Ask Question, Ask an Expert


Ask Other Engineering Expert

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

Discussion-please share with your classmates an experience

Discussion- Please share with your classmates an experience where you have dealt with lack of accommodation for the user in the design of equipment, process, or product. What was done to accommodate the user? Which anthr ...

Problem 1a router is used to cut locating notches on a

Problem 1 A router is used to cut locating notches on a printer circuit board. The vibration level at the surface of the board as it is cut, is considered to be a major source of dimensional variation (lower the better) ...

If you obtain advice from others or use information from

If you obtain advice from others, or use information from any source including the web, these must be acknowledged in your report. Two sample MATLAB codes are provided at the end of the assignment to help you with this a ...

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 ...

1 the 2d diffusion equation ut dnabla2u is discretized

1. The 2D diffusion equation u t = D∇ 2 u is discretized using the Finite Difference method as (u i,j n+1 - u i,j n )/DΔt = γ[(u i+1 n+1 ,j - 2u i,j n+1 + u i-1 n+1 ,j )/Δx 2 + u i,j+1 n+1 ,j - 2u i,j n+1 + u i-1 n+1 /Δy ...

The united states east to west water diversion

The United States East to West Water Diversion Project Background I was recently contacted by a concerned citizen in Naperville, Illinois with the following request: Dear Dr. Adam, I have written up an idea I've been thi ...

Finite element analysis in engineering term assignmentfor

Finite Element Analysis in Engineering Term Assignment For the truss system above, do the following. Q1: (a) Solve for the x,y components of displacement of each joint using one bar element for each link. Show all work i ...

Assignmentactive filter design techniques1refer to chapter

ASSIGNMENT: Active Filter Design Techniques 1. Refer to Chapter 6 in the text as needed. 2. Using the Fast, Practical Filter Design technique presented in section 6.3 design the following. Be sure to show all work for fu ...

Technical memo based on a provided excel sheetsreport your

Technical MEMO based on a provided excel sheets Report your results to Dr. Robin Hood, Director of Applications Department, in a technical memo, no longer than 3 pages. Note that Dr. Hood has a strong background in fuel ...

Assignment air traffic control systemconsider the following

Assignment: Air Traffic Control System Consider the following goal model fragment for an air traffic control system shown below. The parent goal roughly states that aircraft routes should be sufficiently separated. The r ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

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.

Ask Now Help with Problems, Get a Best Answer

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