Nonlinear optical characteristics of an ADP crystal grown in a defined direction

Yafei Lian; Jibin Wen; Fang Wang; Tingting Sui; Jin Huang; Xun Sun; Xiaodong Jiang

doi:10.1364/OME.8.002614

1. Introduction

Ammonium dihydrogen phosphate (NH₄H₂PO4, ADP) crystal is a typical isomorph of potassium dihydrogen phosphate (KH₂PO₄, KDP) crystal, which is the only nonlinear optical material used in inertial confinement fusion (ICF) engineering [1–5]. And owing to its large nonlinear optical (NLO) coefficient, high transmittance and high laser damage threshold (LDT), ADP crystal has various applications as a piezo-electric material, as a monochromator for X-ray fluorescence analysis and as a frequency conversion media of Nd-laser radiation by third or fourth harmonic generation [1, 2]. However, laser induced damage always appears as the high power laser especially in the UV region irradiating the optical media, and is always considered to be induced by the nonlinear effects such as self-induced phase modulation, self-focusing and multi-photon absorption [6]. As reported, the absorption for 1 cm length KDP crystal at 355 nm increases from 4.4% to 6.3% when energy density increases from 0.1 J/cm² to 3 J/cm² [7]. Besides, distinct steps were observed in the laser induced damage threshold (LDT) of DKDP at photon energies of 2.55eV or 3.9eV associated with the multi-photon absorption [8].

As the typical isomorphs of KDP crystals, ADP crystals show similar properties such as the crystal structures and their growth regulation [9–11]. ADP crystals grown in defined crystallographic direction (θ = 90°, φ = 45°) [12–14] can on one hand improve the morphology of ADP crystal with the growth in direction of fourth harmonic generation to the greatest extent, and thus we can obtain ample size and enhance the utilization rate of crystals; On the other hand, it may impede the expansion of the dislocations originating from the seed, decrease the dislocation density and improve the quality of ADP crystals. Due to the simplicity and accuracy, Z-scan technique is popular to gauge the nonlinear refraction and nonlinear absorption [15, 16]. However, beam propagation in thick (L>z₀, z₀ is the Raleigh length) nonlinear media is usually complicated, with for example some coupling effects. As the media of the ADP crystals or (D) KDP crystals utilizing in the super projects or the high power laser systems is thick [17], it is of great significance to directly investigate the nonlinear optical characters of the thick crystal samples. In the early works, absolute measurements of two-photon absorption (2PA) coefficients were presented by John Reintjes and Robert C. Eckardt and the value of β = 11 ± 3 × 10⁻¹¹cm/W at 266.1nm for ADP and 2.7 ± 0.7 × 10⁻¹¹cm/W for KD*P were determined [18]. And the NLA properties of 66% deuterated DKDP crystal about 10mm at 263 nm and 351 nm were investigated and the results indicate that the nonlinear absorption in E⊥Z geometry is stronger than that in E∥Z geometry [19]. However, little work has been done on the NLA properties of thick ADP crystals.

In our work, thick (10 mm) samples in the crystal directions of Z, X(ab) and the non-critical phase matching angle (θ = 90°,φ = 45°) namely type-I (ooe) noncritical phase matching with the direction at 90° to the crystal Z axis (θ = 90°) and at 45° to the crystal X axis (Φ = 45°) were gained from high-quality ADP crystals grown in Z direction and in defined crystallographic direction (θ = 90°, φ = 45°) belonging to [110] via the rapid growth method. Z-scan measurements with Pico-second pulse laser irradiation at λ = 355nm were implemented to systematically investigate their nonlinear characters such as the nonlinear absorption coefficient β, nonlinear refractive index n₂ and the third order nonlinear susceptibility χ⁽³⁾. The results displayed the nonlinear absorption and nonlinear refraction, and the ADP crystals exhibit the reverse saturable absorption and self-focusing effect. And the nonlinear absorption and refraction were anisotropic in the crystal directions of Z, X, and the non-critical phase matching angle (θ = 90°, φ = 45°). The investigations can contribute to elucidate the nonlinear optical characters and the laser induced damage properties of ADP crystals.

2. Experiments

2.1. Sample preparations

The ADP crystals grown in Z direction and in (θ = 90°, φ = 45°) direction ([110]) were prepared from aqueous solution via the point-seed rapid growth method by temperature reduction [9, 13]. And the detailed growth procedures of the two kinds of ADP crystals grown in the same conditions such as the growth temperature interval, supersaturation and the growth velocity et al. were listed in our early works [9, 13]. In addition, the samples tested in our experiments were cut from the as-grown crystals in the directions of Z, X and (θ = 90°,φ = 45°) and were processed and polished to a size of 40mm × 40mm × 10mm as shown in Fig. 1.

Fig. 1 Schematic of samples cut along the direction of (a) Z (sample Z-Z and D-Z), a (sample Z-X and D-X, and (b) (θ = 90°, φ = 45°) (sample Z-[110] and D-[110]).

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2.2. Transmittance

The samples were tested by Hitachi U-3500 spectrograph with a test band of 200–2000 nm at room temperature. And the linear absorption coefficient α can be calculated via the transmittance spectrum according to Ref. [19].

2.3. Z-scan measurements

A picosecond Nd:YAG Gaussian laser with 30ps pulse length and 10Hz pulse repetition rate was utilized in our experiments as shown in Fig. 2. A 355nm laser beam travels along the axis of the experimental set-up and is divided into two beams by the splitter. One beam is detected by the energy meter E₁, and the other one goes through the tested samples and then caught by the energy meter E₂. Additionally, E₂/E₁ is attached to the normalized transmittance to fit the curves and calculate the nonlinear optical parameters. Open-aperture scheme allowed determining the sign and the magnitude of nonlinear absorption coefficient. And the aperture was closed for the measurements of nonlinear refractive index.

Fig. 2 Schematic diagram of experimental set-up for Z-scan measurements.

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2.3. Theories for thick media

For the materials with nonlinear absorption, the absorption coefficient can be expressed by [2, 20]:

α (I) = α + β I + γ I^{2} + \cdot \cdot \cdot \cdot \cdot \cdot

where α is the linear absorption coefficient, β and γ the nonlinear absorption coefficient and I the laser energy intensity.

As a Gaussian beam irradiate a thin nonlinear medium with a small on-axis phase shift, the normalized transmittance of a closed aperture can be written as [21, 22]:

T = 1 + \frac{4 Δ φ_{0} (t) x}{(x^{2} + 1) (x^{2} + 9)} + O [Δ φ_{0} {(t)}^{2}]

where

Δ φ_{0} (t) = k Δ n_{0} (t) L_{e f f}

is the on-axis nonlinear phase shift at focus,

L_{e f f} = (1 - e^{- α L}) / α

is the effective sample thickness, and

x = z / z_{0}

.

z_{0} = π ω_{0}^{2} / λ

is the Rayleigh length of the laser beam, where ω₀ is the waist radius and λ represents the wavelength of the light beam.

A thick nonlinear medium could be acted as a stack of thin medium slices, applying a distributed lens model, and the high power laser beam transmits through each thin medium slice sequentially. If the coupling of nonlinearities between slices can be neglected, the normalized transmittance of a thick nonlinear medium can be expressed as [21, 22]:

T = \prod_{i = 1}^{n} [1 + \frac{4 Δ φ_{0 i} x_{i}}{(x_{i}^{2} + 1) (x_{i}^{2} + 9)}] ≅ \exp [\sum_{i = 1}^{n} \frac{4 Δ φ_{0 i} x_{i}}{(x_{i}^{2} + 1) (x_{i}^{2} + 9)}]

where

x_{i} = z_{i} / z_{0}

,

Δ φ_{0 i} (t) = k Δ n_{0} (t) = Δ φ_{R} (t) Δ x_{i}

and

Δ φ_{R} (t) = k Δ n_{0} (t) z_{0}

. z_i, and L_i are the position and the length of the ith thin medium, respectively. And then it can be calculated as [21, 22]:

T = {\frac{[{(x + l)}^{2} + 1] \times (x^{2} + 9)}{[{(x + l)}^{2} + 9] \times (x^{2} + 1)}}^{Δ φ_{R} (t) / 4}

Where l = L/z₀, L is the length of the medium.

In the high power laser system, a correction function $C_{φ} [Δ φ_{R} (t), x, l]$ must be substituted for $Δ φ_{R} (t)$ in Eq. (4) as the coupling effect between the slices is considered. The correction function $C_{φ} [Δ φ_{R} (t), x, l]$ can be simplified to $C_{φ} [Δ φ_{R} (t), l]$ seeing that the magnitude of nonlinear refraction weakly influences the positions of the peak and valley of the normalized transmittance. In addition, previous numerical simulations [23–25] evince that the coupling of nonlinear refraction with medium length is weak, thus $C_{φ} [Δ φ_{R} (t), x, l]$ can be expressed as the sum of $Δ φ_{R} (t)$ and the product of the functions of nonlinear refraction and of the medium length. Therefore, the correction function can be expressed as [21]:

C_{φ} (t) ≅ Δ φ_{R} (t) + \tan h (l / 3) \times ⌊ {[Δ φ_{R} (t)]}^{2} / 4 + {[Δ φ_{R} (t)]}^{3} / 16 ⌋

As a result, the corrected normalized transmittance can be written as [21]:

T = {\frac{[{(x + l)}^{2} + 1] \times (x^{2} + 9)}{[{(x + l)}^{2} + 9] \times (x^{2} + 1)}}^{C_{φ} (t) / 4}

The normalized transmittance of a thin medium in the open aperture Z-scan measurements with respect to the nonlinear absorption such as the two-photon absorption (2PA) can be obtained as [26]:

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

where

q_{0} (x, t) = q_{0} (t) / (1 + x^{2})

,

q_{0} (t) = β I_{0} (t) L = Q_{R} (t) l

and

Q_{R} (t) l = β I_{0} (t) z_{0}

, β is the 2PA coefficient.

In like manner of the nonlinear refraction in thick media, the normalized transmittance in open aperture for a thick medium by utilizing the distributed lens model and neglecting the effect of nonlinear refraction can be calculated as [21]:

T = \prod_{i = 1}^{n} {\frac{1}{q_{0 i} (x_{i}, t)} \ln [1 + q_{0 i} (x_{i}, t)]} ≅ 1 - \frac{1}{2} \sum_{i = 1}^{n} q_{0 i} (x, t) + {[\frac{1}{2} \sum_{i = 1}^{n} q_{0 i} (x, t)]}^{2} + O {{[\frac{1}{2} \sum_{i = 1}^{n} q_{0 i} (x, t)]}^{3}}

The summation can be transformed to the integral. Then substituting $q_{0} (x, t)$ into Eq. (8), the integral can be finished as follows [21, 27]:

T' = \frac{1}{1 + \frac{1}{2} \sum_{i = 1}^{n} q_{0 i} (x', t)} = \frac{1}{1 + \frac{1}{2} \int_{x}^{x + l'} q_{0} (x', t) d x'} = \frac{1}{1 + \frac{1}{2} Q_{R} (t) [\tan^{- 1} (x + l) - \tan^{- 1} (x)]}

In the high power laser system, the correction function $C_{q} [Δ Q_{R} (t), x, l]$ should be included as the effect of nonlinear refraction on the nonlinear absorption for a thick medium is in consideration. The correction function $C_{q} [Δ Q_{R} (t), x, l]$ can be simplified to $C_{q} [Δ Q_{R} (t), l]$ owing that the magnitude of nonlinear absorption weakly and slowly affects the positions of the valley of the normalized transmittance. And as given in Ref 21, the correction function is shown below:

C_{q} (t) ≅ Q_{R} (t) \times (1 + \tan h (l / 2) \times {3 Δ φ_{R} (t) / 10 + {[Δ φ_{R} (t)]}^{2} / 8})

Therefore, the corrected normalized transmittance can be written as [21]:

T' = \frac{1}{1 + \frac{1}{2} C_{q} (t) [\tan^{- 1} (x + l) - \tan^{- 1} (x)]}

The third-order nonlinear processes are connected with nonlinear light absorption and nonlinear refractive index change in a strong electromagnetic field [2, 20]:

χ^{(3)} = χ_{R}^{(3)} + i χ_{I}^{(3)}

where

χ^{(3)}

is the third-order nonlinear susceptibility,

χ_{R}^{(3)}

is the real part of

χ^{(3)}

related to the nonlinear refractive index and

χ_{I}^{(3)}

is the imaginary part concerned with the nonlinear absorption coefficient:

χ_{R}^{(3)} (e s u) = c n_{0}^{2} n_{2} / 120 π^{2} (m^{2} / W)

χ_{I}^{(3)} (e s u) = c^{2} n_{0}^{2} β / 240 π^{2} ω (m / W)

Where c is the speed of light in a vacuum and n₀ represents the linear refractive index.

3. Experiments

3.1. Transmittance spectrum

The transmittance spectra of the ADP samples are listed in Fig. 3. And as seen in the figure, the transmission spectra of the samples along the same direction cut from the ADP crystals grown in Z or defined direction practically coincide on the wavelengths from 200nm to 2000 nm. All the transmittance spectrum show high transmittance from 400nm to 1000nm, indicating that none macro defects exist in all the samples and the samples were well processed and polished. In the near infrared region (IR), two absorption peaks around 1069nm and 1297nm exist, which are multiple frequency peaks and caused by the vibration of the N-H group [28, 29]. The transmittances show a sharp decline in the UV band in the transmittance spectra of sample Z-X, D-X, Z-Z and D-Z. This phenomenon evinces the quality of sample Z-X, D-X, Z-Z and D-Z native to the prismatic sector are weaker than that of sample Z-[110] and D-[110] belong to the pyramidal sector, mainly owing to the absorption of the impurities i.e. Fe³⁺, Cr³⁺ et al and instinct defects (hydrogen, vacany and interstitial oxygen et al.) [30–32] containing in the prismatic sector of ADP crystals.

Fig. 3 Transmittance spectra of the ADP samples.

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3.2. Nonlinear absorption

The results of open aperture Z-scan measurements are attached to the nonlinear absorption coefficient α and are revealed in Fig. 4. Figure 4(a) and Fig. 4(b) illustrate the nonlinear absorption (NLA) of samples grown in Z direction and in defined direction, respectively. The points are the experimental data and the solid lines are the fitted curves. Compared with the results of thin ADP samples via open aperture Z-scan testing, the valley budges away from z = 0. In the figures, the reverse saturable absorption is obviously observed in all ADP samples. The diffraction length z0 of focused beam at 355nm is about 3.54mm.

Fig. 4 Open-aperture Z-scan measurements results of ADP samples at 355nm. (a) and (b) illustrate the NLA of samples grown in Z direction and in defined direction, respectively.

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3.3. Nonlinear refraction

The results of closed aperture Z-scan measurements are in reference to the nonlinear refractive index n₂ and are exhibited in Fig. 5. And the nonlinear refraction of samples grown in Z direction and in defined direction is shown in Fig. 5(a)-5(c) and Fig. 5(d)-5(f), respectively. The points are the experimental data and the solid lines are the fitted curves. Compared with the results of thin ADP samples via closed aperture Z-scan testing, the valley budges away from z = 0. From the valley-peak configurations indicate that nonlinear refractive index of ADP crystals is positive and the self-focusing effect appears as the high power laser irradiating [33].

Fig. 5 Closed-aperture Z-scan measurements results of ADP samples at 355nm. (a)-(e) illustrate the nonlinear refraction of the samples Z-Z, Z-X, Z-[110], D-Z, D-X and D-[110].

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3.4. Discussions

As shown in Fig. 4 and Fig. 5, the normalized transmittance versus the distance to the focal point are in presentation to calculate the nonlinear absorption coefficient and nonlinear refractive index. The nonlinear absorption is associated with the nonlinear refraction via the correction function and phase shift. Based on the Eq. (6), $C_{R} (t)$ could be calculated. And substituting $C_{R} (t)$ into Eq. (5), $Δ φ_{R} (t)$ is obtained. Then the nonlinear refractive index n₂ can be gained via $Δ φ_{R} (t) = k Δ n_{0} (t) z_{0}$ . Besides, based on Eq. (11) and substituting $Δ φ_{R} (t)$ into Eq. (10), the $Q_{R} (t)$ can be calculated. And the nonlinear absorption coefficient β can be derived from $Q_{R} (t) l = β I_{0} (t) z_{0}$ . What is more, on the strength of Eq. (12)-(14), the third order susceptibility with its imaginary part and real part is calculated. The detailed parameters and computed results are listed in Table 1. Generally speaking, as L>z₀, a nonlinear medium could be acted as a stack of thin medium slices, applying a distributed lens model, and the high power laser beam transmits through each thin medium slice sequentially. As the coupling of nonlinearities between slices cannot be neglected, the third-order nonlinearities of thick medium may be larger than those of thin medium.

Table 1. The detailed parameters and computed results of the nonlinear absorption and nonlinear refraction.

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According to Fig. 4 and 5 and Table 1, the nonlinear absorption coefficient β, the nonlinear refractive index n₂ and the third order susceptibility χ⁽³⁾ are anisotropic along the crystallographic orientations such as Z, X and (θ = 90°, φ = 45°)([110]) in our experiments. The parameters along different directions are sorted as [110] < X < Z. and those of ADP crystals grown in defined direction are slightly smaller than those of ADP crystals grown in defined direction. ADP crystal belongs to the $\bar{4} 2 m$ symmetry and in dispersionless approximation its third-order Kerr nonlinearities have four independent components: χ_xxxx, χ_xxyy, χ_yyzz and χ_zzzz. For extraordinary wave directed at θ and ϕ angles to the crystal axes, the Kerr nonlinearity of the crystal possessing of $\bar{4} 2 m$ symmetry can be expressed via these components as follows [34, 35]:

χ_{k}^{(3)} = \frac{1}{4} [3 (χ_{x x x x} + χ_{x x y y}) + (χ_{x x x x} - χ_{x x y y}) \cos 4 φ] \cos^{4} θ + \frac{3}{2} χ_{y y z z} \sin^{2} 2 θ + χ_{z z z z} \sin^{4} θ

Based on some early works [34], the value of the nonlinearities for all polarized wave components is decreased in angular range from 0 up to 45 degrees and is increased in the ϕ range from 45 up to 90 degrees with growth of ϕ angle, in the case of |χ_xxyy|<<|χ_xxxx|. In the case |χ_yyzz|<<|χ_zzzz|, |χ_xxxx|, the growth of θ must decrease the value of the nonlinearity for e-polarized wave component in angular range closed to 0 degree and increase it in the θ range closed to 90 degree. And the relation of χ_zzzz: χ_xxxx is equal to about 0.6:1 [34]. Therefore, substituting the θ and ϕ into Eq. (13), the χ ⁽³⁾ can be calculated and sorted by [110] < X < Z.

In our early work [13], the six ADP samples were investigated by the laser induced damage experiments and their laser induced damage threshold (LDT) in the manners of R-on-1 and 1-on-1 were obtained. The LDTs by 1-on-1 testing of ADP crystals grown in Z direction and grown in defined direction are listed in Table 2. And the LDT of the samples are greater than 11.5 J/cm² as the limitation of the quality of the front surface. As seen in Table 2, the LDTs of ADP grown in Z or defined direction along different crystal orientations are Z < X < [110] in numerical value. And the total LDT of ADP grown in defined direction is larger than that of ADP grown in Z direction. The quality of ADP grown in defined direction is better than that of ADP grown in Z direction, which is associated with the formation and distributions of dislocations in the two kinds of ADP crystals. In distinction from the seed of Z-cut, similar essential defects are not present at the crystal growing process on the orientation plate at the regeneration area and during the poly-sectorial crystal growth growing on the orientation (θ = 90º, Φ = 45º) plate as shown in Ref. [13].

Table 2. the LDTs of ADP crystals grown in Z direction and grown in defined direction via 1-on-1 method (J/cm²) [13].

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During the process of lase induced damage of DKDP crystals, one classical model is the defect assisted multistep/photon mechanism [8]. In this mechanism, the atoms in the crystal lattice may absorb the photons as high power laser irradiating, altering the energy level and rendering the electrons breaking away from the pinion of the atomic nucleus. Besides, the cross section for multiphoton absorption is altered by the defect states in the gap, changing the process into a series of reduced order absorptions [8, 36]. And multi-photons cross sections for two, third, and fourth order absorption in wide band gap materials are on the order of 10⁻⁵⁰ cm⁴•s, 10⁻⁸¹ cm⁶•s², and 10⁻¹¹⁴ cm⁸•s³, respectively [37–39]. The photon energy at 355 nm is about 3.49 eV and the band gap Eg of ADP crystal is about 6.96 eV at room temperature [40]. That is to say 2PA and 3PA may coexist during the nonlinear optical process of ADP crystals in theory. However, some impurities may are absorbed into the crystal lattice during the growth process of ADP crystals which are typical isomorph of DKDP crystals, giving rise to the appearance of defect energy level which displays lower than the intrinsic band gap. And the 3PA process may not appear as the high power laser irradiating. Therefore, the 2PA come up predominantly in NLA of thick ADP crystals at 355nm, while the appearance probability of 3PA is rather low. And the 3PA process may appear as the high power laser irradiating. Therefore, the 2PA and 3PA come up simultaneously in NLA of thick ADP crystals at 355nm, while 2PA is predominant.

In addition, the third order nonlinearity of the six samples in our experiments is marshaled as: [110] < X < Z, in contrast with the laws of LDT tested as: Z < X < [110]. Besides, the nonlinear absorption coefficient β, the nonlinear refractive index n₂ and the third order susceptibility χ⁽³⁾ of ADP grown in defined are greater than those of ADP grown in Z direction. As literatures pointed out, the laser irradiation direction and polarization make a difference upon the damage threshold of (D) ADP and (D) KDP crystal [41–43]. Generally, the damage anisotropy is ascribed to the variation of mechanical strength on crystal directions [43] and the localized damage initiation in KDP-family crystals involves multi photon absorption assisted by the presence of clusters of intrinsic defects [8]. Additionally, anisotropy of NLA of ADP crystals is closely bound up with the damage anisotropy in our experiments. Besides, weaker NLA coefficient, nonlinear refractive index and third order susceptibility corresponds to greater LDT, and the nonlinearities and LDT possess the same anisotropy. Accordingly, the variation of mechanical strength on crystal directions is associated with the LDT and the LDT is connected with the nonlinearities. Thus we suspect the variation of mechanical strength on crystal directions may be responsible for the anisotropy of nonlinearities of ADP crystals irradiated by high power laser. However, the quantitative relation between the NLA and the damage threshold and between the nonlinearities and the variation of mechanical strength need to be investigated further.

4. Conclusions

In conclusion, thick samples in the crystal directions of Z, X(ab) and the non-critical phase matching angle (θ = 90°,φ = 45°) ([110]) were investigated via the Z-scan measurements with Pico-second pulse laser irradiation at λ = 355nm. The nonlinear absorption coefficient β, nonlinear refractive index n₂ and the third order nonlinear susceptibility χ ⁽³⁾ were calculated and sorted by operating theoretical fits of the theories for thick medium to the experimental data as: [110] < X < Z. What is more, the optical characteristics of ADP crystals grown in defined direction are analogous to those of ADP grown in Z direction, while the nonlinear optical coefficients of D-grown ADP are inferior to those of Z-grown ADP crystals. The third order nonlinear optics exhibit the lowest along [110], while in this direction, the LDTs are utmost and the utilization ratio increases greatly, to realize the I-type non-critical phase matching. Thus, it is of great significance to be applied as a frequency conversion media in the high power laser systems. The remarkable NLA behaviors at 355 nm are identified to the co-existing of 2PA and 3PA, while 2PA is in dominant and the occurrence probability of 3PA is rather low. Anisotropy of NLA of ADP crystals grown in Z and defined directions is closely bound up with the damage anisotropy in our experiments. Besides, weaker NLA coefficient, nonlinear refractive index and third order susceptibility corresponds to greater LDT, and the nonlinearities and LDT possess the same anisotropy. And the variation of mechanical strength on crystal directions may be responsible for the anisotropy of nonlinearities of ADP crystals irradiated by high power laser, which need to be investigated further. We believe that our results will help in elucidating the influence of NLA on the frequency conversion and understanding the LDT mechanism of ADP crystals.

Funding

National Natural Science Foundation of China (Grants No. 51323002, 51402173 and 11704352), the Ministry of Education (Grant No. 625010360).

References and links

1. L. N. Rashkovich, KDP-Family Single Crystal (IOP Publishing Ltd, 1991).

2. D. N. Nikogosyan, Nonlinear Optical Crystals: A Complete Survey (Springer, 2001.

3. N. Zaitseva and L. Carman, “Rapid growth of KDP-type crystals,” Prog: Cryst. Growth Charact. 43(1), 1–118 (2001).

4. N. P. Zaitseva, J. J. De Yoreo, M. R. Dehaven, R. L. Vital, K. E. Montgomery, M. Richardson, and L. J. Atherton, “Rapid growth of large-scale (40–55 cm) KH₂PO₄ crystals,” J. Cryst. Growth 180(2), 255–262 (1997). [CrossRef]

5. S. Ji, B. Teng, W. Kong, D. Zhong, X. Sun, and Z. Wang, “The effect of supersaturation levels on the segregation coefficient of deuterium in K(H_1−xD_x)₂PO₄ crystals using Raman spectroscopy,” CrystEngComm 18(6), 971–976 (2016). [CrossRef]

6. S. C. Jones, Peter Braunlich, R. T Casper, and Xiao-An Shen, “Recent progress on laser-induced modifications and intrinsic bulk damage of wide-gap optical materials,” Opt. Eng. 28(10), 1039–1068 (1989).

7. A. Melninkaitis, M. Šinkevičius, T. Lipinskas, N. Slavinskis, V. Sirutkaitis, H. Bercegol, and L. Lamaignère, “Characterization of the KDP crystals used in large aperture doublers and triplers,” SPIE 5647, 298–305 (2004).

8. C. W. Carr, H. B. Radousky, and S. G. Demos, “Wavelength Dependence of Laser-Induced Damage: Determining the Damage Initiation Mechanisms,” Phys. Rev. Lett. 91(12), 127402 (2003). [CrossRef] [PubMed]

9. Y. Lian, L. Zhu, T. Sui, G. Yu, L. Song, H. Zhou, M. Xu, and X. Sun, “The rapid growth of ADP single crystal,” CrystEngComm 18(39), 7530–7536 (2016). [CrossRef]

10. D. Xu and D. Xue, “Chemical bond analysis of the crystal growth of KDP and ADP,” J. Cryst. Growth 286(1), 108–113 (2006). [CrossRef]

11. D. Xu and D. Xue, “Chemical bond and microscopic growth habit of ADP crystals,” Rengong Jingti Xuebao 34, 823–827 (2005).

12. Y. Lian, G. Yu, F. Liu, L. Zhang, M. Xu, H. Zhou, X. Sun, and Q. Gu, “Prismatic morphology of an ADP crystal grown in a defined crystallographic direction,” RSC Advances 7(83), 52962–52969 (2017). [CrossRef]

13. Y. Lian, M. Xu, L. Zhang, D. Cai, T. Sui, X. Sun, and X. Chai, “the rapid growth of ADP crystal in defined crystallographic direction,” CrystEngComm 20(7), 917–923 (2018). [CrossRef]

14. H. Gao, B. Teng, Z. Wang, D. Zhong, S. Wang, J. Tang, N. Ullah, and S. Ji, “Room temperature noncritical phase matching fourth harmonic generation properties of ADP, DADP, and DKDP crystals,” Opt. Mater. Express 7(11), 4050–4057 (2017).

15. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n₂ measurements,” Opt. Lett. 14(17), 955–957 (1989). [CrossRef] [PubMed]

16. H. Zhang, Stéphane Virally, Qiaoliang Bao, L. K. Ping, Serge Massar, Nicolas Godbout, and Pascal Kockaert, “Z-scan measurement of the nonlinear refractive index of grapheme,” Opt. Lett. 37(11), 1856 (2012). [CrossRef] [PubMed]

17. J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH₂PO₄ and KD₂PO₄ crystals for the world’s most powerful laser,” Int. Mater. Rev. 47(3), 113–152 (2002). [CrossRef]

18. John Reintjes and R. C. Eckardt, “Two-photon absorption an ADP and KD*P at 266.1 nm,” IEEE J. Quantum Electron. QE-13(9), 791 (1977).

19. X. Chai, Q. Zhu, B. Feng, F. Li, X. Feng, F. Wang, W. Han, and L. Wang, “Nonlinear absorption properties of DKDP crystal at 263nm and 351nm,” Opt. Mater. 64, 262–267 (2017). [CrossRef]

20. R. Desalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Z-scan measurements of the anisotropy of nonlinear refraction and absorption in crystals,” Opt. Lett. 18(3), 194–196 (1993). [CrossRef] [PubMed]

21. W.-P. Zang, J.-G. Tian, Z.-B. Liu, W.-Y. Zhou, F. Song, and C.-P. Zhang, “Analytic solutions to Z-scan characteristics of thick media with nonlinear refraction and nonlinear absorption,” J. Opt. Soc. Am. B 21(1), 63–66 (2004). [CrossRef]

22. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n₂ measurements,” Opt. Lett. 14(17), 955–957 (1989). [CrossRef] [PubMed]

23. J.-G. Tian, W.-P. Zang, C.-Z. Zhang, and G. Zhang, “Analysis of beam propagation in thick nonlinear media,” Appl. Opt. 34(21), 4331–4336 (1995). [CrossRef] [PubMed]

24. W. Zang, J. Tian, and G. Zhang, “Theoretical analysis of Z-scan in thick optical nonlinear media,” Wuli Xuebao 3, 476–482 (1994).

25. J.-G. Tian, W.-P. Zang, and G.-Y. Zhang, “Analysis of beam propagation through thick nonlinear media by the variational approach,” Wuli Xuebao 43, 1712–1717 (1994).

26. M. Sheik-Bahae, A. A. Said, T. 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]

27. P. B. Chapple, J. A. Hermann, and R. G. McDuff, “Power saturation effects in thick single-element optical limiters,” Opt. Quantum Electron. 31(5/7), 555–569 (1999). [CrossRef]

28. H. Zhou, Q. Zhang, B. Wang, X. Xu, Z. Wang, X. Sun, F. Zhang, L.-S. Zhang, B.-A. Liu, and X.-X. Chai, “Raman gains of ADP and KDP crystals,” Chin. Phys. B 24(4), 227–230 (2015). [CrossRef]

29. S. Yu, C.-H. Yang, Z. Jiang, S. Hao, and C. Zhu, “Raman spectra analysis for lattice vibration modes in ADP crystals,” Chinese J. Inorgan. Chem . 28(4), 733–738 (2012).

30. G. G. Gurzadyan and R. K. Ispiryan, “Two-photon absorption peculiarities of potassium dihydrogen phosphate crystal at 216 nm,” Appl. Phys. Lett. 59(6), 630–631 (1991). [CrossRef]

31. C. S. Liu, Q. Zhang, and N. Kioussis, “Electronic structure calculations of intrinsic and extrinsic hydrogen point defects in KH₂PO₄,” Phys. Rev. B 68(224107), 1–11 (2003).

32. K. P. Wang, C. S. Fang, J. X. Zhang, C. S. Liu, R. I. Boughton, S. L. Wang, and X. Zhao, “First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals,” Phys. Rev. B 72, 184105 (2005).

33. S. B. Mansoor, A. A. Said, and T. H. Wei, “Senstive measurement of optical nonlinearities using a single beam,” J. Quantum Electron 26(3), 760–769 (1990).

34. I. A. Kulagin, R. A. Ilya, A. Kulagin, R. A. Ganeev, V. A. Kim, A. I. Ryasnyansky, R. I. Tugushev, T. Usmanov, and A. V. Zinoviev, “Nonlinear refractive indices and third-order susceptibilities of nonlinear-optical crystals,” Proc. SPIE 4972, 182–189 (2003).

35. X. L. Yang and S. W. Xie, “Expression of third-order effective nonlinear susceptibility for third-harmonic generation in crystals,” Appl. Opt. 34(27), 6130–6135 (1995). [CrossRef] [PubMed]

36. G. Duchateau, M. D. Feit, and S. G. Demos, “Transient material properties during defect-assisted laser breakdown in deuterated potassium dihydrogen phosphate crystals,” J. Appl. Phys. 115(10), 103506 (2014). [CrossRef]

37. F. Zhang, Z. X. Wu, Zh. P. Wang, W. D. Liang, Sh. L. Wang, and X. G. Xu, “Strong optical limiting behavior discovered in black phosphorus,” RSC Advances 6(24), 20027–20033 (2016). [CrossRef]

38. D. S. Correa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonc, “Z-scan theoretical analysis for three-, four-and five-photon absorption,” Opt. Commun. 277, 440–445 (2007). [CrossRef]

39. C. Görling, U. Leinhos, and K. Mann, “Comparative studies of absorptance behaviour of alkaline-earth fluorides at 193 nm and 157 nm,” Appl. Phys. B 74(3), 259–265 (2002). [CrossRef]

40. T. Sui, Y. Lian, M. Xu, L. Zhang, Y. Li, X. Zhao, and X. Sun, “Stability and electronic structure of hydrogen vacancies in ADP: hybrid DFT with vdW correction,” RSC Advances 8(13), 6931–6939 (2018). [CrossRef]

41. Y. B. Zheng, L. Ding, X. D. Zhou, R. S. Ba, J. Yuan, H. L. Xu, J. Na, Y. J. Li, X. Y. Yang, L. Q. Chai, B. Chen, and W. G. Zheng, “Characterization of the influence of polarization orientation on bulk damage in KDP crystal at different wavelengths,” Opt. Mater. 58, 248–252 (2016). [CrossRef]

42. B. A. Liu, G. H. Hu, Y. A. Zhao, M. X. Xu, S. H. Ji, L. L. Zhu, L. S. Zhang, X. Sun, Z. P. Wang, and X. G. Xu, “Laser induced damage of DKDP crystals with different deuterated degrees,” Opt. Laser Technol. 45, 469–472 (2013). [CrossRef]

43. H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, and K. Yoshida, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. B 70(2), 195–201 (2000). [CrossRef]

Sample	α ₀ cm⁻¹	I ₀ GW·cm⁻²	β₂ cm·GW⁻¹ ( × 10⁻²)	n ₂ m² W⁻¹ ( × 10⁻¹⁹)	Imχ³ esu ( × 10⁻¹⁴)	Reχ³ esu ( × 10⁻¹⁴)	χ⁽³⁾ esu ( × 10⁻¹⁴)
Z-Z	0.062	37.8	2.124	2.71	3.34	1.60	3.70
Z-X	0.136	38.0	1.598	2.25	2.51	1.33	2.84
Z-[110]	0.052	39.0	1.491	1.14	2.34	0.67	2.43
D-Z	0.047	37.8	2.064	2.61	3.24	1.54	3.59
D-X	0.109	39.0	1.571	2.17	2.47	1.28	2.78
D-[110]	0.043	39.5	1.489	1.03	2.34	0.61	2.42

samples	Z	X	[110]
Z	1.15	1.65	Inhomogeneous
D	1.46	2.65	11.5

Sample	α ₀ cm⁻¹	I ₀ GW·cm⁻²	β₂ cm·GW⁻¹ ( × 10⁻²)	n ₂ m² W⁻¹ ( × 10⁻¹⁹)	Imχ³ esu ( × 10⁻¹⁴)	Reχ³ esu ( × 10⁻¹⁴)	χ⁽³⁾ esu ( × 10⁻¹⁴)
Z-Z	0.062	37.8	2.124	2.71	3.34	1.60	3.70
Z-X	0.136	38.0	1.598	2.25	2.51	1.33	2.84
Z-[110]	0.052	39.0	1.491	1.14	2.34	0.67	2.43
D-Z	0.047	37.8	2.064	2.61	3.24	1.54	3.59
D-X	0.109	39.0	1.571	2.17	2.47	1.28	2.78
D-[110]	0.043	39.5	1.489	1.03	2.34	0.61	2.42

samples	Z	X	[110]
Z	1.15	1.65	Inhomogeneous
D	1.46	2.65	11.5

Nonlinear optical characteristics of an ADP crystal grown in a defined direction

Abstract

1. Introduction

2. Experiments

2.1. Sample preparations

2.2. Transmittance

2.3. Z-scan measurements

2.3. Theories for thick media

3. Experiments

3.1. Transmittance spectrum

3.2. Nonlinear absorption

3.3. Nonlinear refraction

3.4. Discussions

4. Conclusions

Funding

References and links

Cited By

Figures (5)

Tables (2)

Equations (15)

Optical Materials Express