UNIT-II WAVES AND OPTICS

1. UNIT-II WAVES AND OPTICS PREPARED BY Dr.G.VIJAYASRI ASSISTANT PROFESSOR DEPARTMENT OF PHYSICS MOHAMED SATHAK ENGINEERING COLLEGE KILAKARAI

2. UNIT II WAVES AND OPTICS

3. OUTLINE • Simple Harmonic Motion revision • Displacement, velocity and acceleration in SHM • Energy in SHM • Damped harmonic motion • Forced Oscillations • Resonance

4. Simple Harmonic Motion

5. Simple Harmonic Motion Light Displacement of oscillating object = projection on x-axis of object undergoing circular motion y(t) = Acos For rotational motion with angular frequency , displacement at time t: y(t) = Acos(t + ) = angular displacement at t=0 (phase constant) A = amplitude of oscillation (= radius of circle)

7. Damped Oscillations In most “real life” situations, oscillations are always damped (air, fluid resistance etc) In this case, amplitude of oscillation is not constant, but decays with time.

8. Damped Oscillations For damped oscillations, simplest case is when the damping force is proportional to the velocity of the oscillating object In this case, amplitude decays exponentially: Equation of motion:

9. Damped Oscillations NB: in addition to time dependent amplitude, the damped oscillator also has modified frequency: Critical Damping Light Damping (small b/m) Heavy Damping (large b/m)

10. Forced Oscillations & Resonance If we apply a periodically varying driving force to an oscillator (rather than just leaving it to vibrate on its own) we have a FORCED OSCILLATION Free Oscillation with damping: Frequency Forced Oscillation with damping: MAXIMUM AMPLITUDE WHEN DENOMINATOR MINIMISED: k = mD2 ie when driving frequency = natural frequency of the UNDAMPED oscillator

12. WAVES

13. Plane wave

14. Lasers and Fiber optics

15. What is Laser? Light Amplification by Stimulated Emission of Radiation • A device produces a coherent beam of optical radiation by stimulating electronic, ionic, or molecular transitions to higher energy levels • When they return to lower energy levels by stimulated emission, they emit energy.

16. Properties of Laser • The light emitted from a laser is monochromatic, that is, it is of one color/wavelength. In contrast, ordinary white light is a combination of many colors (or wavelengths) of light. • Lasers emit light that is highlydirectional, that is, laser light is emitted as a relatively narrow beam in a specific direction. Ordinary light, such as from a light bulb, is emitted in many directions away from the source. • The light from a laser is said to be coherent, which means that the wavelengths of the laser light are in phase in space and time. Ordinary light can be a mixture of many wavelengths. • These three properties of laser light are what can make it more hazardous than ordinary light. Laser light can deposit a lot of energy within a small area.

17. Monochromacity Nearly monochromatic light Example: He-Ne Laser λ0 = 632.5 nm Δλ = 0.2 nm Diode Laser λ0 = 900 nm Δλ = 10 nm Comparison of the wavelengths of red and blue light

18. Directionality Conventional light source Divergence angle (θd) Beam divergence: θd= β λ /D β ~ 1 = f(type of light amplitude distribution, definition of beam diameter) λ = wavelength D = beam diameter

19. Coherence Incoherent light waves Coherent light waves

20. Incandescent vs. Laser Light • Many wavelengths • Multidirectional • Incoherent • Monochromatic • Directional • Coherent

21. Basic concepts for a laser • Absorption • Spontaneous Emission • Stimulated Emission • Population inversion

22. Absorption • Energy is absorbed by an atom, the electrons are excited into vacant energy shells.

23. Spontaneous Emission • The atom decays from level 2 to level 1 through the emission of a photon with the energy hv. It is a completely random process.

24. Stimulated Emission atoms in an upper energy level can be triggered or stimulated in phase by an incoming photon of a specific energy.

25. Stimulated Emission The stimulated photons have unique properties: • In phase with the incident photon • Same wavelength as the incident photon • Travel in same direction as incident photon

26. Population Inversion • A state in which a substance has been energized, or excited to specific energy levels. • More atoms or molecules are in a higher excited state. • The process of producing a population inversion is called pumping. • Examples: →by lamps of appropriate intensity →by electrical discharge

27. Pumping • Optical: flashlamps and high-energy light sources • Electrical: application of a potential difference across the laser medium • Semiconductor: movement of electrons in “junctions,” between “holes”

28. Two level system E2 E2 hn hn hn absorption Spontaneous emission Stimulated emission E1 E1 hn =E2-E1

29. E2 E1 Boltzmann’s equation example: T=3000 K E2-E1=2.0 eV • n1 - the number of electrons of energy E1 • n2 - the number of electrons of energy E2 • Population inversion- n2>>n1

30. Resonance Cavities and Longitudinal Modes Since the wavelengths involved with lasers and masers spread over small ranges, and are also absolutely small, most cavities will achieve lengthwise resonance L = nλ Plane parallel resonator Hemifocal resonator f c Concentric resonator c Hemispherical resonator f Confocal resonator Unstable resonator c: center of curvature, f: focal point

31. Transverse Modes Due to boundary conditions and quantum mechanical wave equations TEM00: I(r) = (2P/πd2)*exp(-2r2/d2) (d is spot size measured to the 1/e2 points)

32. Einstein’s coefficients Probability of stimulated absorption R1-2 R1-2 = r (n) B1-2 Probability of stimulated and spontaneous emission : R2-1 = r (n) B2-1 + A2-1 assumption: n1 atoms of energy e 1 and n2 atoms of energy e 2 are in thermal equilibrium at temperature T with the radiation of spectral density r (n): n1 R1-2 = n2 R2-1 n1r (n) B1-2 = n2 (r (n) B2-1 + A2-1) E2 E1

33. According to Boltzman statistics: • r (n) = = Planck’s law B1-2/B2-1 = 1

34. The probability of spontaneous emission A2-1 /the probability of stimulated emission B2-1r(n ): • Visible photons, energy: 1.6eV – 3.1eV. • kT at 300K ~ 0.025eV. • stimulated emission dominates solely when hn /kT <<1! • (for microwaves: hn <0.0015eV) • The frequency of emission acts to the absorption: • if hn /kT <<1. x~ n2/n1

35. E2 E1 Condition for the laser operation Ifn1 > n2 • radiation is mostly absorbed absorbowane • spontaneous radiation dominates. if n2>> n1 - population inversion • most atoms occupy level E2, weak absorption • stimulatedemission prevails • light is amplified Necessary condition:population inversion

36. E2 E1 How to realize the population inversion? Thermal excitation: impossible. The system has to be „pumped” Optically,electrically.

37. Laser Diodes • Laser diodes generate coherent, intense light of a very narrow bandwidth • A laser diode has an emission linewidth of about 2 nm, compared to 50 nm for a common LED • Laser diodes are constructed much like LEDs but operate at higher current levels

38. Laser Diode Construction

39. Fiber Optics

40. Introduction • An optical fiber is essentially a waveguide for light • It consists of a core and cladding that surrounds the core • The index of refraction of the cladding is less than that of the core, causing rays of light leaving the core to be refracted back into the core • A light-emitting diode (LED) or laser diode (LD) can be used for the source • Advantages of optical fiber include: • Greater bandwidth than copper • Lower loss • Immunity to crosstalk • No electrical hazard

41. Optical Fiber & Communications System

42. Optical Fiber • Optical fiber is made from thin strands of either glass or plastic • It has little mechanical strength, so it must be enclosed in a protective jacket • Often, two or more fibers are enclosed in the same cable for increased bandwidth and redundancy in case one of the fibers breaks • It is also easier to build a full-duplex system using two fibers, one for transmission in each direction

43. Total Internal Reflection • Optical fibers work on the principle of total internal reflection • With light, the refractive index is listed • The angle of refraction at the interface between two media is governed by Snell’s law:

44. Refraction & Total Internal Reflection

45. Numerical Aperture • The numerical aperture of the fiber is closely related to the critical angle and is often used in the specification for optical fiber and the components that work with it • The numerical aperture is given by the formula: • The angle of acceptance is twice that given by the numerical aperture

46. Modes and Materials • Since optical fiber is a waveguide, light can propagate in a number of modes • If a fiber is of large diameter, light entering at different angles will excite different modes while narrow fiber may only excite one mode • Multimode propagation will cause dispersion, which results in the spreading of pulses and limits the usable bandwidth • Single-mode fiber has much less dispersion but is more expensive to produce. Its small size, together with the fact that its numerical aperture is smaller than that of multimode fiber, makes it more difficult to couple to light sources

47. Types of Fiber • Both types of fiber described earlier are known as step-index fibers because the index of refraction changes radically between the core and the cladding • Graded-index fiber is a compromise multimode fiber, but the index of refraction gradually decreases away from the center of the core • Graded-index fiber has less dispersion than a multimode step-index fiber

48. Losses • Losses in optical fiber result from attenuation in the material itself and from scattering, which causes some light to strike the cladding at less than the critical angle • Bending the optical fiber too sharply can also cause losses by causing some of the light to meet the cladding at less than the critical angle • Losses vary greatly depending upon the type of fiber • Plastic fiber may have losses of several hundred dB per kilometer • Graded-index multimode glass fiber has a loss of about 2–4 dB per kilometer • Single-mode fiber has a loss of 0.4 dB/km or less

49. Types of Losses

50. Fiber-Optic Cables • There are two basic types of fiber-optic cable • The difference is whether the fiber is free to move inside a tube with a diameter much larger than the fiber or is inside a relatively tight-fitting jacket • They are referred to as loose-tube and tight-buffer cables • Both methods of construction have advantages • Loose-tube cables—all the stress of cable pulling is taken up by the cable’s strength members and the fiber is free to expand and contract with temperature • Tight-buffer cables are cheaper and generally easier to use