Abstract

We utilize the conventional Z-scan technique to provide absolute measurements of third-order nonlinear refraction coefficients (n2) in the mid-wave infrared at 2 µm and 3.9 µm of common optical materials that have transparency windows spanning this regime. We study a variety of narrow band gap and wide band gap semiconductors, fluoride crystals (BaF2, CaF2, LiF, and MgF2) and optical glasses, and a series of chalcogenide glasses. The n2 is found to span on the order of ∼10−15 to ∼10−12 cm2/W for the semiconductors, ∼10−16 cm2/W for the fluoride crystals and glasses, and ∼10−14 to ∼10−13 cm2/W for the chalcogenides. The experimental results are compared to previous measurements of n2 conducted in the visible and near-infrared along with empirical and theoretical formulations.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (3)

2018 (1)

M. Seidel, X. Xiao, S. A. Hussain, G. Arisholm, A. Hartung, K. T. Zawilski, P. G. Schunemann, F. Habel, M. Trubetskov, V. Pervak, O. Pronin, and F. Krausz, “Multi-watt, multi-octave, mid-infrared femtosecond source,” Sci. Adv. 4(4), eaaq1526 (2018).
[Crossref]

2017 (2)

B.-U. Sohn, C. Monmeyran, L. C. Kimerling, A. M. Agarwal, and D. T. H. Tan, “Kerr nonlinearity and multi-photon absorption in germanium at mid-infrared wavelengths,” Appl. Phys. Lett. 111(9), 091902 (2017).
[Crossref]

R. Lin, F. Chen, X. Zhang, Y. Huang, B. Song, S. Dai, X. Zhang, and W. Ji, “Mid-infrared optical properties of chalcogenide glasses within tin-antimony-selenium ternary system,” Opt. Express 25(21), 25674–25688 (2017).
[Crossref]

2016 (3)

B. Qiao, F. Chen, Y. Huang, P. Zhang, S. Dai, and Q. Nie, “Investigation of mid-infrared optical nonlinearity of Ge20SnxSe80−x ternary chalcogenide glasses,” Mater. Lett. 162, 17–19 (2016).
[Crossref]

E. A. Anashkina, A. V. Andrianov, V. V. Dorofeev, and A. V. Kim, “Toward a mid-infrared femtosecond laser system with suspended-core tungstate–tellurite glass fibers,” Appl. Opt. 55(17), 4522–4530 (2016).
[Crossref]

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

2015 (3)

2014 (3)

2013 (2)

X. Gai, Y. Yu, B. Kuyken, P. Ma, S. J. Madden, J. Van Campenhout, P. Verheyen, G. Roelkens, R. Baets, and B. Luther-Davies, “Nonlinear absorption and refraction in crystalline silicon in the mid-infrared,” Laser Photonics Rev. 7(6), 1054–1064 (2013).
[Crossref]

T. Wang, N. Venkatram, J. Gosciniak, Y. Cui, G. Qian, W. Ji, and D. T. H. Tan, “Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths,” Opt. Express 21(26), 32192–32198 (2013).
[Crossref]

2012 (1)

2010 (1)

2009 (1)

J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Chalcogenide Glass-Fiber-Based Mid-IR Sources and Applications,” IEEE J. Sel. Top. Quantum Electron. 15(1), 114–119 (2009).
[Crossref]

2007 (3)

W. C. Hurlbut, Y.-S. Lee, K. L. Vodopyanov, P. S. Kuo, and M. M. Fejer, “Multiphoton absorption and nonlinear refraction of GaAs in the mid-infrared,” Opt. Lett. 32(6), 668–670 (2007).
[Crossref]

A. D. Bristow, N. Rotenberg, and H. M. v. Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[Crossref]

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[Crossref]

2005 (3)

2003 (1)

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[Crossref]

2000 (1)

1998 (1)

1996 (1)

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n/sub 2/in wide bandgap solids,” IEEE J. Quantum Electron. 32(8), 1324–1333 (1996).
[Crossref]

1994 (1)

T. D. Krauss and F. W. Wise, “Femtosecond measurement of nonlinear absorption and refraction in CdS, ZnSe, and ZnS,” Appl. Phys. Lett. 65(14), 1739–1741 (1994).
[Crossref]

1993 (1)

1992 (1)

R. Adair, L. L. Chase, and S. A. Payne, “Dispersion of the nonlinear refractive index of optical crystals,” Opt. Mater. 1(3), 185–194 (1992).
[Crossref]

1991 (3)

M. E. Lines, “OXIDE GLASSES FOR FAST PHOTONIC SWITCHING - A COMPARATIVE-STUDY,” J. Appl. Phys. 69(10), 6876–6884 (1991).
[Crossref]

H. Ma, A. S. L. Gomes, and C. B. d. Araujo, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59(21), 2666–2668 (1991).
[Crossref]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

1990 (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

1989 (2)

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39(5), 3337–3350 (1989).
[Crossref]

S. Adachi, “Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, AlxGa1−xAs, and In1−xGaxAsyP1−y,” J. Appl. Phys. 66(12), 6030–6040 (1989).
[Crossref]

1987 (1)

1985 (1)

1984 (2)

M. Debenham, “Refractive indices of zinc sulfide in the 0.405–13-µm wavelength range,” Appl. Opt. 23(14), 2238–2239 (1984).
[Crossref]

M. E. Lines, “Scattering losses in optic fiber materials. I. A new parametrization,” J. Appl. Phys. 55(11), 4052–4057 (1984).
[Crossref]

1980 (2)

H. H. Li, “Refractive index of alkaline earth halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(1), 161–290 (1980).
[Crossref]

D. Depatie and D. Haueisen, “Multiline phase conjugation at 4 µm in germanium,” Opt. Lett. 5(6), 252–254 (1980).
[Crossref]

1978 (1)

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting non-linear refractive-index changes in optical solids,” IEEE J. Quantum Electron. 14(8), 601–608 (1978).
[Crossref]

1977 (1)

D. Milam, M. J. Weber, and A. J. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31(12), 822–825 (1977).
[Crossref]

1976 (2)

H. H. Li, “Refractive index of alkali halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 5(2), 329–528 (1976).
[Crossref]

D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: Application to optical materials for high-power neodymium lasers,” J. Appl. Phys. 47(6), 2497–2501 (1976).
[Crossref]

1974 (1)

M. Levenson, “Feasibility of measuring the nonlinear index of refraction by third-order frequency mixing,” IEEE J. Quantum Electron. 10(2), 110–115 (1974).
[Crossref]

1965 (1)

Abouraddy, A. F.

Adachi, S.

S. Adachi, “Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, AlxGa1−xAs, and In1−xGaxAsyP1−y,” J. Appl. Phys. 66(12), 6030–6040 (1989).
[Crossref]

Adair, R.

R. Adair, L. L. Chase, and S. A. Payne, “Dispersion of the nonlinear refractive index of optical crystals,” Opt. Mater. 1(3), 185–194 (1992).
[Crossref]

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39(5), 3337–3350 (1989).
[Crossref]

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive-index measurements of glasses using three-wave frequency mixing,” J. Opt. Soc. Am. B 4(6), 875–881 (1987).
[Crossref]

Agarwal, A. M.

B.-U. Sohn, C. Monmeyran, L. C. Kimerling, A. M. Agarwal, and D. T. H. Tan, “Kerr nonlinearity and multi-photon absorption in germanium at mid-infrared wavelengths,” Appl. Phys. Lett. 111(9), 091902 (2017).
[Crossref]

Aggarwal, I. D.

J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Chalcogenide Glass-Fiber-Based Mid-IR Sources and Applications,” IEEE J. Sel. Top. Quantum Electron. 15(1), 114–119 (2009).
[Crossref]

G. Lenz, J. Zimmermann, T. Katsufuji, M. E. Lines, H. Y. Hwang, S. Spalter, R. E. Slusher, S. W. Cheong, J. S. Sanghera, and I. D. Aggarwal, “Large Kerr effect in bulk Se-based chalcogenide glasses,” Opt. Lett. 25(4), 254–256 (2000).
[Crossref]

Agrawal, G. P.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[Crossref]

Agrell, E.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Albrow-Owen, T.

Allen, T.

J. M. Hales, S.-H. Chi, T. Allen, S. Benis, N. Munera, J. W. Perry, D. McMorrow, D. J. Hagan, and E. W. Van Stryland, “Third-Order Nonlinear Optical Coefficients of Si and GaAs in the Near-Infrared Spectral Region,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), JTu2A.59.

Anashkina, E. A.

Andrianov, A. V.

Arisholm, G.

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Figures (6)

Fig. 1.
Fig. 1. Schematic of Z-scan experiment. “CM” stands for concave mirror, “SF” for spatial filter, “50/50” for a 50/50 beamsplitter, “Ir” for iris diaphragm used as the aperture for the closed aperture (CA) detector, “OA” for open-aperture detector, and “Ref” for the reference detector.
Fig. 2.
Fig. 2. Linear transmission from 300 nm to 20 $\upmu \textrm{m}$ for the measured (a) semiconductors, (b) glasses and fluoride crystals, and (c) chalcogenide glasses. The legend in (a) is as follows: ZnS/Cleartran (black), ZnSe (red), GaAs (green), InP (blue), Si (orange), Ge (magenta), and GaSb (dark yellow). Fresnel reflections are included in the spectra.
Fig. 3.
Fig. 3. (a) CA Z-scans of ZnS/Cleartran at 3.9 $\upmu \textrm{m}$. The energies of 46 nJ, 94 nJ, 190 nJ, and 382 nJ correspond to peak irradiances of 3.9, 8.0, 16, and 32 GW/cm2, respectively. (b) Theoretical prediction (solid black line) of the ${n_2}$ dispersion of ZnS plotted with experimental data. The experimental data is taken from Ref. [15] for the black circles, Ref. [16] for the green top-pointing triangles, Ref. [13] for the cyan bottom-pointing triangle, Ref. [17] for the blue diamonds, and Ref. [18] for the dark blue left-pointing triangle. The theoretical curve is calculated from Ref. [13]. The red squares are measurements from this work.
Fig. 4.
Fig. 4. Log-linear plot of the theoretical ${n_2}$ dispersion of ZnSe (solid black line), GaAs (solid red line), InP (solid blue line), and GaSb (solid green line) calculated from Ref. [13]. Experimental results obtained via Z-scans at $2 \,\upmu \textrm{m}$ and 3.9 $\upmu \textrm{m}$ from this work are shown as solid squares for each respective sample. The open red circles are experimental data from Ref. [21] and open red triangles from Ref. [22] of GaAs and open black circles from Ref. [23] of ZnSe. The data point at 3.9 $\upmu \textrm{m}$ of ZnSe is a previously published result from Ref. [24]. The inset shows a linear plot of the ${n_2}$ dispersion of GaSb along with the experimental data point at $2 \,\upmu \textrm{m}$ with the horizontal axis expanded having the same horizontal and vertical axes titles as the main figure. The dashed line in the inset represents ${n_2} = 0$.
Fig. 5.
Fig. 5. CA Z-scans of (a) CaF2 and (b) MgF2 at $2 \,\upmu \textrm{m}$. The input energies of 383 nJ, 749 nJ, and 1.19 $\upmu$J correspond to incident peak irradiances of 260 GW/cm2, 520 GW/cm2, and 820 GW/cm2, respectively. The open symbols represent the data and the solid lines represent fits to the data.
Fig. 6.
Fig. 6. CA Z-scans of (a) AMTIR-1 and (b) AMTIR-5 at 3.9 $\upmu \textrm{m}$. The input energies of 10 nJ, 20 nJ, and 40 nJ correspond to incident peak irradiances of 0.98 GW/cm2, 2.0 GW/cm2, and 3.9 GW/cm2, respectively. The open symbols represent the data and the solid lines represent fits to the data.

Tables (3)

Tables Icon

Table 1. n 2 coefficients of the studied semiconductors. Note that the value of ZnSe at 3.9 µ m is a previously published value from Ref. [24]. The direct and indirect band gap energies are taken from Ref. [19]. The error associated with the measurements at 2 µ m and 3.9 µ m are ± 20% and ± 25 %, respectively.

Tables Icon

Table 2. n 2 values of the studied fluoride crystals and glasses at 800 nm and 2 µ m along with previously published literature values at 532 nm and 1.06 µ m of the fluoride crystals and glasses. The error associated with the measurements at 800 nm and 2 µ m are ± 15% and ± 20 %, respectively. The literature values are as follows: aRef. [11], bRef. [37], cRef. [36], dRef. [38], eRef. [39], fRef. [40], gRef. [41], hRef. [18], iRef. [42], jRef. [43], kRef. [44], lRef. [45], and mRef. [46]. The (+), (#), and (*) denote measurements at 525 nm, 810 nm, and 1.03 µ m , respectively.

Tables Icon

Table 3. n 2 coefficients of the selected chalcogenide glasses. The error associated with the measurements at 2 µ m and 3.9 µ m are ± 20% and ± 25 %, respectively.

Equations (2)

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n 2 ( esu ) = 68 ( n d 1 ) ( n d 2 + 2 ) 2 ν d ( 1.517 + ( n d 2 + 2 ) ( n d + 1 ) 6 n d ν d ) 1 / 2 10 13
n 2 ( c m 2 / W ) = 3.4 ( n 0 2 + 2 ) 3 ( n 0 2 1 ) d 2 n 0 2 E s 2 10 16

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