Đây là bộ sách tiếng anh về chuyên ngành vật lý gồm các lý thuyết căn bản và lý liên quan đến công nghệ nano ,công nghệ vật liệu ,công nghệ vi điện tử,vật lý bán dẫn. Bộ sách này thích hợp cho những ai đam mê theo đuổi ngành vật lý và muốn tìm hiểu thế giới vũ trụ và hoạt độn ra sao.
Contents Preface vii 1 Maxwell’s Equations 1 1.1 Maxwell’s Equations, 1 1.2 Lorentz Force, 2 1.3 Constitutive Relations, 3 1.4 Boundary Conditions, 6 1.5 Currents, Fluxes, and Conservation Laws, 8 1.6 Charge Conservation, 9 1.7 Energy Flux and Energy Conservation, 10 1.8 Harmonic Time Dependence, 12 1.9 Simple Models of Dielectrics, Conductors, and Plasmas, 13 1.10 Problems, 21 2 Uniform Plane Waves 25 2.1 Uniform Plane Waves in Lossless Media, 25 2.2 Monochromatic Waves, 31 2.3 Energy Density and Flux, 34 2.4 Wave Impedance, 35 2.5 Polarization, 35 2.6 Uniform Plane Waves in Lossy Media, 42 2.7 Propagation in Weakly Lossy Dielectrics, 48 2.8 Propagation in Good Conductors, 49 2.9 Propagation in Oblique Directions, 50 2.10 Complex Waves, 53 2.11 Problems, 55 3 Propagation in Birefringent Media 60 3.1 Linear and Circular Birefringence, 60 3.2 Uniaxial and Biaxial Media, 61 3.3 Chiral Media, 63 3.4 Gyrotropic Media, 66 3.5 Linear and Circular Dichroism, 67 3.6 Oblique Propagation in Birefringent Media, 68 3.7 Problems, 75 ii CONTENTS iii 4 Reflection and Transmission 81 4.1 Propagation Matrices, 81 4.2 Matching Matrices, 85 4.3 Reflected and Transmitted Power, 88 4.4 Single Dielectric Slab, 91 4.5 Reflectionless Slab, 94 4.6 Time-Domain Reflection Response, 102 4.7 Two Dielectric Slabs, 104 4.8 Problems, 106 5 Multilayer Structures 109 5.1 Multiple Dielectric Slabs, 109 5.2 Antireflection Coatings, 111 5.3 Dielectric Mirrors, 116 5.4 Propagation Bandgaps, 127 5.5 Narrow-Band Transmission Filters, 127 5.6 Equal Travel-Time Multilayer Structures, 132 5.7 Applications of Layered Structures, 146 5.8 Chebyshev Design of Reflectionless Multilayers, 149 5.9 Problems, 156 6 Oblique Incidence 159 6.1 Oblique Incidence and Snell’s Laws, 159 6.2 Transverse Impedance, 161 6.3 Propagation and Matching of Transverse Fields, 164 6.4 Fresnel Reflection Coefficients, 166 6.5 Total Internal Reflection, 168 6.6 Brewster Angle, 174 6.7 Complex Waves, 177 6.8 Geometrical Optics, 185 6.9 Fermat’s Principle, 187 6.10 Ray Tracing, 189 6.11 Problems, 200 7 Multilayer Film Applications 202 7.1 Multilayer Dielectric Structures at Oblique Incidence, 202 7.2 Single Dielectric Slab, 204 7.3 Antireflection Coatings at Oblique Incidence, 207 7.4 Omnidirectional Dielectric Mirrors, 210 7.5 Polarizing Beam Splitters, 220 7.6 Reflection and Refraction in Birefringent Media, 223 7.7 Brewster and Critical Angles in Birefringent Media, 227 7.8 Multilayer Birefringent Structures, 230 7.9 Giant Birefringent Optics, 232 7.10 Problems, 237 iv Electromagnetic Waves & Antennas – S. J. Orfanidis 8 Waveguides 238 8.1 Longitudinal-Transverse Decompositions, 239 8.2 Power Transfer and Attenuation, 244 8.3 TEM, TE, and TM modes, 246 8.4 Rectangular Waveguides, 249 8.5 Higher TE and TM modes, 251 8.6 Operating Bandwidth, 253 8.7 Power Transfer, Energy Density, and Group Velocity, 254 8.8 Power Attenuation, 256 8.9 Reflection Model of Waveguide Propagation, 259 8.10 Resonant Cavities, 261 8.11 Dielectric Slab Waveguides, 263 8.12 Problems, 271 9 Transmission Lines 273 9.1 General Properties of TEM Transmission Lines, 273 9.2 Parallel Plate Lines, 279 9.3 Microstrip Lines, 280 9.4 Coaxial Lines, 284 9.5 Two-Wire Lines, 289 9.6 Distributed Circuit Model of a Transmission Line, 291 9.7 Wave Impedance and Reflection Response, 293 9.8 Two-Port Equivalent Circuit, 295 9.9 Terminated Transmission Lines, 296 9.10 Power Transfer from Generator to Load, 299 9.11 Open- and Short-Circuited Transmission Lines, 301 9.12 Standing Wave Ratio, 304 9.13 Determining an Unknown Load Impedance, 306 9.14 Smith Chart, 310 9.15 Time-Domain Response of Transmission Lines, 314 9.16 Problems, 321 10 Coupled Lines 330 10.1 Coupled Transmission Lines, 330 10.2 Crosstalk Between Lines, 336 10.3 Weakly Coupled Lines with Arbitrary Terminations, 339 10.4 Coupled-Mode Theory, 341 10.5 Fiber Bragg Gratings, 343 10.6 Problems, 346 11 Impedance Matching 347 11.1 Conjugate and Reflectionless Matching, 347 11.2 Multisection Transmission Lines, 349 11.3 Quarter-Wavelength Impedance Transformers, 350 11.4 Quarter-Wavelength Transformer With Series Section, 356 11.5 Quarter-Wavelength Transformer With Shunt Stub, 359 11.6 Two-Section Series Impedance Transformer, 361 CONTENTS v 11.7 Single Stub Matching, 366 11.8 Balanced Stubs, 370 11.9 Double and Triple Stub Matching, 371 11.10 L-Section Lumped Reactive Matching Networks, 374 11.11 Pi-Section Lumped Reactive Matching Networks, 377 11.12 Problems, 383 12 S-Parameters 386 12.1 Scattering Parameters, 386 12.2 Power Flow, 390 12.3 Parameter Conversions, 391 12.4 Input and Output Reflection Coefficients, 392 12.5 Stability Circles, 394 12.6 Power Gains, 400 12.7 Generalized S-Parameters and Power Waves, 406 12.8 Simultaneous Conjugate Matching, 410 12.9 Power Gain Circles, 414 12.10 Unilateral Gain Circles, 415 12.11 Operating and Available Power Gain Circles, 418 12.12 Noise Figure Circles, 424 12.13 Problems, 428 13 Radiation Fields 430 13.1 Currents and Charges as Sources of Fields, 430 13.2 Retarded Potentials, 432 13.3 Harmonic Time Dependence, 435 13.4 Fields of a Linear Wire Antenna, 437 13.5 Fields of Electric and Magnetic Dipoles, 439 13.6 Ewald-Oseen Extinction Theorem, 444 13.7 Radiation Fields, 449 13.8 Radial Coordinates, 452 13.9 Radiation Field Approximation, 454 13.10 Computing the Radiation Fields, 455 13.11 Problems, 457 14 Transmitting and Receiving Antennas 460 14.1 Energy Flux and Radiation Intensity, 460 14.2 Directivity, Gain, and Beamwidth, 461 14.3 Effective Area, 466 14.4 Antenna Equivalent Circuits, 470 14.5 Effective Length, 472 14.6 Communicating Antennas, 474 14.7 Antenna Noise Temperature, 476 14.8 System Noise Temperature, 480 14.9 Data Rate Limits, 485 14.10 Satellite Links, 487 14.11 Radar Equation, 490 14.12 Problems, 492 vi Electromagnetic Waves & Antennas – S. J. Orfanidis 15 Linear and Loop Antennas 493 15.1 Linear Antennas, 493 15.2 Hertzian Dipole, 495 15.3 Standing-Wave Antennas, 497 15.4 Half-Wave Dipole, 499 15.5 Monopole Antennas, 501 15.6 Traveling-Wave Antennas, 502 15.7 Vee and Rhombic Antennas, 505 15.8 Loop Antennas, 508 15.9 Circular Loops, 510 15.10 Square Loops, 511 15.11 Dipole and Quadrupole Radiation, 512 15.12 Problems, 514 16 Radiation from Apertures 515 16.1 Field Equivalence Principle, 515 16.2 Magnetic Currents and Duality, 517 16.3 Radiation Fields from Magnetic Currents, 519 16.4 Radiation Fields from Apertures, 520 16.5 Huygens Source, 523 16.6 Directivity and Effective Area of Apertures, 525 16.7 Uniform Apertures, 527 16.8 Rectangular Apertures, 527 16.9 Circular Apertures, 529 16.10 Vector Diffraction Theory, 532 16.11 Extinction Theorem, 536 16.12 Vector Diffraction for Apertures, 538 16.13 Fresnel Diffraction, 539 16.14 Knife-Edge Diffraction, 543 16.15 Geometrical Theory of Diffraction, 549 16.16 Problems, 555 17 Aperture Antennas 558 17.1 Open-Ended Waveguides, 558 17.2 Horn Antennas, 562 17.3 Horn Radiation Fields, 564 17.4 Horn Directivity, 569 17.5 Horn Design, 572 17.6 Microstrip Antennas, 575 17.7 Parabolic Reflector Antennas, 581 17.8 Gain and Beamwidth of Reflector Antennas, 583 17.9 Aperture-Field and Current-Distribution Methods, 586 17.10 Radiation Patterns of Reflector Antennas, 589 17.11 Dual-Reflector Antennas, 598 17.12 Lens Antennas, 601 17.13 Problems, 602 CONTENTS vii 18 Antenna Arrays 603 18.1 Antenna Arrays, 603 18.2 Translational Phase Shift, 603 18.3 Array Pattern Multiplication, 605 18.4 One-Dimensional Arrays, 615 18.5 Visible Region, 617 18.6 Grating Lobes, 618 18.7 Uniform Arrays, 621 18.8 Array Directivity, 625 18.9 Array Steering, 626 18.10 Array Beamwidth, 628 18.11 Problems, 630 19 Array Design Methods 632 19.1 Array Design Methods, 632 19.2 Schelkunoff’s Zero Placement Method, 635 19.3 Fourier Series Method with Windowing, 637 19.4 Sector Beam Array Design, 638 19.5 Woodward-Lawson Frequency-Sampling Design, 643 19.6 Narrow-Beam Low-Sidelobe Designs, 647 19.7 Binomial Arrays, 651 19.8 Dolph-Chebyshev Arrays, 653 19.9 Taylor-Kaiser Arrays, 665 19.10 Multibeam Arrays, 668 19.11 Problems, 671 20 Currents on Linear Antennas 672 20.1 Hall ´ en and Pocklington Integral Equations, 672 20.2 Delta-Gap and Plane-Wave Sources, 675 20.3 Solving Hall ´ en’s Equation, 676 20.4 Sinusoidal Current Approximation, 678 20.5 Reflecting and Center-Loaded Receiving Antennas, 679 20.6 King’s Three-Term Approximation, 682 20.7 Numerical Solution of Hall ´ en’s Equation, 686 20.8 Numerical Solution Using Pulse Functions, 689 20.9 Numerical Solution for Arbitrary Incident Field, 693 20.10 Numerical Solution of Pocklington’s Equation, 695 20.11 Problems, 701 21 Coupled Antennas 702 21.1 Near Fields of Linear Antennas, 702 21.2 Self and Mutual Impedance, 705 21.3 Coupled Two-Element Arrays, 709 21.4 Arrays of Parallel Dipoles, 712 21.5 Yagi-Uda Antennas, 721 21.6 Hall ´ en Equations for Coupled Antennas, 726 21.7 Problems, 733 viii Electromagnetic Waves & Antennas – S. J. Orfanidis 22 Appendices 735 A Physical Constants, 735 B Electromagnetic Frequency Bands, 736 C Vector Identities and Integral Theorems, 738 D Green’s Functions, 740 E Coordinate Systems, 743 F Fresnel Integrals, 745 G MATLAB Functions, 748 References 753 Index 779 1 Maxwell’s Equations 1.1 Maxwell’s Equations Maxwell’s equations describe all (classical) electromagnetic phenomena: ∇ ∇ ∇×E =− ∂ B ∂t ∇ ∇ ∇× H = J + ∂ D ∂t ∇ ∇ ∇· D = ρ ∇ ∇ ∇· B = 0 (Maxwell’s equations) (1.1.1) The first is Faraday’s law of induction, the second is Amp ` ere’s law as amended by Maxwell to include the displacement current ∂D/∂t, the third and fourth are Gauss’ laws for the electric and magnetic fields. The displacement current term ∂D /∂t in Amp ` ere’s law is essential in predicting the existence of propagating electromagnetic waves. Its role in establishing charge conser- vation is discussed in Sec. 1.6. Eqs. (1.1.1) are in SI units. The quantities E and H are the electric and magnetic field intensities and are measured in units of [volt/m] and [ampere/m], respectively. The quantities D and B are the electric and magnetic flux densities and are in units of [coulomb/m 2 ] and [weber/m 2 ], or [tesla]. B is also called the magnetic induction. The quantities ρ and J are the volume charge density and electric current density (charge flux) of any external charges (that is, not including any induced polarization charges and currents.) They are measured in units of [coulomb/m 3 ] and [ampere/m 2 ]. The right-hand side of the fourth equation is zero because there are no magnetic mono- pole charges. The charge and current densities ρ, J may be thought of as the sources of the electro- magnetic fields. For wave propagation problems, these densities are localized in space; for example, they are restricted to flow on an antenna. The generated electric and mag- netic fields are radiated away from these sources and can propagate to large distances to 2 Electromagnetic Waves & Antennas – S. J. Orfanidis the receiving antennas. Away from the sources, that is, in source-free regions of space, Maxwell’s equations take the simpler form: ∇ ∇ ∇×E =− ∂ B ∂t ∇ ∇ ∇× H = ∂ D ∂t ∇ ∇ ∇· D = 0 ∇ ∇ ∇·B = 0 (source-free Maxwell’s equations) (1.1.2) 1.2 Lorentz Force The force on a charge q moving with velocity v in the presence of an electric and mag- netic field E , B is called the Lorentz force and is given by: F = q(E +v × B ) (Lorentz force) (1.2.1) Newton’s equation of motion is (for non-relativistic speeds): m d v dt = F = q(E + v ×B) (1.2.2) where m is the mass of the charge. The force F will increase the kinetic energy of the charge at a rate that is equal to the rate of work done by the Lorentz force on the charge, that is, v ·F. Indeed, the time-derivative of the kinetic energy is: W kin = 1 2 m v · v ⇒ dW kin dt = m v · d v dt = v · F = q v ·E (1.2.3) We note that only the electric force contributes to the increase of the kinetic energy— the magnetic force remains perpendicular to v, that is, v ·(v ×B)= 0. Volume charge and current distributions ρ, J are also subjected to forces in the presence of fields. The Lorentz force per unit volume acting on ρ, J is given by: f = ρE +J × B (Lorentz force per unit volume) (1.2.4) where f is measured in units of [newton/m 3 ]. If J arises from the motion of charges within the distribution ρ, then J = ρv (as explained in Sec. 1.5.) In this case, f = ρ(E +v ×B) (1.2.5) By analogy with Eq. (1.2.3), the quantity v · f = ρ v · E = J · E represents the power per unit volume of the forces acting on the moving charges, that is, the power expended by (or lost from) the fields and converted into kinetic energy of the charges, or heat. It has units of [watts/m 3 ]. We will denote it by: dP loss dV = J · E (ohmic power losses per unit volume) (1.2.6) 1.3. Constitutive Relations 3 In Sec. 1.7, we discuss its role in the conservation of energy. We will find that elec- tromagnetic energy flowing into a region will partially increase the stored energy in that region and partially dissipate into heat according to Eq. (1.2.6). 1.3 Constitutive Relations The electric and magnetic flux densities D, B are related to the field intensities E, H via the so-called constitutive relations, whose precise form depends on the material in which the fields exist. In vacuum, they take their simplest form: D = 0 E B = µ 0 H (1.3.1) where 0 ,µ 0 are the permittivity and permeability of vacuum, with numerical values: 0 = 8.854 ×10 −12 farad/m µ 0 = 4π ×10 −7 henry/m (1.3.2) The units for 0 and µ 0 are the units of the ratios D/E and B/H, that is, coulomb/m 2 volt/m = coulomb volt · m = farad m , weber/m 2 ampere/m = weber ampere · m = henry m From the two quantities 0 ,µ 0 , we can define two other physical constants, namely, the speed of light and characteristic impedance of vacuum: c 0 = 1 √ µ 0 0 = 3 ×10 8 m/sec ,η 0 = µ 0 0 = 377 ohm (1.3.3) The next simplest form of the constitutive relations is for simple dielectrics and for magnetic materials: D = E B = µH (1.3.4) These are typically valid at low frequencies. The permittivity and permeability µ are related to the electric and magnetic susceptibilities of the material as follows: = 0 (1 + χ) µ = µ 0 (1 + χ m ) (1.3.5) The susceptibilities χ, χ m are measures of the electric and magnetic polarization properties of the material. For example, we have for the electric flux density: D = E = 0 (1 + χ)E = 0 E + 0 χE = 0 E + P [...]... discuss simple models of (ω) for dielectrics, conductors, and plasmas, and clarify the nature of Ohm s law: J = σE (Ohm s law) (1.3.12) One major consequence of material dispersion is pulse spreading, that is, the progressive widening of a pulse as it propagates through such a material This effect limits the data rate at which pulses can be transmitted There are other types of dispersion, such as intermodal... of values For example, assuming a frequency of 1 GHz and using (for illustration purposes) the dc-values of the dielectric constants and conductivities, we find: 20 Electromagnetic Waves & Antennas – S J Orfanidis Jcond Jdisp 109 σ 1 = = ω −9 10 for copper with σ = 5.8×107 S/ m and = for seawater with σ = 4 S/ m and = 72 0 for a glass with σ = 10−10 S/ m and = 2 0 0 Thus, the ratio varies over... that its dielectric behavior is determined from Dx ± jDy = ± (ω)(Ex ± jEy ), where ± (ω)= 0 1− ω2 p ω(ω ± ωB ) where ωp is the plasma frequency Thus, the plasma exhibits birefringence 2 Uniform Plane Waves 2.1 Uniform Plane Waves in Lossless Media The simplest electromagnetic waves are uniform plane waves propagating along some fixed direction, say the z-direction, in a lossless medium { , µ} The assumption... Using Eq (1.9.26), we have: tan θ = σc (ω)+ω d (ω) σc (ω) = + ω d (ω) ω d (ω) d (ω) d (ω) = tan θc + tan θd (1.9.29) The ohmic loss per unit volume can be expressed in terms of the loss tangent as: dPloss 1 = ω dV 2 d (ω)tan θ E 2 (ohmic losses) (1.9.30) 1.10 Problems 21 Plasmas To describe a collisionless plasma, such as the ionosphere, the simple model considered in the previous sections can be specialized... materials exhibit, of course, several such resonant frequencies corresponding to various vibrational modes and polarization types (e.g., electronic, ionic, polar.) The dielectric constant becomes the sum of such terms: (ω)= 2 0 ωip 0 + i ω20 − ω2 + j αi i 16 Electromagnetic Waves & Antennas – S J Orfanidis Fig 1.9.1 Real and imaginary parts of dielectric constant Conductors The conductivity properties of... electrons and describes the case of good ˙ conductors The frictional term αx arises from collisions that tend to slow down the electron The parameter α is a measure of the rate of collisions per unit time, and therefore, τ = 1/α will represent the mean-time between collisions 14 Electromagnetic Waves & Antennas – S J Orfanidis In a typical conductor, τ is of the order of 10−14 seconds, for example,... regions Fig 1.6.1 Flux outwards through surface 10 Electromagnetic Waves & Antennas – S J Orfanidis Another consequence of Eq (1.6.1) is that in good conductors, there cannot be any accumulated volume charge Any such charge will quickly move to the conductor s surface and distribute itself such that to make the surface into an equipotential surface Assuming that inside the conductor we have D = E and J. .. z ˆ· ˆ× z z † The ∂H ∂z shorthand notation ∂x stands for = ˆ· z ∂ ∂x ∂E =0 ∂t ⇒ ∂Ez =0 ∂t 26 Electromagnetic Waves & Antennas – S J Orfanidis Because also ∂z Ez = 0, it follows that Ez must be a constant, independent of z, t Excluding static solutions, we may take this constant to be zero Similarly, we have Hz = 0 Thus, the fields have components only along the x, y directions: ˆ ˆ E(z, t) = x Ex (z,... per unit volume is JE = σE2 Multiplying this by the resistor volume Al and equating it to the circuit expression V2 /R = RI2 will give: (J · E)(Al)= σE2 (Al)= V2 E 2 l2 = R R ⇒ R= 1 l σA 12 Electromagnetic Waves & Antennas – S J Orfanidis The same circuit expressions can, of course, be derived more directly using Q = CV, the magnetic flux Φ = LI, and V = RI Conservation laws may also be derived for... (source-free boundary conditions) (1.4.5) 8 Electromagnetic Waves & Antennas – S J Orfanidis 1.5 Currents, Fluxes, and Conservation Laws The electric current density J is an example of a flux vector representing the flow of the electric charge The concept of flux is more general and applies to any quantity that flows.† It could, for example, apply to energy flux, momentum flux (which translates into pressure . conditions) (1.4.5) 8 Electromagnetic Waves & Antennas – S. J. Orfanidis 1.5 Currents, Fluxes, and Conservation Laws The electric current density J is an. fields are radiated away from these sources and can propagate to large distances to 2 Electromagnetic Waves & Antennas – S. J. Orfanidis the receiving antennas.