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Section questions 1) Explain why x² for any uniform glass (in the dipole approximation). 2) You havebeen given nonlinear crystal with x(2) 0. Explain whether the material will demonstrate the Pockels effect or the Kerr effect. 3) Amaterialwith x(3) as the lowest order nonlinearity will drives wide variety of output frequencies driven by the term pNL & where Eis: E Eleived (1) Write down five output frequencies that will be generated by the x(3) nonlinear term. One approach to answering this would be to write down the product EEE in full without calculating the final answer. i.e. the full version of: (Equitivet Ei.. E2 Ei Ej.+.+.) (2) 4) Using 72.1 n21 and 12/2 2.6 x 10 20m²/W calculate the change in refractive index for a power of 10 kW propagating in fiber with effective mode area of 10 pm² 5) In lectures. the frequency change caused by SPM was plotted for Gaussian pulse. In between the times where the magnitude of the frequency change is largest, is the chirp positive or negative? continued on following page. 1 6) a) Write down the nonlinear Schrödinger equation without loss. b) Explain which term leads todispersive and to nonlinear effects c) For an JV = 1 soliton, describe any changes in the pulse as it propagates (Comment on the shape in both the time and the frequency domains.) ')(i)Calculate at 1550nm for SMF28 fiber using a mode field diameter of 10. 4 pm for your calculation of the effective area and 2.6 10 -30m²/W (ii) Ignoring dispersion, calculate the peak nonlinear phase shift (radians) for pulse with peak power of 100W propagated through 10m of this fiber. (iii) The fiber dispersioni D= 18 ps/( Assume that the pulse has the same 100W peak power and the correct input shape for soliton. Calculate the input pulse duration. To. that would give N=1. (iv) Give the wavelength where the dispersion of silica changes from normal to anoma lous. 8) A fiber has D: 18.8 ps/nm km at the 1000 nm input wavelength of a pulsed laser (a) Is the dispersion normal or anomalous? (b) Will the fiber support solitons? (c) Explain whether 10Ofs Gaussian pulse is mainly linearly chirped after propagation through (i) 10em and (ii) 100m of fiber by calculating the ratic of fiber length to the dispersion length. 9)(i) Write down two differences between the process of generating a Stokes wave by stimulated Brillouin scattering and of generating sidebands by four-wave-mixing. (ii) Calculatethe wavelength of the Brillouin Stokes wave for laserat 1550.0 nm ina fiber with peal Brillouin gain at frequency offset of GHz. (Assume that the laser linewidth is less than the Brillouin gain bandwidth.) (iii) Express this SBS frequency offset and the SRS frequency offset (13 THz) in wavenumbers with units em -1 Continued on next page: Section questions 10) For third harmonic generation the output intensity, las depends on the driving intensity, In, and the parameter Ak Ata 3k1 121) as follows: (waxTHg)² sin² law(2) 1.3 (3) deferman3 AN° (i) (a) [1 + 3 2+ 2 marks Derive the equation for law. Start by sketching the crystal and any thin slab within crystal that generates Eaw Write down the phase of the nonlinear polarisation in the thin slab and then write the phase of Eas at the crystal output. Finally perform the integral for all slabs along the crystal and show your calculated answers for Eaw Law (b) marks] Use the result from (a) to derive the equation for the coherence length. (ii) Rearrange the equation so la. becomes function of ARL/2 (iii)plot L/ Looh when t o. (Loohi the Coherence Length. Use the axes shown below. (iv) [Repeat (iii) for che case when AR using the same axes. (v) For: nonlinear crystalof length, Lo. Laser hasoutput at the phasematched wavelength for THG and similar laser. Laser 2. has frequency offset so Leah = Ln Calculate the ratio of the powers at the third harmonic that are produced from the lasers at the crystal output. (vi)A continuous wave laser and laser producing rectangular pulses with rep-etition frequency, fo. and pulse duration 1/(10/0). have the same average power, Po. All other characteristics of the lasers are the same. Calculate the ratio of the output power from the third harmomic generation process produced from the two lasers.

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