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ENEE 486 – Basic Optics

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ENEE 486 – Basic Optics Powered By Docstoc
					ENEE 486 - Optoelectronics Laboratory - Fall 2000


Instructor: Dr. Julius Goldhar
Teaching Assistant: Ms. Sukanya Tachatraiphop
 Lecture: Mondays 1-1:50, Jasmine Computer Classroom
 Lab: Mondays 2-5 PM; Rm 1170, Eng Lab Bldg.
Website

    http://www.ece.umd.edu/courses/enee486.F2000/

          Course Information
          Instructor Infomation
          Calendar
          Laboratory instructions
          Lecture slides (preliminary)
          Guidelines for writing reports
Instructor information

   Instructor: Julius Goldhar
   Office: Room 2317 A.V.Williams Bldg.
   Phone: (301) 405-3738
   email: jgoldhar@eng.umd.edu
   Office Hours: M,W 10-11, or by appointment


   Teaching Assistant: Ms. Sukanya Tachatraiphop
   Office: Room 4448 A.V. Williams Bldg
   Phone: (301) 405-3730
   email: sukanya@eng.umd.edu
   Office Hours:
Grading

 The grade will be based on the laboratory reports
 and two quizzes.

 The quizzes determine 50% of the grade.


 For details look at the web:
 Guidelines for writing reports for ENEE 486
Calendar of events- tentative

First lecture: Monday September 11, 1:00-1:50 PM.
Lab tour and demos: Monday September 11, 2 –2:45 PM.
Labs 1,2,3,4 - September 18th, September 25th, October 2nd,
              October 9th
Labs 5,6,7 - October 16th, October 23rd, October 30th, November 6th,
   Quiz #1 - October 30th
Labs 8,9,10 - November 13th, November 20th, November 27th,
               December 4th
Quiz #2 - December 11th
Schedule of rotation for different groups between the labs will be posted
Rotation schedule

         Lab#       Groups
          1     A     D      C   B
          2     B     A      D   C
          3     C     B      A   D
          4     D     C      B   A

          5     A     D      C   B
          6     B     A      D   C
          7     C     B      A   D

          8     A     C      B   x
          9     B     A      C   x   New 3 groups
          10    C     B      A   x
ENEE 486 – Basic Optics


1. Detectors of light: Power, Resolution in time, Resolution in space


2. Refraction of light: Prisms, Index of refraction, TIR


3. Reflection of light: Index of refraction, Brewster’s angle


4. Diffraction: Gaussian beam propagation, slit pattern
ENEE 486 – Applications of Optics

5. Image Formation: Simple and compound lenses, telescope, microscope

6. Gratings & spectrometers: The grating formula, blaze angle
7. E/O and A/O modulators: Natural and induced birefringence,
                    Pockels’ cell, diffraction of light by sound

8. N2 pumped dye laser: Spontaneous emission, gain, feedback, tunability

9. Fiber optics: Numerical aperture, transverse modes, bandwidth,
                optical communication
10. Fourier Optics: Diffraction, 2-D fourier transforms, filtering,
                     pattern recognition
Lab# 1. Detectors of light



       Measuring optical power,
       Neutral density filters,
       Optical density,
       Photocell, Quantum efficiency,
       Resolution in time, PIN diode
       Resolution in space, CCD array
Optical power can be measured directly
with a commercial power meter



                                          MilliWats
laser beam


                                           Range
                                                      on

                                                      off



                         Turn off the meter after use!
Neutral density filters are used to vary light power

             ND filter
                                           MilliWats
laser beam



   OD = Optical density
 Transmission = 10 -OD
             OD      T
               0   100%
             0.3    50%
               1    10%
               2     1%
Photocell generates current from light
                        Photocell

laser beam                          electrical signal




                    Multi- meter
                    Current                  0.1000 mA
                    +       -
Photocell currrent is directly proportional to
light power
             ND filter       Photocell

laser beam


                                             current




                         i


                             Optical power
Photons generate electron-hole pairs in a photocell

                                Photocell

            laser beam                      Current = 2e Ne

 Power = hn Np

h = 6.610-34 Joule-sec
                                        e = 1.6 10-19 Coulombs
n=c/l       l = c/n =632.8 nm           Ne= #of electrons /second
Np= #of photons /second                 factor of 2 is due to e-h pairs


Quantum efficiency = Ne /Np
Electrical power output from the photocell depends
on the load resistance
                            Photocell

       laser beam                                               +
                                                      RL        V
                                        I
                                                                -



 Electrical Power = I V = I2RL = V2/RL

 Photocell acts as a non-ideal current ( or voltage) source.
 Optimal electrical power dissipation in the load occurs when
 RL is equal to the source impedance (which depends on optical power)
PIN diodes are designed for efficient measurement of
fast temporal variations of optical signals
                                         -     +
                                I

                                    p        RL
       Optical signal                                     +
                                    i                     V
                                                          -
                                    n



       Reverse bias in PIN diode quickly sweeps out the
       optically generated carriers
Chopper provides temporal modulation of
optical beam

                                          oscilloscope



                          PIN
                          diode   RL
                                               C
Load resistance and parasitic capacitance
determine the signal’s rise and fall times
      Voltage        tF         tR




                                                          time


                                     tR = tF ~ 2RC
      PIN
                RL
      diode                 C = Cdiode+Ccable+Cscope

                                     Ccable~ 30 pf/foot
CCD array detects spatial variation in optical
illumination

      Diode Array                                   Oscilloscope


                                     Diodes
       1024 diodes                   Video
                                     Trigger         Vert.   Horiz.




    The signals from photodiode array are read out in serial fashon
Lab#2. Refraction of light


      Snell’s law,
      Prisms,
       Index of refraction,
      Angle of minimum deviation
      Critical angle,
      Total internal reflectionn
Snell’s law describes refraction of light


                 n1                   n2

               1
                                      2




          n1 sin 1 = n2 sin 2
It is easy to calculate beam deflection for
normal incidence to first surface of prism
                                             n2 =1
                              n1
                 1 =30o
                                                 a
     HeNe
                                        2
                            30o
            No refraction
                                  n1 sin 1 = sin 2
                                   a = 2 - 1
   n1 can be calculated from measured value of a
Calculation is more complicated for an
arbitrary angle of incidence


               n                4
                                         a
     1

                     30o   n sin 3 = sin 4
 sin 1 = n sin 2
                           a = 1 + 4 - 30o
  2 + 3 = 30o
The plot of angle of deflection vs angle of
incidence has a minimum


            n =1.5
                                           a
                                 0.8

     1                          0.7


                                 0.6



                     30o
                             a
                                 0.5


                                 0.4


                                 0.3


                                 0.2

                                 0.1




                                       0
                                               1
  angle of minimum deviation
Variation in index of refraction with
wavelength causes dispersion

                                        rainbow
                           n1
   white light
                         30o



                                              screen
Total Internal Reflection occurs when 1 exceeds
the critical angle

                n1
                                       n2

            1=C              2 = p / 2




          n1 sin C = n2
Lab #3. Reflection of light


   Reflection form a dielectric interface
   Index of refraction,
   Brewster’s angle
Optical power reflection coefficient can be readily
calculated for normal angle of incidence

                      Incident          Transmitted
      HeNe

                      Reflected
     Reflected power
  R=                              n1   n2
     Incident power

                  2
       n1 - n 2
    R=
       n1 + n 2
Multiple reflections need to be considered for
reflection from a parallel plate
                           Incident         Transmitted
       HeNe
                   Reflected
Incoherent addition of power
                                      n1 n2 n1=1
   Rtot ~ R+(1-R)R(1-R)+ ....
   Rtot ~ 2R - 2R2 + ...
   R can be calculated from the measured value of Rtot

   n2 can be calculated from R                     2
                                           n2 -1
                                        R=
                                           n2 +1
We can define two orthogonal states of polarization
for a beam incident on a surface at an angle

           TM polarization (P)




             TE polarization (S)
                   .
Reflection from a dielectric interface depends
on the polarization of light
                       n1 n2 n1=1


                                1

Field reflection coefficients                  n1sinθ1 = n 2sinθ2
       n1 cos θ1 - n 2 cos θ2
 rTE =
       n1 cos θ1 + n 2 cos θ2
                                     Power reflection coefficient
       n 2 cos θ1 - n1 cos θ2
 rTM =                                     R = |r|2
       n 2 cos θ1 + n1 cos θ2
Beam with TM polarization has zero reflectivity at
                     0.7


the Brewster’s angle 0.6
                                        0.5




                     Power Reflection
                                                                            TE
    n1 n2 n1=1                          0.4


                                        0.3


   1                                   0.2


                                        0.1
                                                                            TM

                                         0
                                          0   10   20   30   40   50   60    70   80



        tan B= n2/n1                         Brewster’s angle
Lab#4. Diffraction




    Gaussian beam propagation,
    Rayleigh range
    slit pattern
Laser beam profile is measured by using a rotating
mirror to sweep the beam across the apperture

       laser beam                         rotating
                                          mirror




                    apperture


 to oscilloscope            detector
A good laser mode has a Gaussian beam profile

        1


                                                                   - 2 (r/w)   2
                                             I(r) = I 0 e
       0.8
I/I0
       0.6


       0.4

                                         w
       0.2
   0.135
                                                             e-2

        0
            -5   -4   -3   -2   -1   0   1   2   3   4   5
                                                             r/w
Laser beam expands as it propagates
                                                                  r 2
                                                          - 2(        )
                           w(z)           I(r, z) = I0e          w(z)


                                                                     2
                                                             z
                                             w(z) = w 0   1+  
                                                             b
              propagation distance
                                      z
        z=b
                                              2
                                         w0
Beam area doubles when z = b         b=π           Rayleigh range
                                          λ
The diffraction angle is inversely proportional to w0

                                                               2
                                                         z
                                       w(z) = w 0     1+  
                      w(z)                              b
                               z
                                                                   2
                                                           w0
      z=b
                                     Rayleigh range    b=π
                                                            λ
    for z >> b
              z       zl       zl             w(z)    l
    w(z) = w 0 = w 0        =              =      =
              b      pw 0
                          2
                              pw 0             z     pw 0
Small slit produces a characteristic diffraction pattern




                                    




                                                      sin 2 
               πdsinθ π d θ                    I ()  2
            β                                         
                 λ      λ
        I () = 0   when  = np or  = nl /d
The size of a slit can be calculated from the
diffraction angle



   d                                      1




        Angle for the first minimum:

         1 = l /d                     d = l / 1
The size of a slit can be also measured directly by
projecting and magnifying its image

              Microscope
     d        objective


                            Y
              Principal
              plane
         f=16 mm                    Magnified image
                                    on a screen

              Magnification = Y/f
Lab#5. Image Formation



Thin lens imaging equation,
Simple and compound lenses,
telescope,
microscope
Image formation with a thin lens of focal length f

  Object                                 Image


           X                  Y


               1 1 1
                + =
               X Y f
For objects located distance 2f from the lens, the
image is also 2f away from the lens

                              real, inverted, same size
                                             image
                f      f
                                  2f



                    1   1 1
                      +  =
                    2f 2f f
For objects located further than 2f from the lens, the
image is real and smaller



                                real, inverted, same size
                                               image
                 f      f
                                   2f
For objects located closer than 2f from the
lens, the image is real and larger

                                real, inverted, larger
                                              image
             f       f
Objects located at a distance f from the lens
form the image at infinity




               f       f



                              no image
For objects located closer than f from the lens,
the image is virtual and larger

                       image

virtual, not-inverted, larger

                       f        f
A lens with a negative focal length always
forms a virtual image


 virtual, not inverted, smaller


                           image


                      f           f

                             concave lenz
Simple lens with large f# produces a distorted image




                                             Distorted
                                             image
Camera lenses produce great images




                                     Good
                                     image
Complex lens can be modeled by a simple
lens located at the principal plane
The thin lens equation can be generalized to
complex lenses
Calculating focal length of a two lens system




             1   1 1    L
                = + -
            feff f1 f2 f1f2
Maximum size of the image is determined by
how close the object is to the eye


    object
                                                         image

                       X                            Y

                                            Magnification = X/Y
X~ 25 cm for comfortable viewing
Y~ f1 = focal length of the eye’s lens

             If the object is brought closer,
             the image is larger and out of focus
Magnifying glass permits bringing the object
closer to the eye


                object
                                                   image

                         X                   Y

                             Magnification ~ X/Y

     X~ fe , focal length of the eye piece         Y~ f1

      The image is increased in size by Me~ 25/fe
Microscope has two stages of magnification


          Objective                          Eyepiece

object

                                   image 1
                                                             image 2
         X1               Y1                    X2      Y2

         Mo= Y1/X1 ~25/fo           Me~ 25/fe

              Total magnification M = Mo * Me
Telescope magnifies image of a distant object

                                 fo
                                                           fe   f1
object
                                               image 1
                                                                     image 2
               L >> fo, fe


     Without the telescope M1= f1/L
         With the telescope M= (fo/L) * (f1/fe) = M1 * fo/fe
Lab#6 Gratings & spectrometers


      Transmission gratings,
      The grating formula,
      Reflection gratings
      Littrow angle,
      Absorption spectrometer
      Blaze
      Monochromator
Transmission grating can produce several
diffracted beams
                          m= -1
                                  m=0 beam is undeflected




   in                               m=1 first order
                           out
                             m=2 second order

          d(sin in + sinout) =ml
Diffracted beams are observed for the angles for
which there is constructive interference


                                      A+B= ml

         in        d          out
The grating formula is obtained with simple geometry




  in
                     d                   out
                    in out




              d(sin in + sinout) =ml
The same grating formula applies to
a reflection grating
                                              m= -1
             grating acts like a mirror m=0


                  first order   m=1

                                      in 
                                           out
   d(sin in + sinout) =ml
                                      m=2
                                      second order
Littrow angle means that a diffracted beam
is reflected back on itself




      in = out


     2dsin in =ml
Grating disperses white light
Absorption spectrometer can be constructed with a
rotating grating

                       sample
                                             rotating
beam of white light                          grating




                      apperture


 to oscilloscope                  detector
Converting time to wavelength




                                             α             2π
                                          θ = - (t - t 0 )
                                             2             T

    d (sin in + sin out) = nl

    with   in= -     and    out= a-
Monochromator is used for precise
wavelength measurement

                   output slit




   input     
   slit
Lab #7 E/O and A/O modulators


  Induced birefringence,
  Natural birefringence in crystals
  Pockels’ cell,
  Diffraction of light by sound
  Acousto-optical modulator
Stress induced birefringence is observed by placing
the sample between crossed polarizers
                               Polarizer

            Diffuser
     HeNe



                       Plexiglass
                       under stress        Screen
Rotation of polarization is stongest when the stress is
at 45o to the polarization direction
                                Polarizer

            Diffuser
     HeNe



                       Plexiglass
                       under stress
                                             Screen
Natural birefringence results in characteristic
isogyre pattern



        Diffuser
 HeNe
                                                   c




                   Uniaxial
                   Birefringent
                   crystal
                                              Screen
                                  Polarizer
Electric field of incident beam can be decomposed
into components along eigen directions

              ^
              x                x’ and y’ are eigen directions
   ^
   y’

          a                   ^
                              x’



   Propagation distance
           z =0
                        jt                                  jt
        E(0) = E 0 xe
                   ˆ          = E 0 (x' cosa + y' sin a) e
                                     ˆ         ˆ
Beam components along eigen directions propagate
as plane waves with different k’s

              ^
              x         x’ and y’ are eigen directions
   ^
   y’                   have propagation constants k1 and k2

          a              ^
                         x’                    k1 =n1/c
                                               k2 =n2/c

  After propation through
  crystal the field is given by:
                                                                       jt
        E(l ) = E 0 (x' cosa e
                     ˆ           -jk1l
                                         + y' sin a e
                                           ˆ            -jk 2 l
                                                                  )e
Polarization of the output light depends on the
phase shift between the two eigen directions

                                                  j      jt
      E(l ) = E 0 e   -jk1l
                              (x' cosa + y' sin a e ) e
                               ˆ         ˆ

                            
           = (k1 + k 2 )l = (n1 - n 2 )l
                            c
   No change in polarization (dark rings) when  =2mp

                                                       2p c
         Δnl = 2mp                Δnl = ml 0       l0 =
       c                                                 
Dark rings in isogyre pattern indicate no change of
polarization
                                               jt
    E(0) = E 0 (x' cosa + y' sin a) e
                ˆ         ˆ
                                                     j   jt
     E(l ) = E 0 e   -jk1l
                             (x' cosa + y' sin a e ) e
                              ˆ         ˆ
   No change in polarization (dark rings) when  =2mp

                                                          2p c
        Δnl = 2mp                 Δnl = ml 0          l0 =
      c                                                     
 Dark cross corresponds to propagation directions for
 which the polarization was along one of the eigen direction
In uniaxial crystal one index of refraction is constant
(ordinary) and the other (extraordinary) varies with 
  n1=n0         Ordinary

  n2=ne()     Extraordinary


          cos 2  sin 2θ 
         
  n() =      2
                  +    2 
                            n o + (n o - n e ) sin 2 
          no       ne 
No change in polarization (dark rings) when  =2mp




                                         d
                                      l=
                                         cosθ
              d

      |ne() – ne| l = mlo

                       d
                                     Birefringence:
    (n 0 - n e )sin θ
                  2
                           = mλ o
                      cosθ                    mλ o cosθ
                                    n0 - ne =
                                               d sin 2θ
Pockels’ cell consists of an electro-optical
crystal with attached electrodes



        Diffuser Pockels’
                 cell
 HeNe
                                                    c




                 V=0
                                               Screen
                              Polarizer
Voltage applied across an electro-optical
crystal changes the isogyre pattern


                Pockels’
                cell




                 +V-
                                            Screen
                             Polarizer
Voltage applied to the Pockels’ cell modulates
the transmission through the polarizer

                                            V p
                                   T = sin   
                                          2

                                           Vp 2 




When the applied voltage is Vp the transmission is maximum
Double pass through the Pockes’ cell reduces
Vp by a factor of two
Inside AO modulator RF excited acoustical wave acts
as a grating and diffracts the laser beam
                       AO modulator



                                        in=0
 RF oscillator      Amplifier
                                    d sinout =ml

                    d = L = vs /n
                 speed of sound/frequency
At normal incidence the diffraction efficiency is the
same for + / - orders


                                             m=1
                                             m=0
                                              m= -1
               Acoustical
                 wave
At Bragg angle the diffraction efficiency is
highest for one of the orders
                                           strong order

Bragg angle

                Acoustical                weak order
                  wave


   The direction for diffraction corresponds to reflection
   from the acoustical wavefronts
Lab #8 N2 pumped dye laser


Spontaneous emission,
Stimulated emission: gain,
 feedback,
tunable laser
Ultra violet light causes emission of flourescence
from a dye



         Unfocused                           Spontaneous
         UV laser                            emision

                                   Rhodamin 6G
                   Excited state

                                             Emission

                     Ground state
Directed Amplified Spontaneous Emission is observed
when UV laser is focused


   Focusing
   UV laser
                                    ASE
Aligning the gain line perpendicular to the cell walls
causes laser oscillations

   Focusing
   UV laser




                 Longitudinal laser
Cylindrical lens focuses UV beam to a line on the
surface of the cell




                             Transverse laser

        Cyindrical lens
External cavity can be used to provide laser feedback




     Laser output

                                 Gain

                    microscope
                                            Aluminum
                    slide
                                            mirror
Grating at Littrow angle forms laser cavity




Laser output

                            Gain

               microscope
                                          Grating
               slide
       Rotating the grating changes laser wavelength
Spectrometer for monitoring dye laser output


 laser beam           multimode fiber


      grating
                             lens               slit
  


                                                oscilloscope
                                        ccd
                                        array
Lab#9. Fiber optics


Numerical aperture,
transverse modes,
bandwidth,
optical communication
Optical fiber is a very thin cylinder of glass with a
core that has higher index of refraction than cladding



                                   n2
            core                    n1 > n 2
                                   cladding
Light rays at entering the optical fiber at sufficiently
small angles will be trapped by the TIR



                                     n2
                                          n1
            


   is the largest angle    Numerical apperture:
  for trapped rays              NA =sin
Numerical aperture depends only on indexes
of refraction
      air: n=1               cladding: n2

                                          C
                               1
                            core: n1

  sinθ = n1sinθ1      C = p/2 - 2     n1sin C = n 2

                           NA = sin  =           - n2
                                              2          2
    Numerical apperture:                    n1
The light is trapped when the fiber’s acceptance
angle is greater than the numerical apperture

                                                  d
      core diameter =d
                                 cladding

  A laser beam of diameter d will have the diffracion angle
                 l
            θd 
                 d
  The beam is trapped if d < NA

  Single mode criterion: d ~ NA
Number of allowed modes in a fiber can be
easily estimated


                                            d
        NA
                    d
                            cladding

                                  2
                          NA 
       Number of modes      
                         l 
                          d
Numerical aperture of a fiber can be determined
by measuring the cone angle of the output


     lens
                   fiber
                                         




                  NA = sin 
                                             screen
Number of modes in a fiber can be estimated
from the measured NA and the given core diameter
                  fiber
                                        

                             NA = sin 

                                    2
                            NA 
         Number of modes      
                           l 
                            d
Fiber optic transmission line is used to
transmit data

Electronic data                      Electronic data

                         fiber

   E/O converter                           O/E converter

    Transmitter                              Receiver
Light emitting diode or laser diode can be
used as a simple optical transmitters


                          R       V2
               +V1

       I = (V1 – V2) /R
                          LED
                          or LD
LED exhibits same electrical characteristics as
common rectifying diodes


                  I




                                      V2


                 Find this voltage experimentally
Optical power output from LED increases
monotonically with current


  Optical power




                                 I
Laser diode optical output power has a threshold

                      Optical power
   I




                      V2                           I
 Electrically, LED and LD
                                Laser threshold
 look the same
Reverse biased PIN diode acts as a receiver

               +Vbias


                        PIN

                                      oscilloscope

                              Rload
A simple fiber optic transmission line

          R                     +Vbias
 signal
 input    LED                            PIN



                     fiber                     signal
                                     Rload
                                               output
Direct modulation of LED can be used for
demonstration of optical transmission of audio signals
Lab #10. Fourier Optics



  Fourier transforms
  Diffraction,
  near and far fields
  2-D Fourier transforms,
  filtering,
  pattern recognition
Time and frequency representation of signals
                            


                            
                       1                   jt
                f(t) =           X( j)e
                       2π
                            -
         f(t)                                    f()
Simple example: f(t) =constant


                                 f()= 2p d()
     f(t) =1

                      t
  This is DC signal                              
                                     0
Another simple example: f(t)= cos(w0t)


   f(t)= cos(w0t)         f() =p[d(-0)+ d(+0)]

  f(t)


                    t                             
                                          0




                       2
                           (
                       1 j 0 t
             cos 0 t = e       +e - j 0 t
                                              )
Diffraction in far field naturally produces
Fourier transform of a 2-D image




                             Diffraction

   Plane Wave
                Near Field
                                           Far Field
Propagation distance to the far field increases
rapidly with the size of an object


Diffraction angle:       θl
                               d
Size of the beam:         D   L
Far field requierment:     D >> d      L  l  d
                                            d
                                   2
                              d
                         L 
                              l
Far field is also observed in a focus of a beam


                             focal length
Very simple example: one plane wave

x

z
                                 One small spot
     constant

    E(x)

                      x
                                                  x
    Think of this as DC signal          0
Another simple example: two plane waves

x

z

                                      Two small spots
    Sinusindal modulation

    E(x)
                                                        x
                                           0

                     x
                                    2
                                      (
                                    1 jkx
                            cos kx = e + e - jkx
                                                   )
FFT Discrete Fourier transform.

  FFT(X) is the discrete Fourier transform (DFT) of vector X. If the
 length of X is a power of two, a fast radix-2 fast-Fourier
 transform algorithm is used. If the length of X is not a
 power of two, a slower non-power-of-two algorithm is employed.
 For matrices, the FFT operation is applied to each column.
 For N-D arrays, the FFT operation operates on the first
 non-singleton dimension.
fft



               N
      X(k) =       sum x(n)*exp(-j*2*pi*(k-1)*(n-1)/N), 1 <= k <= N.
               n=1

				
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posted:8/19/2012
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