+1-415-315-9853

info@mywordsolution.com

## Engineering

 Civil Engineering Chemical Engineering Electrical & Electronics Mechanical Engineering Computer Engineering Engineering Mathematics MATLAB Other Engineering Digital Electronics Biochemical & Biotechnology

1. A very narrow laser beam in air is shone into a sphere of solid glass that has a uniform refractive index n>1 and radius ρ . The beam makes an angle α in air with the normal to the surface of the sphere. Sketch the path of the beam in the circular cross-section of the sphere defined by the normal and the beam direction, and show all reflected and transmitted rays.  describe why the beam cannot become a bound whispering gallery ray propagating around the inside the glass-air surface of the sphere.

2. An asymmetric, multimode, step-profile slab waveguide has a core index of 1.49. The cladding index above the core has value 1.47 and the cladding index below the core has value 1.48. Rays propagate in the core in the x-z plane and make an angle θz relative to the z-axis along the centre of the waveguide.

(a) Determine the range of (positive) values of θz in degrees for which only bound rays will propagate along the waveguide.

(b) How many different types of rays can propagate along the waveguide? Sketch a typical path for each type of ray.

(c) Determine the values of θz in degrees that delineate between the 3 types of ray paths.

3. An asymmetric, multimode slab waveguide has a core width 2ρ, a uniform cladding index ncl in the regions above and below the core, and a variable refractive-index profile nco(x) in the core defined by:

nco(x)= nco[1-2Δ(x/ρ)2]1/2  for 0≤x≤ ρ

nco(x)= nco for - ρ ≤x≤0

Where nco is a constant, Δ is the relative index difference with standard definition and the x-axis is orthogonal to the z-axis of symmetry of the waveguide. Assume that all ray paths are periodic and start at x=z=0. The initial angle the ray path makes with the z-axis at x=0 is θz, i.e. dx/dz=tanθz at z=0.

(a) Sketch, approximately, the shape of a periodic bound ray path along the waveguide.

(b) Substitute the above core profile into the second-order differential equation for ray    paths as given in lectures and solve the resulting equation to determine the curved bound ray paths for 0≤x≤ ρ as a function of z, θz and σ. What is the maximum permissible value of θz for a curved bound ray path?

(c) Use the path equation derived in (a) to determine an analytical expression for the bound ray half-period zp, i.e. the distance between successive crossing points of the ray path on the z-axis.

4. A weakly guiding, step-profile slab waveguide has a core half-width of 4 microns. The core index is 1.47 and the cladding index is 1.46. Determine the range of source wavelength values in nanometres for which the waveguide will support: (i) a single mode; (ii) two modes; (iii) three modes; (iv) more than three modes.

5. Consider a fibre whose core index is 1.5 and whose cladding index is 1.485.  The core radius is 100 mm.  At what bending radius does a ray traveling along the fibre axis strike the cladding at the critical angle in the bend?

6. A weakly guiding optical fibre propagates just the first three bound modes. The three modes have scalar transverse electric fields ψ1(x,y), ψ2(x,y) and ψ3(x,y) with respective propagation constants β1, β2 and β3 respectively. At the beginning of the fibre, a source on the end-face excites the three modes with electric field amplitudes a1, a2 and a3, respectively.

(a) prepare down an algebraic expression for the total bound electric field at any position along the fibre.

(b) Starting with the expression for the total field in (a), use lecture notes to determine an integral expression for the total guided mode power in the fibre in terms of ψ1(x,y), ψ2(x,y) and ψ3(x,y).

(c) Confirm that the resulting expression in (b) is equal to the sum of the powers carried by each of the three modes.

7. A multimode, step-profile fibre has a core radius of 40 microns, a core index of 1.51 and a cladding index of 1.49.

(a) If the fibre end-face is excited by a source with a wavelength of 900nm, what is the maximum number of bound modes that can be excited?

(b) What is the minimum number of bound modes that can be excited regardless of the wavelength of the source?

(c) If the end-face of the fibre in (a) is now illuminated simultaneously by 2 sources that emit light at wavelengths of 800 and 1,000nm, respectively, what is the total number of different bound modal states that can be excited in the fibre?

Other Engineering, Engineering

• Category:- Other Engineering
• Reference No.:- M9767

Have any Question?

## Related Questions in Other Engineering

### 1given the following transfer function modelsy1su1s g11s

1. Given the following transfer function models: y 1 (s)/u 1 (s) = g 11 (s) = 2/(s+3) y 1 (s)/u 2 (s) = g 12 (s) = -1/(s+1) y 2 (s)/u 1 (s) = g 21 (s) = -1/(s+7) y 2 (s)/u 2 (s) = g 22 (s) = 0.5/(s+4) a) Draw the 2x2 ope ...

### Exercise 1charity is a big business in the united states

Exercise 1 Charity is a big business in the United States. The Web site charitynavigator.com gives information on roughly 5500 charitable organizations, and there are many smaller charities that fly below the navigator's ...

Assignment Discussion Analog Integrated Circuits & Lab Filter Design Directions: Please answer BOTH of the questions and respond to a minimum of two of your classmates. Question A Discuss the various compromises that mus ...

Assignment Discussion Analog Integrated Circuits & Lab Op-Amp Application and Datasheets Directions: Please answer BOTH of the questions and respond to a minimum of two of your classmates. Question A Discuss why it is im ...

### Electronics lab transistor biasing1given a bjt unloaded

Electronics Lab: Transistor Biasing 1. Given a BJT unloaded amplifier shown in figure 1 below with β=100. o Draw DC equivalent circuits of this unloaded amplifier. o Draw the DC load line of the circuit. o Determine the ...

### Microprocessorsmodule-simple automation systemsoverviewin

MICROPROCESSORS Module-Simple Automation Systems OVERVIEW In the final module, we cut the umbilical cord and try standalone operations of UNO board. You will learn about the applications of the AVR in various areas. We a ...

### Microcomputers lab exploring pwmobjectives to gain a better

Microcomputers Lab: Exploring PWM Objectives: To gain a better understanding of Pulse Width Modulation. What you will need: Arduino UNO, Analog Discovery Kit (ADK), LU EE Component Kit, jump wires, a computer with instal ...

### Life cycle and risk management assignment 4 a

Life Cycle and Risk Management Assignment 4: A workplace-based report This assessment task involves collaborative team arrangement efforts and designed to explore the key issues of risk management and how these issues ar ...

### Project proposal -objectives to get more familiar with the

Project Proposal - Objectives: To get more familiar with the Hadoop Ecosystem (Spark specifically) and Scala Programming. Resources: Files of tweets about election Project Topic: The election of 2016 seems to be a very c ...

### 1 represent the following decimal numbers in both binary

1. Represent the following decimal numbers in both binary sign/magnitude and two's complement using 16 bits: -29. 2. A Computer uses IEEE-754 format to represent floating points. What value (in decimal) the computer repr ...

• 13,132 Experts

## Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

### WalMart Identification of theory and critical discussion

Drawing on the prescribed text and/or relevant academic literature, produce a paper which discusses the nature of group

### Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

### Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

### Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

### Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro