Method and apparatus for the two-dimensional mapping of the electro-optical coefficient

Method for measuring and two-dimensional mapping of the electro-optical properties of materials transparent to the electromagnetic radiation, the method using a Reflective Grating Interferometer (5) wherein a substantially coherent and monochromatic electromagnetic beam is projected onto the transparent material to be analysed, which is subjected to an homogeneous electrical field, in such a way that the beam is enlarged as far as to have a two-dimensional cross section comparable with the dimensions of the material (10) to be analysed, and dividing said electromagnetic beam in two parts, in such a way that one part crosses the material (O), the other part travels undisturbed (R), the two beams (O,R) being recomposed on a recombination element (5a) of the Reflective Grating Interferometer (5), the beam exiting from said Reflective Grating Interferometer (5) being detected by means of a device (7) suited to two-dimensionally detection of such beam, the method further comprising the following subsequent steps:

• E. obtaining, by means of an algorithm of digital holography, from the detected electromagnetic beam, which is representative of a two-dimensional image, the phase variation Δø(x,y) of the electromagnetic beam (O) which has crossed the material (10) with respect to that of the undisturbed electromagnetic beam (R);
• F. for a number of P times, varying the applied electrical field value and repeating the preceding detection steps;
• G. calculating the two-dimensional electro-optical properties of the material (10) under examination using the formula:
• Δ
• ⁢
• ⁢
• Φ
• ⁡
• (
• x
• ,
• y
• )
• =
• (
• π
• λ
• )
• ·
• [
• -
• n
• 0
• 3
• ⁡
• (
• x
• ,
• y
• )
• ·
• r
• 13
• ′
• ⁡
• (
• x
• ,
• y
• )
• ·
• V
• ]
• where Δφ is the phase difference, V is the value of the voltage difference applied to the material (10) to be analysed, r′13 is the electro-optical parameter, and n0 is the ordinary refraction index.