We had previously seen Mechanics and Theory of Relativity, and Electricity and Magnetism by *A. N. Matveev*. In this post we will see another book, *Optics* by this great author.

## 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.

This link was pointed out by Amit in a comment on Matveev’s Electricity and Magnetism. Many thanks to him.

All credits to the original uploader.

PDF | OCR | 24 MB

You can get the book here (original link posted in the comment above) here. (IA Link)

## Contents

Preface

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?

Night vision.

Sec. 2. Properties of Electromagnetic Waves 22

Electromagnetic nature of light.

Wave equation.

Plane waves.

Spherical waves.

Plane harmonic waves.

Wave vector.

Complex representation of a plane wave.

Complex representation of a spherical wave.

Plane electromagnetic wave.

Invariance of a plane wave.

Phase invariance.

Four-dimensional wave vector.

Transformation formulas for frequency and direction of propagation of a plane

wave.

Doppler effect.

Sec. 3. Flux Densities of Energy and Momentum of Electromagnetic Waves. Light Pressure 35

Energy flux density.

Flux density distribution over beam cross section.

Gaussian beam.

Momentum density of electromagnetic waves.

Light pressure.

Effect of light pressure on small particles.

Laser fusion.

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.

Beats.

Standing waves.

Energy transformation in a standing electromagnetic wave.

Experimental proof of the electromagnetic nature of light.

Sec. 5. Polarization of Electromagnetic Waves 49

Polarization.

Linear polarization.

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 operation.

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 quantities.

Radiant intensity.

Radiance.

Radiant emittance (exitance).

Radiant illuminance.

Photometric quantities.

Luminous flux.

Luminance.

Luminous emittance.

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.

Negative frequencies.

Parseval’s theorem.

Plancherel’s theorem.

Sec. 9. Natural linewidth of Radiation 79

Classical model of a radiator.

Spectral composition of radiation.

Lorentz shape and width of emission line.

Emission time.

Shape of absorption line.

Quantum interpretation of the shape of emission line.

Quasi-monochromatic wave.

Sec. 10. Spectral Line Broadening 86

Reasons for broadening.

Uniform and nonuniform broadening.

Natural width of emission line as a uniform broadening.

Collision broadening.

Doppler broadening.

Shape of a composite emission line.

Sec. 11. Modulated Waves 91

Modulation.

Amplitude modulation.

Frequency and phase modulation.

Oscillation spectrum with harmonic frequency modulation.

Sec. 12. Wave Packets 94

Wave packet formed by two waves.

Group velocity.

Superposition of oscillations with equidistant frequencies.

Quasi-plane wave.

Sec. 13. Random Light 98

Superposition of waves with random phases.

Resolution time.

Averaging over oscillation period.

Effect of increasing time interval on the result of averaging.

Coherence time.

Coherence length.

Gaussian light.

Energy flux density fluctuations for random light.

Polarization.

Sec. 14. Fourier Analysis of Random Processes 103

Power spectrum (spectral function).

Autocorrelation function.

Wiener-Khintchine theorem.

Correlation interval.

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

Monochromatic waves.

Dispersion.

Normal dispersion.

Anomalous dispersion.

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

Boundary conditions.

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.

Brewster effect.

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.

Penetration depth.

Phase velocity. Reflected wave.

Sec. 18. Energy Relations for Reflection and Refraction of Light 139

Energy flux densities.

Reflection coefficient.

Transmission coefficient.

Law of energy conservation.

Polarization of light upon reflection and refraction.

Sec. 19. Propagation of Light in Conducting Media 142

Complex permittivity.

Penetration depth.

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

Boundary conditions.

Relation between wave amplitudes.

Reflection coefficient.

Connection between reflecting and absorbing properties.

4. Geometrical Optics

Sec. 21. Geometrical Optics Approximation 153

Eikonal equation.

Ray of light.

Range of applicability of the ray approximation.

Fermat’s principle.

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

Paraxial approximation.

Refraction at a spherical surface.

Matrix notation.

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.

Lens equation.

Thin lenses.

A system of thin lenses.

Utilization of computers.

Sec. 24. Optical Aberration 173

Sources of aberration.

Exact transformation matrices.

Spherical aberration.

Coma.

Aberration caused by off-axis inclined rays.

Chromatic aberration.

Oil-immersion lens.

Abbe’s sine condition.

Sec. 25. Optical Instruments 180

Diaphragming.

Basic concepts associated with diaphragming.

Eye as an optical system.

Photographic camera.

Magnifying glass.

Microscope.

Telescope.

Optical projectors.

5. Interference

Sec. 26.

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

interferometer.

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.

Mach-Zehnder interferometer.

Twyman-Green interferometer.

Jamin refractometer.

Sec. 27. Two-beam Interference Through Wave Front Splitting 205

Huygens’ principle.

Young’s two-slit interferometer.

White light interference.

Finite-sized source.

Source with a uniform distribution of emission intensity.

Space and time coherence.

Coherence angle and coherence width.

Stellar interferometer.

Measurement of the diameters of stars.

Measurement of the distance between components of a double star.

Fresnel biprism.

Billet split lens.

Lloyd’s mirror interference.

Fresnel mirrors.

Law of energy conservation in interference.

Sec. 28. Multiple-beam Interference Through Amplitude Divisio 216

Fabry-Perot interferometer.

Intensity distribution in interference pattern.

Interference rings.

Resolving power.

Factors limiting the resolving power.

Dispersion region.

Fabry-Perot scanning interferometer.

Interference filters.

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).

Newton rings.

Multiple reflection.

Layer with zero reflectivity.

Layer with a high reflectivity.

Matrix method of computations for multilayer films.

Multilayer dielectric mirrors.

Translucent materials.

Sec. 30. Partial Coherence and Partial Polarization 239

Partial coherence.

Mutual coherence function.

Normalized coherence function.

Coherence function.

Brown-Twiss experiment.

Partial polarization.

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.

Van-Zittert-Zemike theorem.

6. Diffraction

Sec. 31. Fresnel Z ne Method 263

Huygens-Fresnel principle.

Fresnel zones.

Graphic computation of amplitude.

Poisson’s spot.

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

Green’s formula.

Helmholtz-Kirchhoff theorem.

Radiation condition.

Kirchhoffs approximation.

Optical approximation.

Fresnel-Kirchhoff diffraction relation.

Helmholtz’ reciprocity theorem.

Secondary sources.

Fresnel’s approximation.

Sec. 33. Fraunhof er Diffraction 277

Fraunhofer diffraction region.

Diffraction at a rectangular aperture.

Diffraction at a slit.

Diffraction at a circular aperture.

Diffraction grating.

Diffraction of white light at a grating.

Dispersion region.

Resolving power.

Reflection gratings.

Diffraction at a slit for a continuously varying wave phase.

Phase gratings.

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.

Fresnel integrals.

Cornu’s spiral.

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.

Phase-contrast method.

Sec. 37. Spatial Filtering of Images 313

The essence of spatial filtering of images.

Spatial filtering of the diffraction grating images.

Abbe-Porter experiment.

Sec. 38. Holography 315

Synchronous detection.

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).

Bragg’s law.

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.

Permittivity tensor.

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.

Fresnel equation.

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.

Optical axis.

Biaxial and uniaxial crystals.

Index ellipsoid.

Ray surface.

Sec. 42. Birefringence 344

Ordinary and extraordinary rays.

Essence of birefringence.

Huygens’ construction.

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.

Polaroid.

Polarizing prisms and birefringent prisms.

Nicol prism.

Birefringent prism.

Polychroism.

Sec. 43. Interference of Polarized Waves 349

Interference of rays with mutually perpendicular directions of linear polarization.

Quarter-wave plate.

Half-wave plate.

Wave plate.

Analysis of linearly polarized light.

Analysis of elliptically polarized light.

Analysis of circularly polarized light.

Compensators.

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.

Optical isomerism.

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.

Pockels effect.

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.

Multiple scattering.

Model of an elementary scatterer.

Rayleigh scattering.

Rayleigh law.

Angular distribution and polarization of light in Rayleigh scattering.

Attenuation of light intensity.

Mie scattering.

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 components.

Undisplaced component.

Brillouin scattering in solids.

Classical interpretation.

Experimental facts.

Quantum interpretation.

Applications of Raman scattering.

10. Generation of Light

Sec. 50. Blackbody Radiation 38

Radiation density.

Equilibrium density of radiation.

Kirchhoff’s first law of radiation.

Absorptive power and radiant emittance.

Kirchhoff’s second law of radiation.

Blackbody.

Number density of oscillation modes.

Rayleigh-Jeans formula.

Wien’s formula.

Planck’s formula.

Stefan-Boltzmann law.

Wien’s displacement law.

Elementary quantum theory.

Spontaneous and induced transitions.

Einstein’s coefficients.

Sec. 51. Optical Amplifiers 391

Passage of light through a medium.

Burger’s law.

Amplification conditions.

Effect of light flux on the population density of levels.

Saturation conditions.

Creation of population inversion.

Sec. 52. Lasers 394

Schematic diagram of a laser.

Lasing threshold.

Steady-state lasing conditions.

Q-factor.

Continuous-wave (CW) and pulsed lasers.

Enhancement of the emission power.

Q-switching method.

Sec. 53. Laser Radiation 398

Radiation modes.

Resonator with plane rectangular mirrors.

Axial (longitudinal) modes.

Width of emission lines.

Side modes.

Cylindrical resonator with spherical mirrors.

Mode synchronization.

Pulse duration.

Attainment of mode synchronization.

Laser speckles.

Sec. 54. Characteristics of Some Lasers 406

Various types of lasers.

Ruby laser.

Helium-neon laser.

Closed-volume C02 laser.

CW-mode C0 2 -laser.

T-laser.

Gasdynamic lasers.

Dye lasers.

11. Nonlinear Phenomena in Optics

Sec. 55. Nonlinear Polarization 413

Linear polarization.

Nonlinear polarization.

Quadratic nonlinearity.

Nonlinear susceptibility.

Combination frequencies.

Sec. 56. Generation of Harmonics 417

Linear polarization waves.

Nonlinear polarization waves.

Spatial synchronism

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.

Self-focussing length.

Threshold energy flux.

Main reasons behind nonlinearity of the refractive index.

Time lag.

Appendix. SI units used in the book 432

Conclusion 434

Subject Index 441