Lecturer: Ivan Kassamakov, Docent Assistants: Risto Montonen and Anton Nolvi, Doctoral

Transcription

1 Lecturer: Ivan Kassamakov, Docent Assistants: Risto Montonen and Anton Nolvi, Doctoral students Course webpage: Course webpage:

2 Personal information Ivan Kassamakov office: PHYSICUM - PHY C 318 (9:00-19:00) Risto Montonen risto.montonen@helsinki.fi office: PHYSICUM - PHY A 312 Anton Nolvi anton.nolvi@helsinki.finolvi@helsinki office: PHYSICUM - PHY C 317

3 Schedule: Lectures: Tuesdays: 10:15 12:00, , Lecture Room: PHYSICUM - PHY D116 SH; Exercises: Tuesdays: 12:15 14:00, , Lecture Room: PHYSICUM - PHY D116 SH; Demonstrations: Demonstrations: Electronics Laboratory: PHYSICUM - PHY C

4 Lectures Lecture # Week # Place - Lecture Room Date Starting time Ending time 01 OPTIIKKA : LUENTO 3 PHYSICUM - PHY D116 SH :15 12:00 02 OPTIIKKA : LUENTO 4 PHYSICUM - PHY D116 SH :15 12:00 03 OPTIIKKA : LUENTO 5 PHYSICUM - PHY D116 SH :15 12:00 04 OPTIIKKA : LUENTO 6 PHYSICUM - PHY D116 SH :15 12:00 05 OPTIIKKA : LUENTO 7 PHYSICUM - PHY D116 SH :15 12:00 06 OPTIIKKA : LUENTO 8 PHYSICUM - PHY D116 SH :15 12:00 07 OPTIIKKA : LUENTO 9 PHYSICUM - PHY D116 SH :15 12:00 08 OPTIIKKA : LUENTO 11 PHYSICUM - PHY D116 SH :15 12:00 09 OPTIIKKA : LUENTO 12 PHYSICUM - PHY D116 SH :15 12:00 10 OPTIIKKA : LUENTO 14 PHYSICUM - PHY D116 SH :15 12:00 11 OPTIIKKA : LUENTO 15 PHYSICUM - PHY D116 SH :15 12:00 12 OPTIIKKA : LUENTO 16 PHYSICUM - PHY D116 SH :15 12:00 13 OPTIIKKA : LUENTO 17 PHYSICUM - PHY D116 SH :15 12:00 14 OPTIIKKA : LUENTO 18 PHYSICUM - PHY D116 SH :15 12:00

5 Exercises Exercises # Week # Place - Lecture Room Date Starting time Ending time 01 OPTIIKKA : LUENTO 3 PHYSICUM - PHY D116 SH :15 16:00 02 OPTIIKKA : LUENTO 4 PHYSICUM - PHY D116 SH :15 16:00 03 OPTIIKKA : LUENTO 5 PHYSICUM - PHY D116 SH :15 16:00 04 OPTIIKKA : LUENTO 6 PHYSICUM - PHY D116 SH :15 16:00 05 OPTIIKKA : LUENTO 7 PHYSICUM - PHY D116 SH :15 16:00 06 OPTIIKKA : LUENTO 8 PHYSICUM - PHY D116 SH :15 16:00 07 OPTIIKKA : LUENTO 9 PHYSICUM - PHY D116 SH :15 16:00 08 OPTIIKKA : LUENTO 11 PHYSICUM - PHY D116 SH :15 16:00 09 OPTIIKKA : LUENTO 12 PHYSICUM - PHY D116 SH :15 16:00 10 OPTIIKKA : LUENTO 14 PHYSICUM - PHY D116 SH :15 16:00 11 OPTIIKKA : LUENTO 15 PHYSICUM - PHY D116 SH :15 16:00 12 OPTIIKKA : LUENTO 16 PHYSICUM - PHY D116 SH :15 16:00 13 OPTIIKKA : LUENTO 17 PHYSICUM - PHY D116 SH :15 16:00 14 OPTIIKKA : LUENTO 18 PHYSICUM - PHY D116 SH :15 16:00

6 What is light? Aristotle - Light was emitted from our eyes Christian Huygens - Wave theory of light Sir Isaac Newton - Particle theory of light Thomas Young - Wave theory of light Albert Einstein - Particle theory of light de Broglie - Wave-particle duality of all matter

7 What is light? Light is a form of electromagnetic energy detected through its effects, e.g. heating of illuminated objects, conversion of light to current, mechanical pressure ( Maxwell force ) etc. Light energy is conveyed through particles: photons ballistic behavior, e.g. shadows Light energy is conveyed through waves wave behavior, e.g. interference, diffraction Quantum mechanics reconciles the two points of view, through the wave/particle duality assertion

8 What is light? Light exhibits either wave characteristics or particle (photon) characteristics, but never both at the same time. The wave theory of light and the quantum theory of light are both needed d to explain the nature of light and therefore complement each other.

9 Properties of Light The wave-particle duality. A principle of quantum mechanics which implies that light (and, indeed, all other subatomic particles) sometimes act like a wave, and sometimes act like a particle, depending on the experiment you are performing. Light as a wave. E E 0 cos 2 t c E = amplitude of electric field (J) = frequency (Hz) = wavelength (m) c = speed of light (2.998 x 10 8 m/s in vacuum) Light is also viewed as particles or packets of energy - photons. Energy of a photon: Also written as: E h E hc E energy (J) 34 h Planck's constant ( J s) hc ~ ~ 1 wavenumber One photon of visible light contains about Joules

10 Photons Photons are stable, chargeless, massless elementary yparticles that exist only at the speed c. Unlike ordinary objects, photons cannot be seen directly; what is known of them comes from observing the results of their being either created or annihilated Photons begin and end on charged particles; most often they are emitted from and absorbed by electrons.

11 Why can t we see a light beam? Unless the light beam is propagating right into your eye or is scattered into it, you won t see it. This is true for laser light and flashlights. This is due to the facts that: air is very sparse (N is relatively small), air is also not a strong scatterer, and the scattering is incoherent. This eye sees almost no light. This eye is blinded (don t try this at home ) To photograph light beams in laser labs, you need to blow p g p g, y some smoke into the beam

12 Photons "What is known of [photons] comes from observing the results of their being created or annihilated. " Eugene Hecht What is known of nearly everything comes from observing the results of photons being created or annihilated. Prof. Rick Trebino Georgia Institute of Technology School of Physics Atlanta

13 Light is not particles, not waves, but BOTH! Louis de Broglie Light is, in short, the most refined form of matter.

14 Sources of light When a charge moves nonuniformly, it radiates Linearly accelerating charge Synchrotron radiation - light emitted by charged particles deflected by a magnetic field Bremsstrahlung (Braking radiation) - light emitted when charged particles collide with other charged particles B

15 Тhe majority of light in the universe comes from molecular vibrations emitting light. Electrons vibrate in their motion around nuclei High frequency: ~ cycles per second. Nuclei in molecules vibrate with respect to each other Intermediate frequency: ~ cycles per second. Nuclei in molecules rotate Low frequency: ~ cycles per second.

16 The Emission of Light from Atoms Surely the most significant ifi mechanism responsible for the natural emission and absorption of radiant energyespecially of light - is the bound charge, electrons confined within atoms. Excitation of the ground state De-excitation ti with emission i of a photon Ground state ~ 10-8 seconds later

17 Einstein showed that stimulated i i l emission can also occur. Before After Spontaneous emission Absorption Stimulated emission

18 Boltzmann population factors Ene ergy E 3 E 2 E1 N 3 Population density N exp E / k T i i B N 2 N 1 N i is the number density of molecules in state i (i.e., the number of molecules per cm 3 ). T is the temperature, and k B is Boltzmann s constant. t

19 Light in a Medium The light may encounter an electron The electron may absorb the light, oscillate, and reradiate the light The absorption and radiation cause the average speed of the light moving through the material to decrease

20 A light wave in a medium Vacuum (or air) Medium n = 1 n = 2 Absorption depth = 1/ k 0 nk 0 n Wavelength decreases E( zt, ) E(0) exp[ ikz ( t)] 0 0 E0(0) exp[( / 2) z] exp[ i( nk0z t)] The speed of light the wavelength (and k) and the amplitude change The speed of light, the wavelength (and k), and the amplitude change, but the frequency, ν, doesn t change.

21 Light in Bulk Matter The response of dielectric or nonconducting materials to electromagnetic fields is of special concern in Optics. We will, of course, be dealing with transparent dielectrics in the form of lenses,,p prisms,,p plates, films, and so forth, not to mention the surrounding sea of air. The net effect of introducing a homogeneous, isotropic dielectric into a region of free space is to change Ɛ 0 to Ɛ and µ 0 to µ in Maxwell's Equations. The phase speed in the medium now becomes 1 v The ratio of the speed of an electromagnetic wave in vacuum to that in matter is known as the absolute index of refraction n c v o o o permittivity of free space

22 Refractive index and speed of light vacuum (or air) m water (n = 1.33) m glass (n = 1.5) m diamond (n = 2.42) m

23 Refractive index and speed of light vacuum (or air) m water (n = 1.33) m m fastest glass (n = 1.5) m Refractive index Speed of light slowest diamond (n = 2.42) m

24 Some Indices of Refraction n is wavelength and temperature dependent

25 Wave travels via transparent media Remember: E = h F i th Frequency remains the same Velocity and wavelength change

26 Refractive indices for glasses We ll use n = 1.5 for the refractive index of the glass we usually encounter. Dispersion corresponds to the phenomenon whereby the p p p y index of refraction of a medium is frequency dependent.

27 Refractive Index vs. Wavelength Since resonance frequencies exist in many spectral ranges, the refractive index varies in a complex manner. Electronic resonances usually occur in the UV; vibrational and rotational resonances occur in the IR; and inner-shell electronic resonances occur in the x-ray region. n increases with frequency, except in anomalous dispersion regions.

28 Absorption Coefficient and the Irradiance The irradiance is proportional to the (average) square of the field. Since E(z) exp(- z/2), the irradiance is then: I(z) = I(0) exp(- z) where I(0) is the irradiance at z = 0, and I(z) is the irradiance at z. Thus, due to absorption, a beam s irradiance exponentially decreases as it propagates through a medium. The 1/e distance, 1/, is a rough measure of the distance light can propagate into a medium (the penetration depth).

29 Refractive index and Absorption coefficient Refractive index Absorption coefficient n Frequency, Ne /2 Ne 2 ( ) ( /2) 4 ( ) ( /2) n cm 0 e 0 0 me 0

30 The Sellmeier Equation approximates the refractive-index curve for most materials. Coefficient Value B B x10-1 B C x10-3 C x10-2 C x10 2 These values are obtained by measuring n for numerous wavelengths and then curve-fitting.

31 Practical numbers for material dispersion dn/d m Plots borrowed from

32 Propagation of Light Photons interact with matter in a variety of ways Photons encountering an opaque solid can be absorbed (black surface) or reflected (metal surface) Photons encountering a transparent surface can be scattered if path length is long enough (no substance is perfectly transparent) Enhanced scattering of bluer light in atmosphere makes sky blue Molecules can be visualized as absorbing photons and then emitting them in a new direction (physics is complex) Huygen s Principle Behavior of light can be understood as the scattering of wavelets. A surface (real or imaginary) can be thought of as a number of scattering centers. Provides an explanation for the laws of reflection and refraction

33 Light Scattering When light encounters matter, matter not only reemits light in the forward direction (leading to absorption and refractive index), but it also re-emits light in all other directions. This is called scattering. Light scattering is everywhere: All molecules scatter light. Surfaces scatter light. Scattering causes milk and clouds to be white and water to be blue. It is the basis of nearly all optical phenomena. Scattering can be coherent or incoherent.

34 Scattering from molecules and small particles A plane pa wave impinging g on a molecule oecueor particle patcescatterss into a spherical wave. Huygens Principle says that waves propagate p as if each point on a wavefront emits a spherical wave (whether or not there s a molecule or particle involved). Scattering from an individual molecule or particle is weak, but many such scatterings can add up - especially if interference is coherent and constructive.

35 Scattering of light The scattering of light in the atmosphere depends on the size of the scattering particles, R, and on the wavelength,, of the scattered light. Geometric scattering: R>> Rain drops (R~ m) All wavelengths equally scattered Optical effects: white clouds Mie scattering: R~ Aerosols (R~ m) Red scattered better than blue Blue moon, blue sun Rayleigh scattering: R<< Air molecules (R~ m) Blues scattered better than red Blue sky, blue mountains, red sunsets R R R

36 Rayleigh Scattering Elastic ( does not change) Random direction of emission Little energy loss

37 Rayleigh Scattering Rayleigh scattering refers to the scattering of light off of the molecules of the air, and can be extended to scattering from particles up to about a tenth of the wavelength of the light. It is Rayleigh scattering off the molecules of the air which gives us the blue sky. Lord Rayleigh calculated the scattered intensity from dipole scatterers much smaller than the wavelength to be:

38 Scattering from molecules and small particles A small point with a different refractive index to its surroundings oscillates as a dipole under the influence of the incident electric field, and reradiates energy in all directions. In 3D this is known as Rayleigh scattering and atmospheric examples are scattering of sunlight by molecules and scattering of weather radar beams by cloud and rain droplets. Total field (incident plus scattered) Scattered field (total minus incident)

39 Scattering from molecules and small particles A small point with a different refractive index to its surroundings oscillates as a dipole under the influence of the incident electric field, and reradiates energy in all directions. The point is illuminated with two frequencies simultaneously. It is found that the higher frequency is scattered much more effectively than the lower frequency, explaining why the sky is blue. Total field (incident plus scattered) Scattered field (total minus incident)

40 Mie Scattering For particle sizes larger than a wavelength, Mie scattering predominates. This scattering produces a pattern like an antenna lobe, with a sharper and more intense forward lobe for larger particles. Mie scattering is not strongly wavelength dependent and produces the almost white glare around the sun when a lot of particulate material is present in the air. It also gives us the white light from mist and fog.

41 Scattering from large particles Even larger particles exhibit more complex scattering patterns; scattering by large spheres of constant refractive index can be calculated exactly using Mie theory. The preferential scattering in particular directions leads to rainbows Total field (incident plus scattered) Scattered field (total minus incident)

42 Rayleigh and Mie Scattering

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44 White Clouds

45 White clouds Description: the clouds appear white or grey. Physical process: geometric scattering by rain drops. Explanation: Visible light at all is scattered in all directions. Clouds are optically thick with respect to light scattering but they do not absorb light well. The thicker the cloud is the more light is scattered backwards and less solar light reaches the bottom of the cloud. Therefore thicker clouds appear darker. At the bottom of very thick clouds the raindrops are even larger and absorb sun light better. These clouds look even darker.

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47 Wavelength-dependent incoherent molecular scat- tering: Why the sky is blue. Light from the sun Air Air molecules scatter light, and the scattering is proportional to ν 4. Shorter-wavelength light is scattered out of the beam, leaving longer- wavelength light behind, so the sun appears yellow. In space, there s no scattering, so the sun is white, and the sky is black.

48 The Color of the Sun

49 The Color of The Sun Description: at sunrise and sunset the sun is yellow, orange or red Physical process: Rayleigh scattering by air molecules and fine dust particles. Explanation: on clear days only the blue light is scattered away, on hazy days the yellow and the orange wavelengths are also scattered and only the red remains in the direct solar light. Conclusion: Red sunsets suggest that there is dust in the air (pollution, haze over the ocean, volcanic activity, dust storms).

50 Blue Moon Description: the moon appears blue. Physical process: Mie scattering by dust particles. Explanation: When the size of the dust particles is approximately equal to the visible wavelengths the red light is scattered better than the blue light. Conclusion: one can guess what is the size of the particles in the air.

51 Construction of an Optical Fiber Numerical Aperture (NA): A dimensionless number that characterizes the range of angles over which the system can accept or emit light. NA n outside sin c n 2 1 n 2 2 noutside n air ; c air 8

52 Absorption & scattering losses in fibers Two types of absorption exist: Intrinsic Absorption, caused by interaction with one or more of the components of the glass Extrinsic Absorption, caused by impurities within the glass

53 Intrinsic absorption losses in optical fibers Attenuation spectrum for pure silica glass. Intrinsic absorption is very low compared to other forms of loss Intrinsic absorption in the ultraviolet region is caused by electronic absorption bands. The main cause of intrinsic absorption in the infrared region is the characteristic vibration frequency of atomic bonds. In silica glass, absorption is caused by the vibration of silicon-oxygen (Si-O) bonds. The interaction ti between the vibrating bond and dthe electromagnetic ti field of the optical signal causes intrinsic absorption. Light energy is transferred from the electromagnetic field to the bond.

54 Extrinsic Absorption (metallic ions) Extrinsic absorption is much more significant than intrinsic Caused by impurities introduced into the fiber material during manufacture Iron, nickel, and chromium Caused by transition of metal ions to a higher energy level Modern fabrication techniques can reduce impurity levels below 1 part in For some of the more common metallic impurities in silica fibre the table shows the peak attenuation wavelength and the attenuation caused by an impurity concentration of 1 in 10 9

55 Extrinsic Absorption (OH ions) Extrinsic absorption caused by dissolved water in the glass, as the hydroxyl y or OH ion. In this case absorption due to the same fundamental processes (between 2700 nm and 4200 nm) gives rise to so called absorption overtones at 1380, 950 and 720 nm. Typically a 1 part per million impurity level causes 1 db/km of attenuation at 950 nm. Typical levels are a few parts per billion. Absorption Spectrum for OH in Silica

56 Rayleigh scattering loss Dominant scattering mechanism in silica fibres Scattering causes by inhomogeneities in the glass, of a size smaller than the wavelength. Inhomogeneities manifested as refractive index variations, present in the glass after manufacture. Difficult to eliminate with present manufacturing methods For 1550 nm the loss is approximately 0.18 db per km.

57 Total oa Fibre beattenuation Three low loss transmission windows exist circa 850, 1320, 1550 nm Earliest systems worked at 850 nm, latest t systems at Attenuation falls with increasing wavelength, so that the loss at 1550 nm is Attenuation falls with increasing wavelength, so that the loss at 1550 nm is only about 0.25 db/km, compared to about 2.5 db/km at 850 nm

58 Scattering in tenuous media (d > ) Separation between the molecular scatterers is roughly a wavelength or more, as it is in a tenuous gas. The theory of Rayleigh Scattering has independent molecules randomly arrayed in space so that the phases of the secondary wavelets scattered off to the side have no particular relationship to one another and there is no sustained pattern of interference Lateral scattering: random phase Summation is a random walk (no interference).

59 Forward Propagation For a forward point P all the different paths taken by the light are about the same length; scattering alters path lengths by very little. Two molecules A and B, interacting with an incoming primary plane wave. In the forward direction the scattered wavelets arrive in-phase on planar wavefronts- trough with trough, peak with peak.

60 What about light that scatters on transmission i through h a surface? Again, a beam can remain a plane wave if there is a direction for which constructive interference occurs. Constructive interference will occur for a transmitted beam if Snell's Law is obeyed.

61 Reflection and Refraction of Light The speed of light in vacuum is c=300,000 km/s Snell s law: The angle of incidence is equal to the angle of reflection. Light that enters a more-dense medium slows down and bends toward the normal. Light that exits a more-dense medium speeds up and bends away from the normal.

62 True and apparent position of objects Due to the refraction of light the objects on the sky appear higher than they actually are. Star location and scintillations; Timing of the sunset and the sunrise; The sun on the horizon looks flattened; Twilight.

63 The Timing of the Sunset & Sunrise We see the sun before it actually rises above the horizon and after it We see the sun before it actually rises above the horizon and after it sets below the horizon.

64 Twilight

65 Flattening of the Sun s Disk at Sunset Green flash

66 Flattening of the Moon Refraction by the Earth s atmosphere (image from ISS)