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MiePlot’s calculations for Gaussian beams are based on the algorithms in the following papers:

- J. A. Lock,
*Contribution of high-order rainbows to the scattering of a Gaussian laser beam by a spherical particle*

JOSA A Vol. 10, No. 4, p. 693, April 1993 Free download - J. A. Lock,
*Improved Gaussian beam-scattering algorithm*

Applied Optics, Vol. 34, No. 3, p. 559, January 1995 Free download

Reproduced by kind permission of J. A. Lock ©

Equation 47 from Lock's 1993 paper (reproduced above) calculates the amplitude S1 of the scattered light for perpendicular polarisation as a function of the scattering angle θ and the tilt φ of the scattering plane. Most of the results on this page assume the conditions specified in Lock's 1993 paper which considered scattering from a sphere of radius 43.3 μm and refractive index

Evaluation of the above equation involves three separate terms, each of which involves summation of terms involving

For the conditions assumed in Lock's 1993 paper, x ≅ 528.7 and the resulting value of

The previous page illustrated the importance of using the correct value of

This page addresses the general issue of setting appropriate values of

Fig. 1 shows the amplitudes of the various contributions to S1 in in the 3 terms of Lock's equation 47 as a function of

The very rapid decline in the amplitudes of the contributions above

Although Fig. 1 shows the results for θ = 120°, similar patterns appear at other values of θ. Computation time could be reduced by performing only those calculations for values of

The previous page indicated that

Although Fig. 2 shows the results for scattering angle θ = 120° (the most sensitive value of θ for Debye

To address this issue, another type of false-colour map has been developed - as shown in Fig. 3 above. Note that this map covers the entire range of scattering angles from θ = -180° to θ = 180° (rather than the single value of θ used in Figs. 1 and 2). In this case, the inner sums involving

Fig. 3 shows that the value of

Fig. 4 is particularly interesting because, unlike the other diagrams shown above, the amplitudes of the contributions do not display a monotonic decrease with increasing values of

Fig. 5 shows equivalent results for Debye

Fig. 6 shows equivalent results for Debye

Fig. 7 shows equivalent results for Debye

MiePlot's results have been examined for two conditions:

- scattering from a sphere of radius 43.3 μm and refractive index
*n*= 1.33, refractive index of medium = 1, λ = 0.5145 μm, φ = 90° with the incident Gaussian beam defined by x_{0}= 0, y_{0}= -40 μm, z_{0}= 0 and ω_{0}= 20 μm; - scattering from a sphere of radius 1000 μm and refractive index
*n*= 1.336, refractive index of medium = 1, λ = 0.5145 μm, φ = 90° with the incident Gaussian beam defined by x_{0}= 0, y_{0}= -950 μm, z_{0}= 0 and ω_{0}= 100 μm.

For condition 2, equations 57 and 58 in Lock's 1995 paper suggest m

The above results indicate that the ampltudes of the contributions for a given value of θ do not always decline monotonically with increasing value of

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