Dr Qian D. Zhuang

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• OPTICS OPTICAL INSTRUMENTS
• Dr Qian D. Zhuang
• C37, Physics Department
• Email q.zhuang_at_lancaster.ac.uk
• Tel [phone]

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Introduction

• Teaching plan
• 11 lectures
• 4 seminars
• Academic aims
• To teach the principles of geometrical optics
  physical optics
• To investigate optical phenomena
• To display the applications of principles in
  modern optical systems and optoelectronics
• To understand the functions and basic principles
  of operation of some important optical
  instruments and applications
• Assessment
• Course Work 70
• Examination 30

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Content
Part 1 The Nature of Light Propagation

• Dual-nature of light
• The law of reflection refraction
• Dispersion polarization
• Huygens principle

Part 2 Geometrical Optics

• Particle nature of light - Ray approximation
• Images formation by spherical surfaces, thin
  lenses
• Introduction of optical instruments

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Content
Part 3 Physical Optics - Wave-nature of Light

• Interference its applications
• interference coherent sources
• two-source interference
• interference in thin film
• applications of interference ? Michelson
  Interferometer
• Diffraction its applications
• diffraction from single slit multi slits
• applications ? Diffraction Grating

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• The nature and propagation of light

• Dual nature of light
• Description of light propagation waves,
  particles, rays, wavelets
• Laws of reflection diffraction
• Concepts of dispersion, polarization, and
  scattering
• Huygens principle

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Nature of Light Particle-wave duality of light

• particle property light is a stream consists
  tiny particles
• predictable reflection
• photoemission
• wave nature is kind of electromagnetic wave
• diffraction and interference
• ability to bend through obstacle

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Particle nature ? predictable reflection

• Isaac Newton proposed that light consists of a
  stream of small particles, because it
• travels in straight lines at great speeds
• is reflected from mirrors in a predictable way

Newton observed that the reflection of light from
a mirror resembles the rebound of a steel ball
from a steel plate
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Evidence 2 ? Photoelectric effect

• When blue light is shone on the emitter plate a
  current flows in the circuit
• But for red light, no current flows in the circuit

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Photoelectric Effect

• Only light with a frequency greater than a
  certain threshold will produce a current
• Current begins almost instantaneously, even for
  light of very low intensity
• Current is proportional to the intensity of the
  incident light

light carries energy in discrete bundles ? photons
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Wave theory of light (1802)

• Thomas Young showed that light is a wave, because
  it
• undergoes diffraction and interference (Youngs
  double-slit experiment)

Thomas Young (1773-1829)
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Wave theory of light (1802)

• Interference

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Maxwells electromagnetic theory

• Light consists of an oscillating electric and
  magnetic field
• E-field and H-field are perpendicular each other
• And perpendicular to the propagate direction
• Light travels at
• constant speed c
• different frequency f ? number of cycles per
  second (Hertz)

f c / l
James Clerk Maxwell (1831-1879)
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The electromagnetic spectrum

• Evidence for the wave nature of light

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Problems with wave theory of light

• The wave theory of light is unable to explain
  photoemission
• For waves, energy depends on amplitude and not
  frequency
• This implies that a current should be produced
  when say, high-intensity red light is used
• Einsteins Explanation (1905)
• Light consists of particles, now known as
  photons
• A photon hitting the emitter plate will eject an
  electronif it has enough energy
• Each photon has energy

Albert Einstein won a Nobel Prize for his work
on the photoelectric effect
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WAVE-PARTICLE DUALITY OF LIGHT
In 1924 Einstein wrote There are therefore now
two theories of light, both indispensable, and
without any logical connection.

• Evidence for wave-nature of light
• Diffraction and interference
• Evidence for particle-nature of light
• Photoelectric effect

• Light exhibits diffraction and interference
  phenomena that are only explicable in terms of
  wave properties
• Light is always detected as packets (photons) if
  we look, we never observe half a photon
• Number of photons proportional to energy density
  (i.e. to square of electromagnetic field strength)

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Energy imparted by a photon

• Light can be considered to propagate through
  space as a stream of vast numbers of particles.
  
• This particle is not a hard lump of
  well-defined mass, but a massless, quantum of
  energy
• Each photon carries with it a precisely defined
  amount of energy which depends only on its
  characteristic frequency or wavelength
• The energy of a single photon is

• h 663 x 10-36 J s Planck's constant
• c is the velocity of propagation of the photon in
  free space

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Practice energy of a photon

• A particular photon has a wavelength of 600 nm.
  This photon would be in the red part of the
  spectrum
• what is the energy of a single photon?
• what is the energy in electronvolt (eV)? If a
  parallel beam of this light has energy of 0.5 J,
  what is the number of photons contained in this
  beam?

Electronvolt is defined as the energy obtained by
an electron when it is accelerated through a
potential difference of 1 volt 1 eV 160x10-21 J
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• Ray Approximation
• to describe light propagation

• Ray approximation to represent beams of light
• Wave front to present the physical displacement ?
  applies to wave-nature of light

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Ray approximation

• Light travels in a straight-line path in a
  homogeneous medium until it encounters a boundary
  between two different media
• The ray approximation is used to represent beams
  of light
• A ray of light is an imaginary line drawn along
  the direction of travel of the light beams
• in particle theory it was used for particle path
• from wave viewpoint, a ray is an imaginary line
  along the direction of travel of the wave

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Wave front

• Wave front the locus of all adjacent points at
  which the phase of vibration of a physical
  quantity associated with the wave is the same

• Near a point source, the wave fronts (i.e.,
  surfaces of constant phase) are circular in two
  dimensions (? stone in the water) and spherical
  in three dimensions.
• Far from a point source, the wave fronts are
  approximately linear or planar. A line
  perpendicular to a wave front in direction of the
  waves propagation is called a ray.

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Wave front
Far field
Near field

• To describe wave motion in diagrams
• only draw parts of a few consecutive wave fronts
• Ray to present propagate direction

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Plane waves

• For most purposes we may represent a travelling
  light wave as ? Plane wave
• a one-dimensional, scalar wave, propagating in a
  given direction
• all the surfaces upon which the wave has equal
  phase are parallel to each other and
  perpendicular to the direction of propagation.
• The planes can be considered as the wavefronts of
  the wave and usually represent the peak amplitude
  of the wave and are separated by the wavelength
• We need only describe such a wave in terms of
  either the electric field or the magnetic field
• Both are not necessary, since we can always
  extract one from the other

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Continued

• Conventionally, amplitude of electric field
  vector E, describes a plane wave of angular
  frequency ? and wave vector k, propagating in the
  z direction
• E E0 cos(?t - kz - ?)

? - initial phase of the wave t and z - the
respective time and space co-ordinates E0 - peak
amplitude of the wave ? 2?f rad s-1, f is
linear frequency of light

• Wavefronts correspond to the peaks of the sine
  wave ? They are perpendicular (normal) to
  direction of propagation

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Continued

• The propagation constant is
• k 2?/? m-1
• ? is the wavelength.
• The velocity of propagation of the light wave in
  a vacuum,
• c f? m s-1
• The velocity of the wave in any medium is related
  to its free-space velocity
• ? c/n f(?/n)
• The refractive index itself is related to the
  relative magnetic and electric constants, ?r and
  ?r
• n c/ ? ?(?r.?r)/(?0.?0)
• ?0 8.87 x 10-12 F m-1 the primary electric
  constant of free space
• ?0 4 x 10-7 H m-1 the primary magnetic
  constant of free space
• The velocity of propagation of an electromagnetic
  wave in free space
• c ?(?0?0)-1 2.998x108 m s-1 3x108 m s-1

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Geometrical optics

• Plane waves are very important in understanding
  the properties of mirrors and lenses.  
• For light waves, the ray concept is particularly
  convenient for showing the path taken by the
  light.
•  
• Geometrical Optics
• We will make frequent use of light rays, and they
  can be regarded essentially as narrow beams of
  light much like those lasers produce.

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Reflection

• Using Ray Approximation to explore two important
  aspects of light propagation reflection and
  refraction

• A ray of light, the incident ray, travels in a
  medium
• When it encounters a boundary with a second
  medium, part of the incident ray is reflected
  back into the first medium ? This means it is
  directed backward into the first medium

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Specular reflection diffuse reflection

• Specular reflection is reflection from a smooth
  surface
• The reflected rays are parallel to each other
• All reflection in this text is assumed to be
  specular

• Diffuse reflection is reflection from a rough
  surface
• The reflected rays travel in a variety of
  directions

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• Diffuse reflection makes the road easy to see at
  night

Diffuse
Specular
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Law of reflection

• Incident and reflected ray are in the same plane
• The angle of reflection is equal to the angle of
  incidence

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Law of refraction

• When a ray of light traveling in a transparent
  medium encounters a boundary leading into a
  second medium, part of the ray is reflected and
  part of the ray enters the second medium
• The ray that enters the second medium is bent at
  the boundary

This bending of the ray is called refraction
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Law of refraction

• The incident ray, the reflected ray, the
  refracted ray, and the normal all lie on the same
  plane
• The angle of refraction, ?2, depends on the
  properties of the medium

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Law of refraction
sinq1v1t/d (yellow triangle) sinq2v2t/d (green
triangle)
light velocity depends on the medium refractive
index n
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Reflection details

• Light may refract into a material where its speed
  is higher
• The angle of refraction is greater than the angle
  of incidence
• The ray bends away from the normal

• Light may refract into a material where n is
  higher
• The angle of refraction is less than the angle of
  incidence
• The ray bends toward the normal

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Total internal reflection

• what happens if we raise incident angel for
  second case?

• Red ray bended with angle ?2
• Blue ray is bended further towards interface
• Green ray is bended along tangent to the
  interface ? critical angle
• beyond critical angle, no ray transmitted into
  the second medium, all is completely reflected
  back ? total internal reflection

setting ?b90oC
? critical angle
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Total internal reflection

• We can define the two conditions necessary for
  TIR to occur
• The refractive index of the first medium is
  greater than the refractive index of the second
  one.
• The angle of incidence is greater than or equal
  to the critical angle
• The phenomenon of TIR causes 100 reflection. In
  no other situation in nature, where light is
  reflected, does 100 reflection occur. So TIR is
  unique and very useful

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Application 1 Periscope

• Porro prism used to change propagation direction
• Periscope consists of two right angle prisms
• To observe subjects at high level

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Application 1 Porro prism

• In submarine to see above the sea surface

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Application 1 periscope
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Trapping and guiding of light

• Water flow or plastic pipe could trap light

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Application 2 light pipe

• Light pipe a bundle consisting thousands of
  individual fibres can be used to transmit image

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Application optical fibre

• Optical fibre
• Consists of core fire and surrounding cladding
  layer and supported in sheath tube
• Very low attenuation for wavelength of 1.3 um or
  1.55um
• Carries 8000 phone channels (copper coaxial
  cable 36)

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Application 3 optical fibre

• Bundle of fibres
• 2432 fibres

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Application 4 LED

• Semiconductor Light Emitting Diode (LED)
• Extraction efficiency

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Application 4 LED

• Initial emitting light is reflected back partly
  Fresnel losses
• Only the emitting light towards surface with
  incident angle smaller than critical angle could
  contribute to external light escape cone

• Improved by using quater-wavelength deposit film
  (discuss later)
• Improved by using dome shaped encapsulates or
  advanced die shape

LED mesa side view
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High extraction efficiency LED

• dome shaped encapsulates

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High extraction efficiency LED

• Advanced die shape to minimize trapping of light

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Handout 1 Optical fibre cables

• The optical fibres are then placed in cables to
  ensure conditioning (in tubes or ribbons), as
  well as mechanical and chemical protection. The
  reduced size and weight of optical fibres cables
  allow laying of lengths in excess of 4800 m
  compared to only 300 m with coaxial copper cable.
  To take into account the railway environment, the
  length of Telecom cables is limited to 2100 m.
• The main structures of optical fibres cable are
  - free tubed structure cable (N fibres in m free
  protection tubes helically placed around a
  central carrier). Standard capacity is 2 to 432
  fibres, - central tube cable (N free fibres in 1
  central tube, rigidity being ensured by
  mini-carriers placed in the sheath), - Ribbon
  cable with central tube (N fibres next to each
  other in m ribbons in 1 central tube). Standard
  capacity is 18 ribbons of 12 fibres, that is to
  say 216 fibres. The advantage of this type of
  cable is the possibility to splice all fibres in
  one ribbon at the same time, - Ribbon cable with
  free tubes (N fibres next to each other in m
  ribbons in p helical free tubes around a central
  carrier).

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Handout 2 Acceptance angle

• Only the light incident with angle smaller than
  acceptance angle ?m is allowed to transit with
  low attenuation