## Simulation

A numerical calculation of the polarization plane rotation was performed. The discharge current waveform was defined as that of the lightning return stroke (peak current: 2kA, 1/10 of the typical return current of cloud-to-ground discharge).6-8 The ionized electron density is assumed that the atmospheric molecules were perfectly ionized as 100% (=1025/m3) around the discharge path of 2 cm diameter and partially ionized (<1015/m3) in other areas. The magnetic flux density was calculated with the considerations of the distance from the discharge path and its orientation.

Figure 3 shows an example of calculated results for the experimental model. The sides of the square mirror were 28 cm in length. The beam reflection step was 2 cm. The propagating beam was reflected multiple times by the four sides of the square mirror, as shown in Fig. 3(a). Mirror M' returns the propagating beam to the output from the square mirror. Fig. 3. Calculation result. (a) Optical path, (b) Magnetic flux density B, (c) distance and (d) Rotation angle.

B vs

Fig. 3. Calculation result. (a) Optical path, (b) Magnetic flux density B, (c) distance and (d) Rotation angle.

B vs

 Mirror Number of Necessary Total optical Discharge Rotation Polarization length reflections/ reflectance path length gap angle (max) ratio (mm) step (mm) (%) (m) (cm) (deg.) 280 12/21.4 91 19 10 0.21 1 1.007 (21 dB) 280 28/10.0 96 44 10 0.51 1 1.018 (18 dß) 280 56/05.0 98 89 10 0.95 1 1.034 (15 dß) 500 12/41.7 91 34 10 0.074 1 1.003 (26 dß) 500 50/10.0 98.3 141 10 0.51 1 1.018 (18 dß) 500 12/41.7 91 34 20 0.074 1 1.003 (26 dß) 500 50/10.0 98.3 141 20 0.52 1 1.018 (17 dß)

The magnetic flux densities along the beam propagation projected on a side of the square mirror are shown in Fig. 3(b). Multiplying the magnetic flux density B by the electron density ne along the propagation distance, the rotation angle of the beam polarization was estimated by Eq. (2). Figure 3(c) shows the change of the magnetic flux density with respect to the distance from the discharge path at 13 ^s after the discharge. The flux density changes its value along the elapsed time. The magnetic flux density B is inversely proportional to the distance from the discharge path.

The electron density ne is assumed to be high only within 2 cm of the discharge path. Based on the results of Fig. 3(a)-(c), the rotation angle of the polarization was estimated, and is shown in Fig. 3(d). The change of the rotation angle had the same time response as the discharge current. The result shows that the frequency response of a few MHz was sufficient for the detector and amplifiers. Other calculations with different discharge gaps and the beam propagation conditions are summarized in Table 2. Selecting those conditions, we can distinguish the rotation angle of the beam polarization by differential detection with a dynamic range of 30 dB.

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