Introduction to Photonics PHYC 302, Fall 2014 Lectures: M-W-F, - PowerPoint PPT Presentation

Introduction to Photonics PHYC 302, Fall 2014 Lectures: M-W-F, 10:00-10:50 am, P&A room 184 Instructor: Prof. Francisco Elohim Becerra email: fbecerra@unm.edu Office: P&A, room 1136 Phone: 505-277-2673 Teaching Assistant: Zhixiang Ren email: zxren@unm.edu Office: P&A, room 1132 Class: http://physics.unm.edu/Courses/Becerra/Phys302Fa14/

Photonics • Study of: Generation, emission, transmission, processing, modulation, amplification & detection of light. (wiki … ) • Involves: the control of photons (free space & matter), and the study of the photon nature of light in describing the operation of optical devices . Data handling Applications Communications Laser Micro- Fundamental science

Overview • Introduction to Photonics (302) • PHYC302 provides an introduction to optics and its applications. It covers fundamental properties of light, and the analysis of simple optical elements and their applications for optical systems. • Topics: fundamentals of electromagnetic theory, propagation of light, reflection, refraction, interference, diffraction, polarization, coherence, and geometrical and wave optics for the study of lenses and other optical systems. • Goals • Learn the fundamental properties of light • Examine the behavior of light and its interaction with matter • Analyze optical systems: lenses, mirrors, interferometers, apertures, etc. • Obtain a general knowledge of optics

Introduction to Photonics (302) Class Syllabus: http://physics.unm.edu/Courses/Becerra/Phys302Fa14/ • Lectures: M-W-F, 10:00-10:50 am. • Instructor: Prof. Francisco Elohim Becerra email: fbecerra@unm.edu • Office hours: Tuesday 9-11 am. You may also arrange a meeting for another time via email • Teaching Assistant: Zhixiang Ren email: zxren@unm.edu (office hours: TBD).

Introduction to Photonics (302) Class Syllabus: http://physics.unm.edu/Courses/Becerra/Phys302Fa14/ • Class textbook: “Optics” (4th Edition), by Eugene Hecht. (Chapters 2-12) • Homework: Assignments of problems from the textbook, which also may contain additional exercises. (~one set per week) – Posted in the class page about one week before they are due. – Assignments are due at the beginning of the class. – No late work will be accepted .

Introduction to Photonics (302) Class Syllabus: http://physics.unm.edu/Courses/Becerra/Phys302Fa14/ • Grading: – Homework: 20% – Two midterm exams: 25% each – Final: 30% • Tentative Exam Dates (subject to change): September 26 and November 7. The final exam is currently scheduled for Friday, December 12.

General Properties of Waves (Overview: already seen in PHYC 262) • Waves: disturbance that travels through matter or space; transfer of energy. – Longitudinal waves : Medium is displaced in the direction of motion of the wave. • Sound waves • Seismic P-waves (pressure wave) • Springs, etc… – Transverse waves : Medium is displaced in a direction perpendicular to the motion of the wave. • Waves in water (mainly) • Seismic S-waves (shear waves) • Electric (E) and magnetic (M) fields :

Traveling Wave  ( t x , ) Traveling wave : wave that propagates in time: . The a mplitude of the wave: transverse (longitudinal) displacement.   • Assume a wave at t 0 . ( x , t ) f ( x ) 0 The wave moves to the right x>0 with velocity V: with no distortion  ( t x , )   f ( x ) ( x , t )  S g ( x , t ) f ( x , t ) 0 V O x

Traveling Wave  g ( x ') f ( x ') We want to describe the traveling wave at time “t” in the reference frame S’ , which is the “lab” frame at rest S : in the coordinate system x . Moving frame of reference S′ with coordinates x’ moving at the wave  speed V. ( t x , )   f ( x ) ( x , t ) S’  S 0 g ( x ') f ( x ') V p O O ' Vt x ' x For a point p wit position x’ in the frame S’ which Traveling wave to the right (x>0) is moving with velocity V , the position of this     ( x , t ) f ( x ') f ( x Vt ) point in the frame at rest S will be:  '    x x Vt x ' x Vt

Traveling Wave In general: for a traveling wave with no distortion “ - ” Traveling wave to the right (x>0)     ( x , t ) f ( x ') f ( x Vt ) “ + ” Traveling wave to the left (x<0) For any wave with any shape we can generate a traveling wave by changing: f ( x )   x x Vt Example: 00   Sinusoidal wave traveling to the right (x>0) A sin( x ) A sin( x Vt )    2  2 ax a ( x Vt ) Gaussian wave traveling to the left (x<0) Ae Ae  Question: What is the equation that the general traveling wave function satisfies? f ( x Vt )

Wave Equation •    For a general function of “x” and “t”  f ( x ') f ( x Vt )     2 2 1  Partial derivatives with   Respect to: 2 2 2 x V t   " x "  General Solution (important) x t constant      ( x , t ) c f ( x Vt ) c g ( x Vt )   " t " 1 2  t x constant To see proof: book Ch 2.1.1 First derivatives Second derivatives        f ( x ') f ( x ') x '       f '' f '      x x x x ' x        f ( x ') f ( x ') x ' 2 f        V '' Vf '      t t t x ' t

Harmonic Waves Harmonic waves : have a profile of a sine or cosine function. k : propagation number     ( x , t ) ( x ) A sin( kx )  t 0 units [rad/m]   • Harmonic traveling wave x x Vt Angular Frequency       ( x , t ) A sin( k ( x Vt )) A sin( kx t )    A sin Phase : depends on ( t x , ) “x” and “t” Amplitude  ( t x , ) A  ( t x , )    2 3  A

Harmonic Waves    2   ( t x , ) is an harmonic wave, and it repeats itself every .             ( x , t ) kx t ( x , t ) A sin( ) A sin( )   For t=0: ( x , t ) kx  Wavelength: Wave number (spatial period) (spatial frequency)   ( x , 0 ) A sin( kx )    2 1 K    x        k x 2 k Wavelength of Light Propagation   number 400 nm Blue  ( t x , )   Red 700 nm A x  3    2 2  2 A

Harmonic Waves    2   ( t x , ) Is an harmonic wave, and it repeats itself every .             ( x , t ) kx t ( x , t ) A sin( ) A sin( )     For x=0: ( x , t ) kVt t  Period Frequency       2 2 1   ( 0 , t ) A sin( t )        V t    kV V        t 2 Speed of Light Angular Frequency  c    V ( t x , )   8 A c 3 10 m / s t  3    2 2  2 A

Harmonic Waves  ( t x , ) Amplitude Initial phase Phase  2       k  ( x , t ) A sin( kx t )    2 Propagation  position time  number Angular frequency   V k  ( t x , ) A  ( t x , )     2 3  A

Harmonic Waves  ( t x , ) Amplitude Initial phase Phase  2       k  ( x , t ) A sin( kx t )    2 Propagation  position time  number Angular frequency   V Phase Velocity : k Velocity that travels a point P of constant phase. Velocity of P Position of P Constant phase:            dx t  ( x , t ) kx t    V x  dt k constant k

Harmonic Waves  ( t x , ) Amplitude Initial phase Phase  2       k  ( x , t ) A sin( kx t )    2 Propagation  position time  number Angular frequency   V Phase k We can express an harmonic wave with: either Sine or Cosine              ( x , t ) A cos( kx t ) A sin( kx t / 2 )  '

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