{ "id": "epg9hrv7e3", "slug": "z-scan-technique", "title": "Z-scan technique", "updated": "2026-09-30", "topic_path": [ { "id": "physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical" }, { "id": "physical.physics", "label": "Physics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.physics" }, { "id": "physical.physics.matter-and-radiation", "label": "Matter and radiation physics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.physics.matter-and-radiation" }, { "id": "physical.physics.matter-and-radiation.quantum-optics-and-photonics", "label": "Quantum optics and photonics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.physics.matter-and-radiation.quantum-optics-and-photonics" } ], "geo": [ { "id": "geo.nongeo.t1946.physical.physics.matter-and-radiation", "label": "Non-geographic · 1946 to 2000: Matter and radiation physics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.physics.matter-and-radiation", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1946", "label": "Non-geographic · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946" }, { "id": "geo.nongeo.t1946.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical" }, { "id": "geo.nongeo.t1946.physical.physics", "label": "Physics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.physics" }, { "id": "geo.nongeo.t1946.physical.physics.matter-and-radiation", "label": "Matter and radiation physics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.physics.matter-and-radiation" } ] } ], "excerpt": "The Z-scan technique is a single-beam optical method that measures nonlinear refraction and absorption by moving a sample through a laser focus, introduced in 1989.", "snippet": "The Z-scan technique is a single-beam optical method that measures nonlinear refraction and absorption by moving a sample through a laser focus, introduced in 1989.", "node": "physical.physics.matter-and-radiation.quantum-optics-and-photonics", "markdown": "# Z-scan technique\n\nThe Z-scan technique is a single-beam optical characterization method that measures nonlinear refraction and nonlinear absorption by translating a sample through the focus of a laser beam and recording the transmitted intensity as a function of sample position. It yields the nonlinear refractive index \\( n_{2} \\) (often written \\( \\gamma \\)) and the nonlinear absorption coefficient \\( \\beta \\), the real and imaginary parts of the third-order susceptibility \\( \\chi^{(3)} \\).[1](https://opg.optica.org/abstract.cfm?uri=OAM-1989-TUY3) • [2](http://materias.df.uba.ar/onla2020c2/files/2020/10/1990_Sheik-Bahae_IEEE-QE_Sensitive-Measurement-of-Optical-Nonlinearities-using-a-single-beam.pdf) Presented in 1989 and given a full theoretical treatment in 1990, it remains the standard technique for nonlinear characterization of transparent materials.[3](https://api.p1.mks.com/medias/sys_master/images/images/hb4/h45/8797308878878/Z-Scan-for-the-Characterization-of-Transparent-Optical-Materials-App-Note-34.pdf)\n\n| Key fact | Value |\n|---|---|\n| Measured quantities | Nonlinear refraction \\( n_{2} \\) (\\( \\gamma \\)) and nonlinear absorption \\( \\beta \\), real and imaginary parts of \\( \\chi^{(3)} \\)[3](https://api.p1.mks.com/medias/sys_master/images/images/hb4/h45/8797308878878/Z-Scan-for-the-Characterization-of-Transparent-Optical-Materials-App-Note-34.pdf) |\n| Sign of \\( n_{2} \\) | Peak before focus (negative, self-defocusing); peak after focus (positive, self-focusing)[2](http://materias.df.uba.ar/onla2020c2/files/2020/10/1990_Sheik-Bahae_IEEE-QE_Sensitive-Measurement-of-Optical-Nonlinearities-using-a-single-beam.pdf) |\n| Peak-valley relation | \\( \\Delta T_{p-v} \\approx 0.405|\\Delta \\Phi_{0}| \\) for an on-axis aperture, accurate to 0.5%[4](https://api.creol.ucf.edu/Publications/9431.pdf) |\n| Thin-sample condition | \\( L \\le n_{0} Z_{0} \\), with \\( Z_{0} = \\pi w_{0}^{2}/\\lambda \\); scan range about \\( \\pm 5 Z_{0} \\)[5](https://api.creol.ucf.edu/Publications/933.pdf) |\n| Aperture placement | Far field, typically \\( 20 Z_{0} \\) to \\( 100 Z_{0} \\) from focus; most closed-aperture work uses \\( 0.1 < S < 0.5 \\)[6](http://www.phys.unm.edu/msbahae/publications/z-scan.pdf) |\n| Demonstrated sensitivity | Better than \\( \\lambda/300 \\) wavefront distortion in \\( n_{2} \\) of BaF₂ at 532 nm[2](http://materias.df.uba.ar/onla2020c2/files/2020/10/1990_Sheik-Bahae_IEEE-QE_Sensitive-Measurement-of-Optical-Nonlinearities-using-a-single-beam.pdf) |\n| Typical accuracy | Closed-form analysis within 3%; single-scan separation within ±10%[3](https://api.p1.mks.com/medias/sys_master/images/images/hb4/h45/8797308878878/Z-Scan-for-the-Characterization-of-Transparent-Optical-Materials-App-Note-34.pdf) • [7](https://phyweb.physics.nus.edu.sg/~phyjiwei/APB-Yin-2000.pdf) |\n\n## How it works\n\nA focused [Gaussian beam](https://www.edgepedia.org/gaussian-beam) induces a lens-like phase shift in the sample proportional to the local irradiance. Under self-focusing (positive \\( n_{2} \\)) or self-defocusing (negative \\( n_{2} \\)), the beam divergence at a distant aperture changes depending on where the sample sits relative to the waist, so the aperture transmittance traces a characteristic peak-valley curve as the sample scans through focus. A prefocal transmittance maximum followed by a postfocal minimum is the signature of a negative refractive nonlinearity; positive nonlinear refraction gives the opposite valley-peak configuration.[2](http://materias.df.uba.ar/onla2020c2/files/2020/10/1990_Sheik-Bahae_IEEE-QE_Sensitive-Measurement-of-Optical-Nonlinearities-using-a-single-beam.pdf) The magnitude of the normalized peak-to-valley transmittance change \\( \\Delta T_{p-v} \\) follows a linear relation with the on-axis nonlinear phase shift \\( \\Delta \\Phi_{0} \\).[1](https://opg.optica.org/abstract.cfm?uri=OAM-1989-TUY3)\n\nThe central quantities are the diffraction length \\( Z_{0} = \\pi w_{0}^{2}/\\lambda \\), the on-axis phase shift at the waist\n\n\\[ \\Delta \\Phi_{0} = \\frac{2\\pi}{\\lambda} n_{2} I_{0} L_{\\mathrm{eff}}, \\]\n\nthe effective length \\( L_{\\mathrm{eff}} = (1 - e^{-\\alpha L})/\\alpha \\) for a sample of linear absorption \\( \\alpha \\), the peak-valley separation \\( \\Delta Z_{pv} \\approx 1.7 Z_{0} \\), and \\( \\Delta T_{pv} = |T_{p} - T_{v}| \\).[6](http://www.phys.unm.edu/msbahae/publications/z-scan.pdf) For an on-axis aperture (\\( S \\approx 0 \\)), \\( \\Delta T_{p-v} \\approx 0.405|\\Delta \\Phi_{0}| \\) holds to within 0.5%; with 1% resolvable transmittance change, phase shifts below \\( \\lambda/250 \\) wavefront distortion are measurable.[4](https://api.creol.ucf.edu/Publications/9431.pdf) The esu conversion is \\( n_{2}(\\mathrm{esu}) = (c \\cdot n_{0}/40\\pi) \\cdot \\gamma(\\mathrm{m^2/W}) \\).[4](https://api.creol.ucf.edu/Publications/9431.pdf)\n\nNonlinear absorption modifies this curve: multiphoton absorption suppresses the peak and enhances the valley, while saturable absorption produces the opposite effect. With the aperture fully open (\\( S = 1 \\)), the scan is insensitive to nonlinear refraction in the thin-sample approximation and responds only to absorption.[2](http://materias.df.uba.ar/onla2020c2/files/2020/10/1990_Sheik-Bahae_IEEE-QE_Sensitive-Measurement-of-Optical-Nonlinearities-using-a-single-beam.pdf) A further practical advantage is that the sign of the nonlinearity is read directly from the curve order, which other techniques do not provide so directly.[8](https://cdn.intechopen.com/pdfs/83013.pdf)\n\n## How it is done\n\nThe standard apparatus uses a long-focal-length lens, a motorized translation stage carrying a thin sample (under 5 mm), and a beamsplitter feeding two photodiodes: one records total transmitted power (open aperture) and one sits behind an iris clipping roughly half the beam (closed aperture), so both scans are acquired simultaneously.[3](https://api.p1.mks.com/medias/sys_master/images/images/hb4/h45/8797308878878/Z-Scan-for-the-Characterization-of-Transparent-Optical-Materials-App-Note-34.pdf) A reference detector arm, optionally with an identical lens and aperture, normalizes the signal against laser power and spatial beam fluctuations.[5](https://api.creol.ucf.edu/Publications/933.pdf)\n\nA thin sample is defined as having thickness \\( L \\le n_{0} Z_{0} \\). Although all information lies within \\( \\pm Z_{0} \\), scanning over about \\( \\pm 5 Z_{0} \\) or more establishes the linear-transmission baseline. The aperture is placed in the far field, typically \\( 20 Z_{0} \\) to \\( 100 Z_{0} \\) from focus, and most closed-aperture experiments use \\( 0.1 < S < 0.5 \\), where \\( S \\) is the aperture's linear transmittance.[6](http://www.phys.unm.edu/msbahae/publications/z-scan.pdf) The measured curve is then fitted, or its peak-valley height read directly, to extract \\( n_{2} \\) and \\( \\beta \\). Both detectors can be replaced by a single CCD camera: integrating over the array gives the open-aperture result and tracking the beam radius gives closed-aperture-analogous information.[3](https://api.p1.mks.com/medias/sys_master/images/images/hb4/h45/8797308878878/Z-Scan-for-the-Characterization-of-Transparent-Optical-Materials-App-Note-34.pdf)\n\nThese closed-form relations assume the slowly varying envelope approximation, \\( L < Z_{0} \\) and \\( L < Z_{0}/\\Delta \\Phi_{0} \\), and are accurate to within 3%; higher precision comes from the Gaussian Decomposition (GD) method, in which the field at the aperture is expanded in Gaussian components.[3](https://api.p1.mks.com/medias/sys_master/images/images/hb4/h45/8797308878878/Z-Scan-for-the-Characterization-of-Transparent-Optical-Materials-App-Note-34.pdf) The GD approach builds on earlier work by D. Weaire and colleagues on low-power nonlinear refraction in InSb.[9](https://doi.org/10.1364/ol.4.000331)\n\n## Origin\n\nThe technique was reported in 1989 by M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland's group at CREOL: a CLEO paper described the z-scan trace as containing the sign, magnitude, and order of the nonlinearity,[10](https://stars.library.ucf.edu/scopus1980/405/) an SPIE paper set out the analysis,[4](https://api.creol.ucf.edu/Publications/9431.pdf) and an OSA Annual Meeting abstract (paper TUY3, Orlando, October 1989) presented the single-beam scheme with constant input pulse energy.[1](https://opg.optica.org/abstract.cfm?uri=OAM-1989-TUY3) The comprehensive theory, with the \\( \\lambda/300 \\) sensitivity demonstration in BaF₂, appeared in IEEE Journal of Quantum Electronics 26, 760.[2](http://materias.df.uba.ar/onla2020c2/files/2020/10/1990_Sheik-Bahae_IEEE-QE_Sensitive-Measurement-of-Optical-Nonlinearities-using-a-single-beam.pdf)\n\nIt built on earlier work: a similar scanning approach had been used to measure thermally induced beam distortion by chemicals in solvents,[2](http://materias.df.uba.ar/onla2020c2/files/2020/10/1990_Sheik-Bahae_IEEE-QE_Sensitive-Measurement-of-Optical-Nonlinearities-using-a-single-beam.pdf) and A. E. Kaplan had analyzed external self-focusing of light by a nonlinear layer in 1969 in Radiophysics and Quantum Electronics.[11](https://doi.org/10.1007/bf01031251) Its sensitivity is comparable to interferometric methods while being simpler than nonlinear interferometry, degenerate four-wave mixing, nearly-degenerate three-wave mixing, ellipse rotation, and beam distortion measurements, which explains its rapid adoption as a standard technique.[4](https://api.creol.ucf.edu/Publications/9431.pdf) • [5](https://api.creol.ucf.edu/Publications/933.pdf)\n\n## Variants\n\nDividing the closed-aperture curve by the open-aperture curve recovers a purely refractive scan, agreeing with a true refractive Z-scan within ±10%.[5](https://api.creol.ucf.edu/Publications/933.pdf) A single closed-aperture scan can also separate refraction from absorption by symmetry: \\( T_{\\Delta\\Phi}(z) = [T(z) - T(-z)]/2 \\) isolates the odd (refractive) part and \\( T_{\\Delta\\Psi}(z) = [T(z) + T(-z)]/2 - 1 \\) the even (absorptive) part, with about ±10% uncertainty.[7](https://phyweb.physics.nus.edu.sg/~phyjiwei/APB-Yin-2000.pdf) A later Gaussian-decomposition model with symmetric analysis obtains both quantities simultaneously from one scan regardless of their relative magnitudes.[12](https://opg.optica.org/josab/abstract.cfm?uri=josab-21-2-349)\n\nNamed variants include:\n\n- **Top-hat beam Z-scan**, produced by expanding a coherent beam and aperturing it at the focusing lens, with the empirical relation \\( \\Delta T_{pv} \\approx 0.28(1-S)^{0.37} \\Delta \\Phi_{0} \\tanh(0.14 \\Delta \\Phi_{0}) \\); the top-hat profile raises the peak-to-valley response by a factor of 2.5 over a Gaussian beam, at the cost of pulse energy discarded in beam shaping.[5](https://api.creol.ucf.edu/Publications/933.pdf) • [13](https://doi.org/10.1364/ol.20.001821)\n- **Non-Gaussian and thick-sample Z-scan**, in which Robert E. Bridges, George L. Fischer, and [Robert W. Boyd](https://www.edgepedia.org/robert-w-boyd) compared a test sample against a reference sample, removing the need to know the pulse temporal profile and allowing samples thicker than a Rayleigh range (distance over which a focused laser beam stays nearly collimated).[13](https://doi.org/10.1364/ol.20.001821)\n- **Two-color Z-scan**, reported by H. Ma and Cid B. de Araújo with enhanced sensitivity.[14](https://doi.org/10.1063/1.113858)\n- **Eclipsing Z-scan (EZ-scan)**, with a circular board replacing the aperture; S. V. Kershaw published its analysis in 1995.[15](https://doi.org/10.1080/09500349514551191)\n- **Time-resolved pump-probe Z-scan**, in which a filter before the detector blocks the pump and transmits the probe, allowing \\( \\Delta n(t) \\) and \\( \\Delta \\alpha(t) \\) and slow versus fast responses to be separated.[5](https://api.creol.ucf.edu/Publications/933.pdf)\n- **Reflection Z-scan**, in which the open-aperture configuration provides \\( n_{2} \\) through the nonlinear modification of the surface reflection coefficient, suited to surfaces and single nano-objects.[16](https://arxiv.org/html/2411.02315)\n\n## Applications\n\nThe founding measurements covered semiconductors (InSb, ZnSe, CdTe), glasses (BaF₂, MgF₂), semiconductor-doped glasses, and CS₂.[1](https://opg.optica.org/abstract.cfm?uri=OAM-1989-TUY3) For ZnSe (2.7 mm, 27 ps pulses at 532 nm) the fitted values were \\( \\beta = 5.8 \\) cm/GW and \\( \\gamma \\approx 6.8 \\times 10^{-14} \\) cm²/W, with about ±25% uncertainty dominated by irradiance calibration.[2](http://materias.df.uba.ar/onla2020c2/files/2020/10/1990_Sheik-Bahae_IEEE-QE_Sensitive-Measurement-of-Optical-Nonlinearities-using-a-single-beam.pdf) CS₂ measured at 10.6, 1.06, and 0.53 µm gave consistent \\( n_{2} \\) of \\( (1.5 \\pm 0.6) \\), \\( (1.3 \\pm 0.3) \\), and \\( (1.2 \\pm 0.2) \\times 10^{-11} \\) esu, with thermal and reorientational Kerr mechanisms distinguished by pulse duration.[4](https://api.creol.ucf.edu/Publications/9431.pdf) [Femtosecond](https://www.edgepedia.org/femtosecond) measurements with a 35 fs, 1 kHz amplifier and a 500 mm lens (\\( Z_{0} = 18 \\) mm, \\( I_{0} = 6 \\times 10^{14} \\) W/m²) gave \\( n_{2} = 2.9 \\times 10^{-20} \\) m²/W for fused silica and \\( 9.7 \\times 10^{-20} \\) m²/W for BK7.[3](https://api.p1.mks.com/medias/sys_master/images/images/hb4/h45/8797308878878/Z-Scan-for-the-Characterization-of-Transparent-Optical-Materials-App-Note-34.pdf) Pulse regimes range from picosecond and femtosecond amplified systems to continuous-wave beams, and current use spans perovskite films, doped nanopowders, and organic liquids.[17](https://pubs.rsc.org/en/content/articlelanding/2022/ma/d2ma00724j) • [18](https://www.nature.com/articles/s41598-025-94079-x) • [19](https://google.iopscience.iop.org/article/10.1088/2053-1591/ae7e4a)\n\n## Limitations and alternatives\n\nZ-scan is mechanism-blind: it responds to any process that changes the index or the absorption, so thermal refraction, electrostriction, molecular reorientation, and excited-state effects all contribute to the same curve. Cumulative (slow) nonlinearities are fluence dependent while ultrafast effects remain irradiance dependent, a diagnostic that, together with scans at varying pulsewidths, frequencies, and focal geometries, helps identify the underlying process.[5](https://api.creol.ucf.edu/Publications/933.pdf) Experimental parameters that can seriously distort the extracted response include sample length, self-focusing, cell lensing and wedging, laser repetition rate, temporal and spatial beam profile, and multiple internal reflections.[20](https://www.spiedigitallibrary.org/conference-proceedings-of-spie/5131/0000/Influence-of-experimental-conditions-on-the-determination-of-nonlinear-optical/10.1117/12.513674.full) The original formulation also assumes a diffraction-limited Gaussian beam and a sample much thinner than a Rayleigh range; common Nd:YAG lasers can have \\( M^{2} \\) of roughly 2 to 2.4, violating the beam-quality assumption.[13](https://doi.org/10.1364/ol.20.001821) [Irradiance](https://www.edgepedia.org/irradiance) calibration contributes about ±25% uncertainty to absolute values.[2](http://materias.df.uba.ar/onla2020c2/files/2020/10/1990_Sheik-Bahae_IEEE-QE_Sensitive-Measurement-of-Optical-Nonlinearities-using-a-single-beam.pdf)\n\nAgainst alternatives, the Z-scan offers interferometry-comparable sensitivity with simpler apparatus than nonlinear interferometry, degenerate four-wave mixing, nearly-degenerate three-wave mixing, ellipse rotation, and beam distortion methods.[4](https://api.creol.ucf.edu/Publications/9431.pdf) Conventional focusing over tens of µm² requires intensities of order GW/cm², which risks damaging delicate nanomaterials and prevents measurement of single nanoscale objects.[16](https://arxiv.org/html/2411.02315) Recent work extends the framework in other directions: a [Fresnel diffraction](https://www.edgepedia.org/fresnel-diffraction) model handles large nonlinear phase shifts under continuous-wave illumination beyond the small-phase-shift regime of the original treatment,[21](https://journal.hep.com.cn/ol/EN/10.1007/s11801-024-3123-4) and a reflection Z-scan inside a plasmonic nanocavity reached kW/cm² intensities, down to two photons per pulse, extracting \\( n_{2} \\) and \\( \\beta \\) of perovskite and gold nano-objects and a molecular monolayer.[16](https://arxiv.org/html/2411.02315)\n\n## References\n\n1. [z-scan: a simple sensitive technique for measuring refractive nonlinearities (OSA Annual Meeting 1989, paper TUY3)](https://opg.optica.org/abstract.cfm?uri=OAM-1989-TUY3)\n2. [Sensitive measurement of optical nonlinearities using a single beam (Sheik-Bahae, Said, Wei, Hagan, Van Stryland, IEEE J. Quantum Electron. 26(4):760–769, 1990)](http://materias.df.uba.ar/onla2020c2/files/2020/10/1990_Sheik-Bahae_IEEE-QE_Sensitive-Measurement-of-Optical-Nonlinearities-using-a-single-beam.pdf)\n3. [Z-Scan for the Characterization of Transparent Optical Materials (Newport/MKS Application Note 34)](https://api.p1.mks.com/medias/sys_master/images/images/hb4/h45/8797308878878/Z-Scan-for-the-Characterization-of-Transparent-Optical-Materials-App-Note-34.pdf)\n4. [Simple and sensitive technique for determining refractive nonlinearities (Sheik-Bahae et al., SPIE Proceedings, 1989)](https://api.creol.ucf.edu/Publications/9431.pdf)\n5. [Z-Scan Measurements of Organic Nonlinearities (Van Stryland & Sheik-Bahae, CREOL review chapter)](https://api.creol.ucf.edu/Publications/933.pdf)\n6. [Z-Scan Measurements of Optical Nonlinearities (book chapter, Kuzyk & Dirk eds., Marcel Dekker, 1998)](http://www.phys.unm.edu/msbahae/publications/z-scan.pdf)\n7. [Determination of nonlinear absorption and refraction by single Z-scan method (Yin et al., Appl. Phys. B, 2000)](https://phyweb.physics.nus.edu.sg/~phyjiwei/APB-Yin-2000.pdf)\n8. [Third-Order Nonlinearity (book chapter, IntechOpen)](https://cdn.intechopen.com/pdfs/83013.pdf)\n9. [D. Weaire and colleagues (1979). Effect of low-power nonlinear refraction on laser-beam propagation in InSb. Optics Letters.](https://doi.org/10.1364/ol.4.000331)\n10. [Simple And Sensitive Technique For Determining Refractive Nonlinearities (CLEO 1989, UCF STARS record)](https://stars.library.ucf.edu/scopus1980/405/)\n11. [A. E. Kaplan (1969). ?External? self-focusing of light by a nonlinear layer. Radiophysics and Quantum Electronics.](https://doi.org/10.1007/bf01031251)\n12. [Accurate determination of nonlinear refraction and nonlinear absorption by a single Z-scan method (J. Opt. Soc. Am. B 21(2):349, 2004)](https://opg.optica.org/josab/abstract.cfm?uri=josab-21-2-349)\n13. [Robert E. Bridges, George L. Fischer, Robert W. Boyd (1995). Z-scan measurement technique for non-Gaussian beams and arbitrary sample thicknesses. Optics Letters.](https://doi.org/10.1364/ol.20.001821)\n14. [H. Ma, Cid B. de Araújo (1995). Two-color Z-scan technique with enhanced sensitivity. Applied Physics Letters.](https://doi.org/10.1063/1.113858)\n15. [S.V. Kershaw (1995). Analysis of the EZ Scan Measurement Technique. Journal of Modern Optics.](https://doi.org/10.1080/09500349514551191)\n16. [Few photons probe third-order nonlinear properties of nanomaterials in a plasmonic nanocavity (arXiv, November 2024)](https://arxiv.org/html/2411.02315)\n17. [Femtosecond induced third-order optical nonlinearity in quasi 2D Ruddlesden–Popper perovskite film deciphered using Z-scan (Materials Advances, RSC, 2022)](https://pubs.rsc.org/en/content/articlelanding/2022/ma/d2ma00724j)\n18. [Study of Z-scan technique, dispersion energy, and Wemple–DiDomenico model on Cu, Cr and Fe doped NiO nanopowder (Scientific Reports, 2025)](https://www.nature.com/articles/s41598-025-94079-x)\n19. [Z-scan study of nonlocal nonlinear optical response in different organic oils under CW visible illumination (Materials Research Express, IOPscience)](https://google.iopscience.iop.org/article/10.1088/2053-1591/ae7e4a)\n20. [Influence of experimental conditions on the determination of nonlinear optical parameters of a medium using the Z-scan technique (Aloukos & Couris, Proc. SPIE 5131, 2003)](https://www.spiedigitallibrary.org/conference-proceedings-of-spie/5131/0000/Influence-of-experimental-conditions-on-the-determination-of-nonlinear-optical/10.1117/12.513674.full)\n21. [Numerical calculation of Z-scan measurements for nonlinear media with large phase shift (Optoelectronics Letters, 2024)](https://journal.hep.com.cn/ol/EN/10.1007/s11801-024-3123-4)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Physics › Matter and radiation physics › Quantum optics and photonics*\n\n*Initially written Sep 29, 2026 · Reviewed: Sep 30, 2026 · Edited: Sep 30, 2026 · Last review: Sep 30, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [], "url": "https://www.edgepedia.org/z-scan-technique", "markdown_url": "https://www.edgepedia.org/z-scan-technique.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Z-scan technique\", Edgepedia (EdgeChat), https://www.edgepedia.org/z-scan-technique. Edgepedia Community License 1.0.", "credit_md": "\"[Z-scan technique](https://www.edgepedia.org/z-scan-technique)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/z-scan-technique](https://www.edgepedia.org/z-scan-technique). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Z-scan technique\", Edgepedia (EdgeChat), https://www.edgepedia.org/z-scan-technique. Edgepedia Community License 1.0.", "speakable": "The Z-scan technique is a single-beam optical method that measures nonlinear refraction and absorption by moving a sample through a laser focus, introduced in 1989." }