Nonlinear refractive index measurements of solids and the impact of B-integral on the phase of generated high-order harmonics

Roy Van der Linden; Nataliia Kuzkova; Peter M. Kraus

doi:10.1364/OE.579736

Nonlinear refractive index measurements of solids and the impact of B-integral on the phase of generated high-order harmonics

Roy Van der Linden
, Nataliia Kuzkova
, Peter M. Kraus^*

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

We present an interferometric method that employs a birefringent common-path interferometer to measure absolute nonlinear refractive indices in 5 mm thick CaF₂, SiO₂, NBK-7 and KBr for femtosecond pulses at 804 nm center wavelength. The measured nonlinear refractive indices are found to be in agreement with previous literature, over a broad range of pulse energies. In addition, we show and highlight the importance of thorough B-integral characterization when using this birefringent common-path interferometer for high-harmonic generation driven extreme-ultraviolet interferometry. The accumulated third-order nonlinear phase is shown to have significant impact on the harmonic phase after up-conversion to higher orders, but can be accounted for if correctly characterized.

Original language	English
Pages (from-to)	53268-53278
Number of pages	11
Journal	Optics Express
Volume	33
Issue number	25
Early online date	10 Dec 2025
DOIs	https://doi.org/10.1364/OE.579736
Publication status	Published - 15 Dec 2025

Bibliographical note

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© 2025 Optica Publishing Group (formerly OSA). All rights reserved.

Funding

HORIZON EUROPE European Research Council (101041819); Nederlandse Organisatie voor Wetenschappelijk Onderzoek (VI.Vidi223.133). We thank the mechanical workshop and the design, electronic, and software departments of ARCNL for the construction of the setup and highlight Dr. Stefan Lehman’s contribution for his technical support and insight.

Funders	Funder number
ARCNL
HORIZON EUROPE European Research Council	101041819
Nederlandse Organisatie voor Wetenschappelijk Onderzoek	VI.Vidi223.133

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abstract = "We present an interferometric method that employs a birefringent common-path interferometer to measure absolute nonlinear refractive indices in 5 mm thick CaF2, SiO2, NBK-7 and KBr for femtosecond pulses at 804 nm center wavelength. The measured nonlinear refractive indices are found to be in agreement with previous literature, over a broad range of pulse energies. In addition, we show and highlight the importance of thorough B-integral characterization when using this birefringent common-path interferometer for high-harmonic generation driven extreme-ultraviolet interferometry. The accumulated third-order nonlinear phase is shown to have significant impact on the harmonic phase after up-conversion to higher orders, but can be accounted for if correctly characterized.",

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N2 - We present an interferometric method that employs a birefringent common-path interferometer to measure absolute nonlinear refractive indices in 5 mm thick CaF2, SiO2, NBK-7 and KBr for femtosecond pulses at 804 nm center wavelength. The measured nonlinear refractive indices are found to be in agreement with previous literature, over a broad range of pulse energies. In addition, we show and highlight the importance of thorough B-integral characterization when using this birefringent common-path interferometer for high-harmonic generation driven extreme-ultraviolet interferometry. The accumulated third-order nonlinear phase is shown to have significant impact on the harmonic phase after up-conversion to higher orders, but can be accounted for if correctly characterized.

AB - We present an interferometric method that employs a birefringent common-path interferometer to measure absolute nonlinear refractive indices in 5 mm thick CaF2, SiO2, NBK-7 and KBr for femtosecond pulses at 804 nm center wavelength. The measured nonlinear refractive indices are found to be in agreement with previous literature, over a broad range of pulse energies. In addition, we show and highlight the importance of thorough B-integral characterization when using this birefringent common-path interferometer for high-harmonic generation driven extreme-ultraviolet interferometry. The accumulated third-order nonlinear phase is shown to have significant impact on the harmonic phase after up-conversion to higher orders, but can be accounted for if correctly characterized.

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Nonlinear refractive index measurements of solids and the impact of B-integral on the phase of generated high-order harmonics

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