The Combined Ellipsometric Method of Complete Optical Characterization of Crystals. Ii. Determination of the Optical Constants of Crystal

Abstract

This part of the article describes the second stage of the combined ellipsometric method of complete optical characterization of crystals. The testing of the second stage was carried out on crystals of lithium niobate (LiNbO3) and cadmium tungstate (CdWO4). The obtained results of measurements of an optically uniaxial LiNbO3 crystal fully confirmed the correctness of the proposed method and its applicability for optical characterization of crystals. In particular, the values of the principal refractive indices {no = 2.280(±0.003), ne = 2.202(±0.002)} and birefringence {Δn = -0.0775(±0.0015)} of the LiNbO3 crystal are in good agreement with the values of these quantities, obtained by other researchers by other methods. Studies of the optically biaxial CdWO4 crystal were important for analyzing the accuracy of determining the optical constants. For generality of this analysis, measurements were performed in different measurement configurations at several angles of incidence of the laser beam. In particular, according to the results of measurements in two configurations (angle of incidence 45°), the following values of the principal refractive indices of the CdWO4 crystal (doped from the melt 0.375 wt.% PbO) were obtained: ng = 2.249±0.002, nm = 2.185±0.002, np = 2.130±0.008. Based on these values of ng, nm, and np, the angle between the optical axes and the optical sign of the crystal were determined. It has been shown experimentally that the CdWO4 crystal is a pronounced biaxial crystal with an angle between the optical axes close to 90°. Possible ways to improve the accuracy of determining the optical constants of crystals are also analyzed.

The Combined Ellipsometric Method of Complete Optical Characterization of Crystals. Iv. Application to Uniaxial Crystal.

“…Therefore, it was necessary to refine the orientation of the main planes of this sample in order to perform the necessary measurements. As mentioned in the second part of this article [2], the necessary measurements to determine the optical constants of the LiNbO3 crystal can be performed on any plane perpendicular to the (001) plane. Therefore, it was only necessary to refine the orientation of the (001) plane and prepare for measurements any plane perpendicular to it.…”

“…In particular, tables 1 and 2 present the results of determining the optical constants of samples LN-P2 and LN-DM5. The results for sample LN-P1 were published in the second part of the article (see Table 1 in [2]). As in [2], the values of n and k given in Tables 1 and 2 are the average values of the corresponding ranges, the boundaries of which are indicated in brackets.…”

“…The results for sample LN-P1 were published in the second part of the article (see Table 1 in [2]). As in [2], the values of n and k given in Tables 1 and 2 are the average values of the corresponding ranges, the boundaries of which are indicated in brackets. Thus, the numbers in brackets determine the range of n and k values that satisfies the measured set of  and  values (and for uniaxial crystals, these are two pairs of  and  values), taking into account the measurement accuracy.…”

“…In other words, the numbers in parentheses actually indicate the sensitivity of a given method. Recall that we called it the local measurement accuracy for each angle of incidence in a certain measurement configuration, since the measurements were performed at one point on the surface (for more details, see [2]). It is to demonstrate local accuracy that we use the presentation of measurement results in the form of tables.…”

The Combined Ellipsometric Method of Complete Optical Characterization of Crystals. Iv. Application to Uniaxial Crystal.

“…Therefore, it was necessary to refine the orientation of the main planes of this sample in order to perform the necessary measurements. As mentioned in the second part of this article [2], the necessary measurements to determine the optical constants of the LiNbO3 crystal can be performed on any plane perpendicular to the (001) plane. Therefore, it was only necessary to refine the orientation of the (001) plane and prepare for measurements any plane perpendicular to it.…”

“…In particular, tables 1 and 2 present the results of determining the optical constants of samples LN-P2 and LN-DM5. The results for sample LN-P1 were published in the second part of the article (see Table 1 in [2]). As in [2], the values of n and k given in Tables 1 and 2 are the average values of the corresponding ranges, the boundaries of which are indicated in brackets.…”

“…The results for sample LN-P1 were published in the second part of the article (see Table 1 in [2]). As in [2], the values of n and k given in Tables 1 and 2 are the average values of the corresponding ranges, the boundaries of which are indicated in brackets. Thus, the numbers in brackets determine the range of n and k values that satisfies the measured set of  and  values (and for uniaxial crystals, these are two pairs of  and  values), taking into account the measurement accuracy.…”

“…In other words, the numbers in parentheses actually indicate the sensitivity of a given method. Recall that we called it the local measurement accuracy for each angle of incidence in a certain measurement configuration, since the measurements were performed at one point on the surface (for more details, see [2]). It is to demonstrate local accuracy that we use the presentation of measurement results in the form of tables.…”

The Combined Ellipsometric Method of Complete Optical Characterization of Crystals. Iii. Experimental Determination of the Orientation of Optical Axis in Crystal

“…This is how we determined the angle V in the second part of this article [2] in a CdWO4 crystal. Thus, knowing the value of the angle 2V, we determine both the orientation of the optical axes in a biaxial crystal and the optical sign of the crystal.…”

The Combined Ellipsometric Method of Complete Optical Characterization of Crystals. Iv. Application to Uniaxial Crystal.

“…Therefore, it was necessary to refine the orientation of the main planes of this sample in order to perform the necessary measurements. As mentioned in the second part of this article [2], the necessary measurements to determine the optical constants of the LiNbO3 crystal can be performed on any plane perpendicular to the (001) plane. Therefore, it was only necessary to refine the orientation of the (001) plane and prepare for measurements any plane perpendicular to it.…”

“…In particular, tables 1 and 2 present the results of determining the optical constants of samples LN-P2 and LN-DM5. The results for sample LN-P1 were published in the second part of the article (see Table 1 in [2]). As in [2], the values of n and k given in Tables 1 and 2 are the average values of the corresponding ranges, the boundaries of which are indicated in brackets.…”

“…The results for sample LN-P1 were published in the second part of the article (see Table 1 in [2]). As in [2], the values of n and k given in Tables 1 and 2 are the average values of the corresponding ranges, the boundaries of which are indicated in brackets. Thus, the numbers in brackets determine the range of n and k values that satisfies the measured set of  and  values (and for uniaxial crystals, these are two pairs of  and  values), taking into account the measurement accuracy.…”

“…In other words, the numbers in parentheses actually indicate the sensitivity of a given method. Recall that we called it the local measurement accuracy for each angle of incidence in a certain measurement configuration, since the measurements were performed at one point on the surface (for more details, see [2]). It is to demonstrate local accuracy that we use the presentation of measurement results in the form of tables.…”

The Combined Ellipsometric Method of Complete Optical Characterization of Crystals. Iii. Experimental Determination of the Orientation of Optical Axis in Crystal

“…This is how we determined the angle V in the second part of this article [2] in a CdWO4 crystal. Thus, knowing the value of the angle 2V, we determine both the orientation of the optical axes in a biaxial crystal and the optical sign of the crystal.…”

The Combined Ellipsometric Method of Complete Optical Characterization of Crystals. Iv. Application to Uniaxial Crystal.

“…Therefore, it was necessary to refine the orientation of the main planes of this sample in order to perform the necessary measurements. As mentioned in the second part of this article [2], the necessary measurements to determine the optical constants of the LiNbO3 crystal can be performed on any plane perpendicular to the (001) plane. Therefore, it was only necessary to refine the orientation of the (001) plane and prepare for measurements any plane perpendicular to it.…”

“…In particular, tables 1 and 2 present the results of determining the optical constants of samples LN-P2 and LN-DM5. The results for sample LN-P1 were published in the second part of the article (see Table 1 in [2]). As in [2], the values of n and k given in Tables 1 and 2 are the average values of the corresponding ranges, the boundaries of which are indicated in brackets.…”

“…The results for sample LN-P1 were published in the second part of the article (see Table 1 in [2]). As in [2], the values of n and k given in Tables 1 and 2 are the average values of the corresponding ranges, the boundaries of which are indicated in brackets. Thus, the numbers in brackets determine the range of n and k values that satisfies the measured set of  and  values (and for uniaxial crystals, these are two pairs of  and  values), taking into account the measurement accuracy.…”

“…In other words, the numbers in parentheses actually indicate the sensitivity of a given method. Recall that we called it the local measurement accuracy for each angle of incidence in a certain measurement configuration, since the measurements were performed at one point on the surface (for more details, see [2]). It is to demonstrate local accuracy that we use the presentation of measurement results in the form of tables.…”

The Combined Ellipsometric Method of Complete Optical Characterization of Crystals. Iii. Experimental Determination of the Orientation of Optical Axis in Crystal

“…This is how we determined the angle V in the second part of this article [2] in a CdWO4 crystal. Thus, knowing the value of the angle 2V, we determine both the orientation of the optical axes in a biaxial crystal and the optical sign of the crystal.…”