Syllabus

This lecture presents the fundamental equations of electromagnetism and the resulting concepts.

• Vector calculus refreshers
• Fundamental equations and relationships in electromagnetism: Maxwell’s equations, complete presentation of Maxwell’s equations, boundary conditions, constitutive relationships, energy considerations and Poynting vector, delayed potentials and Green’s functions
• Electromagnetism in harmonic regime: Maxwell’s equations and boundary conditions in harmonic regime, constitutive relations in harmonic regime and complex permittivity, permittivity of dielectric materials and conductive materials, Kramers-Krönig dispersion relations
• Plane waves in harmonic regime: components of fields in harmonic regime, Helmholtz equation without second member for a LIH medium, plane waves in an absorbing medium, plane waves in an absorbing medium, electromagnetic power in harmonic regime
• Spherical waves – Radiation from an antenna in harmonic mode: orthogonality relations at a large distance from the source, equiphase surfaces and spherical waves, Poynting vector of a spherical wave in a non-absorbing medium, wave polarisation
• Plane wave beams: propagation constants of a plane wave, evanescent and propagating plane waves in a lossless medium, evanescent plane waves in a lossy medium, 3D plane wave beam, 2D plane wave beam, asymptotic behaviour of a plane wave beam, depolarisation of waves by a surface, diffraction by a rough surface and Rayleigh hypothesis
• Propagation in different types of environments
• Equivalence principle, application to aperture diffraction
• Study of periodic surfaces, application to the reflection of rough surfaces
• TD1: Maxwell’s equations with boundary conditions
• TD2: complex permittivity of materials
• TD3: plane waves and spherical waves
• TD4: study of a Gaussian beam (2D)
• TD5: asymptotic behaviour of a 2D plane wave beam
• TD6: field diffracted by a surface – Power balance

• Born M., Wolf E. (1999), Principles of optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, Cambridge University Press, 985 pp.
• Ishimaru A. (1990), Electromagnetic Wave Propagation, Radiation and Scattering, Prentice Hall, 656 pp.
• Petit R. (1997), Ondes électromagnétiques en radioélectricité et en optique, Dunod, 349 pp.
• Stratton J.A. (2007), Electromagnetic theory, Wiley-IEEE Press, 640 pp.

This lecture deals with electromagnetic radiation emitted in free space and in the presence of diffracting objects. It mainly relies on the electric-field integral equation.

Part I: OEM propagation

• Radiation from sources in free space:
  – review of Maxwell’s equations and conditions of application
  – Maxwell’s equations in harmonic regime
  – continuity relations
  – Helmholtz equations
  – solving propagation equations in free space in the presence of sources
• OEM in the presence of obstacles
  – Rayleigh-Gans equivalence principle and solving equations
• Diffraction by:
  – an infinite flat surface
  – a limited flat surface
  – a non-flat surface
• Diffusion/absorption/emission by particules
  – resolution principle
  – Mie solutions/geometric optical limits
  – Rayleigh-Gans approximation
  – Qabs/Qsca/Qext, assymetry parameter, phase fonction
  – consequences and practical case

Part II: matter-EM waves interaction

• Drude and Lorentz models
• Debye model
• Kramers-Krönig relation
• Maxwell-Garnett and Bruggemann mixing rules

• Beckmann A. & Spizzichino A. (1987), The scattering of electromagnetic waves from rough surfaces, Artech House Radar Library, 512 pp.
• Born M. & Wolf E. (1999), Principles of optics: Electromagnetic theory of propagation, interference and diffraction of light, Cambridge University Press, 985 pp.
• Brekhovski L.M. & Godin O.A. (1998), Acoustics of Layered Media I: Plane and Quasi-Plane Waves, Springer, 250 pp.
• Chew W.C. (1999), Waves and Fields in Inhomogeneous Media, Wiley-IEEE Press, 632 pp.
• Dassios G. & Kleinman R. (2000), Low Frequency Scattering, Oxford University Press, 320 pp.
• Fournet G. (1979), Electromagnétisme : à partir des équations locales, Masson, 478 pp.
• Ishimaru A. (1999), Waves Propagation and Scattering in Random Media, Wiley-IEEE Press, 600 pp.
• Kaufman A.A. & Keller G.V. (1985), Inductive Mining Prospecting, Part 1: Theory, Elsevier, 617 pp.
• Kong J.A. (1986), Electromagnetic Wave Theory, John Wiley & Sons Inc, 710 pp.
• Petit R. (2011). Electromagnetic Theory of Gratings, Springer, 304 pp.
• Roubine E. & Bolomey J.C. (1978), Antennes – Tome I, Masson, 2020 pp.
• Tai C.T. (1994), Dyadic Green Function in Electromagnetic Theory, IEEE, 343 pp.

This lecture introduces the fundamentals of monochromatic and transitional propagation of acoustic waves in fluid media.

• Elements of physical acoustics: introduction, sound sources, receivers, frequency of acoustic waves, sound level, propagation speed, polarisation of acoustic waves, acoustic waves in fluid media, solving the one-dimensional wave equation, acoustic impedance, propagation in three-dimensional space.
• Reflection and transmission of acoustic waves: introduction, linear and translation-invariant systems, reflection of an acoustic wave on a rigid wall, reflection of an acoustic wave on a soft wall, acoustic diopter, geometric approximation of transmission, application to wavefront calculation, reflection and transmission by two parallel interfaces
• Two-dimensional signal theory: introduction, review, signal theory in acoustics, study of complex exponentials
• Scalar theory of diffraction: introduction, diffraction by a flat screen, transient diffraction
• Fresnel and Fraunhofer diffraction: introduction, first approximations, Fresnel approximation, Fraunhofer approximation, examples of Fraunhofer diffraction
• Impulse diffraction by a circular piston: impulse formalism of diffraction, application to the case of a circular piston

• Brekhovskikh L.M. (1980), Waves in layered media, Academic Press, 503 pp.
• Brekhovskikh L.M., Goncharov V.V. (1985), Mechanics of continua and wave dynamics, Springer-Verlag, 342 pp.
• Bruneau M.(1998), Manuel d’acoustique fondamentale, Hermes Science Publications, 576 pp.
• Davis J.L. (1988), Wave propagation in solids and fluids, Springer-Verlag, 386 pp.
• Filippi P., Collectif (1994), Acoustique générale, Editions de Physique , 371 pp.
• Goodman J.W. (1968), Introduction to Fourier optics, McGraw-Hill, 287 pp.
• Gordon S.K. (1987), Acoustic waves: Devices, imaging, and analog signal processing, Prentice Hall, 601 pp.
• 2Guyader J.L. (2002), Vibrations des milieux continus, Hermes Science Publications, 445 pp.
• Royer D., Dieulesaint E. (1999), Ondes élastiques dans les solides. Tome 2 . Génération, interaction acousto-optique, applications, Masson, 410 pp..

• Tarantola A. (2005), Inverse problem theory and methods for model parameter estimation, Siam, 342 pp.

Molecular spectroscopy is a key method to determine the spectral signature of the Earth and the other planets of the Solar system, as well as the exoplanets. It aims at recording the electromagnetic radiation reflected or emitted by a target (surface or atmosphere) in very narrow wavebands. In particular it plays an essential role in the monitoring of the evolution of our atmosphere (aerosols and gas molecules).

In the next decades, large telescopes will extend observation to new spectral domains and boost the search for life on exoplanets. New instruments designed to analyze the chemical composition of the Earth’s lower atmosphere (greenhouse gases, pollutants, etc.) use technologies that allow measurements of spectra with very high spectral resolution and signal-to-noise ratios. The interpretation of these spectra requires mastering theoretical and experimental spectroscopic analysis techniques.

• J.M. Flaud (1992), Spectroscopie des molécules d’intérêt atmosphérique, Ecole d’été du CNRS.
• J.M. Hollas (2003), Spectroscopie, Dunod, 400 pp.
• J.M. Hollas (2004), Modern spectroscopy, John Wiley & Sons, Inc., 482 pp.
• S. Payan (2013), Radiative transfer and inversion, Ecole d’été du CNRS “HiResMIR@CAES-Frejus-2013”, Fréjus (France), 3-7 June 2013.
• L. Régalia, H. Tran, M. Leperec (2015), SpecAtmo summer school trainings, Fréjus (France).
• J. Vander Auwera (2013), Principles of vibration-rotation spectroscopy, Ecole d’été du CNRS “HiResMIR@CAES-Frejus-2013”, Fréjus (France), 3-7 June 2013.

This lecture introduces the concepts of direct and inverse radiative transfer, which underlie the study of the Earth’s atmosphere using remote sensing satellites, in the context of climate studies. The physical variables and fundamental laws are reminded, leading to the derivation of the radiative transfer equation that calculates the electromagnetic radiation transmitted or emitted by the atmosphere and measured at the top of it. This equation involves various thermodynamic, spectroscopic and instrumental information. The main radiative transfer codes are described. Finally, the inverse problem that consist in extracting atmospheric variables from radiometric measurements is discussed and illustrated by numerous examples involving present space missions.

• Principle of antenna radiation
• Description of different types of antennas and their uses
• Characteristics of antennas
• Radiation from currents
• Radiation from flat apertures
• Link budget
• Antenna arrays and multi-antenna systems
• Principle of radiometry
• Radiometric qualities of an antenna

Picon O. (2009), Les Antennes : théorie, conception et applications, Dunod, 371 pp.

This lecture is an introduction to Earth observation techniques by passive and active microwave.

• Le Chevalier F. (2000), Principes de traitement des signaux Radar et Sonar, Masson, 270 pp.
• Ulaby F.T., Moore R.K., Fung A.K. (1986), Microwave Remote Sensing: Active and Passive, Volume I: Fundamentals and Radiometry, Artech House Publishers, 456 pp.
• Ulaby F.T., Moore R.K., Fung A.K. (1986), Microwave Remote Sensing: Active and Passive, Volume II: Radar Remote Sensing and Surface Scattering and Emission Theory, Artech House Publishers, 608 pp.
• Ulaby F.T., Moore R.K., Fung A.K. (1986), Microwave Remote Sensing: Active and Passive, Volume III: From Theory to Applications, Artech House Publishers, 1120 pp.

Overview of Earth observation satellite imaging systems in the reflective domain.

Lier P., Valorge C., Briottet X. (2008), Imagerie spatiale : des principes d’acquisition au traitement des images optiques pour l’observation de la Terre, Cepadues Editions, 844 pp.

This lecture aims to give a general background on the scientific issues related to societal problems such as climate change, pollution, etc. and on the space observation tools used to monitor, analyze and understand such problems.

• Boucher O. (2012), Aérosols atmosphériques – Propriétés et impacts climatiques, Collection : Ingénierie et développement durable, XIV, Springer, 248 pp.
• Burrows J.P., Platt U., Borrell P. (2011), The remote sensing of tropospheric composition from space, Physics of Earth and Space Environments, XXXII, Springer, 549 pp.
• Lee K.H., Li Z., Kim Y.J., Kokhanovsky A. (2009), Atmospheric aerosol monitoring from satellite observations: A history of three decades, in Atmospheric and biological environmental monitoring, Springer, pp 13-38.

This lecture is an introduction to the characterization of terrestrial surfaces by remote sensing, mainly in the solar domain. At first, the different modes of interaction of solar radiation with continental surfaces are discussed. The second part of the lecture is devoted to the determination of the biochemical and structural parameters of vegetation by hyperspectral and multiangular remote sensing, from the leaf scale to the ecosystem. In the last part, we discuss the quantification of energy balance on the surface of the Earth and its importance in climate models. Emphasis is put on physical modeling at different scales.

• Asrar G. (1989), Theory and applications of optical remote sensing, Wiley Interscience, 734 pp.
• Berthier S. (1993), Optique des milieux composites, Polytechnica, 300 pp.
• Campbell G.S., Norman J.M. (1998), An introduction to environmental biophysics, Springer, 286 pp.
• Elias M., Lafait J. (2006), La couleur. Lumière, vision et matériaux, Belin, 352 pp.
• Gates D.M. (2003), Biophysical ecology, Dover, 611 pp.
• Hapke B. (1993), Theory of reflectance and emittance spectroscopy, Cambridge University Press, 455 pp.
• Hufty A. (2001), Introduction à la climatologie, De Boeck-Université, 542 pp.
• Jones H.G., Vaughan R.A. (2010), Remote sensing of vegetation: principles, techniques, and applications, Oxford University Press, 353 pp.
• Liang S. (2003), Quantitative remote sensing of land surfaces, Wiley-Interscience, 560 pp.
• Monteith J.L., Unsworth M.H. (2008), Principles of environmental physics, Academic Press, 418 pp.
• Myneni R.B., Ross J. (1991), Photon-vegetation interactions: applications in optical remote sensing and plant ecology, Springer-Verlag, 565 pp.