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

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/

Introduction to Photonics

PHYC 302, Fall 2014

Photonics

• Study of: Generation, emission, transmission, processing, modulation,

amplification & detection of light. (wiki…)

• Involves: the control of photons (free space & matter), and the study
• f the photon nature of light in describing the operation of optical

devices.

Applications

Laser Data handling Communications Micro- Fundamental science

• 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

Overview

Class Syllabus:

• 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)

http://physics.unm.edu/Courses/Becerra/Phys302Fa14/

Class Syllabus:

• 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)

http://physics.unm.edu/Courses/Becerra/Phys302Fa14/

Class Syllabus:

• 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.

Introduction to Photonics (302)

http://physics.unm.edu/Courses/Becerra/Phys302Fa14/

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: wave that propagates in time: . The amplitude of the wave: transverse (longitudinal) displacement.

• Assume a wave at t0.

The wave moves to the right x>0 with velocity V: with no distortion

) , ( t x 

Traveling Wave

) , ( t x  x V ) , ( ) , ( t x f t x g  O ) , ( ) ( t x x f  

S

) ( ) , ( x f t 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.

) ( ') ( ) , ( Vt x f x f t x    

For a point p wit position x’ in the frame S’ which is moving with velocity V, the position of this point in the frame at rest S will be:

Traveling Wave

Vt x x   ' ') ( ') ( x f x g  ) , ( t x 

x V ') ( ') ( x f x g  O ) , ( ) ( t x x f   ' O ' x

S

Vt p Vt x x   '

Traveling wave to the right (x>0)

S’

Moving frame of reference S′ with coordinates x’ moving at the wave speed V.

In general: for a traveling wave with no distortion

) ( ') ( ) , ( Vt x f x f t x    

For any wave with any shape we can generate a traveling wave by changing:

Traveling Wave

“-” Traveling wave to the right (x>0) “+” Traveling wave to the left (x<0) Sinusoidal wave traveling to the right (x>0)

) (x f Vt x x  

Example:

) sin( ) sin( Vt x A x A  

2 2

) ( Vt x a ax

Ae Ae

  



Gaussian wave traveling to the left (x<0) Question: What is the equation that the general traveling wave function satisfies?

) ( Vt x f 

00

• For a general function of “x” and “t”

Wave Equation

" "x

) ( ') ( Vt x f x f    

2 2 2 2 2

1 t V x       

constant t

x  

Partial derivatives with Respect to:

" "t

constant x

t  

To see proof: book Ch 2.1.1 First derivatives

' ' ' ') ( ') ( f x x x x f x x f x            ' ' ' ') ( ') ( Vf t x x x f t x f t            

Second derivatives

'' f x       ''

2 f

V t      

) ( ) ( ) , (

2 1

Vt x g c Vt x f c t x     

General Solution (important)

Harmonic waves: have a profile of a sine or cosine function.

) sin( ) ( ) , ( kx A x t x

t

 



 

Harmonic Waves

k: propagation number units [rad/m]

• Harmonic traveling wave

) , ( t x 

Vt x x  

) sin( )) ( sin( ) , ( t kx A Vt x k A t x      

 sin A 

Phase: depends on “x” and “t” Amplitude

) , ( t x 

) , ( t x 

A A    2  3

Angular Frequency

is an harmonic wave, and it repeats itself every .

) , ( t x 

For t=0:

Harmonic Waves

  2  

Propagation number

k x   2   

t kx t x     ) , ( ) sin( ) sin( ) , (         A A t x   2     x k kx t x  ) , ( 

Wavelength: (spatial period)

Wavelength of Light

nm 400   nm 700  

Blue Red

 1

 K

Wave number (spatial frequency)



x

) , ( t x 

A A  2  

) sin( ) , ( kx A x  

 2 2 3

Angular Frequency

      1 2 2       V kV t    2     t t kVt t x     ) , (

Period

Speed of Light





V



Frequency



Is an harmonic wave, and it repeats itself every .

) , ( t x 

Harmonic Waves

  2  

t kx t x     ) , (

For x=0:

  c V

t

) , ( t x 

A A  

s m c / 10 3

8

 

2 

) sin( ) sin( ) , (         A A t x ) sin( ) , ( t A t   

2 3  2

Harmonic Waves

) sin( ) , (      t kx A t x 

Phase Amplitude Propagation number position Angular frequency time Initial phase

) , ( t x 

) , ( t x 

A A    2  3



) , ( t x 

  2  k    2  k V  

Harmonic Waves

) sin( ) , (      t kx A t x 

Phase Amplitude

) , ( t x 

Propagation number position Angular frequency time Initial phase

Phase Velocity: Velocity that travels a point P of constant phase.

     t kx t x  ) , (

Constant phase:

k t x    constant 

Position of P Velocity of P

V k dt dx     

  2  k    2  k V  

Harmonic Waves

) sin( ) , (      t kx A t x 

Phase Amplitude

) , ( t x 

Propagation number position Angular frequency time Initial phase

Phase We can express an harmonic wave with: either Sine or Cosine

) 2 / sin( ) cos( ) , (            t kx A t kx A t x  

' 

  2  k    2  k V  

The electromagnetic spectrum