From the preface
The subject matter of the book is completely reflected in Contents. Statistical properties of light and its spectral representation are covered in greater detail than usual. Diffraction of light is described in the framework of Kirchhoffs integral. The effectiveness of the matrix methods is shown in sections covering geometrical optics and interference of light in thin films. A unified approach involving Fourier optics has been adopted for describing the diffraction theory of image formation, spatial filtration of images, holography, and other allied topics. Analysis of partial coherence and partial polarization is carried out in terms of the first correlation function. The mathematical aspect of the material presented in this book has been kept as simple as possible, and at the same time in line with the rigorous scientific approach.
The most significant aspect in which this book differs from the books dealing with mechanics, molecular physics and electricity is that its basic principles lie beyond the scope of this course. Because of this, considerable emphasis has been laid on the deductive method of description. The material of this course
is therefore presented in deductive form and in most cases (though not always) the experimental results are analyzed to show the agreement between the theoretical results and the experimental data, or to explain the observed phenomena. The book is based on the author’s experience of teaching physics for many years at the Physics Faculty of the Lomonosov State University, Moscow.
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1. Electromagnetic Waves
Sec. 1. Optical Range of Electromagnetic Waves 15
Wavelengths of the visible range.
Wave frequencies in the visible range.
Optical and other ranges of electromagnetic waves.
Why can we see only in the visible range?
Why is microwave range unsuitable for vision?
Sec. 2. Properties of Electromagnetic Waves 22
Electromagnetic nature of light.
Plane harmonic waves.
Complex representation of a plane wave.
Complex representation of a spherical wave.
Plane electromagnetic wave.
Invariance of a plane wave.
Four-dimensional wave vector.
Transformation formulas for frequency and direction of propagation of a plane
Sec. 3. Flux Densities of Energy and Momentum of Electromagnetic Waves. Light Pressure 35
Energy flux density.
Flux density distribution over beam cross section.
Momentum density of electromagnetic waves.
Effect of light pressure on small particles.
Transformation of amplitude and normal vector of a plane electromagnetic wave.
Energy of a plane wave train.
Momentum of a plane wave train.
Sec. 4. Superposition of Electromagnetic Waves 43
Superposition of field vectors of a wave.
Superposition of travelling monochromatic electromagnetic plane waves.
Energy transformation in a standing electromagnetic wave.
Experimental proof of the electromagnetic nature of light.
Sec. 5. Polarization of Electromagnetic Waves 49
Superposition of linearly polarized waves.
Elliptical and circular polarizations.
Variation of the electric field vector in space for elliptical and circular polarizations.
Degenerate case of elliptical polarization.
Number of independent polarizations.
Linearly polarized wave as a superposition of circularly polarized waves.
Sec. 6. Averaging 52
Averaging of harmonic functions.
Averaging of squares of harmonic functions.
Linearity of the averaging operation.
Calculations involving complex scalars.
Calculations involving complex vector quantities.
Sec. 7. Photometric Concepts and Quantities 57
Radiant and photometric quantities.
Radiant emittance (exitance).
Illuminance. Light exposure.
Relations between radiant and luminous characteristics of radiation.
2. Nonmonochromatic and Random Radiation
Sec. 8. Spectral Composition of Functions 71
Fourier series in real form.
Fourier series in complex form.
Fourier integral in real form.
Fourier integral in complex form.
Amplitude spectrum and phase spectrum.
Determination of the amplitude and phase spectra from complex form of Fourier series.
Continuous spectrum. Spectrum of rectangular pulses.
Spectrum of sawtooth pulses.
Spectrum of a single rectangular pulse.
Spectrum of an exponentially decreasing function.
Relation between the pulse duration and the spectral width.
Displacement of the time reference point.
Frequency displacement of spectrum.
Sec. 9. Natural linewidth of Radiation 79
Classical model of a radiator.
Spectral composition of radiation.
Lorentz shape and width of emission line.
Shape of absorption line.
Quantum interpretation of the shape of emission line.
Sec. 10. Spectral Line Broadening 86
Reasons for broadening.
Uniform and nonuniform broadening.
Natural width of emission line as a uniform broadening.
Shape of a composite emission line.
Sec. 11. Modulated Waves 91
Frequency and phase modulation.
Oscillation spectrum with harmonic frequency modulation.
Sec. 12. Wave Packets 94
Wave packet formed by two waves.
Superposition of oscillations with equidistant frequencies.
Sec. 13. Random Light 98
Superposition of waves with random phases.
Averaging over oscillation period.
Effect of increasing time interval on the result of averaging.
Energy flux density fluctuations for random light.
Sec. 14. Fourier Analysis of Random Processes 103
Power spectrum (spectral function).
Relation between the correlation interval and the normalized spectral function.
3. Propagation of Light in Isotropic Media
Sec. 15. Propagation of Light in Dielectrics 111
Scattering of light.
Propagation of a wave packet.
Replacement of a light wave in a medium.
Dispersion of light in interstellar space.
Colour of bodies.
Sec. 16. Reflection and’ Refraction of Light at the Interface Between Two Dielectrics. Fresnel’s Formulas 121
Constancy of the wave frequency upon reflection and refraction.
The plane of incident, reflected and refracted rays.
Relation between the angles of incidence, reflection and refraction.
Decomposition of a plane wave into two waves with mutually perpendicular linear polarizations.
Vector E is perpendicular to the plane of incidence.
Fresnel’s formulas for the perpendicular components of the field vector.
Vector E lies in the plane of incidence.
Fresnel’s formulas for parallel components of field vector.
Relation between the phases of reflected and refracted waves.
Degrees of polarization.
Sec. 17. Total Reflection of Light 135
Formulas for angles \theta_in >= \theta_lim
Wave in the second medium.
Phase velocity. Reflected wave.
Sec. 18. Energy Relations for Reflection and Refraction of Light 139
Energy flux densities.
Law of energy conservation.
Polarization of light upon reflection and refraction.
Sec. 19. Propagation of Light in Conducting Media 142
Physical reason behind absorption.
Phase velocity and wavelength.
Relation between the phases of field vector oscillations.
Relation between amplitudes of field vectors.
Media with low conductivity.
Media with high conductivity.
Sec. 20. Reflection of Light from a Conducting Surface 147
Relation between wave amplitudes.
Connection between reflecting and absorbing properties.
4. Geometrical Optics
Sec. 21. Geometrical Optics Approximation 153
Ray of light.
Range of applicability of the ray approximation.
Derivation of the law of refraction from Fermat’s principle.
Propagation of a ray in a medium with varying refractive index.
Sec. 22. Lenses, Mirrors and Optical Systems 159
Refraction at a spherical surface.
Propagation of a ray in a lens.
Refraction of the ray at the second spherical surface.
Refraction of a ray by a lens.
Propagation of a ray through an optical system.
Reflection from spherical surfaces.
Sec. 23. Optical Image 165
Matrix of an optical system.
Transformation of a ray from object plane to image plane.
Cardinal elements of an optical system.
Physical meaning of the Gauss constants.
Construction of images.
A system of thin lenses.
Utilization of computers.
Sec. 24. Optical Aberration 173
Sources of aberration.
Exact transformation matrices.
Aberration caused by off-axis inclined rays.
Abbe’s sine condition.
Sec. 25. Optical Instruments 180
Basic concepts associated with diaphragming.
Eye as an optical system.
Two-beam Interference Caused by Amplitude Division 189
Definition of interference.
Light intensity upon superposition of two monochromatic waves.
Methods of producing coherent waves in optics.
Interference of monochromatic waves propagating strictly along the axis of a Michelson
Interference of monochromatic waves propagating at an angle to the interferometer axis.
The reason behind the blurring of interference fringes.
Interference of nonmonochromatic light.
Fourier transform spectroscopy.
Visibility for a Gaussian line.
Visibility for a Lorentz line.
Michelson’s interferometer with linear fringes.
White light interference pattern.
Sec. 27. Two-beam Interference Through Wave Front Splitting 205
Young’s two-slit interferometer.
White light interference.
Source with a uniform distribution of emission intensity.
Space and time coherence.
Coherence angle and coherence width.
Measurement of the diameters of stars.
Measurement of the distance between components of a double star.
Billet split lens.
Lloyd’s mirror interference.
Law of energy conservation in interference.
Sec. 28. Multiple-beam Interference Through Amplitude Divisio 216
Intensity distribution in interference pattern.
Factors limiting the resolving power.
Fabry-Perot scanning interferometer.
Lummer-Gehrcke plate. Michelson echelon grating.
Sec. 29. Interference in Thin Films 226
Optical path length.
Reflection from parallel surfaces.
Uniform inclination fringes.
The role of source size.
The role of plate thickness and monochromaticity of radiation.
Uniform thickness fringes (isopachic fringes).
Layer with zero reflectivity.
Layer with a high reflectivity.
Matrix method of computations for multilayer films.
Multilayer dielectric mirrors.
Sec. 30. Partial Coherence and Partial Polarization 239
Mutual coherence function.
Normalized coherence function.
Coherence matrix for a quasi-monochromatic plane wave.
Normalized coherence function for mutually perpendicular projections of the electric field strength of a wave.
Natural (nonpolarized) light.
Completely polarized light.
Degree of polarization of a light wave.
Expression of degree of polarization in terms of extremal intensities.
Representation of natural light. Relation between the degrees of polarization and coherence function.
Sec. 31. Fresnel Z ne Method 263
Graphic computation of amplitude.
Diffraction at the knife-edge of a semi-infinite screen.
Zone plate as a lens.
Drawbacks of the Fresnel zone method.
Sec. 32. Kirchhoff s Approximation 269
Fresnel-Kirchhoff diffraction relation.
Helmholtz’ reciprocity theorem.
Sec. 33. Fraunhof er Diffraction 277
Fraunhofer diffraction region.
Diffraction at a rectangular aperture.
Diffraction at a slit.
Diffraction at a circular aperture.
Diffraction of white light at a grating.
Diffraction at a slit for a continuously varying wave phase.
Amplitude and phase gratings.
Oblique incidence of rays on a grating.
Diffraction at continuous periodic and aperiodic structures.
Diffraction by ultrasonic waves.
Comparison of the characteristics of spectral instruments.
Sec. 34. Fresnel Diffraction 29
Fresnel’s diffraction region.
Diffraction at a rectangular aperture.
7. Basic Concepts of Fourier Optics
Sec. 35. Lens as an Element Accomplishing a Fourier Transformation 299
Phase transformation by a thin lens.
Evaluation of the thickness function.
Types of lenses.
Lens as an element accomplishing a Fourier transformation.
Sec. 36. Diffraction Formation of Images by a Lens 303
Fourier transformation of amplitudes between the focal planes of a lens.
Image formation by a lens.
Limiting resolving power of optical instruments.
Dark-field illumination method.
Sec. 37. Spatial Filtering of Images 313
The essence of spatial filtering of images.
Spatial filtering of the diffraction grating images.
Sec. 38. Holography 315
Hologram of a plane wave.
Reconstruction of the image.
Hologram of a point object.
Hologram of an arbitrary object.
Quality of a photographic plate and the exposure time.
Three-dimensional reproduction of the object.
Thick holograms (Denisyuk’s method).
Recording of holograms and reconstruction of a plane wave.
Recording of holograms and reconstruction of a spherical wave.
Holographic recording and reconstruction of the image of an arbitrary object.
Three-dimensional coloured image.
Peculiarities of holograms as carriers of information.
Applications of holography.
8. Propagation of Light in Anisotropic Media
Sec. 39. Anisotropic Media 331
Sources of anisotropy.
Anisotropic dielectric media.
Sec. 40. Propagation of a Plane Electromagnetic Wave in an Anisotropic Medium 334
Plane electromagnetic wave in anisotropic medium.
Dependence of phase velocity on the direction of wave propagation and oscillations of vector D.
Possible types of waves.
Sec. 41. Passage of Rays Through an Anisotropic Medium 338
Dependence of ray (group) velocity on direction.
Ellipsoid of group velocities.
Analysis of ray path through ellipsoid of group velocities.
Biaxial and uniaxial crystals.
Sec. 42. Birefringence 344
Ordinary and extraordinary rays.
Essence of birefringence.
Optical axis is perpendicular to the crystal surface.
Optical axis is parallel to the crystal surface.
Optical axis is at an angle to the crystal surface.
Malus’ law of rays.
Polarization in birefringence.
Polarizing prisms and birefringent prisms.
Sec. 43. Interference of Polarized Waves 349
Interference of rays with mutually perpendicular directions of linear polarization.
Analysis of linearly polarized light.
Analysis of elliptically polarized light.
Analysis of circularly polarized light.
Colours of crystal plates.
Phenomena occurring in convergent rays.
Sec. 44. Rotation of the Polarization Plane 354
Rotation of polarization plane in crystalline bodies.
Rotation of polarization plane in amorphous substances.
Phenomenological theory of the rotation of polarization plane.
Rotation of polarization plane in a magnetic field.
Sec. 45. Artificial Anisotropy 358
Anisotropy due to deformation.
Anisotropy caused by an electric field.
Anisotropy caused by a magnetic field.
9. Scattering of Light
Sec. 46. Scattering Pro.cesses · 365
Sec. 47. Rayleigh Scattering and M e Scattering 366
Nature of scattering.
Types of scattering.
Model of an elementary scatterer.
Angular distribution and polarization of light in Rayleigh scattering.
Attenuation of light intensity.
Angular intensity distribution and polarization of radiation in Mie scattering.
Manifestations of Mie scattering.
Sec. 48. Brillouin Scattering 375
Sec. 49. Raman Scattering 376
Brillouin scattering in solids.
Applications of Raman scattering.
10. Generation of Light
Sec. 50. Blackbody Radiation 38
Equilibrium density of radiation.
Kirchhoff’s first law of radiation.
Absorptive power and radiant emittance.
Kirchhoff’s second law of radiation.
Number density of oscillation modes.
Wien’s displacement law.
Elementary quantum theory.
Spontaneous and induced transitions.
Sec. 51. Optical Amplifiers 391
Passage of light through a medium.
Effect of light flux on the population density of levels.
Creation of population inversion.
Sec. 52. Lasers 394
Schematic diagram of a laser.
Steady-state lasing conditions.
Continuous-wave (CW) and pulsed lasers.
Enhancement of the emission power.
Sec. 53. Laser Radiation 398
Resonator with plane rectangular mirrors.
Axial (longitudinal) modes.
Width of emission lines.
Cylindrical resonator with spherical mirrors.
Attainment of mode synchronization.
Sec. 54. Characteristics of Some Lasers 406
Various types of lasers.
Closed-volume C02 laser.
CW-mode C0 2 -laser.
11. Nonlinear Phenomena in Optics
Sec. 55. Nonlinear Polarization 413
Sec. 56. Generation of Harmonics 417
Linear polarization waves.
Nonlinear polarization waves.
condition. Coherence length.
Attainment of spatial synchronism.
Generation of higher harmonics.
Vector condition for spatial synchronism.
Generation of sum and difference frequencies.
Spontaneous decay of a photon.
Parametric amplification of light.
Parametric generators of light.
Sec. 57. Self-focussing of Light in a Nonlinear Medium 427
Nonlinear correction to the refractive index.
Self-focussing and defocussing of a beam.
Threshold energy flux.
Main reasons behind nonlinearity of the refractive index.
Appendix. SI units used in the book 432
Subject Index 441