Refraction Modulation Z-Scan for Measurement of Nonlinear Refractive Index
DOI:
https://doi.org/10.15407/ujpe71.4.275Keywords:
Z-scan technique, nonlinear refractive index, two-photon absorption coefficientAbstract
We present a novel single-beam refraction-modulation Z-scan technique that combines elements of the standard Z-scan and loss-modulation methods to enable sensitive measurement of third-order refractive nonlinearities in the closed-aperture configuration. Compared with the original Z-scan technique, the proposed method provides an almost background-free signal. An analytical expression relating the nonlinear refractive index n2 to the powers of the incident beam and the transmitted beam components at the first and second modulation harmonics is derived and experimentally verified using SiO2 and LiF samples.
References
1. M. Sheik-Bahae. Sensitive measurement of optical nonlinearities using a single beam. IEEE J. Quantum Electronics 26 (4), 760 (1990).
https://doi.org/10.1109/3.53394
2. T. Xia, D.J. Hagan, M. Sheik-Bahae, E.W. Van Stryland. Eclipsing Z-scan measurement of λ/10^4 wavefront distortion. Opt. Lett. 19, 317 (1994).
https://doi.org/10.1364/OL.19.000317
3. A.S.L. Gomes, E.L. Falc˜ao Filho, Cid B. de Ara'ujo, D. Rativa, R.E. de Araujo. Thermally managed eclipse Z-scan. Opt. Express 15, 1712 (2007).
https://doi.org/10.1364/OE.15.001712
4. Magnus K. Pereira, Ricardo R.B. Correia. Z-scan and eclipsing Z-scan analytical expressions for third-order optical nonlinearities. J. Opt. Soc. Am. B 37, 478 (2020).
https://doi.org/10.1364/JOSAB.376541
5. M. Sheik-Bahae, A.A. Said, D.J. Hagan, M.J. Soileau, E.W. Van Stryland. Nonlinear refraction and optical limiting in "Thick" media. Opt. Eng. 30, 1228 (1990).
https://doi.org/10.1117/12.55902
6. P.B. Chapple, J. Staromlynska, R.G. McDuff. Z-scan studies in the thin- and the thick-sample limits. J. Opt. Soc. Am. B 11, 975 (1994).
https://doi.org/10.1364/JOSAB.11.000975
7. D.I. Kovsh, S. Yang, D.J. Hagan, E.W. Van Stryland. Nonlinear Optical Beam Propagation for Optical Limiting. Appl. Optics 38, 5168 (1999).
https://doi.org/10.1364/AO.38.005168
8. Wei-ping Zang et al. Analytic solutions to Z-scan characteristics of thick media with nonlinear refraction and nonlinear absorption. J. Opt. Soc. America B 21, 63 (2004).
https://doi.org/10.1364/JOSAB.21.000063
9. M. Sheik-Bahae, J. Wang, J.R. DeSalvo, D.J. Hagan, E.W. Van Stryland. Measurement of nondegenerate nonlinearities using a 2-color Z-scan. Opt. Lett. 17, 258 (1992).
https://doi.org/10.1364/OL.17.000258
10. C.M. Cirloganu, L.A. Padilha, D.A. Fishman, S. Webster, D.J. Hagan, E.W. Van Stryland. Extremely nondegenerate two-photon absorption in direct-gap semiconductors. Opt. Express 19 (23), 22951 (2011).
https://doi.org/10.1364/OE.19.022951
11. M. Balu, J. Hales, D.J. Hagan, E.W. Van Stryland. Dispersion of nonlinear refraction and two-photon absorption using a white-light continuum Z-scan. Opt. Express 13 (10), 3594 (2005).
https://doi.org/10.1364/OPEX.13.003594
12. M. Balu, J. Hales, D.J. Hagan, E.W. Van Stryland. Whitelight continuum Z-scan technique for nonlinear materials characterization. Opt. Express 12 (16), 3820 (2004).
https://doi.org/10.1364/OPEX.12.003820
13. J. Wang, M. Sheik-Bahae, A.A. Said, D.J. Hagan, E.W. Van Stryland. Time-resolved Z-scan measurements of optical nonlinearities. JOSA B 11, 1009 (1994).
https://doi.org/10.1364/JOSAB.11.001009
14. Junyi Yang, Yinglin Song, Yuxiao Wang, Changwei Li, Xiao Jin, Min Shui. Time-resolved pump-probe technology with phase object for measurements of optical nonlinearities. Opt. Express 17, 7110 (2009).
https://doi.org/10.1364/OE.17.007110
15. W. Zhao, P. Palffy-Muhoray. Z-scan measurements of χ(3) using top-hat beams. Appl. Phys. Lett. 65, 673 (1994).
https://doi.org/10.1063/1.112264
16. Bing Gu, Hui-Tian Wang. Theoretical study of saturable Kerr nonlinearity using top-hat beam Z-scan technique. Opt. Commun. 263 (2), 322 (2006).
https://doi.org/10.1016/j.optcom.2006.01.053
17. Xiao-Qing Yan, Zhi-Bo Liu, Xiao-Liang Zhang, Wen-Yuan Zhou, Jian-Guo Tian. Polarization dependence of Z-scan measurement: Theory and experiment. Opt. Express 17 (8), 6397 (2009).
https://doi.org/10.1364/OE.17.006397
18. S. Wang, E.J. Lipchus, M.A. Gharbi, C.S. Yelleswarapu. Polarization Z-scan studies revealing plasmon coupling enhancement due to dimer formation of gold nanoparticles in nematic liquid crystals. Micromachines (Basel) 14 (12), 2206 (2023).
https://doi.org/10.3390/mi14122206
19. J.-M. M'enard, M. Betz, I. Sigal, H.M. van Driel. Singlebeam differential Z-scan technique. Appl. Opt. 46 (11), 2119 (2007).
https://doi.org/10.1364/AO.46.002119
20. R. Kolkowski, M. Samoc. Modified Z-scan technique using focus-tunable lens. J. Opt. 16 125202 (2014).
https://doi.org/10.1088/2040-8978/16/12/125202
21. J. Serna, A. Hamad, H. Garcia, E. Rueda. Measurement of nonlinear optical absorption and nonlinear optical refraction in CdS and ZnSe using an electrically focus-tunable lens. In: Proc. of the 12th International Conference on Fibre Optics and Photonics, 13-16 December 2014, Kharagpur, India (Optica Publishing Group, 2014), T2C.2 paper.
https://doi.org/10.1364/PHOTONICS.2014.T2C.2
22. D.V. Petrov, A.S. Gomes, C.B. Ara'ujo. Reflection Z-scan technique for measurements of optical properties of surfaces. Appl. Phys. Lett. 65, 1067 (1994).
https://doi.org/10.1063/1.112175
23. M. Martinelli, S. Bian, J.R. Leite, R.J. Horowicz. Sensitivity-enhanced reflection Z-scan by oblique incidence of a polarized beam. Appl. Phys. Lett. 72 (12), 1427 (1998).
https://doi.org/10.1063/1.120584
24. P. Tian, W.S. Warren. Ultrafast measurement of two-photon absorption by loss modulation. Opt. Lett. 27 (18), 1634 (2002).
https://doi.org/10.1364/OL.27.001634
25. M.G. Kuzyk, C.W. Dirk. Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials (Marcel Dekker, 1998).
26. D. Bhattacharyya et al. Electronic structure of liquid methanol and ethanol from polarization-dependent twophoton absorption spectroscopy. J. Phys. Chem. A 123 (27), 5789 (2019).
https://doi.org/10.1021/acs.jpca.9b04040
27. V. Kadan, I. Pavlov, A. Dmytruk, I. Blonskyi, T. Pavlova, Yu. Serozhkin, A. Goodarzi, M. Bondar. Single-beam lowfrequency loss modulation technique for two-photon absorption measurement. Opt. Commun. 569, 130809 (2024).
https://doi.org/10.1016/j.optcom.2024.130809
28. S.R. Flom, G. Beadie, S.S. Bayya, B. Shaw, J.M. Auxier. Ultrafast Z-scan measurements of nonlinear optical constants of window materials at 772, 1030, and 1550 nm. Appl. Opt. 54, F123 (2015).
https://doi.org/10.1364/AO.54.00F123
29. T.R. Ensley, N.K. Bambha. Ultrafast nonlinear refraction measurements of infrared transmitting materials in the mid-wave infrared. Opt. Express 27, 37940 (2019).
https://doi.org/10.1364/OE.27.037940
30. P. Kabaci'nski, T.M. Kardas, Y. Stepanenko, C. Radzewicz. Nonlinear refractive index measurement by SPM-induced phase regression. Opt. Express 27, 11018 (2019).
https://doi.org/10.1364/OE.27.011018
31. G. Jansonas, R. Budriunas, M. Vengris, A. Varanaviˇcius. Interferometric measurements of nonlinear refractive index in the infrared spectral range. Opt. Express 30, 30507 (2022).
https://doi.org/10.1364/OE.458850
32. D. Milam. Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica. Appl. Opt. 37, 546 (1998).
https://doi.org/10.1364/AO.37.000546
33. R. Adair, L.L. Chase, S.A. Payne. Nonlinear refractive index of optical crystals. Phys. Rev. B 39, 3337 (1989).
https://doi.org/10.1103/PhysRevB.39.3337
34. R. DeSalvo, A.A. Said, D.J. Hagan, E.W. Van Stryland, M. Sheik-Bahae. Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids. IEEE J. Quantum Electron. 32, 1324 (1996).
Downloads
Published
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.










