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

Lab half and full wave rectified sine wavesin this lab you

Lab: Half and Full Wave Rectified Sine Waves In this lab you will construct and measure the output of a half wave and a full wave rectifier and the filtered output. In addition you will learn to use the Math function on ...

A continuous stirred tank reactor is a reactor in which

A continuous stirred tank reactor is a reactor in which reactants are continuously added and products are continuously withdrawn. On the other hand, a plug flow reactor is a reactor in which the flow is continuous and th ...

Digital fundamentalspart a-q1 in which of the following

DIGITAL FUNDAMENTALS Part A- Q1: In which of the following base systems is 123 not a valid number? (a) Base 10 (b) Base 16 (c) Base 8 (d) Base 3 Q2: A NAND gate is called a universal logic element because (a) it is used ...

Csc00240 - data communications and networks - network

CSC00240 - Data Communications and Networks - Network Design for a Modern High School Background: A private high school is located in 3 adjacent two-story buildings. Each building is approximately 50 metres long and 15 m ...

Introductiona blowout preventer bop is being designed for

Introduction A Blowout Preventer (BOP) is being designed for an offshore drilling facility operating at a depth of 1300m. The drilling operation is from a floating platform rig where monitor and control of the BOP is con ...

Strain gauge measurementsafety your demonstrator acts as

Strain Gauge Measurement Safety: Your demonstrator acts as your safety warden. Follow all instructions given by your demonstrator. If the evacuation siren sounds leave your bags and follow the instructions of your demons ...

Lab assignmentbackgroundin electronics a low pass filter is

Lab Assignment Background In electronics, a low pass filter is utilized to remove high-frequency noise from a signal. One example would be static present in a radio or cell phone transmission. A simplest low-pass filter ...

The design of the processor is also included language for

The design of the processor is also included. language for the processor is in system verilog - In this assignment you will design the instruction set architecture of a simple microprocessor. - Assignemt 2 is a group ass ...

Youre responsible for a portion of the logic in an

You're responsible for a portion of the logic in an electronic vending machine. Specifically, your subsystem determines the change to be returned. All items cost 75¢ and the machine accepts dollar bills, so your system m ...

Problem - consider the cmos inverter shown in page 3

Problem - Consider the CMOS Inverter shown in page 3 supplied with a bias of VDD = 5 V. The technology file for this CMOS is provided in Page 4. Only key design parameters are shown in CMOS mask layout. Grid size shown i ...

  • 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

A cola-dispensing machine is set to dispense 9 ounces of

A cola-dispensing machine is set to dispense 9 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manuf

What is marketingbullwhat is marketing think back to your

What is Marketing? • "What is marketing"? Think back to your impressions before you started this class versus how you

Question -your client david smith runs a small it

QUESTION - Your client, David Smith runs a small IT consulting business specialising in computer software and techno

Inspection of a random sample of 22 aircraft showed that 15

Inspection of a random sample of 22 aircraft showed that 15 needed repairs to fix a wiring problem that might compromise

Effective hrmquestionhow can an effective hrm system help

Effective HRM Question How can an effective HRM system help facilitate the achievement of an organization's strate