Short-distance propagation of nonlinear optical pulses
T. Bienaimé,Q. Fontaine,Q. Glorieux,M. Isoard,A.M. Kamchatnov andN. Pavloff
LKB Paris,LPTMS Orsay,ISAN Troitsk March 27, 2019
RNL 2019
General context
L z
I I ENTRANCE
OUTPUT
NONLINEARMEDIUM
x
Stationary propagation of the complex amplitude of the electric field :
i∂zA=− 1 2n0k0
∇~⊥2A+k0n2|A|2A, (1)
−40 −20 0 20 40 x
0.0 0.5 1.0 1.5 2.0
ρ(x,t=0)
ρ(x, t= 0) =ρ0+ρ1exp (−2x2/x20)
v− v+
• Fluid of light :
,→ ρ∝I =|A|2,t∝z,∇⊥∝ ∂∂x,P =ρ2/2.
ρt+ (ρu)x =0,
ut+uux+ 1
ρPx =0.
RNL 2019 March 27, 2019 2
Results
,→λ±(x,t) = 12u(x,t)±p ρ(x,t),
,→(x,t) =fct(λ−, λ+). ⇒ ∂x
∂ λ± −(3
2λ∓+1
2λ±) ∂t
∂ λ± =0
x
−80−60−40−20 0 20 4060 80
t
0 4
8 12
16 20
24 28
32
ρ(x,t) = I
0.0 0.5 1.0 1.5 2.0
t=0 t=4
t=8 t=12
t=16 t=20
t=24 t=28
t=32
100 200 300 400 500
x
0.3 0.4 0.5 0.6 0.7
0.8 xS
xH
xS(t) =c0t+3A22/3t1/3
t=200
x∝√I−I0 : :
RNL 2019 March 27, 2019 3
[ MI, A. M. Kamchatnov, N. Pavloff, arXiv :1902.06975 (2019)]
