ECE437Spring2010
Fiber&IntegratedOptics
Available on Blackboard.
This is an introductory course to the study of the properties of light in optical fibers and waveguiding structures. Topics include: Fundamental principles of electromagnetic theory, operati
ECE 3250
MORE ON REAL AND COMPLEX NUMBERS
Fall 2008
My purpose in this handout is to summarize fairly briskly the main results on sequences and series of real and complex numbers. Ill be lifting some of the denitions (e.g. convergent sequences, Cauchy seq
Solution to Midterm Problem 13 Someone asked me whether Id mind posting a solution to this problem, so here it is.
(a) You might just recognize this system as an averager, but if you dont, you can still nd the impulse response by using h1 = S1 ( ). Accord
ECE 3250
PRIME NUMBERS AND FACTORIZATION
Fall 2008
I think you all know what a prime number is, but lets start from the beginning. Given two natural numbers a and b, we say that a is a divisor of b if and only if b = am for some natural number m. The stan
ECE 3250
PERIODIC SIGNALS AND FOURIER SERIES
Fall 2008
1. Periodic signals You all know intuitively what a periodic signal is. A signal is periodic if it cycles repetitively through a set of values. Heres the formal denition. As usual, F means R or C and
ECE 3250
NUMBERS
Fall 2008
Engineers, scientists, and applied mathematicians think about numbers all the time, but usually in a utilitarian way. We manipulate them, calculate with them, make plans based on them, drive cars and y in airplanes whose design
ECE 3250
DISCRETE-TIME LTI SYSTEMS
Fall 2008
In this handout Id like to summarize the material from class on discrete-time LTI systems. Such systems serve as eective models for a variety of real-world processes that arise in applications. The models are u
ECE 3250
CONTINUOUS-TIME FOURIER TRANSFORMS
Fall 2008
1. Motivation, denition, and derivation The notion of frequency content makes perfect sense for periodic signals. If x is a periodic signal that has To as a period, it might have frequency content at a
ECE 325
THE DTFT AND SAMPLING
Fall 2007
1. The discrete-time Fourier transform The whole frequency-domain concept makes ample sense in continuous time. It starts with periodic signals such as t cos o t, t sin o t, and t ej o t , where o is a given real nu
ECE 3250
SINGULAR-VALUE DECOMPOSITION
Fall 2008
In what follows, Ill be relying on a few essential facts from linear algebra. Some of them are easier to prove than others. As always, F denotes R or C. By Fmn I will mean the set of all (m n) matrices with
ECE 3250
THE z -TRANSFORM
Fall 2008
1. Power series Well have occasion to consider innite series of the form X cn z n ,
n=
where z is a complex variable and the cn are given complex numbers. Well want to know whether the series converges for at least some
ECE 437 Fiber and Integrated Optics: Lab 4 Fiber Bending Loss 12 April, 2010 Report Due Date: 26 April 2010
Read this entire document before starting the laboratory session. The laboratory reports should be clear, concise and written in good English. Ans
ECE 437 Fiber and Integrated Optics: Lab 3 Modes of an Optical Fiber Report Due Date: 7 April 2010
Read this entire document before starting the laboratory session. The laboratory reports should be clear, concise and written in good English. Answer all o
ECE 437 Fiber and Integrated Optics: Lab 2 Polarization Measurement of an Optical Fiber 1 March 2010 Report Due Date: TBA
Read this entire document before starting the laboratory session. The laboratory reports should be clear, concise and written in goo
ECE 4370 Fiber and Integrated Optics: Lab I Optical Fiber Numerical Aperture Measurement 15 February, 2010 Reports due by 03 March 2010
Read this entire document before starting the laboratory session. The laboratory reports should be clear, concise and
ECE4370FiberandIntegratedOptics HomeworkAssignment#7 Due:Monday,April19th,2010at5:00pm 1. Bent Wave Guide Consider the waveguide shown with a=3m, ncore= 1.5, nclad=1.498, and R=5mm at =1.33m. Plot n(r) and and n(r) on the same graph for = 0, 45, and 90o.
Today: Dispersion: Chapter 6
Dispersion
Material Waveguide Modal Dispersion
Real and Imaginary Index
Group Delay and Group Index
g = 1 / v g = dk / d
Group Velocity Dispersion
Ng = n dn d L = N g ( ) c
Material Dispersion
Frequency dependence of the pe
Today: Coupled mode theory (cont) : Chapter 10
Coupling between a source and a waveguide (chapter 11)
A = jKB z B = jKA z
Bragg Gratings
j(+ t) + j( t) A zw A j2 j j zw e e = P ( ) j( ) x x xd 2 pr et z z 2 wt
i ( x ) + r i ( x ) = t t ( x )
H i ( x) rH
Today: Coupled mode theory : Chapter 10
Click to edit Master subtitle style
8/10/10
ECE 437
8/10/10
2 E y ( x, y , z ) =
2 E y ( x, y , z ) t 2
E y ( x, y , z ) =
1 Ai yi ( x)e ( i z wt ) 2
D = oE + P
8/10/10
+ + 1 2A i i A t ) 2 2j i(xe j(izw) i 2i z
Today
Normalizedparameters(review) Circularwaveguides(p.7383)
2 2 a ( 2/n 2 = s n (f n nce =s m st r ) f s) a ayey
2 2 b (f s)nc = ef n / 2 n n (f 2 )
n=/ 0 K e f f
2 V =K ns =m h o 2 n f
2 a ( 2/n 2 = s n (f n nce =s m st r ) 2 s) a ayey f
2 2 b (f s)nc
ECE 3250
THE DFT
Fall 2008
Real-world discrete-time signal processing deals exclusively with nite-duration signals. Innite-duration signals are useful mathematically, but nobody has ever watched such a signal play out in its entirety. When addressing sign
ECE 3250
DISCRETE-TIME CONVOLUTION
Fall 2008
Weve been modeling discrete-time signals as functions x : Z F, where F denotes R or C. I introduced the notation FZ to stand for the set of all F-valued discrete-time signals. If you want, you can view the typi