Scattering from a bubble in water:
impulse response

A previous page shows examples of calculations of the impulse response of a spherical particle of water as a function of scattering angle, thus helping to identify some of the scattering mechanisms.

Figs. 1 and 2 below show the results of such calculations for scattering of red light from a bubble in water assuming the following conditions:

• Nominal wavelength λ = 650 nm;
• Pulse duration: 5 fs (half-amplitude duration, raised-cosine pulse shape);
• Pulse bandwidth: 564 nm 767 nm at -3 dB points; but the bandwidth of the pulse has been truncated at -40 dB points (404 nm 1664 nm);
• Bubble radius r = 10 μm;
• Refractive index of bubble: n₁ = 1
• Refractive index of medium: n₀ = 1.33257 at nominal wavelength λ = 650 nm (N.B. The real part of the refractive index of water is 1.344 at 404 nm and 1.313 at 1664 nm, whilst the imaginary part of the refractive index is ignored.);.

Note that Figs. 1 & 2 have been calculated using the assumption that the refractive index of water is constant across the bandwidth of the 5 fs pulse.   This assumption is NOT correct (as indicated here), but it facilitates comparisons with the results of ray tracing calculations which assume a monochromatic source of light at the nominal wavelength λ = 650 nm).

Fig. 1   Impulse response as a function of scattering angle calculated using Mie theory for scattering of light of λ = 650 nm from a bubble of radius 10 μm and refractive index n = 1 immersed in water of refractive index n₀ = 1.33257

The parametric values along the curves in Figs. 1 – 2 show the value of the impact parameter b calculated using geometrical optics.

Fig. 2   Impulse response as a function of scattering angle calculated using Debye series calculations for p = 0 through p = 5 for scattering of light of λ = 650 nm
from a bubble of radius 10 μm and refractive index n₁ = 1 immersed in water of refractive index n₀ = 1.33257.

Page updated on 1 June 2010