Exact solutions for linear propagation of chirped pulses using a chirped Gauss–Hermite orthogonal basis

P. Lazaridis; G. Debarge; P. Gallion

doi:10.1364/OL.22.000685

Optics Letters
Vol. 22,
Issue 10,
pp. 685-687
(1997)
•https://doi.org/10.1364/OL.22.000685

Exact solutions for linear propagation of chirped pulses using a chirped Gauss–Hermite orthogonal basis

P. Lazaridis, G. Debarge, and P. Gallion

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P. Lazaridis, G. Debarge, and P. Gallion, "Exact solutions for linear propagation of chirped pulses using a chirped Gauss–Hermite orthogonal basis," Opt. Lett. 22, 685-687 (1997)

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Abstract

A generalized solution of the linear propagation equation is proposed in terms of chirped Gauss–Hermite orthogonal functions. Some well-known special cases are pointed out, and the usefulness of this approach in analyzing arbitrarily shaped chirped pulses in rapidly converging series is discussed.

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Basis Function	$c_{m}$	$E_{rms} (%)$
1	$c_{0} = 1.259707$	7.47
2	$c_{4} = 0.091934$	1.69
3	$c_{8} = 0.020216$	0.53
4	$c_{12} = 0.006254$	0.20

$E_{rms} (%)$	Basis Functions
0.01	8
0.001	12
0.0001	17

Distance $z$	CGH $- 4$ Basis Functions	FFT (2048 Points)
Distance $z$	CGH $- 4$ Basis Functions	$t \in (- 40, 40)$	$t \in (- 200, 200)$
0.1	3.16	3.16	2.63
1.0	0.329	0.329	0.343
10.0	0.0994	0.0112	0.0974
100.0	0.0313	0.0682	0.0269

Basis Function	$c_{m}$	$E_{rms} (%)$
1	$c_{0} = 1.259707$	7.47
2	$c_{4} = 0.091934$	1.69
3	$c_{8} = 0.020216$	0.53
4	$c_{12} = 0.006254$	0.20

$E_{rms} (%)$	Basis Functions
0.01	8
0.001	12
0.0001	17

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