- Email: [email protected]
Refractive Index Measurement Using the Laser Profiler
Available online at www.sciencedirect.com
ScienceDirect Physics Procedia 86 (2017) 176 – 180
International Conference on Photonics of Nano- and Bio-Structures, PNBS-2015, 19-20 June 2015, Vladivostok, Russia and the International Conference on Photonics of Nano- and MicroStructures, PNMS-2015, 7-11 September 2015, Tomsk, Russia
Refractive index measurement using the laser profiler Vladislav Kolchinskiya*, Cheng-Hung Shihb, Ikai Lob, Roman Romashkoa,c a
Institute of Automatics and Control Processes, 5 Radio str., Vladivostok 690041, Russia b National Sun Yat-Sen University, 70 Lienhai Rd., Kaohsiung 80424, Taiwan, R.O.C. c Far EasternFederal University, Suhanova 8, Vladivostok690950, Russia
Abstract The paper proposes a method for measuring the refractive index of the plane-parallel samples of the material using laser profiler. The method is based on measurement of the displacement due to refraction of the laser beam passing through a sample of known geometry. The developed method was used to measure the refractive index of gallium nitride on the range of optical wavelengths (470, 561 and 632 nm). The measurement error of the refractive index was 10-3. The experimentally obtained values of the refractive index match with the reference data within measurement error. The relative simplicity of the measurement procedures distinguishes this method. © 2017 2016The TheAuthors. Authors. Published by Elsevier © Published by Elsevier B.V.B.V. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of PNBS-2015 and PNMS-2015. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of PNBS-2015 and PNMS-2015. Keywords: refractive index; laser profiler
The refractive index is one of the most important parameters of optical material. There are various methods for determining the refractive index among which goniometric, refractometric, and ellipsometric (Babichev et al. (1991)). This paper proposes a method for determining the refractive index using an alternative method based on the use of laser profiler. The peculiarity of the method of measuring the refractive index using a laser profiler is that the measured sample should be known geometry. In this case it is possible to apply the laws of geometrical optics and to determine the refractive index by the known formulas. It is known that the geometry in the form of thin plates with parallel to each
* Corresponding author. Tel.: +7-902-488-0486; E-mail address:[email protected]
1875-3892 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of PNBS-2015 and PNMS-2015. doi:10.1016/j.phpro.2017.01.018
177
Vladislav Kolchinskiy et al. / Physics Procedia 86 (2017) 176 – 180
other facets (that often provided automatically when the crystal growth) is the most simple and natural, as well as technologically more easily and more often implemented in practice (Pimpinelli et al. (1998)). Diagram illustrating the principle of measuring the refractive index of the plane-parallel sample using the laser profiler is shown in Figure 1.
Fig. 1. The direction of the rays in a plane-parallel plate (Į - angle of rotation, ȕ - the angle of refraction, h - beam deflection, measured using a laser profiler, d - thickness of the sample).
Thin laser beam falls at an angle Į to one of the face of the plane-parallel investigated sample, whereupon the beam is refracted and shifted due to refraction at the value h determined by a laser profiler. Herewith this beam should be much thinner than the expected shift h. Rotation of the sample leads to a change of the incidence angle ߙ and, respectively, to change of the beam displacement ݄, which can be found by measuring the refractive index according to the formula derived from Snell's law: n
sin D sin( a tan(tan D
h )) d cos D
(1)
where݀ - thickness of the sample. Experimental setup scheme of measuring the refractive index of plane-parallel sample using a laser profiler is shown in Figure 2.
Fig. 2. Scheme of installation: 1- laser, 2 - plano-convex lens, 3 – diaphragm, 4 - plano-convex lens, 5 – polarizer, 6 - Ȝ / 4 plate, 7 – sample, 8 precision rotatory table, 9 - laser profiler.
In the work laser diodes for generating a wavelength of 470 and 561 nm, and He-Ne laser (632.8 nm) were used
178
Vladislav Kolchinskiy et al. / Physics Procedia 86 (2017) 176 – 180
as the radiation source. In case of using laser diodes collimated light beam was formed by means of the lens. In addition, in order to remove distortions in the beam profile the latter was transmitted through the spatial filter is a combination of a plano-convex lens and diaphragm. Optical isolator at the output of the laser was used for the stability of laser operation which provides light transmission in one direction almost without losses, and in the other (opposite) direction with high attenuation. The investigated sample was placed in a vertical position on a precision rotary table by which the accurate rotation (error of 0.25 degrees) of the sample was maintained. Coordinate of the center of the laser beam was determined by a laser profiler NewPort LBP-4-USB accurate to 8 microns. Laser beam moved by rotation the investigated sample on a precision rotary table then new coordinates of the center of the beam were defined, by which displacement h was calculated. The proposed method in this paper, and developed an experimental setup were used to determine the refractive index of the pure sample of gallium nitride GaN having lateral dimensions 10x10 mm2 and a thickness d = 150 Pm. The sample was grown at the National University of Sun Yat-Sen (Taiwan)(Pang et al. (2013)).
Fig. 3. The profiles of the laser beam produced by a laser profiler (a - without the sample, b - after passing through the sample, c - after passing through the sample, rotated axially 35 degrees).
Figure 3 shows the profiles of the laser beam incident on the sample (Figure 3), and after passing through the sample at an incidence angle of 1 degree (3b) and 35 degrees (3c). Figure 4 shows the values of the refractive index of GaN at different angles of rotation for different wavelength (470 , 561 nm and 632.8 nm).The angle of incidence was changed in the range from 0 to 45 degrees since the greater rotation leads to a significant distortion of the profile of the laser beam. As we can see from Fig.4 the distortion of the beam at higher angles of incidence (between 35 and 45 degrees) does not lead to a noticeable increase in measuring errors. Table 1 shows the measurement results for the three wavelengths. As can be seen from the table the refractive index values obtained experimentally match with reference data within the measurement error. Table 1. The values of the refractive index of GaN. Ȝ, nm
nexperimental ± ǻn
n from Ref. data [Barker et al. (1973)]
470
2,4677 ± ͲǡͲͲʹ
2,4668
561
2,4095 ± ͲǡͲͲͷͷ
2,4098
633
2,3844 ± ͲǡͲͲ43
2,3842
Thus, we have determined the refractive index of the investigated sample of gallium nitride (thickness of 150 microns) for a plane-parallel sample. However, the wedge angle should be taken into account for thick crystals or other samples with further post-processing (preparation, grinding, pressing). In this study, we considered the mathematical model that enables determine the refractive index of the test
Vladislav Kolchinskiy et al. / Physics Procedia 86 (2017) 176 – 180
sample for geometry deviating from a plane-parallel plate as a result of the presence of wedge angle ߠ (Fig. 5). Thin laser beam falls on the crystal at angle ߙ and emerges from the crystal at an angle ߰which is dependent on the angle of wedgeߠ of the outputface of crystal. The new beam displacement ݄Ԣcan be determined at a distance ܮ.As can be seen from Figure 5 the greater the distance ܮ, the larger the difference ȟ݄which introduces an error in the calculation of the refractive index.While we cannot eliminate wedge angle of the crystal, in order to reduce errors in the determination of the refractive index, we can handle a distance L reducing it to a minimum The minimum distance L is limited by the size of the measuring head of the laser profiler.
Fig. 4. The refractive index of GaN at different wavelengths (a – 470 nm, b – 561 nm, c – 632.8 nm).
179
180
Vladislav Kolchinskiy et al. / Physics Procedia 86 (2017) 176 – 180
Fig. 5. The direction of the rays in geometry deviating from a plane-parallel plate as a result of the presence of wedge angle ߠ (ߙ - angle of rotation, ȕ - the angle of refraction,d - thickness of the sample,ߠ - wedge angle,݄ - beam deflection, measured using a laser profiler,݄Ԣ – new deflection of the beam due to the presence of wedge angle of the sample, ߰–new angle of the beam at the output of the crystal, ܮ- the distance where the beam displacement is determined, angleߛ ൌ ߙ െ ߚ), ߱ - angle between the output beams of the parallel plate and wedge plate.).
The displacement of the beam ݄Ԣ is determined by the formula (2): h ' h 'h
h L tg (\ B T D )
(2)
According to calculations, the error in determination of the displacement at ൌ ͳͲι, distance ܮൌ ʹǤͷ cm and at the wedge angle ߠ ൌ ͲǤͲͳι݄ᇱ will be 1.67*10-4 m (which is equal to 9.8%.). If we apply this displacement ݄Ԣ to calculate the refractive index, the error in the determination of ݊ will be 15.9%.So, we can conclude that if the wedge we cannot eliminate,itmustbetakenintoaccount since even small angles can give error in the determination of the refractive index using a laser profiler. For example, it is necessary to have a wedge angle ߠ not more than 0.0001°if we want to achieve accuracy of the refractive index determination that the error does not exceed 0.1%. Thus, in this paper we proposed and experimentally proved the method of determining the refractive index using a laser profiler. The refractive index plane-parallel gallium nitride sample was measured at wavelengths of 470, 561 and 633 nm. The experimental values coincide with the reference accurate to 10-3. This method of measuring the refractive index distinguishes simplicity of installation schemes and low cost. Method can be used for expressmeasurement of refractive index of optical elements. This research is supported by the Russian Scientific Foundation (grant No. 14-12-01122). References Babichev A.P., Babushkina N.A., Bratkovsky A.M. et al., 1991. “Physical quantities”. Ed. Grigoriev I.S., MeilikhovE.Z,, Handbook. M.: Energoatomizdat, p.1232 Barker Jr A. S., Ilegems M., 1973. “Infrared lattice vibrations and free-electron dispersion in GaN”, Physical Review B, Vol. 7,N2, p. 743. Pang W.-Y.,LoIkai, et al. 2013. “Growth of wurtzite and zinc-blende phased GaN on silicon(100) substrate with sputtered AlN buffer layer”, Journal of Crystal Growth, Vol. 382, p.1–6. Pimpinelli A., Villain J., 1998. “Physics of crystal growth”, Cambridge university press, p. 374.
ScienceDirect Physics Procedia 86 (2017) 176 – 180
International Conference on Photonics of Nano- and Bio-Structures, PNBS-2015, 19-20 June 2015, Vladivostok, Russia and the International Conference on Photonics of Nano- and MicroStructures, PNMS-2015, 7-11 September 2015, Tomsk, Russia
Refractive index measurement using the laser profiler Vladislav Kolchinskiya*, Cheng-Hung Shihb, Ikai Lob, Roman Romashkoa,c a
Institute of Automatics and Control Processes, 5 Radio str., Vladivostok 690041, Russia b National Sun Yat-Sen University, 70 Lienhai Rd., Kaohsiung 80424, Taiwan, R.O.C. c Far EasternFederal University, Suhanova 8, Vladivostok690950, Russia
Abstract The paper proposes a method for measuring the refractive index of the plane-parallel samples of the material using laser profiler. The method is based on measurement of the displacement due to refraction of the laser beam passing through a sample of known geometry. The developed method was used to measure the refractive index of gallium nitride on the range of optical wavelengths (470, 561 and 632 nm). The measurement error of the refractive index was 10-3. The experimentally obtained values of the refractive index match with the reference data within measurement error. The relative simplicity of the measurement procedures distinguishes this method. © 2017 2016The TheAuthors. Authors. Published by Elsevier © Published by Elsevier B.V.B.V. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of PNBS-2015 and PNMS-2015. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of PNBS-2015 and PNMS-2015. Keywords: refractive index; laser profiler
The refractive index is one of the most important parameters of optical material. There are various methods for determining the refractive index among which goniometric, refractometric, and ellipsometric (Babichev et al. (1991)). This paper proposes a method for determining the refractive index using an alternative method based on the use of laser profiler. The peculiarity of the method of measuring the refractive index using a laser profiler is that the measured sample should be known geometry. In this case it is possible to apply the laws of geometrical optics and to determine the refractive index by the known formulas. It is known that the geometry in the form of thin plates with parallel to each
* Corresponding author. Tel.: +7-902-488-0486; E-mail address:[email protected]
1875-3892 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of PNBS-2015 and PNMS-2015. doi:10.1016/j.phpro.2017.01.018
177
Vladislav Kolchinskiy et al. / Physics Procedia 86 (2017) 176 – 180
other facets (that often provided automatically when the crystal growth) is the most simple and natural, as well as technologically more easily and more often implemented in practice (Pimpinelli et al. (1998)). Diagram illustrating the principle of measuring the refractive index of the plane-parallel sample using the laser profiler is shown in Figure 1.
Fig. 1. The direction of the rays in a plane-parallel plate (Į - angle of rotation, ȕ - the angle of refraction, h - beam deflection, measured using a laser profiler, d - thickness of the sample).
Thin laser beam falls at an angle Į to one of the face of the plane-parallel investigated sample, whereupon the beam is refracted and shifted due to refraction at the value h determined by a laser profiler. Herewith this beam should be much thinner than the expected shift h. Rotation of the sample leads to a change of the incidence angle ߙ and, respectively, to change of the beam displacement ݄, which can be found by measuring the refractive index according to the formula derived from Snell's law: n
sin D sin( a tan(tan D
h )) d cos D
(1)
where݀ - thickness of the sample. Experimental setup scheme of measuring the refractive index of plane-parallel sample using a laser profiler is shown in Figure 2.
Fig. 2. Scheme of installation: 1- laser, 2 - plano-convex lens, 3 – diaphragm, 4 - plano-convex lens, 5 – polarizer, 6 - Ȝ / 4 plate, 7 – sample, 8 precision rotatory table, 9 - laser profiler.
In the work laser diodes for generating a wavelength of 470 and 561 nm, and He-Ne laser (632.8 nm) were used
178
Vladislav Kolchinskiy et al. / Physics Procedia 86 (2017) 176 – 180
as the radiation source. In case of using laser diodes collimated light beam was formed by means of the lens. In addition, in order to remove distortions in the beam profile the latter was transmitted through the spatial filter is a combination of a plano-convex lens and diaphragm. Optical isolator at the output of the laser was used for the stability of laser operation which provides light transmission in one direction almost without losses, and in the other (opposite) direction with high attenuation. The investigated sample was placed in a vertical position on a precision rotary table by which the accurate rotation (error of 0.25 degrees) of the sample was maintained. Coordinate of the center of the laser beam was determined by a laser profiler NewPort LBP-4-USB accurate to 8 microns. Laser beam moved by rotation the investigated sample on a precision rotary table then new coordinates of the center of the beam were defined, by which displacement h was calculated. The proposed method in this paper, and developed an experimental setup were used to determine the refractive index of the pure sample of gallium nitride GaN having lateral dimensions 10x10 mm2 and a thickness d = 150 Pm. The sample was grown at the National University of Sun Yat-Sen (Taiwan)(Pang et al. (2013)).
Fig. 3. The profiles of the laser beam produced by a laser profiler (a - without the sample, b - after passing through the sample, c - after passing through the sample, rotated axially 35 degrees).
Figure 3 shows the profiles of the laser beam incident on the sample (Figure 3), and after passing through the sample at an incidence angle of 1 degree (3b) and 35 degrees (3c). Figure 4 shows the values of the refractive index of GaN at different angles of rotation for different wavelength (470 , 561 nm and 632.8 nm).The angle of incidence was changed in the range from 0 to 45 degrees since the greater rotation leads to a significant distortion of the profile of the laser beam. As we can see from Fig.4 the distortion of the beam at higher angles of incidence (between 35 and 45 degrees) does not lead to a noticeable increase in measuring errors. Table 1 shows the measurement results for the three wavelengths. As can be seen from the table the refractive index values obtained experimentally match with reference data within the measurement error. Table 1. The values of the refractive index of GaN. Ȝ, nm
nexperimental ± ǻn
n from Ref. data [Barker et al. (1973)]
470
2,4677 ± ͲǡͲͲʹ
2,4668
561
2,4095 ± ͲǡͲͲͷͷ
2,4098
633
2,3844 ± ͲǡͲͲ43
2,3842
Thus, we have determined the refractive index of the investigated sample of gallium nitride (thickness of 150 microns) for a plane-parallel sample. However, the wedge angle should be taken into account for thick crystals or other samples with further post-processing (preparation, grinding, pressing). In this study, we considered the mathematical model that enables determine the refractive index of the test
Vladislav Kolchinskiy et al. / Physics Procedia 86 (2017) 176 – 180
sample for geometry deviating from a plane-parallel plate as a result of the presence of wedge angle ߠ (Fig. 5). Thin laser beam falls on the crystal at angle ߙ and emerges from the crystal at an angle ߰which is dependent on the angle of wedgeߠ of the outputface of crystal. The new beam displacement ݄Ԣcan be determined at a distance ܮ.As can be seen from Figure 5 the greater the distance ܮ, the larger the difference ȟ݄which introduces an error in the calculation of the refractive index.While we cannot eliminate wedge angle of the crystal, in order to reduce errors in the determination of the refractive index, we can handle a distance L reducing it to a minimum The minimum distance L is limited by the size of the measuring head of the laser profiler.
Fig. 4. The refractive index of GaN at different wavelengths (a – 470 nm, b – 561 nm, c – 632.8 nm).
179
180
Vladislav Kolchinskiy et al. / Physics Procedia 86 (2017) 176 – 180
Fig. 5. The direction of the rays in geometry deviating from a plane-parallel plate as a result of the presence of wedge angle ߠ (ߙ - angle of rotation, ȕ - the angle of refraction,d - thickness of the sample,ߠ - wedge angle,݄ - beam deflection, measured using a laser profiler,݄Ԣ – new deflection of the beam due to the presence of wedge angle of the sample, ߰–new angle of the beam at the output of the crystal, ܮ- the distance where the beam displacement is determined, angleߛ ൌ ߙ െ ߚ), ߱ - angle between the output beams of the parallel plate and wedge plate.).
The displacement of the beam ݄Ԣ is determined by the formula (2): h ' h 'h
h L tg (\ B T D )
(2)
According to calculations, the error in determination of the displacement at ൌ ͳͲι, distance ܮൌ ʹǤͷ cm and at the wedge angle ߠ ൌ ͲǤͲͳι݄ᇱ will be 1.67*10-4 m (which is equal to 9.8%.). If we apply this displacement ݄Ԣ to calculate the refractive index, the error in the determination of ݊ will be 15.9%.So, we can conclude that if the wedge we cannot eliminate,itmustbetakenintoaccount since even small angles can give error in the determination of the refractive index using a laser profiler. For example, it is necessary to have a wedge angle ߠ not more than 0.0001°if we want to achieve accuracy of the refractive index determination that the error does not exceed 0.1%. Thus, in this paper we proposed and experimentally proved the method of determining the refractive index using a laser profiler. The refractive index plane-parallel gallium nitride sample was measured at wavelengths of 470, 561 and 633 nm. The experimental values coincide with the reference accurate to 10-3. This method of measuring the refractive index distinguishes simplicity of installation schemes and low cost. Method can be used for expressmeasurement of refractive index of optical elements. This research is supported by the Russian Scientific Foundation (grant No. 14-12-01122). References Babichev A.P., Babushkina N.A., Bratkovsky A.M. et al., 1991. “Physical quantities”. Ed. Grigoriev I.S., MeilikhovE.Z,, Handbook. M.: Energoatomizdat, p.1232 Barker Jr A. S., Ilegems M., 1973. “Infrared lattice vibrations and free-electron dispersion in GaN”, Physical Review B, Vol. 7,N2, p. 743. Pang W.-Y.,LoIkai, et al. 2013. “Growth of wurtzite and zinc-blende phased GaN on silicon(100) substrate with sputtered AlN buffer layer”, Journal of Crystal Growth, Vol. 382, p.1–6. Pimpinelli A., Villain J., 1998. “Physics of crystal growth”, Cambridge university press, p. 374.