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

The essay is about a book called spare parts by joshua

The essay is about a book called "Spare parts by Joshua Davis". The requirments are attached (1) an overview of the theme of the book. Ask yourself the question: "What does the book say to me about the field of engineeri ...

Problem - write a matlab program to simulate 2pam baseband

Problem - Write a Matlab program to simulate 2PAM baseband digital transmitter with truncated Sine pulse. The 2PAM signal corresponds to X(t) = i=0 ∑ N-1 Ad i p(t - iT s )                                                  ...

Lab 4 - configuring an interrupt who has the fastest

Lab 4 - Configuring an Interrupt (Who has the Fastest Reflex) 1. Connect the circuit up as shown 2. Develop a game that uses Switch L & R as external input interrupts. 3. Initialize the 7-segments to 9 4. First set the H ...

Practical assignmentconsult the prescribed textbook for the

Practical assignment Consult the prescribed textbook for the assignment. 1.1 An optical fibre communication system (NRZ coding) is operating at a data rate of 20 Mb/s and a bit-error-rate of 10 -9 (at most one error can ...

Assignment computer aided power system design and

Assignment : Computer Aided Power System Design and Analysis 1 Aims of Assignment - To gain a thorough understanding of Load Flow analysis, balanced and unbalanced fault level analysis, power and voltage control in addit ...

Question no 1 write vhdl code for the lfsr circuit given in

Question no. 1 Write VHDL code for the LFSR circuit given in Fig 1. Use the sample entity statement shown in Fig 2. Use the testbench code given with assignment to test your VHDL code. (Note: For the D-flip-flop, make ou ...

Think of a digital system application that utilizes the

Think of a digital system application that utilizes the principle of Finite State Machine (FSM). (Example: Traffic light controller) Describe in detail the application in term of its operational characteristics until the ...

Please review this 10-minute tutorial on multisim make sure

Please review this 10-Minute Tutorial on Multisim, make sure you understand how to capture your circuit and insert it into a word document. Review Example 3-6 and then use Multisim software to do its related problem and ...

Sustainable energy production and utilization1 why do

Sustainable Energy Production and Utilization 1. Why do people perceive change as linear over time? 2. Why is change not linear and ever increasing? 3. Roughly, from what year on, did we consume more "easy" oil than was ...

Proposed max light rail projecttask listyour team has been

Proposed Max Light Rail Project Task List Your team has been asked to determine what a one way ticket price needs to be set to, in order to be able to break even at the end of a 50 year time frame. To help you to provide ...

  • 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