Abstract

Digital inline pump–probe holography can be applied to estimate parameters of samples’ optical nonlinear properties. Here we propose a mathematical model to describe noncollinear degenerate phase modulation in samples with inhomogeneities of nonlinear refractive index over all three dimensions, namely, two-layered samples and samples with local impurities. The impact of sample parameters in the considered configurations is analyzed. We show that analysis of inline digital holograms obtained by time-resolved inline digital holography can be successfully used for rapid detection and characterization of various types of nonlinear refractive index inhomogeneities.

© 2021 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2020 (2)

O. Moskalyuk, A. Belashov, Y. Beltukov, E. Ivan’kova, E. Popova, I. Semenova, V. Yelokhovsky, and V. Yudin, “Polystyrene-based nanocomposites with different fillers: fabrication and mechanical properties,” Polymers 12, 2457 (2020).
[Crossref]

A. V. Belashov, C.-J. Cheng, and N. V. Petrov, “Time-resolved inline digital holography for measurement of optical nonlinear properties of quantum dots on substrates,” Proc. SPIE 11278, 1127810 (2020).
[Crossref]

2019 (3)

2018 (4)

2017 (3)

S. S. Nalegaev, A. V. Belashov, and N. V. Petrov, “Application of photothermal digital interferometry for nonlinear refractive index measurements within a Kerr approximation,” Opt. Mater. 69, 437–443 (2017).
[Crossref]

T. V. Amotchkina, M. K. Trubetskov, F. Krausz, V. Pervak, O. Pronin, L. Smalakys, A. Melninkaitis, and B. Momgaudis, “Time resolved digital holography measurements of the nonlinear optical filters,” Proc. SPIE 10447, 104470Y (2017).
[Crossref]

Y.-D. Wu and M.-H. Cheng, “Analyzing the multilayer metamaterial waveguide structure with the Kerr-type nonlinear cladding,” Opt. Quantum Electron. 49, 181 (2017).
[Crossref]

2015 (2)

M. G. Beygi, R. Karimzadeh, and M. Dashtdar, “Nonlinear refractive index measurement by Fresnel diffraction from phase object,” Opt. Laser Technol. 66, 151–155 (2015).
[Crossref]

S. Bai, Q. Li, H. Zhang, X. Chen, S. Luo, H. Gong, Y. Yang, D. Zhao, and M. Qiu, “Large third-order nonlinear refractive index coefficient based on gold nanoparticle aggregate films,” Appl. Phys. Lett. 107, 141111 (2015).
[Crossref]

2014 (2)

M. Miguez, E. Barbano, S. C. Zilio, and L. Misoguti, “Accurate measurement of nonlinear ellipse rotation using a phase-sensitive method,” Opt. Express 22, 25530–25538 (2014).
[Crossref]

L. Zhu, M. Sun, J. Chen, J. Yu, and C. Zhou, “Integrated digital holography for measuring the photothermal effect induced by femtosecond laser pulses,” Opt. Eng. 53, 112311 (2014).
[Crossref]

2013 (2)

I. Dancus, S. T. Popescu, and A. Petris, “Single shot interferometric method for measuring the nonlinear refractive index,” Opt. Express 21, 31303 (2013).
[Crossref]

J. Yao, P. Meemon, K.-S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52, 112111 (2013).
[Crossref]

2012 (1)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748 (2012).
[Crossref]

2011 (2)

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[Crossref]

A. Orlova, Y. A. Gromova, A. Savelyeva, V. Maslov, M. Artemyev, A. Prudnikau, A. Fedorov, and A. Baranov, “Track membranes with embedded semiconductor nanocrystals: structural and optical examinations,” Nanotechnology 22, 455201 (2011).
[Crossref]

2009 (1)

L.-S. Chen, Z.-M. Huang, G.-H. Dong, C.-L. He, L. Liu, Y.-Y. Hu, and Y. Li, “Development of a transparent PMMA composite reinforced with nanofibers,” Polym. Compos. 30, 239–247 (2009).
[Crossref]

2008 (2)

F. Henari and A. Dakhel, “Linear and nonlinear optical properties of gold nanoparticle-eu oxide composite thin films,” J. Appl. Phys. 104, 033110 (2008).
[Crossref]

Y.-D. Wu, T.-T. Shih, and M.-H. Chen, “New all-optical logic gates based on the local nonlinear Mach-Zehnder interferometer,” Opt. Express 16, 248–257 (2008).
[Crossref]

2001 (1)

P. Apel, “Track etching technique in membrane technology,” Radiat. Meas. 34, 559–566 (2001).
[Crossref]

1995 (1)

1992 (1)

1990 (1)

M. Sheik-Bahae, A. Said, T.-H. Wei, D. Hagan, and E. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[Crossref]

1989 (1)

E. Pope, M. Asami, and J. Mackenzie, “Transparent silica gel–PMMA composites,” J. Mater. Res. 4, 1018–1026 (1989).
[Crossref]

1966 (1)

A. Ashkin, G. Boyd, J. I. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Amotchkina, T. V.

T. V. Amotchkina, M. K. Trubetskov, F. Krausz, V. Pervak, O. Pronin, L. Smalakys, A. Melninkaitis, and B. Momgaudis, “Time resolved digital holography measurements of the nonlinear optical filters,” Proc. SPIE 10447, 104470Y (2017).
[Crossref]

Apel, P.

P. Apel, “Track etching technique in membrane technology,” Radiat. Meas. 34, 559–566 (2001).
[Crossref]

Artemyev, M.

A. Orlova, Y. A. Gromova, A. Savelyeva, V. Maslov, M. Artemyev, A. Prudnikau, A. Fedorov, and A. Baranov, “Track membranes with embedded semiconductor nanocrystals: structural and optical examinations,” Nanotechnology 22, 455201 (2011).
[Crossref]

Asami, M.

E. Pope, M. Asami, and J. Mackenzie, “Transparent silica gel–PMMA composites,” J. Mater. Res. 4, 1018–1026 (1989).
[Crossref]

Ashkin, A.

A. Ashkin, G. Boyd, J. I. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Bai, S.

S. Bai, Q. Li, H. Zhang, X. Chen, S. Luo, H. Gong, Y. Yang, D. Zhao, and M. Qiu, “Large third-order nonlinear refractive index coefficient based on gold nanoparticle aggregate films,” Appl. Phys. Lett. 107, 141111 (2015).
[Crossref]

Ballman, A.

A. Ashkin, G. Boyd, J. I. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Baranov, A.

A. Orlova, Y. A. Gromova, A. Savelyeva, V. Maslov, M. Artemyev, A. Prudnikau, A. Fedorov, and A. Baranov, “Track membranes with embedded semiconductor nanocrystals: structural and optical examinations,” Nanotechnology 22, 455201 (2011).
[Crossref]

Barbano, E.

Belashov, A.

O. Moskalyuk, A. Belashov, Y. Beltukov, E. Ivan’kova, E. Popova, I. Semenova, V. Yelokhovsky, and V. Yudin, “Polystyrene-based nanocomposites with different fillers: fabrication and mechanical properties,” Polymers 12, 2457 (2020).
[Crossref]

N. Petrov, S. Nalegaev, A. Belashov, I. Shevkunov, S. Putilin, Y. Lin, and C. Cheng, “Time-resolved inline digital holography for the study of noncollinear degenerate phase modulation,” Opt. Lett. 43, 3481–3484 (2018).
[Crossref]

Belashov, A. V.

A. V. Belashov, C.-J. Cheng, and N. V. Petrov, “Time-resolved inline digital holography for measurement of optical nonlinear properties of quantum dots on substrates,” Proc. SPIE 11278, 1127810 (2020).
[Crossref]

S. S. Nalegaev, A. V. Belashov, and N. V. Petrov, “Application of photothermal digital interferometry for nonlinear refractive index measurements within a Kerr approximation,” Opt. Mater. 69, 437–443 (2017).
[Crossref]

A. V. Belashov, C.-J. Cheng, and N. V. Petrov, “On the evaluation of nonlinear optical inhomogeneities fraction using time-resolved in-line digital holography,” Tech. Phys. Russ. J. Appl. Phys.5 (to be published).

Beltukov, Y.

O. Moskalyuk, A. Belashov, Y. Beltukov, E. Ivan’kova, E. Popova, I. Semenova, V. Yelokhovsky, and V. Yudin, “Polystyrene-based nanocomposites with different fillers: fabrication and mechanical properties,” Polymers 12, 2457 (2020).
[Crossref]

Beygi, M. G.

M. G. Beygi, R. Karimzadeh, and M. Dashtdar, “Nonlinear refractive index measurement by Fresnel diffraction from phase object,” Opt. Laser Technol. 66, 151–155 (2015).
[Crossref]

Bilde, A.

Boyd, G.

A. Ashkin, G. Boyd, J. I. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Bruno, L.

L. Bruno, “Mechanical characterization of composite materials by optical techniques: a review,” Opt. Lasers Eng. 104, 192–203 (2018).
[Crossref]

Chen, J.

L. Zhu, M. Sun, J. Chen, J. Yu, and C. Zhou, “Integrated digital holography for measuring the photothermal effect induced by femtosecond laser pulses,” Opt. Eng. 53, 112311 (2014).
[Crossref]

Chen, L.-S.

L.-S. Chen, Z.-M. Huang, G.-H. Dong, C.-L. He, L. Liu, Y.-Y. Hu, and Y. Li, “Development of a transparent PMMA composite reinforced with nanofibers,” Polym. Compos. 30, 239–247 (2009).
[Crossref]

Chen, M.-H.

Chen, X.

S. Bai, Q. Li, H. Zhang, X. Chen, S. Luo, H. Gong, Y. Yang, D. Zhao, and M. Qiu, “Large third-order nonlinear refractive index coefficient based on gold nanoparticle aggregate films,” Appl. Phys. Lett. 107, 141111 (2015).
[Crossref]

Cheng, C.

Cheng, C.-J.

A. V. Belashov, C.-J. Cheng, and N. V. Petrov, “Time-resolved inline digital holography for measurement of optical nonlinear properties of quantum dots on substrates,” Proc. SPIE 11278, 1127810 (2020).
[Crossref]

A. V. Belashov, C.-J. Cheng, and N. V. Petrov, “On the evaluation of nonlinear optical inhomogeneities fraction using time-resolved in-line digital holography,” Tech. Phys. Russ. J. Appl. Phys.5 (to be published).

Cheng, M.-H.

Y.-D. Wu and M.-H. Cheng, “Analyzing the multilayer metamaterial waveguide structure with the Kerr-type nonlinear cladding,” Opt. Quantum Electron. 49, 181 (2017).
[Crossref]

Dakhel, A.

F. Henari and A. Dakhel, “Linear and nonlinear optical properties of gold nanoparticle-eu oxide composite thin films,” J. Appl. Phys. 104, 033110 (2008).
[Crossref]

Dancus, I.

Dashtdar, M.

M. G. Beygi, R. Karimzadeh, and M. Dashtdar, “Nonlinear refractive index measurement by Fresnel diffraction from phase object,” Opt. Laser Technol. 66, 151–155 (2015).
[Crossref]

DeSalvo, R.

Dong, G.-H.

L.-S. Chen, Z.-M. Huang, G.-H. Dong, C.-L. He, L. Liu, Y.-Y. Hu, and Y. Li, “Development of a transparent PMMA composite reinforced with nanofibers,” Polym. Compos. 30, 239–247 (2009).
[Crossref]

Dziedzic, J. I.

A. Ashkin, G. Boyd, J. I. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Fedorov, A.

A. Orlova, Y. A. Gromova, A. Savelyeva, V. Maslov, M. Artemyev, A. Prudnikau, A. Fedorov, and A. Baranov, “Track membranes with embedded semiconductor nanocrystals: structural and optical examinations,” Nanotechnology 22, 455201 (2011).
[Crossref]

Gomes, J.

Gong, H.

S. Bai, Q. Li, H. Zhang, X. Chen, S. Luo, H. Gong, Y. Yang, D. Zhao, and M. Qiu, “Large third-order nonlinear refractive index coefficient based on gold nanoparticle aggregate films,” Appl. Phys. Lett. 107, 141111 (2015).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (2004).

Gromova, Y. A.

A. Orlova, Y. A. Gromova, A. Savelyeva, V. Maslov, M. Artemyev, A. Prudnikau, A. Fedorov, and A. Baranov, “Track membranes with embedded semiconductor nanocrystals: structural and optical examinations,” Nanotechnology 22, 455201 (2011).
[Crossref]

Guizard, S.

Guo, B.

B. Guo, Q.-L. Xiao, S.-H. Wang, and H. Zhang, “2d layered materials: synthesis, nonlinear optical properties, and device applications,” Laser Photon. Rev. 13, 1800327 (2019).
[Crossref]

Hagan, D.

M. Sheik-Bahae, A. Said, T.-H. Wei, D. Hagan, and E. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[Crossref]

Hagan, D. J.

He, C.-L.

L.-S. Chen, Z.-M. Huang, G.-H. Dong, C.-L. He, L. Liu, Y.-Y. Hu, and Y. Li, “Development of a transparent PMMA composite reinforced with nanofibers,” Polym. Compos. 30, 239–247 (2009).
[Crossref]

Henari, F.

F. Henari and A. Dakhel, “Linear and nonlinear optical properties of gold nanoparticle-eu oxide composite thin films,” J. Appl. Phys. 104, 033110 (2008).
[Crossref]

Hu, Y.-Y.

L.-S. Chen, Z.-M. Huang, G.-H. Dong, C.-L. He, L. Liu, Y.-Y. Hu, and Y. Li, “Development of a transparent PMMA composite reinforced with nanofibers,” Polym. Compos. 30, 239–247 (2009).
[Crossref]

Huang, Z.-M.

L.-S. Chen, Z.-M. Huang, G.-H. Dong, C.-L. He, L. Liu, Y.-Y. Hu, and Y. Li, “Development of a transparent PMMA composite reinforced with nanofibers,” Polym. Compos. 30, 239–247 (2009).
[Crossref]

Ivan’kova, E.

O. Moskalyuk, A. Belashov, Y. Beltukov, E. Ivan’kova, E. Popova, I. Semenova, V. Yelokhovsky, and V. Yudin, “Polystyrene-based nanocomposites with different fillers: fabrication and mechanical properties,” Polymers 12, 2457 (2020).
[Crossref]

Karimzadeh, R.

M. G. Beygi, R. Karimzadeh, and M. Dashtdar, “Nonlinear refractive index measurement by Fresnel diffraction from phase object,” Opt. Laser Technol. 66, 151–155 (2015).
[Crossref]

Kartashov, Y. V.

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[Crossref]

Kauranen, M.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748 (2012).
[Crossref]

Krausz, F.

T. V. Amotchkina, M. K. Trubetskov, F. Krausz, V. Pervak, O. Pronin, L. Smalakys, A. Melninkaitis, and B. Momgaudis, “Time resolved digital holography measurements of the nonlinear optical filters,” Proc. SPIE 10447, 104470Y (2017).
[Crossref]

A. Zheltikov, A. L’auillier, and F. Krausz, “Nonlinear optics,” in Springer Handbook of Lasers and Optics (2012).

Kudriasov, V.

L’auillier, A.

A. Zheltikov, A. L’auillier, and F. Krausz, “Nonlinear optics,” in Springer Handbook of Lasers and Optics (2012).

Lee, K.-S.

J. Yao, P. Meemon, K.-S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52, 112111 (2013).
[Crossref]

Levinstein, J.

A. Ashkin, G. Boyd, J. I. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Li, Q.

S. Bai, Q. Li, H. Zhang, X. Chen, S. Luo, H. Gong, Y. Yang, D. Zhao, and M. Qiu, “Large third-order nonlinear refractive index coefficient based on gold nanoparticle aggregate films,” Appl. Phys. Lett. 107, 141111 (2015).
[Crossref]

Li, Y.

L.-S. Chen, Z.-M. Huang, G.-H. Dong, C.-L. He, L. Liu, Y.-Y. Hu, and Y. Li, “Development of a transparent PMMA composite reinforced with nanofibers,” Polym. Compos. 30, 239–247 (2009).
[Crossref]

Lin, Y.

Liu, L.

L.-S. Chen, Z.-M. Huang, G.-H. Dong, C.-L. He, L. Liu, Y.-Y. Hu, and Y. Li, “Development of a transparent PMMA composite reinforced with nanofibers,” Polym. Compos. 30, 239–247 (2009).
[Crossref]

Luo, S.

S. Bai, Q. Li, H. Zhang, X. Chen, S. Luo, H. Gong, Y. Yang, D. Zhao, and M. Qiu, “Large third-order nonlinear refractive index coefficient based on gold nanoparticle aggregate films,” Appl. Phys. Lett. 107, 141111 (2015).
[Crossref]

Mackenzie, J.

E. Pope, M. Asami, and J. Mackenzie, “Transparent silica gel–PMMA composites,” J. Mater. Res. 4, 1018–1026 (1989).
[Crossref]

Malomed, B. A.

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[Crossref]

Maslov, V.

A. Orlova, Y. A. Gromova, A. Savelyeva, V. Maslov, M. Artemyev, A. Prudnikau, A. Fedorov, and A. Baranov, “Track membranes with embedded semiconductor nanocrystals: structural and optical examinations,” Nanotechnology 22, 455201 (2011).
[Crossref]

Meemon, P.

J. Yao, P. Meemon, K.-S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52, 112111 (2013).
[Crossref]

Melninkaitis, A.

Miguez, M.

Misoguti, L.

Momgaudis, B.

Moskalyuk, O.

O. Moskalyuk, A. Belashov, Y. Beltukov, E. Ivan’kova, E. Popova, I. Semenova, V. Yelokhovsky, and V. Yudin, “Polystyrene-based nanocomposites with different fillers: fabrication and mechanical properties,” Polymers 12, 2457 (2020).
[Crossref]

Nalegaev, S.

Nalegaev, S. S.

S. S. Nalegaev, A. V. Belashov, and N. V. Petrov, “Application of photothermal digital interferometry for nonlinear refractive index measurements within a Kerr approximation,” Opt. Mater. 69, 437–443 (2017).
[Crossref]

Nassau, K.

A. Ashkin, G. Boyd, J. I. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Orlova, A.

A. Orlova, Y. A. Gromova, A. Savelyeva, V. Maslov, M. Artemyev, A. Prudnikau, A. Fedorov, and A. Baranov, “Track membranes with embedded semiconductor nanocrystals: structural and optical examinations,” Nanotechnology 22, 455201 (2011).
[Crossref]

Panov, A. V.

Pervak, V.

T. V. Amotchkina, M. K. Trubetskov, F. Krausz, V. Pervak, O. Pronin, L. Smalakys, A. Melninkaitis, and B. Momgaudis, “Time resolved digital holography measurements of the nonlinear optical filters,” Proc. SPIE 10447, 104470Y (2017).
[Crossref]

Petris, A.

Petrov, N.

Petrov, N. V.

A. V. Belashov, C.-J. Cheng, and N. V. Petrov, “Time-resolved inline digital holography for measurement of optical nonlinear properties of quantum dots on substrates,” Proc. SPIE 11278, 1127810 (2020).
[Crossref]

S. S. Nalegaev, A. V. Belashov, and N. V. Petrov, “Application of photothermal digital interferometry for nonlinear refractive index measurements within a Kerr approximation,” Opt. Mater. 69, 437–443 (2017).
[Crossref]

A. V. Belashov, C.-J. Cheng, and N. V. Petrov, “On the evaluation of nonlinear optical inhomogeneities fraction using time-resolved in-line digital holography,” Tech. Phys. Russ. J. Appl. Phys.5 (to be published).

Pope, E.

E. Pope, M. Asami, and J. Mackenzie, “Transparent silica gel–PMMA composites,” J. Mater. Res. 4, 1018–1026 (1989).
[Crossref]

Popescu, S. T.

Popova, E.

O. Moskalyuk, A. Belashov, Y. Beltukov, E. Ivan’kova, E. Popova, I. Semenova, V. Yelokhovsky, and V. Yudin, “Polystyrene-based nanocomposites with different fillers: fabrication and mechanical properties,” Polymers 12, 2457 (2020).
[Crossref]

Pronin, O.

T. V. Amotchkina, M. K. Trubetskov, F. Krausz, V. Pervak, O. Pronin, L. Smalakys, A. Melninkaitis, and B. Momgaudis, “Time resolved digital holography measurements of the nonlinear optical filters,” Proc. SPIE 10447, 104470Y (2017).
[Crossref]

Prudnikau, A.

A. Orlova, Y. A. Gromova, A. Savelyeva, V. Maslov, M. Artemyev, A. Prudnikau, A. Fedorov, and A. Baranov, “Track membranes with embedded semiconductor nanocrystals: structural and optical examinations,” Nanotechnology 22, 455201 (2011).
[Crossref]

Putilin, S.

Qiu, M.

S. Bai, Q. Li, H. Zhang, X. Chen, S. Luo, H. Gong, Y. Yang, D. Zhao, and M. Qiu, “Large third-order nonlinear refractive index coefficient based on gold nanoparticle aggregate films,” Appl. Phys. Lett. 107, 141111 (2015).
[Crossref]

Rolland, J. P.

J. Yao, P. Meemon, K.-S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52, 112111 (2013).
[Crossref]

Said, A.

M. Sheik-Bahae, A. Said, T.-H. Wei, D. Hagan, and E. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[Crossref]

Savelyeva, A.

A. Orlova, Y. A. Gromova, A. Savelyeva, V. Maslov, M. Artemyev, A. Prudnikau, A. Fedorov, and A. Baranov, “Track membranes with embedded semiconductor nanocrystals: structural and optical examinations,” Nanotechnology 22, 455201 (2011).
[Crossref]

Semenova, I.

O. Moskalyuk, A. Belashov, Y. Beltukov, E. Ivan’kova, E. Popova, I. Semenova, V. Yelokhovsky, and V. Yudin, “Polystyrene-based nanocomposites with different fillers: fabrication and mechanical properties,” Polymers 12, 2457 (2020).
[Crossref]

Sheik-Bahae, M.

M. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z scan,” Opt. Lett. 17, 258–260 (1992).
[Crossref]

M. Sheik-Bahae, A. Said, T.-H. Wei, D. Hagan, and E. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[Crossref]

Shevkunov, I.

Shih, T.-T.

Smalakys, L.

T. V. Amotchkina, M. K. Trubetskov, F. Krausz, V. Pervak, O. Pronin, L. Smalakys, A. Melninkaitis, and B. Momgaudis, “Time resolved digital holography measurements of the nonlinear optical filters,” Proc. SPIE 10447, 104470Y (2017).
[Crossref]

Smith, R.

A. Ashkin, G. Boyd, J. I. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

Sun, M.

L. Zhu, M. Sun, J. Chen, J. Yu, and C. Zhou, “Integrated digital holography for measuring the photothermal effect induced by femtosecond laser pulses,” Opt. Eng. 53, 112311 (2014).
[Crossref]

Terazima, M.

Torner, L.

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[Crossref]

Trubetskov, M. K.

T. V. Amotchkina, M. K. Trubetskov, F. Krausz, V. Pervak, O. Pronin, L. Smalakys, A. Melninkaitis, and B. Momgaudis, “Time resolved digital holography measurements of the nonlinear optical filters,” Proc. SPIE 10447, 104470Y (2017).
[Crossref]

Van Stryland, E.

M. Sheik-Bahae, A. Said, T.-H. Wei, D. Hagan, and E. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[Crossref]

Van Stryland, E. W.

Vengris, M.

Wang, J.

Wang, S.-H.

B. Guo, Q.-L. Xiao, S.-H. Wang, and H. Zhang, “2d layered materials: synthesis, nonlinear optical properties, and device applications,” Laser Photon. Rev. 13, 1800327 (2019).
[Crossref]

Wei, T.-H.

M. Sheik-Bahae, A. Said, T.-H. Wei, D. Hagan, and E. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[Crossref]

Wu, Y.-D.

Y.-D. Wu and M.-H. Cheng, “Analyzing the multilayer metamaterial waveguide structure with the Kerr-type nonlinear cladding,” Opt. Quantum Electron. 49, 181 (2017).
[Crossref]

Y.-D. Wu, T.-T. Shih, and M.-H. Chen, “New all-optical logic gates based on the local nonlinear Mach-Zehnder interferometer,” Opt. Express 16, 248–257 (2008).
[Crossref]

Xiao, Q.-L.

B. Guo, Q.-L. Xiao, S.-H. Wang, and H. Zhang, “2d layered materials: synthesis, nonlinear optical properties, and device applications,” Laser Photon. Rev. 13, 1800327 (2019).
[Crossref]

Yang, Y.

S. Bai, Q. Li, H. Zhang, X. Chen, S. Luo, H. Gong, Y. Yang, D. Zhao, and M. Qiu, “Large third-order nonlinear refractive index coefficient based on gold nanoparticle aggregate films,” Appl. Phys. Lett. 107, 141111 (2015).
[Crossref]

Yao, J.

J. Yao, P. Meemon, K.-S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52, 112111 (2013).
[Crossref]

Yelokhovsky, V.

O. Moskalyuk, A. Belashov, Y. Beltukov, E. Ivan’kova, E. Popova, I. Semenova, V. Yelokhovsky, and V. Yudin, “Polystyrene-based nanocomposites with different fillers: fabrication and mechanical properties,” Polymers 12, 2457 (2020).
[Crossref]

Yu, J.

L. Zhu, M. Sun, J. Chen, J. Yu, and C. Zhou, “Integrated digital holography for measuring the photothermal effect induced by femtosecond laser pulses,” Opt. Eng. 53, 112311 (2014).
[Crossref]

Yudin, V.

O. Moskalyuk, A. Belashov, Y. Beltukov, E. Ivan’kova, E. Popova, I. Semenova, V. Yelokhovsky, and V. Yudin, “Polystyrene-based nanocomposites with different fillers: fabrication and mechanical properties,” Polymers 12, 2457 (2020).
[Crossref]

Zayats, A. V.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748 (2012).
[Crossref]

Zhang, H.

B. Guo, Q.-L. Xiao, S.-H. Wang, and H. Zhang, “2d layered materials: synthesis, nonlinear optical properties, and device applications,” Laser Photon. Rev. 13, 1800327 (2019).
[Crossref]

S. Bai, Q. Li, H. Zhang, X. Chen, S. Luo, H. Gong, Y. Yang, D. Zhao, and M. Qiu, “Large third-order nonlinear refractive index coefficient based on gold nanoparticle aggregate films,” Appl. Phys. Lett. 107, 141111 (2015).
[Crossref]

Zhao, D.

S. Bai, Q. Li, H. Zhang, X. Chen, S. Luo, H. Gong, Y. Yang, D. Zhao, and M. Qiu, “Large third-order nonlinear refractive index coefficient based on gold nanoparticle aggregate films,” Appl. Phys. Lett. 107, 141111 (2015).
[Crossref]

Zheltikov, A.

A. Zheltikov, A. L’auillier, and F. Krausz, “Nonlinear optics,” in Springer Handbook of Lasers and Optics (2012).

Zhou, C.

L. Zhu, M. Sun, J. Chen, J. Yu, and C. Zhou, “Integrated digital holography for measuring the photothermal effect induced by femtosecond laser pulses,” Opt. Eng. 53, 112311 (2014).
[Crossref]

Zhu, L.

L. Zhu, M. Sun, J. Chen, J. Yu, and C. Zhou, “Integrated digital holography for measuring the photothermal effect induced by femtosecond laser pulses,” Opt. Eng. 53, 112311 (2014).
[Crossref]

Zilio, S. C.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. Ashkin, G. Boyd, J. I. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[Crossref]

S. Bai, Q. Li, H. Zhang, X. Chen, S. Luo, H. Gong, Y. Yang, D. Zhao, and M. Qiu, “Large third-order nonlinear refractive index coefficient based on gold nanoparticle aggregate films,” Appl. Phys. Lett. 107, 141111 (2015).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. Said, T.-H. Wei, D. Hagan, and E. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[Crossref]

J. Appl. Phys. (1)

F. Henari and A. Dakhel, “Linear and nonlinear optical properties of gold nanoparticle-eu oxide composite thin films,” J. Appl. Phys. 104, 033110 (2008).
[Crossref]

J. Mater. Res. (1)

E. Pope, M. Asami, and J. Mackenzie, “Transparent silica gel–PMMA composites,” J. Mater. Res. 4, 1018–1026 (1989).
[Crossref]

Laser Photon. Rev. (1)

B. Guo, Q.-L. Xiao, S.-H. Wang, and H. Zhang, “2d layered materials: synthesis, nonlinear optical properties, and device applications,” Laser Photon. Rev. 13, 1800327 (2019).
[Crossref]

Nanotechnology (1)

A. Orlova, Y. A. Gromova, A. Savelyeva, V. Maslov, M. Artemyev, A. Prudnikau, A. Fedorov, and A. Baranov, “Track membranes with embedded semiconductor nanocrystals: structural and optical examinations,” Nanotechnology 22, 455201 (2011).
[Crossref]

Nat. Photonics (1)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748 (2012).
[Crossref]

Opt. Eng. (2)

J. Yao, P. Meemon, K.-S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52, 112111 (2013).
[Crossref]

L. Zhu, M. Sun, J. Chen, J. Yu, and C. Zhou, “Integrated digital holography for measuring the photothermal effect induced by femtosecond laser pulses,” Opt. Eng. 53, 112311 (2014).
[Crossref]

Opt. Express (4)

Opt. Laser Technol. (1)

M. G. Beygi, R. Karimzadeh, and M. Dashtdar, “Nonlinear refractive index measurement by Fresnel diffraction from phase object,” Opt. Laser Technol. 66, 151–155 (2015).
[Crossref]

Opt. Lasers Eng. (1)

L. Bruno, “Mechanical characterization of composite materials by optical techniques: a review,” Opt. Lasers Eng. 104, 192–203 (2018).
[Crossref]

Opt. Lett. (5)

Opt. Mater. (1)

S. S. Nalegaev, A. V. Belashov, and N. V. Petrov, “Application of photothermal digital interferometry for nonlinear refractive index measurements within a Kerr approximation,” Opt. Mater. 69, 437–443 (2017).
[Crossref]

Opt. Quantum Electron. (1)

Y.-D. Wu and M.-H. Cheng, “Analyzing the multilayer metamaterial waveguide structure with the Kerr-type nonlinear cladding,” Opt. Quantum Electron. 49, 181 (2017).
[Crossref]

Polym. Compos. (1)

L.-S. Chen, Z.-M. Huang, G.-H. Dong, C.-L. He, L. Liu, Y.-Y. Hu, and Y. Li, “Development of a transparent PMMA composite reinforced with nanofibers,” Polym. Compos. 30, 239–247 (2009).
[Crossref]

Polymers (1)

O. Moskalyuk, A. Belashov, Y. Beltukov, E. Ivan’kova, E. Popova, I. Semenova, V. Yelokhovsky, and V. Yudin, “Polystyrene-based nanocomposites with different fillers: fabrication and mechanical properties,” Polymers 12, 2457 (2020).
[Crossref]

Proc. SPIE (2)

T. V. Amotchkina, M. K. Trubetskov, F. Krausz, V. Pervak, O. Pronin, L. Smalakys, A. Melninkaitis, and B. Momgaudis, “Time resolved digital holography measurements of the nonlinear optical filters,” Proc. SPIE 10447, 104470Y (2017).
[Crossref]

A. V. Belashov, C.-J. Cheng, and N. V. Petrov, “Time-resolved inline digital holography for measurement of optical nonlinear properties of quantum dots on substrates,” Proc. SPIE 11278, 1127810 (2020).
[Crossref]

Radiat. Meas. (1)

P. Apel, “Track etching technique in membrane technology,” Radiat. Meas. 34, 559–566 (2001).
[Crossref]

Rev. Mod. Phys. (1)

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[Crossref]

Other (3)

A. Zheltikov, A. L’auillier, and F. Krausz, “Nonlinear optics,” in Springer Handbook of Lasers and Optics (2012).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (2004).

A. V. Belashov, C.-J. Cheng, and N. V. Petrov, “On the evaluation of nonlinear optical inhomogeneities fraction using time-resolved in-line digital holography,” Tech. Phys. Russ. J. Appl. Phys.5 (to be published).

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Figures (5)

Fig. 1.
Fig. 1. (a) TRIDH setup; inset explains the process of NDPM inside the double-layered sample in (b) $xz$ plane; (c) example of phase distribution at the sample output plane; (d) diffraction pattern obtained at the image plane. Gray area indicates pathway of pump and probe pulses overlap area.
Fig. 2.
Fig. 2. (a) Scheme of probe pulse NDPM in the object with LINRI in $xz$ plane; examples of: (b) phase distribution at the object plane; (c) diffraction pattern obtained at the image plane.
Fig. 3.
Fig. 3. Impact of nonlinear refractive index of the second layer on (a) phase profiles and (b) diffraction patterns of the probe beam. Impact of relative thickness of the object first layer on (c) phase profiles and (d) diffraction patterns of the probe beam. Impact of various thicknesses and negative refractive indices of the first layer on (e) phase profiles and (f) diffraction patterns of the probe beam. Reference curve indicated with dotted line corresponds to a single layer sample with ${d_{{\rm ref}}} = 2.5\,{\rm mm}$ and $n_2^{{\rm ref}} = 1.27 \cdot {10^{- 13}}\;{{\rm cm}^2}/{\rm W}$.
Fig. 4.
Fig. 4. Results of numerical simulation of intensity distributions resulted from probe pulse NDPM in glass plate with embedded LINRI with different nonlinear refractive indices: (a) $n_2^{{\rm LINRI}} = 1.56 \cdot {10^{- 13}}\,{{\rm cm}^2}/{\rm W}$, (b) $n_2^{{\rm LINRI}} = 1.25 \cdot {10^{- 12}}{{\rm cm}^2}/{\rm W}$, (c) $n_2^{{\rm LINRI}} = 1 \cdot {10^{- 11}}\,{{\rm cm}^2}/{\rm W}$; and different relaxation times of induced refractive index gradient: (d) ${\tau ^{{\rm LINRI}}} = 15\;{\rm fs} $, (e) ${\tau ^{{\rm LINRI}}} = 0.54\;{\rm ps} $, (f) ${\tau ^{{\rm LINRI}}} = 3.24\;{\rm ps} $.
Fig. 5.
Fig. 5. Examples of (top) diffraction patterns and (bottom) schemes of probe pulse NDPM: (two top rows) at different depths of LINRI location inside 1-mm-thick object: (a) $h \approx 50\,\,\unicode{x00B5}{\rm m}$, (b) $h \approx 500\,\,\unicode{x00B5}{\rm m}$, (c) $h \approx 750\,\,\unicode{x00B5}{\rm m}$; and (two bottom rows) obtained for various relative positions of two LINRIs within the overlap pathway: (d) at the same and (e), (f) various $x$ coordinates, wherein two LINRIs are located (d) beside and (e), (f) far from each other, and one of the LINRIs is located slightly aside from the overlap pathway (e).

Equations (14)

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n 2 ( x , y , z ) = { n 2 , i f 0 < z < d 1 ; n 2 , i f d 1 < z < d 1 + d 2 .
n 2 ( x , y , z ) = { n 2 L I N R I , i f { z 0 < z < z 0 + d L I N R I ; ( x x 0 ) 2 + ( y y 0 ) 2 < R 2 ; n 2 m e d i a , e l s e w h e r e .
Δ n j ( x , y , z ) = Δ n j 1 ( x , y , z ) exp Δ t / τ .
I p u m p j ( x , y , z ) = I p u m p j 1 ( x + c n Δ t sin ( θ ) , y , z + c n Δ t cos ( θ ) ) .
I p u m p j = I p u m p j exp a / ( c n Δ t ) .
Δ n j ( x , y , z ) = Δ n j 1 ( x , y , z ) + I p u m p j ( x , y , z ) n 2 ( x , y , z ) .
z p r j = z p r j 1 + c n Δ t .
φ j ( x , y ) = φ j 1 ( x , y ) + 2 π c n Δ t Δ n ( x , y , z ) δ ( x , y , z z p r ) λ ,
U ( f x , f y , z = 0 ) = u ( x , y , z = 0 ) × exp ( 2 π i ( x f x + y f y ) ) d x d y .
g ( f x , f y , z ) = U ( f x , f y , z = 0 ) H ( f x , f y , Δ z ) ,
H ( f x , f y , Δ z ) = { e i 2 π n λ Δ z 1 λ 2 n 2 ( f x 2 + f y 2 ) , i f ( f x 2 + f y 2 ) n 2 λ 2 ; e 2 π n λ Δ z 1 λ 2 n 2 ( f x 2 + f y 2 ) , i f ( f x 2 + f y 2 ) > n 2 λ 2 .
u ( x , y , Δ z ) = g ( f x , f y , Δ z ) × exp ( 2 π i ( x f x + y f y ) ) d f x d f y .
H ( x , y ) = | u ( x , y , Δ z ) | 2 = | u o | 2 + | u r | 2 + u o u r + u o u r .
u o u r + u o u r = H ( 1 + | u r | 2 ) .

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