Analytic solutions to Z-scan characteristics of thick media with nonlinear refraction and nonlinear absorption

Zang, Wei-Ping; Tian, Jianguo; Liu, Zhibo; Zhou, Wei; Song, Feng; Zhang, Chunping

doi:10.1364/josab.21.000063

Cited by 30 publications

(34 citation statements)

References 11 publications

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“…The nonlinear absorption coefficient can be calculated by fitting the normalized transmittance curves. In Z‐scan theory, the normalized transmittance dependence of nonlinear absorption curve for a thin medium with thickness far below Rayleigh length of laser beam can be expressed as follows:

T (x) = \frac{1}{q_{0} (x, t)} ln [1 + q_{0} (x, t)]

q_{0} (x, t) = \frac{β I_{0} (t) L}{1 + x^{2}}

x = z / z_{0}

where z is the sample position along the optical axis, z 0 is the Rayleigh length of the laser beam, β is the nonlinear absorption coefficient and L is the sample's length. In our experiment, the Rayleigh length of laser beam is calculated to be 3.54 mm, which is less than the sample thickness.…”

Section: Resultsmentioning

confidence: 99%

“…In a thick media with nonlinear refraction, the effect of nonlinear refraction on nonlinear absorption must be included. Q R (t) in Equation must be replaced by the correction function, which can be expressed as follows:

C_{q} false(t false) ≅ Q_{R} false(t false) \times (1 + tanh false(l / 2 false) \times \{\frac{3 Δ φ_{r} false(t false)}{10} + \frac{{false[normalΔ φ_{r} (t) false]}^{2}}{8}\})

Therefore the corrected normalized transmittance can be expressed:

T false(x false) = \frac{1}{1 + 1 / 2 C_{q} false(t false) false[{tan}^{- 1} (x + l) - {prefixtan}^{- 1} (x) false]}

Where

Δ φ_{R} false(t false) = k Δ n_{0} false(t false) z_{0}

is related with nonlinear refraction. For thick media the normalized transmittance of nonlinear refraction can be expressed as

T = {({}, \frac{false[(x^{2} + l) + 1 false] \times false(x^{2} + 9 false)}{false[{false(x^{2} + l false)}^{2} + 9 false] \times false(x^{2} + 1 false)})}^{C_{φ} (t) (t) (/)}

…”

Section: Resultsmentioning

confidence: 99%

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Nonlinear Optical and Laser Damage Properties of KDP Crystal with Trace Impurities in Bulk

Wen

Geng

Wang

et al. 2018

Crystal Research and Technology

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Small-sized potassium dihydrogen phosphate (KDP) samples cut from the pyramid sector of a large KDP boule are observed to have different impurity content. The nonlinear absorption properties of two KDP samples containing different impurities are characterized by Z-scan technique with picosecond laser at 355 nm wavelength. Reverse saturable absorption effects are found in samples, with nonlinear absorption coefficients of 7.35 × 10 −2 cm GW −1 and 15.91 × 10 −2 cm GW −1 . The sample with more impurity contents exhibits stronger nonlinear absorption. Such behavior is considered to be a result of nonlinear energy coupling under 355 nm laser irradiation assisted by impurity defects. Nanosecond laser-induced damage test at 355 nm of the two KDP samples is further investigated. The bulk damage thresholds of the two samples are 4.7 and 0.423 J cm −2 respectively, indicating that impurity-induced nonlinear absorption might play an important role in laser-induced damage processes.

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T (x) = \frac{1}{q_{0} (x, t)} ln [1 + q_{0} (x, t)]

q_{0} (x, t) = \frac{β I_{0} (t) L}{1 + x^{2}}

x = z / z_{0}

Section: Resultsmentioning

confidence: 99%

C_{q} false(t false) ≅ Q_{R} false(t false) \times (1 + tanh false(l / 2 false) \times \{\frac{3 Δ φ_{r} false(t false)}{10} + \frac{{false[normalΔ φ_{r} (t) false]}^{2}}{8}\})

Therefore the corrected normalized transmittance can be expressed:

T false(x false) = \frac{1}{1 + 1 / 2 C_{q} false(t false) false[{tan}^{- 1} (x + l) - {prefixtan}^{- 1} (x) false]}

Where

Δ φ_{R} false(t false) = k Δ n_{0} false(t false) z_{0}

is related with nonlinear refraction. For thick media the normalized transmittance of nonlinear refraction can be expressed as

T = {({}, \frac{false[(x^{2} + l) + 1 false] \times false(x^{2} + 9 false)}{false[{false(x^{2} + l false)}^{2} + 9 false] \times false(x^{2} + 1 false)})}^{C_{φ} (t) (t) (/)}

…”

Section: Resultsmentioning

confidence: 99%

Nonlinear Optical and Laser Damage Properties of KDP Crystal with Trace Impurities in Bulk

Wen

Geng

Wang

et al. 2018

Crystal Research and Technology

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“…For example, two-photon absorption (2PA) has been reported by Zheng et al with picosecond laser radiation at 532 nm in 0.5% Mn 2+ -doped ZnS QDs [7] . Some enhancements in 2PA have been reported in ZnSe/ZnS core/shell at 806 nm and in ZnS quantum structures at 532-nm laser pulses [13,14] . However, to date, there has been no report on the measurement of NLO properties of ZnS and ZnS:Mn QDs in the ultraviolet (UV) region.…”

mentioning

confidence: 96%

“…Therefore, nonlinear refraction (NLR) should be considered in such type of thick medium, i.e., when a Gaussian beam is allowed to pass through the sample. According to the distributed lens model, the on-axis normalized open aperture (OA) transmittance (T OA ) can be written as [14] Twhere}, q 0 = β 2PA I 0 n 0 z 0 , and q 0 =2πγn 0 z 0 /λ. Here, I 0 , β 2PA , and γ are the on-axis peak irradiance at focus in W/cm 2 , the 2PA coefficient, and the NLR coefficient of the sample, respectively, and λ is the wavelength of the radiation used.…”

mentioning

confidence: 99%

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Observation of enhanced two-photon absorption in ZnS quantum dots at an ultraviolet wavelength

Kumbhakar¹,

Chattopadhyay²,

Sarkar³

et al. 2011

中国光学快报

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Two-photon absorption (2PA) in zinc sulphide (ZnS) and Mn 2+ -doped ZnS quantum dots is reported by the z-scan technique, with nanosecond pulsed laser radiation at 355 nm. The observed values of the 2PA cross section of all the samples are 10 5 times larger than that of bulk ZnS. OCIS codes: 190.0190, 160.4236, 190.4180. doi: 10.3788/COL201109.101902. Researchers have recently expanded their research interests to find highly potential multiphoton active materials [1−10] . Amongst others, zinc sulphide (ZnS) and Mn 2+ -doped ZnS (ZnS:Mn) quantum dots (QDs) have been found to be potential materials because of their visible luminescence and interesting nonlinear optical (NLO) properties [5−8,10−12] . Reports on the multiphoton absorption properties of ZnS QDs have been published previously. For example, two-photon absorption (2PA) has been reported by Zheng et al. with picosecond laser radiation at 532 nm in 0.5% Mn 2+ -doped ZnS QDs [7] . Some enhancements in 2PA have been reported in ZnSe/ZnS core/shell at 806 nm and in ZnS quantum structures at 532-nm laser pulses [13,14] . However, to date, there has been no report on the measurement of NLO properties of ZnS and ZnS:Mn QDs in the ultraviolet (UV) region. In this letter, we present our observation of 2PA in undoped ZnS and ZnS:Mn QDs at an UV wavelength of 355 nm. The obtained values of the 2PA cross section in the studied samples are ∼ 10 5 times larger than that of the available reported value of bulk ZnS [11] . The samples used in this work are freshly prepared through the chemical precipitation method [11] . The synthesized undoped ZnS and 1% and 2.5% Mn 2+ -doped ZnS samples are henceforth denoted as R I , R II , and R III , respectively, unless otherwise specified. The UV-visible absorption characteristics of the samples, as obtained from the measurement in a spectrophotometer (Hitachi U-3010), are shown in Fig. 1. An X-ray diffraction measurement of the samples ensures the average particle size (radius) to be ∼1.5 nm [10] . The experimental z-scan set-up used for the measurement of NLO properties is a standard one [2,8,15] . However, in the present experiment, the excitation source of 355-nm radiation is obtained through a third harmonic generation from a Q-switched Nd:YAG laser (10 ns, 10 Hz repetition rate). To avoid the absorption of the input beam in the lens material itself, a quartz lens with a focal length of 7.5 cm is used to focus the 355-nm radiation. The beam waist (w 0 ) and the confocal parameter (z 0 ) at the focus are 7 and 350 µm, respectively. After they are dispersed in methanol, the as-synthesized nanopowders are kept in a quartz cuvette with a path length (L) of 2 mm for the z-scan measurement, satisfying the thick sample condition (L > n 0 z 0 ) in the present experiment. Here, n 0 is the linear refractive index of the samples at a 355-nm wavelength. In Fig. 1, the values of the linear absorption coefficient (α) of R I , R II , and R III samples are 0.50, 0.33, and 0.47 cm −1 , respectively, at the excitation wavelength of 355 ...

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z-Scan characterization of zwitterionic chromophores for optoelectronic switching

et al. 2011

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Analytic solutions to Z-scan characteristics of thick media with nonlinear refraction and nonlinear absorption

Cited by 30 publications

References 11 publications

Nonlinear Optical and Laser Damage Properties of KDP Crystal with Trace Impurities in Bulk

Nonlinear Optical and Laser Damage Properties of KDP Crystal with Trace Impurities in Bulk

Observation of enhanced two-photon absorption in ZnS quantum dots at an ultraviolet wavelength

z-Scan characterization of zwitterionic chromophores for optoelectronic switching

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