Crash Course on Optics I & II. COST Action IC1101 OPTICWISE 4 th Training School

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1 Crash Course on Optics I & II COST Action IC1101 OPTICWISE 4 th Training School

2 Introductory Concepts Fermat s principle Snell s law Total internal refraction Dispersion Aberrations Interference and Diffraction Polarization Gaussian Beam Propagation

3 Introductory Concepts Microwave Waveform Generator Filtering Antenna remoting, L.O. generation/ distribution Fiber Optic Sensors Photonics Smart structure Homeland security Inertial sensors ( gyro, acceler.,.) Acoustic Sensor ( hydrophones,..). Imaging LED-LCD TV Medical imaging Infrared Cameras 3D Imaging Digital Photonics Photonic ADC & wideband digitizer Optical Computing. Optics Fiber Optic Link High data rate interconnections Secure Comms. Optical interconnect In package Chip On board Board to Board.. Quantum Optics Cryptography Optical computers Secure comms Medical Optics LASIK, Surgery with lasers Diagnostic equipment to Chip

4 Introductory Concepts Light is an electromagnetic wave. λ = c n T λ = c nf n: index of refraction

5 Introductory Concepts The Electromagnetic Spectrum: The electromagnetic spectrum spans over 20 orders of magnitude, from radio waves to cosmic rays. The optical portion of that spectrum includes not just visible light (0.4μm< λ < 0.7μm) but the infrared and the ultraviolet radiation as well.

6 Some definitions: Introductory Concepts

7 FERMAT S PRINCIPLE

8 Fermat s Principle Fermat s principle states that: out of the many paths that can connect two given points P and Q, the light ray will follow that path for which the optical path length between the two points is a extremum, i.e. where the variation of the integral means that it is a variation of the path of the integral and the end points P and Q remain fixed.

9 Mirages Fermat s Principle Natural Consequences of Fermat s Principle: Atmospheric Refraction

10 Looming Fermat s Principle Natural Consequences of Fermat s Principle:

11 Fermat s Principle Snell s Law: All of the important laws of geometrical optics can be derived from Fermat s principle (fundamental theorem of geometrical optics). a.) the rectilinear propagation of light in homogeneous media b.) the law of reflection θ ' = θ c.) the law of refraction or Snell's law Snell's law is all anyone needs to know about geometrical optics in order to do optical design. -O. N. Stavroudis

12 Fermat s Principle Derivation of the Law of Reflection:

13 Derivation of the Law of Reflection: Fermat s Principle

14 Fermat s Principle The Critical Angle and Total Internal Reflection:

15 Fermat s Principle Total Internal Reflection Examples:

16 DISPERSION

$Dispersion Most optical materials that are transparent in the visible spectral range (e.g., glass or quartz) have a refractive index between 1.4 and 1.9.$

17 Dispersion Most optical materials that are transparent in the visible spectral range (e.g., glass or quartz) have a refractive index between 1.4 and 1.9. Furthermore, this refractive index varies with wavelength in a manner similar to that indicated below. This variation of index with wavelength is called dispersionbecause it results in light being dispersed by a prism into a spectrum.

18 Dispersion Natural consequences of dispersion

19 OPTICAL ABERRATIONS

20 Aberrations Chromatic aberration (Chromatic Dispersion) Longitudinal Chromatic Aberration Transverse Chromatic Aberration

21 Sub-title Chromatic Dispersion Dispersion on fibers.

22 Aberrations Chromatic aberration, how to correct:

23 Spherical aberration: Aberrations

24 Aberrations Coma A star without correction With correction

25 More on aberration.. There are infinitely many types of aberrations..

26 More on aberration.. Supervision LASIK

27 Wavefront correction First, you need to know how to measure the wavefront. Microlens array:

28 Wavefront correction Second, obtain the iris wavefront

29 Wavefront correction Third, apply laser beam to correct the aberration

30 Adaptive optics Adaptive optics is used to correct the waveform.

31 Military application Adaptive optics

32 Adaptive optics Wireless optical communication

33 Fresnel Lenses Traditional lenses vs Fresnel Lenses

34 Fresnel Lens Examples: Lighthouse Harnassing sunlight

35 INTERFERENCE AND DIFFRACTION

36 Interference and Diffraction There are three fundamental mechanisms for manipulating the propagation of light: Reflection (Law of Reflection) Refraction (Snell's Law) Diffraction (Huygens-Fresnel Principle) Diffraction is a general characteristic of wave phenomena, occurring whenever a region of the wavefront is altered in either amplitude or phase. Hence, if a propagating wavefront encounters an obstacle, either transparent or opaque, the various segments of the wavefront that propagate beyond the obstacle interfere, causing interference fringes to occur in the irradiance pattern observed behind the obstacle. These diffraction effects occur for all wave phenomena, be it sound waves, matter waves, or light waves.

$Interference and Diffraction Diffraction is the ability of light waves to bend around obstacles placed in their path.$

37 Interference and Diffraction Diffraction is the ability of light waves to bend around obstacles placed in their path. Water waves easily bend around obstacles, but light waves also bend, as evidenced by the lack of a sharp shadow on the wall.

$Interference and Diffraction When an opaque body is placed midway between$ intricate shadow made up of bright and dark regions quite unlike anything

intricate shadow made up of bright and dark regions quite unlike anything

$The phenomenon of diffraction has thus been defined as any deviation of$

38 Interference and Diffraction When an opaque body is placed midway between an observing screenand a point source, diffraction effects produce an intricate shadow made up of bright and dark regions quite unlike anything one might expect from the principles of geometrical optics. The phenomenon of diffraction has thus been defined as any deviation of light rays from rectilinear paths that cannot be interpreted as reflection or refraction.

39 Grimaldi Discovers Diffraction (1665) In 1665 Grimaldi observed the gradual transition from light to dark in the shadow region behind an aperture. This observation was contrary to the corpuscular theory of light that was accepted at the time.

40 Huygens Wavefront Construction (1678)

41 Water waves A wave generator sends periodic water waves into a barrier with a small gap, as shown below.

42 Water waves A wave generator sends periodic water waves into a barrier with a small gap, as shown below.

Young s Interference Experiment (1802) Young s interference experiment in 1802 provided indisputable experimental evidence that light exhibits a wave-like nature.

43 Young s Interference Experiment (1802) Young s interference experiment in 1802 provided indisputable experimental evidence that light exhibits a wave-like nature. However, so strong was Newton s influence (Newton was an advocate of the corpuscular theory of light) in the scientific community, that neither Huygens nor Young s work gained widespread acceptance at the time.

44 Interference The resultant displacement of two simultaneous waves (blue and green) is the algebraic sum of the two displacements The composite wave is shown in yellow Constructive Interference Destructive Interference The superposition of two coherent light waves results in light and dark fringes on a screen.

45 Interference s 1 s 2 Constructive Bright fringe s 1 s 2 s 1 Destructive Dark fringe s 2 Constructive Bright fringe

46 Interference s 1 s 2 d q x d sin q p 1 Path difference determines light and dark pattern. p 2 y Dp = p 1 p 2 Dp = d sin q Bright fringes: d sin q = nl, n = 0, 1, 2, 3,... Dark fringes: d sin q = nl/2, n = 1, 3, 5,...

$Diffraction for a Circular$ passing through a circular

47 Diffraction for a Circular Opening The diffraction of light passing through a circular opening produces circular interference fringes

48 Resolution of images Consider two object in the image plane. Clear image of each object Separate images barely seen θ d 1 d 2 θ

49 Resolution of images When the separation of the two point sources is such that it is just possible to determine that there are two points instead of one, the points are said to be resolved.

50 Question If the pupil of your eye in good light is 2 mm in diameter, what s the smallest feature that you can resolve from 1 meter? (visible light is 500 nm)?

51 Phase of light Spatial Phase: E sinkx t n k = 2π λ = 2πn λ 0 Spatial phase Propagation constant Temporal phase Recall, wavelength l changes inside a material c l0 f l fl0 c l n n As a wave passes through any material, its phase shifts For a distance d, we have: Spatial Phase = φ spatial = kd = 2πnd λ 0 d

52 Interference in space s 1 s 2 d q x d sin q p 1 y Phase difference determines light and dark pattern. Δφ = φ 1 φ 2 Δφ = 2πm for BRIGHT FRINGES Δφ = πm for DARK FRINGES p 2 Δφ = 2πnd 1 λ 0 2πnd 2 λ 0 Bright fringes: d sin q = nl, n = 0, 1, 2, 3,... Dark fringes: d sin q = nl/2, n = 1, 3, 5,...

53 Phase of light Temporal Phase: E = E o cos kx wt = E 0 e i(kx ωt) Spatial phase Temporal phase Temporal Phase = φ t = ωt Temporal phase is independent of index of refraction

54 Interference in time When you combine two (or more) waves, you need to know the phase shift between them: The angle φ is the phase shift When the phase shift is zero, the waves add constructively The result is bigger Same thing for any even multiple of π When the phase shift is π, the waves add destructively The result is smaller Same thing for any odd multiple of π sin E Asin x B x Constructive interference Destructive interference

55 Michelson interferometer Configuration: Michelson interferometer consists of a coherent light source, a beam splitter BS a reference mirror,a movable mirror and a screen. Applications: There are many measurements that Michelson interferometer can be used for, absolute distance measurements, optical testing and measure gases refractive index. Work method: The BS divides the incident beam into two parts one travel to the reference mirror and the other to the movable mirror.both parts are reflected back to BS recombined to form the interference fringes on the screen.

56 Michelson interferometer M 2 Mirror M 1 ' d M 1 Laser Mirror G 1 Beam splitter Can you measure the lasers wavelength? G 2 Compensating plate Observation screen

$Applications: refractive index measurement, light modulation Work method: BS1 divides the incident beam into 2 beams, mirrors M1&M2 reflect beams to BS2. BS2 recombine the beams.$

57 Mach-Zehnder interferometer Configuration: consists of a light source, a detector, two mirrors to control the beams directions and two beam splitters to split and recombine the incident beam. Applications: refractive index measurement, light modulation Work method: BS1 divides the incident beam into 2 beams, mirrors M1&M2 reflect beams to BS2. BS2 recombine the beams. interference fringes produced depending on the path difference. measure thickness at constant refractive index measure refractive index at constant thickness

58 POLARISATION

59 Polarization Light wave that propagates in the z direction: E E x y (z,t) (z,t) E E 0x 0y cos(kz -t) cos(kz -t )

60 Linearly Polarized Light Light is linearly polarized if ε = 0 : E E x y (z, t) (z, t) E E 0x 0y cos(kz -t) cos(kz -t)

61 Vertically polarized light If there is no amplitude in y (E oy = 0), there is only one component, in x (vertical). E E x y (z, t) (z, t) E 0 0x cos(kz -t)

62 Polarization at 45º - 1 If there is no phase difference (ε=0) ande0x = E0y, then Ex = Ey E E x y (z, t) (z, t) E E 0 0 cos(kz -t) cos(kz -t)

63 Polarization at 45º - 2 If there is no phase difference (ε=0) ande0x = E0y, then Ex = Ey

64 Circular Polarization - 1 If the phase difference is (ε = π 2 ) and E 0x = E 0y then the light is circularly polarized. E E x y (z, t) (z, t) E E 0 0 cos(kz -t) cos(kz -t 2)

65 Circular Polarization - 2 If the phase difference is (ε = π 2 ) and E 0x = E 0y then the light is circularly polarized.

66 Other polarization states: Elliptical polarization Linear + circular polarization = elliptical polarization

67 Poincaré sphere The polarization state is represented graphically by the Poincaré sphere (diagram below) on the surface of which any possible SOP can be plotted. The equator of the sphere represents linear polarization states, the vertical (V) and the horizontal (H) corresponding to the two defined orthogonal linear polarization axes. The poles of the sphere represent right and left circular polarization. In the coordinate system shown in the diagram, the surface of the northern hemisphere represents any lefthanded elliptical state and the surface of the southern hemisphere represents any right handed elliptical state.

68 Retarders In retarders, one electric field component gets retarded, or delayed, with respect to the other one. There is a final phase difference between the 2 components of the polarization. Therefore, the polarization is changed. Most retarders are based on birefringent materials (quartz, mica, polymers) that have different indices of refraction depending on the polarization of the incoming light.

69 Quarter-Wave plate Special case: incoming light polarized at 45º with respect to the retarder s axis Conversion from linear to circular polarization (vice versa)

70 Half-Wave plate Retardation of ½ wave or 180º for one of the polarizations. Used to flip the linear polarization or change the handedness of circular polarization.

71 Polarizer 1 Linear Polarizer: Input light: unpolarized --- Output light: linear polarized I out = I in 2 Input light polarized, output light polarized Malus law: I out = I in cos 2 (θ)

72 Polarizer 2 Circular Polarizer: Input light: unpolarized --- Output light: circularly polarized Made of a linear polarizer glued to a quarter-wave plate.

73 Polarization Beam Splitter/Combiner Divides/combine to orthogonal polarization states

74 Polarization controller Different types of polarization controller λ 4 λ 2 λ 4

75 GAUSSIAN BEAMS

76 Gaussian Beams

77 Gaussian Beams E r, z = A 0 W(z) e r2 W(z) 2 Gaussian beam at z=0 E A W 0 0 E r, 0 = A 0 W 0 e r 2 W 0 2 A0 ew 0 -W z W z

78 The characteristics of Gaussian beam Thin Lens Beam radius z

79 Intensity of Gaussian beam Intensity of Gaussian beam z=0 z=z 0 z=2z 0 y y y x x x I 1 1 I0 I0 I0 I I W W W The normalized beam intensity as a function of the radial distance at different axial distances

80 Beam Divergence ω z = ω z z 0 2 1/2 z 0 = πω 0 2 λ ω z = ω zλ πω /2 ω(z) 2W0 Beam waist W0 -z0 q0 z0 z The beam radius W(z) has its minimum value W0 at the waist (z=0) reaches at z=±z0 and increases linearly with z for large z. 2W 0

81 Beam Divergence W(z) If z >> z 0 ω z zθ 0 -z0 2W0 W0 q0 Beam waist z0 q 0 l W 0 z The beam radius W(z) has its minimum value W0 at the waist (z=0) reaches at z=±z0 and increases linearly with z for large z. 2W 0 The beam area is doubled at Rayleigh range

82 Depth of Focus Since the beam has its minimum width at z = 0, it achieves its best focus at the plane z = 0. In either direction, the beam gradually grows out of focus. The axial distance within which the beam radius lies within a factor of its minimum value (i.e., its area lies within a factor of 2 of its minimum) is known as the depth of focus. o 0 2 z 2z 0 2W l 2 0 2z o The depth of focus of a Gaussian beam.

83 Radius of Curvature Beam radius z R() z z z z 2 0 z 0 = πω 0 2 λ

84 Beam Shaping Beam focusing Beam expanding

85 Propagation of a Gaussian beam through a lens Gaussian beam propagating in air with beam waist w1 is located at distance d from a lens of focal distance f.

86 Gaussian Beams ) (, 1 1 ) ( ) ( 2 ) ( exp ) ( exp ) ( ),, ( z z z z n w z z R n w z z z w n w z w z w z R kr z kz i z w r z w w E z y x E l l l divergence Beam curvature of Radius ) ( ) Rayleigh range ( spot size Beam width, ) ( aist, Beam w n z R z z z w w w R l q

87 THE END

PRINCIPLES OF PHYSICAL OPTICS

PRINCIPLES OF PHYSICAL OPTICS C. A. Bennett University of North Carolina At Asheville WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION CONTENTS Preface 1 The Physics of Waves 1 1.1 Introduction