16.711 Lecture 1 Review of Wave optics

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16.711 Lecture 1 Review of Wave optics
Today

• Introduction to this course
• Light waves in homogeneous medium
• Monochromatic Waves in inhomogeneous medium
• Polychromatic waves
• Multiple interference and optical resonator
• Diffraction principle and diffraction grating

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16.711 Lecture 1 Review of Wave optics
Syllabus and policy of the course

• Syllabus, course materials, schedules are
  available on the course website
• http//faculty.uml.edu/xlu/16.711

Course contents

1. Introduction of the course, reviews of Wave
   Optics
2. Dielectric waveguides and optical fibers, mode
   and effective index
3. Optical Fiber modal and wavdguide dispersions,
   dispersion management
4. Mode-coupling theory, Mach-zehnder
   interferometer, Directional coupler, taps and WDM
   coupler
5. Electro-optics, polarization and modulation of
   lights
6. Optical Amplifiers. noise figure, gain profile,
   ASE noise. Gain equalization, optical
   filter, bit error rate, amplifier cascade
7. DWDM technology, Gratings, AWG, Fiber Bragg
   grating
8. Photonic switches and all optical switches
9. Nonlinear Fiber optics

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16.711 Lecture 1 Review of Wave optics
Light waves in homogeneous medium

• The Helmholtz equation

Helmholtz equation

• Plane electromagnetic wave

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16.711 Lecture 1 Review of Wave optics
Light waves in homogeneous medium

• The spherical wave

• The Gaussian wave

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16.711 Lecture 1 Review of Wave optics

• The Gaussian wave

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16.711 Lecture 1 Review of Wave optics

• Power of a Gaussian beam

Total Power
The ratio of the power carried within a circle
of radius
The power contained within a circle of radius
86 of the total power.
99 of the total power is contained within a
circle of radius .
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16.711 Lecture 1 Review of Wave optics

• Beam radius of a Gaussian beam

is the spot size.
is the waist radius.
when
86 energy is confined in the cone.
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16.711 Lecture 1 Review of Wave optics

• depth of focus

is the spot size.
is the waist radius.
The gaussian has minimum width at .
The axial distance for the beam width
is called depth of focus.
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16.711 Lecture 1 Review of Wave optics
Monochromatic waves in inhomogeneous medium

• Fresnels equations

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16.711 Lecture 1 Review of Wave optics
Monochromatic waves in inhomogeneous medium

• Fresnels equations

The Fresnels equations is derived from the
boundary conditions.

• phase change

when
At normal incidence, no phase shift if n1gtn2, 180
phase shift if n2gtn1.
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16.711 Lecture 1 Review of Wave optics
Monochromatic waves in inhomogeneous medium

• General case

• polarization angle or Brewsters angle

At
The reflected wave is linear polarized.
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16.711 Lecture 1 Review of Wave optics
Monochromatic waves in inhomogeneous medium

• Total internal reflection

The amplitude of the reflected wave is 1.
At
The phase of the reflected wave changes with the
incident angle.
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16.711 Lecture 1 Review of Wave optics
Monochromatic waves in inhomogeneous medium

• Total internal reflection and evanescent wave

• Evanescence wave

• penetration depth

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16.711 Lecture 1 Review of Wave optics
Monochromatic waves in inhomogeneous medium

• Reflectance and Transmittance

• normal incidence

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16.711 Lecture 1 Review of Wave optics
Polychromatic waves

• group velocity

wave packet speed
is called group index.
Exercise the difference between phase velocity
and group velocity?
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16.711 Lecture 1 Review of Wave optics
Polychromatic waves

• absorption and dispersion

is the absorption or attenuation coefficient.
a wave packet broadening for a length of L is
dispersion parameter
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16.711 Lecture 1 Review of Wave optics
Polychromatic waves

• classical picture of the susceptibility

classical electron moving equation
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16.711 Lecture 1 Review of Wave optics
Multiple interference and optical resonator

• interference of monochromatic waves

• interferometers

Mach-zehnder
Sagnac
Michelson
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16.711 Lecture 1 Review of Wave optics
Multiple interference and optical resonator

• interference of two oblique plane waves

• exercise

interference of a plane wave and spherical wave
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16.711 Lecture 1 Review of Wave optics
Multiple interference and optical resonator

• interference of two monochromatic waves light
  beating

• multiple interference

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16.711 Lecture 1 Review of Wave optics
Multiple interference and optical resonator

• spectral width, finesse,

Diffraction principle and diffraction grating

• Fraunhofer diffraction

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16.711 Lecture 1 Review of Wave optics
Diffraction principle

• The Fourier optics view of Fraunhofer diffraction

In far fields, the spatial frequency is
transferred to position.
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16.711 Lecture 1 Review of Wave optics
Diffraction grating

• Transmission grating

• Reflection grating