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4 phase plate in laser conoscopic method
Optik 161 (2018) 146–150
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Use of /4 phase plate in laser conoscopic method O. Yu Pikoul Far Eastern State Transport University, 47 Seryshev Str., Khabarovsk, Russia
a r t i c l e
i n f o
Article history: Received 16 January 2018 Accepted 9 February 2018 Keywords: Interference Conoscopic pattern Optical activity /4 phase plate Optical sign Optical axes
a b s t r a c t Possibilities of laser conoscopic method expanded due to the introduction of /4 phase plate in the optical system. The introduction of /4 phase plate with known optical sign leads to changes the conoscopic pattern of the investigated crystal plate. Changes conoscopic patterns allow to quickly and reliably determine the optical sign, the presence of optical activity of the crystal, the direction of rotation of the plane of polarization of radiation in optically active crystal for crystal plates of any thickness and any value of the specific rotation. In addition, changes conoscopic pattern of a crystal of known optical sign indicate the location of the optical axis in the plane of the input face the /4 phase plate. © 2018 Published by Elsevier GmbH.
1. Introduction Initially, the conoscopic patterns obtained with a polarizing microscope were used in optical mineralogy in order to identify minerals based on the data on crystal symmetry and orientation. Conoscopic pattern informativity provides for the possibility to determine orientation and nature of optical indicatrix, measure an angle between the optical axes of a biaxial crystal, determine an optical sign of the crystal, detect optical axes dispersion, identify qualitative and quantitative changes in the optical indicatrix in response to external action, etc [1]. At present, capabilities of the conoscopic method have been greatly expanded. Using the method, researchers have got novel scientific results in studying properties of optically active crystals, liquid crystals. Moreover, elements of the conoscopic method are employed in singular optics to study topological and polarization properties of optical beams having a complex wave structure. However, the classical conoscopic method is still in demand under experimental conditions and has not yet been used up as a tool to study optical properties of crystals [2–10]. The /4 phase plate is rather often applied in polarizing measurements to obtaining circular radiation [1]. Addition of /4 phase plate between the polarizers of a polarizing microscope makes easier the optical identification of minerals in thin sections of rocks in particular by allowing deduction of the shape and orientation of the optical indicatrices within the visible crystal sections [1]. Use of /4 phase plate with the known optical sign in the laser conoscopic method expands his opportunities for practical application in various optical devices. The objective of the present paper is to expand potential of the conoscopic method for the study of anisotropic optical crystals. To this end, it is proposed to obtain conoscopic patterns using an optical system where diverging laser radiation is let pass through an anisotropic crystal placed between the polarizer and analyzer, rather than using a polarizing microscope. The pattern on the screen is recorded by a digital camera and displayed on a computer (Fig. 1).
E-mail address: fi[email protected] https://doi.org/10.1016/j.ijleo.2018.02.032 0030-4026/© 2018 Published by Elsevier GmbH.
O.Y. Pikoul / Optik 161 (2018) 146–150
147
Fig. 1. Diagram of the optical sign identifying system: 1 – He-Ne laser (632.8 nm); 2 – polarizer; 3 – /4 phase plate; 4 – diffuser; 5 – investigated crystal plate; 6 – analyzer crossed with polarizer; 7 – screen.
With such observation system, a beam aperture makes 100–150◦ , and the conoscopic pattern on the screen appears large-scale, sharp and high-contrast. This enables one to identify and register fine details of the interference pattern both at the center of viewing field and on the periphery thereof, which appears difficult when using a polarizing microscope. This optical system (Fig. 1) allows placing the /4 phase plate (optical compensator) mounted in front of the diffuser. Such crystal phase plate may be used either as movable [2] or immovable element in determining the optical sign of a crystal. Upon rotation of /4 phase plate of the known optical sign about the vertical axis (Fig. 1), the conoscopic pattern changes and isochromatic rings get shifted. The shift direction of isochromatic rings correspond to the optical sign of the investigated crystal plate [2].
2. Experimental results 2.1. Use of immovable /4 phase plate to simultaneously determine the optical sign and the direction of rotation of the plane of polarization of the optically active crystal It is known that optically active crystals can have two versions – right and left. Thus relative rotation of the two modifications are equal, and the difference is only in the sign of rotation. If the crystal rotates the plane of polarization of clockwise (to the right) it is called dextrorotatory, if counter – clockwise (to the left) it is called levorotatory. The rotation angle of the polarization plane of radiation can be evaluated when observed toward the light beam. Traditionally, the direction of rotation of plane polarized radiation in optically active crystal is determined on the conoscopic pattern obtained with linear light [1]. The conoscopic pattern of the optically active crystal plate represents the light spot at center surrounded by isochromatic ¨ ¨ the periphery of a field of vision [1,8]. This conoscopic pattern has the same form for crosson rings with the black Maltese dextrorotatory and levorotatory optically active crystals. For optically active crystal plates, particularly thin, under review there is a small number of rings. The peripheral area of the conoscopic pattern is darkened. At continuous rotation of /4 phase plate [2] in a conoscopic pattern the shift of isochromatic rings occurs in the darkened area. That doesn’t allow to see the direction of shift of isochromatic rings and to define the optical sign of optically active crystal plate. By means of a immovable plate of /4 phase plate with the known optical sign, established in front of the diffuser, receive the clear conoscopic pattern allowing to define precisely the sign optically of an active crystal plate of any thickness. The conoscopic pattern in this case [9] has an appearance spiral isochrome, twirled on or counterclockwise, with the beginnings of spirals or in the first and third quadrants, or in the second and fourth quadrants (Fig. 2). The experiment has shown that the optical sign of the optically active crystal plate coincides with the optical sign of the /4 phase plate (positive) if the conoscopic pattern has the form of spiral isochrome, twirled clockwise, and with the beginnings of spirals in the first and third quadrants (Fig. 2(ɑ), (b)). If on the screen observe the conoscopic pattern in the form of spiral, twirled clockwise, with the beginnings of spirals in the second and fourth quadrants, then the optical sign of the optically active crystal plate doesn’t coincide with the optical sign of the /4 phase plate (negative) (Fig. 2(c), (d)). If on the screen observe the conoscopic pattern in the form of spiral, twirled counterclockwise, with the beginnings of spirals in the second and fourth quadrants, then the optical sign of the optically active crystal plate coincide with the optical sign of the /4 phase plate (positive) (Fig. 2(e), (f)).
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Fig. 2. Photos conoscopic patterns optically active crystals. Dextrorotatory crystals: a) TeO2 , thickness 7.0 mm; optical sign positive. b) TeO2 , 0.5 mm thickness; optical sign positive. c) LiJO3 , thickness 3.1 mm; a negative optical sign. d) LiJO3 , thickness 1.0 mm; a negative optical sign. Levorotatory crystals: e) TeO2 , the thickness is 3.0 mm; the positive optical sign. f) TeO2 , thickness 1.2 mm; optical sign positive. g) LiJO3 , thickness 3.8 mm; a negative optical sign. h) LiJO3 , thickness 0.3 mm; a negative optical sign.
If on the screen observe the conoscopic pattern in the form of spiral, twirled counterclockwise, with the beginnings of spirals in the first and third quadrants, then the optical sign of the optically active crystal plate coincide with the optical sign of the /4 phase plate (negative) (Fig. 2(g), (h)). At the same time, in the proposed experimental scheme easy to determine the direction of rotation of the plane of polarization [9]. When twisting branches of spirals clockwise draw a conclusion about the right rotation of the plane of polarization of radiation in the investigated crystal plate (Fig. 2(a)–(d)), when twisting branches of spirals counterclockwise – about the left rotation of the plane of polarization of radiation in the investigated crystal plate (Fig. 2(e)–(h)). Thus, the /4 phase plate allows you to quickly and reliably determine the optical sign, and the sign of rotation of plane polarized radiation in optically active crystals. The advantage of the method offered consists in the simplicity and ease of experimental measurements. 2.2. Determination of the optical axis position in the /4 phase plate during its rotation around the axis of the optical system In addition, a conoscopic pattern of an optically inactive crystal with circular light may be used to determine position of an optical axis in the entry face plane of a /4 phase plate. A method is known where positions of fast and slow axes of a phase plate can be identified using a compensator with the known optical axis position, which is introduced into the parallel beam after the phase plate investigated [1]. The experiment has shown that for the said purpose a divergent beam of light may be used to obtain and analyze a conoscopic pattern of a crystal plate of any thickness and known optical sign, which is placed after the /4 phase plate investigated (a 10 mm-thick LiNbO3 crystal plate with the entry face perpendicular to the optical axis was used in the experiment). A /4 phase plate is introduced after the polarizer into an optical system (Fig. 3) and, rotating the plate about the beam axis, one observes the changes in the conoscopic pattern of crystal plate 5. The polarizer and analyzer are crossed. If the optical axis of the /4 phase plate coincides with the polarizer axis, the light after the /4 phase plate will become linearly polarized. A conoscopic pattern of LiNbO3 crystal on the screen acquires a conventional form of concentric isochromatic rings ¨ crossed by a black Maltese cross¨in the center. Upon further rotation of the /4 phase plate, the light after the plate becomes elliptically polarized, which corresponds to the rotation of the optical axis of /4 phase plate at an intermediate angle of 0◦ to 45◦ relative to the polarizer transmission axis. The conoscopic pattern of LiNbO3 crystal plate varies gradually. At a 45◦ angle between the optical axis of the /4 phase plate and the polarizer transmission axis the light after the /4 phase plate will become circularly polarized. With such light, the conoscopic pattern of LiNbO3 will acquire the form shown
O.Y. Pikoul / Optik 161 (2018) 146–150
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Fig. 3. Diagram of the optical system: 1 – He-Ne laser; 2 – polarizer; 3 – quartz /4 phase plate (positive); 4 – diffuser; 5 – crystal plate LiNbO3 (negative); 6 – analyzer crossed with polarizer; 7 – screen.
Fig. 4. Photos conoscopic patterns. (a) /4 phase plate and plane-parallel crystal plate have opposite optical signs; (b) /4 phase plate and plane-parallel crystal plate have the same optical signs. This research did not receive any specific grant from funding agencies in the public, commercial, or not- for-profit sectors.
in Fig. 4. On the whole, upon the complete rotation of /4 phase plate, the conoscopic pattern of the LiNbO3 crystal plate with circular polarized light will appear on the screen four times. The same result may be obtained if the /4 phase plate is introduced into the same optical system and secured rigidly, while the crossed polarizer and analyzer are rotated in synchronism. It has been established that the optical axis in the plane of the entry face of the investigated /4 phase plate is parallel to the line connecting two black dots on the conoscopic pattern, when optical signs of the /4 phase plate and the crystal are different, and is perpendicular, when optical signs of the /4 phase plate and the crystal are the same (Fig. 4). Only two alternative arrangements for the two black dots between the arms of the cross, which are symmetric about the center of the pattern, are possible. The dots are arranged either horizontally or vertically, which is due to the polarizer axis positioned at an angle of 45◦ relative to the vertical line. Position of the optical axis in the plane of the entry face of the investigated /4 phase plate is determined proceeding from the assumption that the optical axis is parallel to the line connecting the two black dots on the conoscopic pattern. Hence, the optical axis is positioned either vertically or horizontally in the plane of the entry face of the /4 phase plate. Note that the conoscopic pattern shown in Fig. 4 may be obtained in the given optical system with any arrangement of the polarizer and analyzer. However, a straight line through the two black dots (minima) in the center of the pattern will be parallel or perpendicular relative to the optical axis of the /4 plate only with the crossed polarizer-analyzer configuration. The method proposed for determination of position of the optical axis in the plane of the entry face of the /4 phase plate is simple and convenient for experiments since it does not require any special expensive devices. Instead, any crystal plate of the known optical sign, which has been cut perpendicularly to the optical axis, may be used. 3. Conclusion This article describes a laser conoscopic method to determine the optical parameters of a crystal, for example, the optical sign, in an optical system that does not employ a polarizing microscope or any special devices such as a quartz wedge, which is a labor-intensive product. We suggest that a /4 phase plate of known optical sign should be used as an auxiliary element.
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When such a plate is introduced into the optical system, the conoscopic pattern of the investigated crystal is changed and the optical sign and other parameters of the crystal are determined by the change. Introduction of a /4 phase plate of a known optical sign into the conoscopic method expands the functional capabilities of the method and allows the simple and reliable determination of the optical sign of crystals and the sense of polarization plane rotation in optically active crystal. Moreover, the use of a conoscopic pattern of auxiliary crystal plate enables determination of position of the optical axis in the plane of the entry face /4 phase plate. References [1] R. Stoiber, S. Morse, New York, in: Microscopic Identification of Crystals, The Ronald Press Company, 1972. [2] O. Pikoul, Determination of the optical sign of a crystal by a conoscopic method, J. Appl. Cryst. 43 (2010) 949–954. [3] L. Dumitrascu, I. Dumitrascu, D.O. Dorohoi, E.C. Subbarao, G.S. Hirane, F. Jona, Conoscopic method for determination of main refractive indices and thickness of a uniaxial crystal cut out parallel to its optical axis, J. Appl. Cryst. 42 (2009) 878–884. [4] F.E. Veiras, M.T. Garea, L.I. Perez, Wide angle conoscopic interference patterns in uniaxial crystals, Appl. Opt. 51 (2012) 3081–3090. [5] Wang Ankai, Y. Ch Gao, J.Q. Xu, H.J. Zhang, Q. Sh Sun, Conoscopic interferometry for probing electro-optic coefficients of strontium calcium barium niobate crystal, Opt. Lasers Eng. 49 (2011) 870–873. [6] R.I. Egorov, A.D. Kiselev, Conoscopic patterns in photonic band gap of cholesteric liquid crystal cells with twist defects, J. Appl. Phys. 29 (2009) 231–234. [7] M. Palatnikov, O. Pikoul, N. Sidorov, O. Makarova, K. Bormanis, Conoscopic studies of optical homogeneity of the LiNbO3 :Mg crystals, Ferroelectrics 436 (2012) 19–28. [8] N.V. Sidorov, A.A. Kruk, O.Y. Pikoul, M.N. Palatnikov, N.A. Teplyakova, A.A. Yanichev, O.V. Makarova, Integrated research of structural and optical homogeneities of the lithium niobate crystal with low photorefractive effect, Optik 126 (2015) 1081–1089. [9] O.Yu Pikul, K.A. Rudoy, A.I. Livashvili, V.I. Doronin, V.I. Stroganov, Spiral structure in conoscopic figures of optically active crystals, J. Opt. Techn. 72 (2005) 69–70. [10] O.Yu Pikoul, Visualization of light polarization forms in the laser conoscopic method, Optik 158 (2018) 349–354.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Use of /4 phase plate in laser conoscopic method O. Yu Pikoul Far Eastern State Transport University, 47 Seryshev Str., Khabarovsk, Russia
a r t i c l e
i n f o
Article history: Received 16 January 2018 Accepted 9 February 2018 Keywords: Interference Conoscopic pattern Optical activity /4 phase plate Optical sign Optical axes
a b s t r a c t Possibilities of laser conoscopic method expanded due to the introduction of /4 phase plate in the optical system. The introduction of /4 phase plate with known optical sign leads to changes the conoscopic pattern of the investigated crystal plate. Changes conoscopic patterns allow to quickly and reliably determine the optical sign, the presence of optical activity of the crystal, the direction of rotation of the plane of polarization of radiation in optically active crystal for crystal plates of any thickness and any value of the specific rotation. In addition, changes conoscopic pattern of a crystal of known optical sign indicate the location of the optical axis in the plane of the input face the /4 phase plate. © 2018 Published by Elsevier GmbH.
1. Introduction Initially, the conoscopic patterns obtained with a polarizing microscope were used in optical mineralogy in order to identify minerals based on the data on crystal symmetry and orientation. Conoscopic pattern informativity provides for the possibility to determine orientation and nature of optical indicatrix, measure an angle between the optical axes of a biaxial crystal, determine an optical sign of the crystal, detect optical axes dispersion, identify qualitative and quantitative changes in the optical indicatrix in response to external action, etc [1]. At present, capabilities of the conoscopic method have been greatly expanded. Using the method, researchers have got novel scientific results in studying properties of optically active crystals, liquid crystals. Moreover, elements of the conoscopic method are employed in singular optics to study topological and polarization properties of optical beams having a complex wave structure. However, the classical conoscopic method is still in demand under experimental conditions and has not yet been used up as a tool to study optical properties of crystals [2–10]. The /4 phase plate is rather often applied in polarizing measurements to obtaining circular radiation [1]. Addition of /4 phase plate between the polarizers of a polarizing microscope makes easier the optical identification of minerals in thin sections of rocks in particular by allowing deduction of the shape and orientation of the optical indicatrices within the visible crystal sections [1]. Use of /4 phase plate with the known optical sign in the laser conoscopic method expands his opportunities for practical application in various optical devices. The objective of the present paper is to expand potential of the conoscopic method for the study of anisotropic optical crystals. To this end, it is proposed to obtain conoscopic patterns using an optical system where diverging laser radiation is let pass through an anisotropic crystal placed between the polarizer and analyzer, rather than using a polarizing microscope. The pattern on the screen is recorded by a digital camera and displayed on a computer (Fig. 1).
E-mail address: fi[email protected] https://doi.org/10.1016/j.ijleo.2018.02.032 0030-4026/© 2018 Published by Elsevier GmbH.
O.Y. Pikoul / Optik 161 (2018) 146–150
147
Fig. 1. Diagram of the optical sign identifying system: 1 – He-Ne laser (632.8 nm); 2 – polarizer; 3 – /4 phase plate; 4 – diffuser; 5 – investigated crystal plate; 6 – analyzer crossed with polarizer; 7 – screen.
With such observation system, a beam aperture makes 100–150◦ , and the conoscopic pattern on the screen appears large-scale, sharp and high-contrast. This enables one to identify and register fine details of the interference pattern both at the center of viewing field and on the periphery thereof, which appears difficult when using a polarizing microscope. This optical system (Fig. 1) allows placing the /4 phase plate (optical compensator) mounted in front of the diffuser. Such crystal phase plate may be used either as movable [2] or immovable element in determining the optical sign of a crystal. Upon rotation of /4 phase plate of the known optical sign about the vertical axis (Fig. 1), the conoscopic pattern changes and isochromatic rings get shifted. The shift direction of isochromatic rings correspond to the optical sign of the investigated crystal plate [2].
2. Experimental results 2.1. Use of immovable /4 phase plate to simultaneously determine the optical sign and the direction of rotation of the plane of polarization of the optically active crystal It is known that optically active crystals can have two versions – right and left. Thus relative rotation of the two modifications are equal, and the difference is only in the sign of rotation. If the crystal rotates the plane of polarization of clockwise (to the right) it is called dextrorotatory, if counter – clockwise (to the left) it is called levorotatory. The rotation angle of the polarization plane of radiation can be evaluated when observed toward the light beam. Traditionally, the direction of rotation of plane polarized radiation in optically active crystal is determined on the conoscopic pattern obtained with linear light [1]. The conoscopic pattern of the optically active crystal plate represents the light spot at center surrounded by isochromatic ¨ ¨ the periphery of a field of vision [1,8]. This conoscopic pattern has the same form for crosson rings with the black Maltese dextrorotatory and levorotatory optically active crystals. For optically active crystal plates, particularly thin, under review there is a small number of rings. The peripheral area of the conoscopic pattern is darkened. At continuous rotation of /4 phase plate [2] in a conoscopic pattern the shift of isochromatic rings occurs in the darkened area. That doesn’t allow to see the direction of shift of isochromatic rings and to define the optical sign of optically active crystal plate. By means of a immovable plate of /4 phase plate with the known optical sign, established in front of the diffuser, receive the clear conoscopic pattern allowing to define precisely the sign optically of an active crystal plate of any thickness. The conoscopic pattern in this case [9] has an appearance spiral isochrome, twirled on or counterclockwise, with the beginnings of spirals or in the first and third quadrants, or in the second and fourth quadrants (Fig. 2). The experiment has shown that the optical sign of the optically active crystal plate coincides with the optical sign of the /4 phase plate (positive) if the conoscopic pattern has the form of spiral isochrome, twirled clockwise, and with the beginnings of spirals in the first and third quadrants (Fig. 2(ɑ), (b)). If on the screen observe the conoscopic pattern in the form of spiral, twirled clockwise, with the beginnings of spirals in the second and fourth quadrants, then the optical sign of the optically active crystal plate doesn’t coincide with the optical sign of the /4 phase plate (negative) (Fig. 2(c), (d)). If on the screen observe the conoscopic pattern in the form of spiral, twirled counterclockwise, with the beginnings of spirals in the second and fourth quadrants, then the optical sign of the optically active crystal plate coincide with the optical sign of the /4 phase plate (positive) (Fig. 2(e), (f)).
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Fig. 2. Photos conoscopic patterns optically active crystals. Dextrorotatory crystals: a) TeO2 , thickness 7.0 mm; optical sign positive. b) TeO2 , 0.5 mm thickness; optical sign positive. c) LiJO3 , thickness 3.1 mm; a negative optical sign. d) LiJO3 , thickness 1.0 mm; a negative optical sign. Levorotatory crystals: e) TeO2 , the thickness is 3.0 mm; the positive optical sign. f) TeO2 , thickness 1.2 mm; optical sign positive. g) LiJO3 , thickness 3.8 mm; a negative optical sign. h) LiJO3 , thickness 0.3 mm; a negative optical sign.
If on the screen observe the conoscopic pattern in the form of spiral, twirled counterclockwise, with the beginnings of spirals in the first and third quadrants, then the optical sign of the optically active crystal plate coincide with the optical sign of the /4 phase plate (negative) (Fig. 2(g), (h)). At the same time, in the proposed experimental scheme easy to determine the direction of rotation of the plane of polarization [9]. When twisting branches of spirals clockwise draw a conclusion about the right rotation of the plane of polarization of radiation in the investigated crystal plate (Fig. 2(a)–(d)), when twisting branches of spirals counterclockwise – about the left rotation of the plane of polarization of radiation in the investigated crystal plate (Fig. 2(e)–(h)). Thus, the /4 phase plate allows you to quickly and reliably determine the optical sign, and the sign of rotation of plane polarized radiation in optically active crystals. The advantage of the method offered consists in the simplicity and ease of experimental measurements. 2.2. Determination of the optical axis position in the /4 phase plate during its rotation around the axis of the optical system In addition, a conoscopic pattern of an optically inactive crystal with circular light may be used to determine position of an optical axis in the entry face plane of a /4 phase plate. A method is known where positions of fast and slow axes of a phase plate can be identified using a compensator with the known optical axis position, which is introduced into the parallel beam after the phase plate investigated [1]. The experiment has shown that for the said purpose a divergent beam of light may be used to obtain and analyze a conoscopic pattern of a crystal plate of any thickness and known optical sign, which is placed after the /4 phase plate investigated (a 10 mm-thick LiNbO3 crystal plate with the entry face perpendicular to the optical axis was used in the experiment). A /4 phase plate is introduced after the polarizer into an optical system (Fig. 3) and, rotating the plate about the beam axis, one observes the changes in the conoscopic pattern of crystal plate 5. The polarizer and analyzer are crossed. If the optical axis of the /4 phase plate coincides with the polarizer axis, the light after the /4 phase plate will become linearly polarized. A conoscopic pattern of LiNbO3 crystal on the screen acquires a conventional form of concentric isochromatic rings ¨ crossed by a black Maltese cross¨in the center. Upon further rotation of the /4 phase plate, the light after the plate becomes elliptically polarized, which corresponds to the rotation of the optical axis of /4 phase plate at an intermediate angle of 0◦ to 45◦ relative to the polarizer transmission axis. The conoscopic pattern of LiNbO3 crystal plate varies gradually. At a 45◦ angle between the optical axis of the /4 phase plate and the polarizer transmission axis the light after the /4 phase plate will become circularly polarized. With such light, the conoscopic pattern of LiNbO3 will acquire the form shown
O.Y. Pikoul / Optik 161 (2018) 146–150
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Fig. 3. Diagram of the optical system: 1 – He-Ne laser; 2 – polarizer; 3 – quartz /4 phase plate (positive); 4 – diffuser; 5 – crystal plate LiNbO3 (negative); 6 – analyzer crossed with polarizer; 7 – screen.
Fig. 4. Photos conoscopic patterns. (a) /4 phase plate and plane-parallel crystal plate have opposite optical signs; (b) /4 phase plate and plane-parallel crystal plate have the same optical signs. This research did not receive any specific grant from funding agencies in the public, commercial, or not- for-profit sectors.
in Fig. 4. On the whole, upon the complete rotation of /4 phase plate, the conoscopic pattern of the LiNbO3 crystal plate with circular polarized light will appear on the screen four times. The same result may be obtained if the /4 phase plate is introduced into the same optical system and secured rigidly, while the crossed polarizer and analyzer are rotated in synchronism. It has been established that the optical axis in the plane of the entry face of the investigated /4 phase plate is parallel to the line connecting two black dots on the conoscopic pattern, when optical signs of the /4 phase plate and the crystal are different, and is perpendicular, when optical signs of the /4 phase plate and the crystal are the same (Fig. 4). Only two alternative arrangements for the two black dots between the arms of the cross, which are symmetric about the center of the pattern, are possible. The dots are arranged either horizontally or vertically, which is due to the polarizer axis positioned at an angle of 45◦ relative to the vertical line. Position of the optical axis in the plane of the entry face of the investigated /4 phase plate is determined proceeding from the assumption that the optical axis is parallel to the line connecting the two black dots on the conoscopic pattern. Hence, the optical axis is positioned either vertically or horizontally in the plane of the entry face of the /4 phase plate. Note that the conoscopic pattern shown in Fig. 4 may be obtained in the given optical system with any arrangement of the polarizer and analyzer. However, a straight line through the two black dots (minima) in the center of the pattern will be parallel or perpendicular relative to the optical axis of the /4 plate only with the crossed polarizer-analyzer configuration. The method proposed for determination of position of the optical axis in the plane of the entry face of the /4 phase plate is simple and convenient for experiments since it does not require any special expensive devices. Instead, any crystal plate of the known optical sign, which has been cut perpendicularly to the optical axis, may be used. 3. Conclusion This article describes a laser conoscopic method to determine the optical parameters of a crystal, for example, the optical sign, in an optical system that does not employ a polarizing microscope or any special devices such as a quartz wedge, which is a labor-intensive product. We suggest that a /4 phase plate of known optical sign should be used as an auxiliary element.
150
O.Y. Pikoul / Optik 161 (2018) 146–150
When such a plate is introduced into the optical system, the conoscopic pattern of the investigated crystal is changed and the optical sign and other parameters of the crystal are determined by the change. Introduction of a /4 phase plate of a known optical sign into the conoscopic method expands the functional capabilities of the method and allows the simple and reliable determination of the optical sign of crystals and the sense of polarization plane rotation in optically active crystal. Moreover, the use of a conoscopic pattern of auxiliary crystal plate enables determination of position of the optical axis in the plane of the entry face /4 phase plate. References [1] R. Stoiber, S. Morse, New York, in: Microscopic Identification of Crystals, The Ronald Press Company, 1972. [2] O. Pikoul, Determination of the optical sign of a crystal by a conoscopic method, J. Appl. Cryst. 43 (2010) 949–954. [3] L. Dumitrascu, I. Dumitrascu, D.O. Dorohoi, E.C. Subbarao, G.S. Hirane, F. Jona, Conoscopic method for determination of main refractive indices and thickness of a uniaxial crystal cut out parallel to its optical axis, J. Appl. Cryst. 42 (2009) 878–884. [4] F.E. Veiras, M.T. Garea, L.I. Perez, Wide angle conoscopic interference patterns in uniaxial crystals, Appl. Opt. 51 (2012) 3081–3090. [5] Wang Ankai, Y. Ch Gao, J.Q. Xu, H.J. Zhang, Q. Sh Sun, Conoscopic interferometry for probing electro-optic coefficients of strontium calcium barium niobate crystal, Opt. Lasers Eng. 49 (2011) 870–873. [6] R.I. Egorov, A.D. Kiselev, Conoscopic patterns in photonic band gap of cholesteric liquid crystal cells with twist defects, J. Appl. Phys. 29 (2009) 231–234. [7] M. Palatnikov, O. Pikoul, N. Sidorov, O. Makarova, K. Bormanis, Conoscopic studies of optical homogeneity of the LiNbO3 :Mg crystals, Ferroelectrics 436 (2012) 19–28. [8] N.V. Sidorov, A.A. Kruk, O.Y. Pikoul, M.N. Palatnikov, N.A. Teplyakova, A.A. Yanichev, O.V. Makarova, Integrated research of structural and optical homogeneities of the lithium niobate crystal with low photorefractive effect, Optik 126 (2015) 1081–1089. [9] O.Yu Pikul, K.A. Rudoy, A.I. Livashvili, V.I. Doronin, V.I. Stroganov, Spiral structure in conoscopic figures of optically active crystals, J. Opt. Techn. 72 (2005) 69–70. [10] O.Yu Pikoul, Visualization of light polarization forms in the laser conoscopic method, Optik 158 (2018) 349–354.