Dispersion Measurement of Electro-Optic Coefficient <i>γ</i>₂₂ of Lithium Niobate Based on Photoelastic Modulation

A novel method for determining the electro-optic (EO) coefficient <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>&#947;</mi> <mrow> <mn>22</mn> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> of lithium niobate and its dispersion using photoelastic modulation is presented. A spectroscopic polarimetry was constructed with the photoelastic modulator (PEM), and a monochromator was selected to automatically scan the wavelength of a light source. Phase retardation induced by an EO sample was loaded into the modulation signals to demodulate the EO coefficients. The PEM and data processing were controlled in the same field programmable gate array (FPGA), and the DC and harmonic terms were extracted simultaneously by employing digital phase-locked technology. An experimental system was built to analyze the principle of this scheme in detail. After the modulation phase retardation amplitude of the PEM was precisely calibrated, the EO coefficient <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>&#947;</mi> <mrow> <mn>22</mn> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> of a Y-cut lithium niobate crystal plate was measured in the spectral range from 0.42 to 0.8 &#181;m. The experimental results demonstrated that the measurement sensitivity of the system was <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1.1</mn> <mo>&#215;</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>&#8722;</mo> <mn>14</mn> </mrow> </msup> <mo>&nbsp;</mo> <mi mathvariant="normal">m</mi> <mo>/</mo> <mi mathvariant="normal">V</mi> </mrow> </semantics> </math> </inline-formula> for a sampling time of 198.9 ms. Plotting the measured results against the light wavelength, the dispersion of the EO coefficients was obtained similar to the Cauchy dispersion formula <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>&#947;</mi> <mrow> <mn>22</mn> </mrow> </msub> <mo>=</mo> <mn>5.31</mn> <mo>&nbsp;</mo> <mo>&#215;</mo> <mo>&nbsp;</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>&#8722;</mo> <mn>12</mn> </mrow> </msup> <mo>+</mo> <mfrac> <mrow> <mn>4.071</mn> <mo>&nbsp;</mo> <mo>&#215;</mo> <mo>&nbsp;</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>&#8722;</mo> <mn>13</mn> </mrow> </msup> </mrow> <mrow> <msup> <mi>&#955;</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mn>7.184</mn> <mo>&nbsp;</mo> <mo>&#215;</mo> <mo>&nbsp;</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>&#8722;</mo> <mn>14</mn> </mrow> </msup> </mrow> <mrow> <msup> <mi>&#955;</mi> <mn>4</mn> </msup> </mrow> </mfrac> </mrow> </semantics> </math> </inline-formula> in the visible light range. This method is suitable for studying dispersion of the EO coefficients of crystals as well as of thin films and two-dimensional materials.