Answer Happy

Problem 4. Pulse evolution when propagating in fused silica Consider an unchirped Gaussian pulse with a width Ti = 30 fs at a central wavelength of 800 nm. It propagates through a piece of fused silica. The Sellmeier equation for the index of fused silica glass is (with λ in microns) 0.69622² 0.407942² 0.89752² n²-1= + λ² − (0.068404)² + x² − (0.11624)² * x² − (9.89616)² (a) Calculate the phase velocity at the wavelength of 800 nm (in the unit of m/s). (b) Calculate the group velocity (in the unit of m/s). (c) Calculate the group velocity dispersion (in the unit of fs²/μm). * Hint: Make a Taylor's expansion of ß (w) to the second order. An easier way is to do the derivative numerically. f(x + h) − f (x − h) - f'(x) ≈ 2h

f(x+h)-2f(x) + f(x - h) f"(x) ≈ h² Here h is a small number. Ref: http://www2.math.umd.edu/~dlevy/classes ... n-chap.pdf (d) Calculate the output pulse width To after propagating through 50 cm of fused silica (in the unit of fs). (e) Calculate the chirp parameter of the output pulse after propagating through 50 cm of fused silica (in the unit of fs-²).