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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 = 6.610-34 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 + sinout) =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 + sinout) =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 + sinout) =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 jt jt 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: jt 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 jt 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 jt E(0) = E 0 (x' cosa + y' sin a) e ˆ ˆ j jt 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 sinout =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 jt 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: θl 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