## Programme Information

## Course Descriptions

- PH501 Acoustics Propagation and Modelling
- PH503 Advanced Optics
- PH505 Acoustic System Analysis
- PH507 Remote Sensing
- PH509 Radio Astronomy
- PH511 Electromagnetic Theory
- PH513 Ferroelectric Transduction Materials: Properties and Applications
- PH515 Thermal and Statistical Physics
- PH517 Selected Topics in Physics
- PH521 Synoptic Oceanography
- PH531 Astrodynamics
- PH537 Satellite Communication and Navigation
- PH539 Spacecraft Mission Geometry
- PH541 Surveillance of Space
- PH543 Space Weather 1-Solar Physics and Activity
- PH545 Space Weather II- the Near Earth Space Environment
- PH547 Space Mission Analysis
- PH549 Space Mission Design
- PH551 Ocean Dynamics
- PH553 Dynamic Oceanography
- PH581 Space Systems
- PH583 Surveillance of and from Space
- PH585 Theory and Observation of Stellar Atmospheres
- PH587 Physical Principles of Non-Destructive Evaluation
- PH589 Radar Polarimetry
- PH591 Galaxies in the Universe
- PH593 Astronomical Instrumentation
- PH595 Gaussian Optics: Light Propagation in Optical Systems and Waveguide Structures
- PH596 Grating and Waveguide Structures
- PH597 Galactic Astronomy
- PH599 Optical Observational Techniques and Data for Space Surveillance
- PH601 Measurement and Modelling of Stellar Magnetic Fields
- PR500 Project
- TH500 Thesis (Master's Level)
- TH600 Thesis (Doctoral Level)
- CP600 Comprehensive Examination (Doctoral Level)

## Contact

- Department Head
- Ribal Georges Sabat, PhD
- Graduate Studies Committee Chair
- Ron Vincent, PhD
- Telephone
- 613-541-6000 ext. 6288
- Fax
- 613-541-6040
- Web Page
- Department of Physics and Space Science

## General Information

### Programmes Offered

The Department of Physics and Space Science offers programmes leading to the degrees of Master of Science (MSc) and Doctor of Philosophy (PhD) in Physics, with the following fields of specialization:

- Acoustics and Oceanography
- Space Science
- Materials Science

### Admission

Candidates for the degrees of Master of Science and Doctor of Philosophy will be admitted under the General Admission Requirements. Details regarding admission to the Royal Military College as a graduate student can be found in the Admission to Graduate Studies section of this calendar.

## Programme Requirements

**Important:**All students must complete the zero-credit course AI500: Academic Integrity or an equivalent course by the end of their first term of study.

### Master of Science Programme

Admission to the Master of Science (MSc) programme normally requires an honours baccalaureate in Physics or a related field.

Two Master of Science programme patterns are available:

- a "thesis" Master of Science which requires at least 4 graduate courses and a research thesis, and
- a "project" Master of Science which requires at least 8 graduate courses and a research project.

Exceptional thesis Master of Science (MSc) students may be eligible for direct transfer to the Doctor of Philosophy (PhD) programme.

A Master's when pursued full-time in the residential programme normally requires five academic terms or two academic years plus the intervening summer to complete.

### Doctor of Philosophy

Admission to the Doctor of Philosophy (PhD) programme normally requires an MSc in Physics or a related field.

## Course Descriptions

### PH501 Acoustics Propagation and Modelling

A study of the fundamental equations used to describe acoustic propagation in the ocean is undertaken in the context of military acoustic requirements. The effect of oceanic variability in one, two and three dimensions on acoustic propagation forecasting is evaluated and discussed to better understand the limitations imposed by the environment upon prediction capabilities. The approximations inherent in such models for transmission loss calculation as FACT, Generic Sonar Model, Ray Mode, and Parabolic Equation are studied to gain understanding of the physical principles behind these models and the implicit strengths and weaknesses of each. Through assignments and class projects the student will have an opportunity to work with some of these current acoustic models and to conduct numerical experiments to show some of the characteristics of each model tested. Oceanic factors affecting acoustic propagation which are discussed include temporal and spatial variability of sound speed profiles, interpolation and digitization of sound speed profiles, calculation of sound speed without using salinity data, reflection characteristics of the ocean surface and bottom, fronts and various kinds of eddy structures. The student is expected to understand the implications of the course and to be able to describe the limitations imposed by the environment on the choice of a particular model to predict transmission loss.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH503 Advanced Optics

This course will start with a review of geometrical optics, including matrices methods and notation for paraxial optics, as well as a review of wave optics and light polarization, including Jones vectors and matrices. After that, the student will be introduced to electromagnetic waves propagation in anisotropic crystals, the optical index ellipsoid and the electro-optic effect in crystals. This will be followed by a study on non-linear optics, including second harmonic generation, and a description of the Fabry-Pérot interferometer. The student will also be introduced to the fundamentals of light propagation and coupling inside slab optical waveguides using diffraction gratings. Finally, detailed theory will be given on surface plasmon resonance and Fourier optics.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH505 Acoustic System Analysis

Using a system approach, the student will learn the characteristics and limitations of a number of active and passive acoustic detection and tracking systems. The design, construction and deployment of passive and active acoustic transducers are discussed from the viewpoint of overall system performance. Fourier methods are introduced so that signal decomposition in frequency space and in wave number space can be described. This leads ultimately to a discussion of spatial beam forming using such systems as difar, vertical line arrays, and towed arrays. A study of correlation methods as applied to random noise lead to a discussion of oceanic ambient noise in both temperate and polar seas and the detection of signals in noisy environments.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH507 Remote Sensing

This course assesses sensors and platforms used in the remote sensing of the earth, and the use of data from them to describe the terrestrial and oceanic environments. The physics of passive and active sensors operating in the visible, infrared and microwave is discussed, as are the algorithms necessary to transform sensor data into geophysical meaningful output, such as land elevation vegetation index, sea surface temperature, wave height and wind speed. Remote sensing of solid surfaces is discussed to illustrate the applicability of modern sensor systems or terrestrial environments. Processing and analysis of remotely sensed imagery is discussed to lead the students to an understanding of how to extract information on oceanic and terrestrial features and conditions using modern professional computational techniques. Emphasis is placed on the use of remotely sensed data for tactical and strategic purposes.

- Lectures:
- 3 periods per week (one term)
- Laboratory:
- 2 periods per week (one term)
- Credit(s):
- 1

### PH509 Radio Astronomy

This course presents an introduction to the fundamental concepts of radio astronomy. The goals are to provide the background needed to read and understand the radio astronomy literature, to recognize when radio observations might help solve an astrophysical problem, and to design, propose, and analyze radio observations. Topics covered include radiation fundamentals, radio telescopes and radiometers, free-free and synchrotron radio radiation, and radio spectral lines.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH511 Electromagnetic Theory

Reviews of electrostatics, magneto statics, and Maxwell's equations in a vacuum and in matter. Scalar and vector potentials. Charge conservation, momentum and angular momentum conservation. Constitutive relations, D(E) and H(B), for linear and non-linear systems, symmetries. Kramers-Kronig relations. Radiation from localized charges and currents, Green's function method, Poynting's theorem, radiated power, retarded potentials. Multipole moments of the scalar and vector potentials. Dipolar antenna. Motion of charges in electromagnetic fields, relativity and Maxwell's equations. Lorentz force law. Electromagnetic tensor. Covariant form of Maxwell's equations, 4-vectors. Analytical and computer-based solutions to electromagnetic boundary value problems: separation of variables, Bessel functions, Fourier series and Finite Element methods.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH513 Ferroelectric Transduction Materials: Properties and Applications

This course presents an understanding of the behaviour of piezoelectric and electrostrictive ceramic materials with particular reference to their use in electromechanical transducers. The properties of other electromechanical transduction materials such as piezoelectric polymers and composites, magnetostrictive materials and shape memory alloys will also be discussed briefly. The use of these materials in acoustic transducers for particular applications such as underwater sonar for submarine detection and mine-hunting, underwater stealth, ceramic motors and actuators and smart structures will be reviewed. Other types of functional ceramic materials will be discussed briefly and these will include: conducting, dielectric, electro-optical, magnetic and superconducting ceramics.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH515 Thermal and Statistical Physics

Review of classical thermodynamics. Review of Maxwell-Boltzmann, Fermi-Dirac and Bose- Einstein statistics. Applications to Brownian motion, thermal properties of matter, superfluidity, and superconductivity. Irreversible flow processes, Onsager relations, thermoosmosis and thermoelectric phenomena.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH517 Selected Topics in Physics

The emphasis in this course will be placed on those areas of particular interest to the student as dictated by his or her research topic.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH521 Synoptic Oceanography

A detailed study of the nature and distribution of synoptic scale and mesoscale features of the oceans is made with particular emphasis on the waters contiguous with Canada, including the Arctic Ocean. Modern knowledge and theories of meandering currents, oceanic eddies and fronts are examined using recent scientific literature. Data and imagery from remote sensing satellites are used to identify and examine these features. Data analysis techniques required for such examinations are also presented.

- Lectures:
- 3 periods per week (one term)
- Credit(s):

### PH531 Astrodynamics

A review of satellite orbital motion as a Keplerian motion, orbit determination, and orbital manoeuvring. Perturbations to the Keplerian motion-oblate earth (J2 and other terms), third body perturbations (solar, lunar), atmospheric drag, solar-radiation pressure. Techniques to treat perturbations-SP (Special Perturbationsnumerical methods), GP-(General Perturbationsanalytical methods) and hybrid methods. Statistical orbit determination using least squares and Kalman filters.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH537 Satellite Communication and Navigation

This course is an introduction to communication between spacecraft and ground stations. Students are introduced to antenna theory: dipole antenna, antenna gain, antenna patterns, directivity and signal strength. The theory is then applied to modulation, transmission, propagation, reception and demodulation of signals between the ground and a satellite. Fundamentals of ionospheric effects, frequency bands, communication lin equations and telemetry are covered. Space-based navigation systems are examined. Topics include positioning using RF Doppler and GPS positioning. Precision navigation and surveying, personal communication systems as well as search and rescue systems are also examined. Satellite tracking is discussed.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH539 Spacecraft Mission Geometry

This course is an introduction to the factors affecting a spacecraft's mission. After a brief review of orbital mechanics with special emphasis on orbital maneuvers and satellite station keeping, the students are introduced to the theory of spacecraft attitude dynamics and kinematics. The theory is then applied to spacecraft attitude stabilization and control, including a brief introduction to the sensors used to measure the spacecraft position and attitude. Earth coverage, the relative motion of satellites, as well as viewing and lighting conditions are discussed in order to illustrate the effects of the spacecraft mission geometry on the overall mission. The process of orbit selection and design will be introduced with special emphasis on constellations, including constellation patterns, coverage, station keeping and collision avoidance. The Analytical Graphics software package, Satellite Tool Kit (STK) will be used to provide a simulation of the spacecraft orbits and mission geometry.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH541 Surveillance of Space

The course presents an overview of factors involved in the tracking of objects in space. It examines the space environment and EM propagation effects that impact on ground-based tracking. It surveys space-time co-ordinates, Keplerian orbits, orbit perturbations and ground track considerations. The course then examines in depth the Analytical Graphics software package STK/PRO and all its associated modules. Included in this are PODS, SKY, IRAF and Streak Detection Algorithms that are being presently used at the Space Surveillance Research and Analysis Laboratory at RMC. The course also examines current topics in space control using the proceedings of research conferences.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH543 Space Weather I - Solar Physics and Activity

This course provides a graduate-level introduction to the physics of the solar outer layers, with concentration on the generation, emergence and evolution of the magnetic field, and its interaction with the solar plasma. This course represents the first half of the space weather curriculum and serves as a basic introduction to the characteristics of stellar atmospheres. Topics: Basic properties of the sun and sun-like stars: bulk characteristics and interior structure; atmospheric structure: photosphere, chromosphere, transition region and corona. Solar magnetic activity: the 22-year cycle; emergence, structure and variability of the solar magnetic field. Solar dynamo: basic principles mean field dynamo theory, alpha and omega effects. Active regions and sunspots, sunspot classification; field evolution in active regions, magnetic shear, field reconnection, current sheets; prominences, flares and CMEs. Origin, structure and variability of the solar wind. Recent solar observations from ground and space; predictions of solar activity and relation to space weather prediction; comparison of solar activity properties with those of other stars.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH545 Space Weather II - The Near Earth Space Environment

This course studies the interplanetary medium and the near-Earth environment from the rigorous perspective of plasma physics. Theoretical topics include: single particle motions in plasmas, plasmas as fluids, waves in plasmas, diffusion and resistivity (magnetohydrodynamics), equilibrium and stability, kinetic theory and nonlinear effects. Applications to the space environment include: the solar wind, the Earth's magnetic field, Van Allen belts, the South Atlantic Anomaly, aurorae, particles and currents in the magnetosphere, magnetospheric waves, and instabilities and shocks in the magnetosphere.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH547 Space Mission Analysis

This represents the first half of the space mission analysis and design curriculum. The course consists of lectures and case study assignments covering various aspects of space missions, including systems engineering, propulsion systems, launch vehicles, power systems, thermal control, communication and navigation, ground systems, mission operations, safety, tolerance, risk and failure management.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH549 Space Mission Design

This represents the second half of the space mission analysis and design curriculum. The students develop the preliminary design of the space and ground segment for a realistic space mission.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH551 Ocean Dynamics

The physics and mathematics of motion in the ocean will be examined at scales ranging from the microscale to basin scale. The hydrodynamic equations governing fluid motion will be developed from the fundamental laws of physics and examined in various forms to study such phenomena as geostrophic currents, inertial currents, Ekman spirals, barotropic and baroclinic currents, the large scale, wind-forced oceanic circulation, thermohaline circulation and western intensification. Wave theory for an unstratified ocean will also be covered and will include an investigation of the tides and Rossby, surface gravity, Poincaré and Kelvin waves.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH553 Dynamic Oceanography

Long waves such as shelf, Rossby, Poincaré and Kelvin waves will be studied for two-layer and continuously stratified fluids. The quasigeostrophic potential vorticity equation will be derived. Barotropic and baroclinic instability of mean flows will be investigated both by doing linear stability analysis and by examining eddy resolving numerical models. Modern theories of the ocean circulation that incorporate the ventilated thermocline and the homogenization of potential vorticity will be covered and compared with observations.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH581 Space Systems

This course is intended for MA students in Space Policy. Review of the history of space with emphasis on Canadian contributions to typical satellite orbits: effects of the environment, satellite function considerations. Satellite systems and subsystems: structure, electrical power, thermal control, propulsion and attitude and altitude control. Systems: sensors, telemetry, surveillance, navigation, meteorology, and remote sensing. Military and scientific satellite systems launch systems.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH583 Surveillance of and From Space

This course is intended for candidates for the MA in Space Policy. This course discusses the observation of the earth's solid and liquid surface from space, and the observation of the space environment from the earth's surface and from low earth orbit. Remote sensing systems operating in the visible, thermal infrared and microwave regions are examined. The fundamentals of the orbits of space objects and the methods of tracking them from the ground are presented. Historical, current and future observing systems will be discussed, with a focus on applications important to the Canadian Forces. Biweekly computer laboratory sessions will give the student hands-on experience in remote sensing image analysis and interpretation, and in satellite and spacecraft orbit determination and prediction using software tools currently in use within the CAF.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH585 Theory and Observation of Stellar Atmospheres

This course provides an introduction to the physics of stellar atmospheres, including bulk stellar properties, concepts of local thermodynamic equilibrium, excitation and ionization equilibria, radiative energy transport, convective instability, continuous opacity, model stellar atmospheres, and stellar continua. This is followed by a development of the basic tools of quantitative spectroscopy, including concepts of line opacity and line profiles, contribution functions, hydrogen line profiles, stellar abundance determinations, and microscopic and macroscopic velocity fields. The course concludes with a discussion of advanced topics such as stellar magnetic fields, non-LTE, stellar winds, stellar pulsation, and stellar activity including chromospheres and coronae.

- Lectures:
- 3 periods per week (1 term)
- Credit(s):
- 1

### PH587 Physical Principles of Non-destructive Evaluation

Physical principles of Nondestructive Evaluation (NDE) techniques are examined. Including: Ultrasonics (stress waves in materials, wave types, beam characteristics), Eddy Current (equivalent circuit models, impedance plane, skin depth), Magnetic Techniques (magnetic fields, ferromagnetism, flux leakage), Radiography (sources, attenuation, shadowing), Liquid Penetrant (surface tension), Thermography (heat diffusion, infrared detection) and Probability of Detection (NDE reliability data analysis).

- Lectures:
- 3 periods per week (1 term)
- Credit(s):
- 1

### PH589 Radar Polarimetry

This course is a thorough introduction to the remote sensing of the earth's surface using polarimetric radar. Topics covered include: SAR processing from signal data to imagery, fundamental concepts in radar polarimetry, speckle statistics and their influence on magnitude and phase information, polarimetric speckle filtering, polarimetric decompositions for discrete and distributed target analysis, polarimetric classification and analysis of natural phenomena and a comparison of polarimetric modes: full, dual, compact, hybrid.

The material will be covered through readings, assignments, seminars and laboratory exercises involving analysis of polarimetric radar imagery. Material from the assigned textbook will form the basis of the course, and will be supplemented by readings from reference books and current literature from international journals.

- Lectures:
- 3 periods per week (1 term)
- Credit(s):
- 1

### PH591 Galaxies in the Universe

This course will provide an overview of the physical properties of galaxies and their environments, as well as the observational techniques used to infer these properties. Topics covered include the orbits of stars, the local population of spiral and elliptical galaxies, groups and clusters of galaxies and galaxy formation. The course material will be put to practise in biweekly problem sets, and a term project will afford students an in-depth look at various aspects of local galaxy physics.

- Lectures:
- 3 periods per week (1 term)
- Credit(s):
- 1

### PH593 Astronomical Instrumentation

This course provides a survey of instrumentation and techniques for astronomical observations. Topics covered include theory of measurement (statistics); detector technology and basic data reduction techniques; imaging and spectroscopy of electromagnetic radiation at radio, infrared, optical, and X-ray wavelengths; data analysis and numerical methods. This course will provide a working base for experimental astronomers and space scientists, as well as a comprehensive background for the more theoretically inclined.

- Lectures:
- 3 periods per week (1 term)
- Credit(s):
- 1

### PH595 Gaussian Optics: Light Propagation in Optical Systems and Waveguide Structures

This course is divided into two main parts. The first part of the course will introduce Gaussian beam and laser beam propagation in the air when focusing or collimating of a Gaussian beam with simple optical systems. Laser-matter interaction in glass and in biological tissues will be covered with some examples in micro-machining and health sciences. Heat transfer in glass material and in biological tissue will be presented in great details for focused and collimated Gaussian beams. The second part of this course will give an overview of laser beams interactions with grating waveguide structure. In this portion of the course, numerical techniques to compute diffraction efficiency in rectangular groove gratings will be presented in detail. Rigorous coupled wave analysis will be derived and applied to binary dielectric and metallic gratings.

- Lectures:
- 3 periods per week (1 term)
- Credit(s):
- 1

### PH596 Grating and Waveguide Structures

This course will be dealing with laser beams interacting with grating waveguide structure. This course will be divided into two parts. In the first part of this course, students will learn about numerical techniques to compute diffraction efficiency in rectangular and sinusoidal gratings, which will be presented in details in class. Rigorous coupled wave analysis will be derived and applied to both binary dielectric and metallic gratings. In the second part of the course, the periodic grating will be applied to optical fibers such as Fiber Bragg gratings and Surface Nanoscale Axial Photonics (SNAP). In this course, students will be taught to use Matlab to calculate the diffraction efficiencies numerically and solve eigenvalue problems in grating waveguide structures.

- Lectures:
- 3 periods per week (1 term)
- Credit(s):
- 1

### PH597 Galactic Astronomy

This course describes the material content, energetics, formation and evolution of the Galaxy and places our Galaxy in the context of galaxies, in general. Topics include the interstellar medium, stellar populations, dynamics, the Galactic centre and the Galactic halo.

- Lectures:
- 3 periods per week (1 term)
- Credit(s):
- 0.5

### PH599 Optical Observational Techniques and Data for Space Surveillance

The course presents an overview of the optical observational techniques that are commonly used to track and characterize artificial Earth-orbiting objects, namely active spacecraft and space debris objects. The course will cover the planning of observations of artificial Earth-orbiting objects. It then introduces charged-coupled detectors (CCD) focussing on the instrument characteristics that have the most important impact on observation activities. Image processing of CCD images will then be studied. Next, the course surveys optics for astronomy namely image quality, telescope types and aberration. Artificial Earth-orbiting object tracking considerations are then reviewed in addition to photometry and spectrometry techniques applied to space surveillance.

- Lectures:
- 3 periods per week (one term)
- Credit(s):
- 1

### PH601 Measurement and Modelling of Stellar Magnetic Fields

This is a PhD-level course on the theory and practice of the diagnosis of stellar magnetic fields. The course is structured based on 5 topics of study: the physics of the Zeeman Effect, polarised radiative transfer in stellar atmospheres, polarization of light and polarimetric instrumentation, methods of measurement of stellar magnetic fields, and modeling and simulation techniques. Evaluation will be based on extensive topic reports, including thorough literature review, original calculations and computations, and well as group discussion.

- Lectures:
- 3 periods per week (1 term)
- Credit(s):
- 1

### PR500 Project

This code is used to capture students registered in a Project. The object of this course is to provide students with an opportunity to be involved in a project that requires them to assimilate knowledge gained from a variety of sources and apply it to a specific, well-defined problem. A formal report is required for presentation in the Winter Term. This course will be offered concurrently with PHE420 (Senior Project) and follow the same curriculum.

### TH500 Thesis; Master's Level

This code is used to capture students registered in a Master's-level Thesis.

### TH600 Thesis; Doctoral Level

This code is used to capture students registered in a Doctoral-level Thesis.

### CP600 Comprehensive Examination; Doctoral Level

This code is used to capture students registered in a Comprehensive Exam.