Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

Three-photon absorption in ZnO and ZnS crystals

Jun He, Yingli Qu, Heping Li, Jun Mi, and Wei Ji

Open Access Open Access

Abstract

We report a systematic investigation of both three-photon absorption (3PA) spectra and wavelength dispersions of Kerr-type nonlinear refraction in wide-gap semiconductors. The Z-scan measurements are recorded for both ZnO and ZnS with femtosecond laser pulses. While the wavelength dispersions of the Kerr nonlinearity are in agreement with a two-band model, the wavelength dependences of the 3PA are found to be given by (3E photon/Eg -1)5/2(3E photon/Eg )-9. We also evaluate higher-order nonlinear optical effects including the fifth-order instantaneous nonlinear refraction associated with virtual three-photon transitions, and effectively seventh-order nonlinear processes induced by three-photon-excited free charge carriers. These higher-order nonlinear effects are insignificant with laser excitation irradiances up to 40 GW/cm2. Both pump-probe measurements and three-photon figures of merits demonstrate that ZnO and ZnS should be a promising candidate for optical switching applications at telecommunication wavelengths.

©2005 Optical Society of America

Full Article  |  PDF Article
More Like This
Nonlinear spectra of ZnO: reverse saturable, two- and three-photon absorption

M.G. Vivas, T. Shih, T. Voss, E. Mazur, and C. R. Mendonca
Opt. Express 18(9) 9628-9633 (2010)

Three-photon absorption spectra and bandgap scaling in direct-gap semiconductors

Sepehr Benis, Claudiu M. Cirloganu, Nicholas Cox, Trenton Ensley, Honghua Hu, Gero Nootz, Peter D. Olszak, Lazaro A. Padilha, Davorin Peceli, Matthew Reichert, Scott Webster, Milton Woodall, David J. Hagan, and Eric W. Van Stryland
Optica 7(8) 888-899 (2020)

Extremely nondegenerate two-photon absorption in direct-gap semiconductors [Invited]

Claudiu M. Cirloganu, Lazaro A. Padilha, Dmitry A. Fishman, Scott Webster, David J. Hagan, and Eric W. Van Stryland
Opt. Express 19(23) 22951-22960 (2011)

View More...

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)
Fig. 1.
Fig. 1. (a) OA Z-scans measured with different excitation irradiances at a wavelength of 780 nm and a pulse repetition rate of 90 MHz. The solid and dashed lines are the fitting curves by employing the Z-scan theory, described in the text, on 3PA and 2PA respectively. (b) Plots of Ln(1-T OA) vs. Ln(I 0) at different wavelengths, the solid lines are the examples of the linear fit at 740 nm with a slope of s = 0.86 and at 840 nm with a slope of s = 1.96.

Download Full Size | PDF

Fig. 2.
Fig. 2. 3PA coefficients plotted as a function of E photon/Eg , where E photon is the photon energy and Eg is the band-gap energy. The solid stars and squares are the experimental data, while the solid and dashed lines are calculated from the theory of Brandi and de Araujo [19] and the theory of Wherrett [25], respectively. For comparison, the experimental result (the empty square) of Catalano et al. is also displayed [17].

Download Full Size | PDF

Fig. 3.
Fig. 3. (a) OA Z-scans and (b) CA Z-scans divided by OA Z-scans measured with 1-kHz repetition rate laser pulses at various excitation irradiances. The inset in (a) and (b) shows the irradiance dependence of the 3PA coefficient and the irradiance dependence of the n 2 value, respectively.

Download Full Size | PDF

Fig. 4.
Fig. 4. (a) OA Z-scan, CA Z-scan and CA Z-scan divided by OA Z-scan; and (b) Kerr-type nonlinear refraction plotted as a function of E photon/Eg . The solid scatters are the experimental data, while the solid lines are calculated from the theory of Sheik-Bahae et al. [26]. For comparison, the experimental results of Adair et al. (the empty triangles) [5], Zhang et al. (the empty square) [6], and Krauss et al. (the empty circles) [7], are also displayed.

Download Full Size | PDF

Fig. 5.
Fig. 5. Calculated nonlinear refraction n 4 plotted against E photon/Eg , for both ZnO (the dashed line) and ZnS (the solid line).

Download Full Size | PDF

Fig. 6.
Fig. 6. Calculated nonlinear refraction changes (n 2 I, n 4 I 2, σ r N e-h) vs. the irradiance for (a) ZnO and (b) ZnS; and calculated changes in nonlinear absorption (α 3 I 2, σ a N e-h) vs. the irradiance for (c) ZnO and (d) ZnS. Herein, wavelength is 780 nm, n 2 is 1.0 × 10-5 cm2/GW (0.69 × 10-5 cm2/GW), n 4 is -1.4 × 10-26 cm4/W2 (3.1 × 10-27 cm4/W2), α 3 is 0.016 cm3/GW2 (0.0021 cm3/GW2) for ZnO (ZnS) crystal, and α r = -1.1×10-21 cm3 and σ a = 6.5×10-18 cm2 are assumed for both ZnO and ZnS crystals [6].

Download Full Size | PDF

Fig. 7.
Fig. 7. Normalized OKE signal (the solid squares for ZnO) and pump-probe signals (the solid stars for ZnO and the solid circles for ZnS) measured at a wavelength of 780 nm as a function of the delay time. The experiment data were measured under the same excitation irradiance (~ 9.0 GW/cm2) with 1-kHz pulse repetition rate. The dashed line and solid lines are the 2PA and 3PA intensity autocorrelation functions of the laser pulses, respectively.

Download Full Size | PDF

Tables (1)

Tables Icon

Table 1. Measured 3PA or 2PA coefficient, Kerr-type refractive nonlinearity, and calculated nonlinear FOM for ZnO and ZnS. The relative errors are estimated as ±20%

View Table

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

d Δ ϕ dz ′ = k ∑ m = 2 n 2 m − 2 I m − 1 + kσ r N e − h
dI dz ′ = − ( α 0 + ∑ m = 2 α m I m − 1 + σ a N e − h ) I
T OA ( z ) = 1 π 1 2 q 0 ∫ − ∞ ∞ ln [ 1 + q 0 exp ( − x 2 ) ] dx
T OA ( z ) = 1 π 1 2 p 0 ∫ − ∞ ∞ ln { [ 1 + p 0 2 exp ( − 2 x 2 ) ] 1 2 + p 0 exp ( − x 2 ) } dx
T OA = ∑ m = 0 ∞ ( − 1 ) m q 0 m ( m + 1 ) 3 2
T OA = ∑ m = 1 ∞ ( − 1 ) m − 1 p 0 2 m − 2 ( 2 m − 1 ) ! ( 2 m − 1 ) 1 2
T OA = 1 − α 2 I 0 L eff 2 3 2
T OA = 1 − α 3 I 0 2 L eff ′ 3 3 2
α 3 = 3 10 2 1 2 8 π 2 ( e 2 ħc ) 3 ħ 2 P 3 n 0 3 E g 7 ( 3 E photon E g − 1 ) 1 2 ( 3 E photon − E g ) 9
α 3 = 2 9 2 3 10 π 2 5 ( e 2 ħc ) 3 ħ 2 S 3 ( 3 E photon E g − 1 ) 5 2 ( 3 E photon − E g ) 9
n 4 ω 1 ω 2 ω 3 = c π ∫ 0 ∞ α 3 ( Ω ; ω 2 , ω 3 ) Ω 2 − ω 1 2 d Ω
dN e − h dt = α 3 I 3 3 ħω − N e − h τ
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use