Z-scan Measurements

Dr. Rüdiger Paschotta

doi:10.61835/k76

Z-scan Measurements

Author: the photonics expert Dr. Rüdiger Paschotta (RP)

Definition: a technique for measuring the strength of the Kerr nonlinearity of a material, relying on self-focusing

Categories: article belongs to category nonlinear optics nonlinear optics, article belongs to category optical metrology optical metrology, article belongs to category methods methods

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DOI: 10.61835/k76 Cite the article: BibTex BibLaTex plain text HTML Link to this page! LinkedIn

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What are z-scan Measurements?

The z-scan measurement technique [1, 2] is often used for measuring the strength of the Kerr nonlinearity (i.e. the magnitude of the nonlinear index ($n_2$)) of an optical material. Essentially, a sample of the material under investigation is moved through the focus of a laser beam, and the beam radius (or the on-axis intensity, or the power transmitted through an aperture) is measured at some point behind the focus as a function of the sample position. These quantities are affected by the self-focusing effect. If the nonlinear index is positive, and the sample is placed behind the focus (as in Figure 1), self-focusing reduces the beam divergence and thus increases the detector signal. If the sample is moved to the left-hand side of the focus, the focus is moved to the left, and the stronger divergence after the focus decreases the detector signal. From the measured dependence of the detector signal on the sample position, it is possible to calculate the magnitude of the nonlinear index.

Figure 1: Setup for z-scan measurements. The transmission through the aperture is measured as a function of the sample position. The left detector is used for monitoring the incident pulse energy.

Note that nonlinear absorption, e.g. two-photon absorption, can also affect the measured signal. This, however, can be measured separately by recording the power of the whole transmitted beam. With these data, the measurement of nonlinearity can be corrected.

Frequently Asked Questions

This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).

What is the z-scan technique used for?

The z-scan technique is primarily used to measure the strength of the Kerr effect, specifically the magnitude of the nonlinear index ($n_2$), in an optical material. It can also be used to measure nonlinear absorption.

How does a z-scan measurement work?

In a z-scan measurement, a sample of the material is moved along the optical axis (the z-axis) through the focus of a laser beam. The self-focusing effect within the sample alters the beam's divergence, and this change is measured by a detector located behind the sample.

How does the sample's position affect the z-scan signal?

For a material with a positive nonlinear index, placing the sample before the beam focus increases beam divergence, reducing the signal at a detector behind an aperture. Placing the sample after the focus reduces divergence and increases the signal. The measured dependence of the signal on the position allows for the calculation of the nonlinear index.

Bibliography

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[2] M. Sheik-Bahae et al., “Sensitive measurement of optical nonlinearities using a single beam”, IEEE J. Quantum Electron. 26 (4), 760 (1990); doi:10.1109/3.53394

[3] J. Wang et al., “Time-resolved Z-scan measurements of optical nonlinearities”, J. Opt. Soc. Am. B 11 (6), 1009 (1994); doi:10.1364/JOSAB.11.001009

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[6] R. de Nalda et al., “Limits to the determination of the nonlinear refractive index by the Z-scan method”, J. Opt. Soc. Am. B 19 (2), 289 (2002); doi:10.1364/JOSAB.19.000289

[7] I. P. Nikolakakos et al., “Broadband characterization of the nonlinear optical properties of common reference materials”, IEEE J. Sel. Top. Quantum Electron. 10 85), 1164 (2004); doi:10.1109/JSTQE.2004.836007

[8] B. Gu et al., “Theory of Gaussian beam Z scan with simultaneous third- and fifth-order nonlinear refraction based on a Gaussian decomposition method”, J. Opt. Soc. Am. B 22 (12), 2651 (2005); doi:10.1364/JOSAB.22.002651

[9] M. C. Fischer et al., “Simultaneous self-phase modulation and two-photon absorption measurement by a spectral homodyne Z-scan method”, Opt. Express 16 (6), 4192 (2008); doi:10.1364/OE.16.004192

[10] L. C. Oliveira and S. C. Zilio, “Single-beam time-resolved z-scan measurements of slow absorbers”, Appl. Phys. Lett. 65, 2121 (1994)

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[12] L. Pálfalvi et al., “A general Z-scan theory”, Appl. Phys. B 97 (3), 679 (2009)

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Questions and Comments from Users

2021年04月12日

What are the functions of the two detectors in the figure?

The author's answer:

The first one would not be strictly necessary, but is used to compensate possible fluctuations in the laser pulse energy.

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