiodes
        7.4.2 Amplifiers
            7.4.2.1 Circuits for photodiodes
            7.4.2.2 Circiits for avalanche photodiodes
            7.4.2.3 Amplifier noise
        7.4.3 Receiver performance
            7.4.3.1.Bandwidth
            7.4.5.2 Bit error rate (BER)

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