Measurement of nonlinear optical refraction of composite material based on sapphire with silver by Kerr-lens autocorrelation method

Xiang-xiang Yu; Yu-hua Wang

doi:10.1364/OE.22.000177

1. Introduction

The nonlinear optical properties of dielectric materials doped with metallic nanoparticles have been studied due to the application of these materials in optical switching, beam steering, image processing and amplification [1–3].One of the suitable techniques to fabricate composite materials (dielectric materials doped with metallic nanoparticles) is ion implantation. It can accurately control the thickness of the doped layer and the metal concentration. The promising implants used to realize nonlinear optical properties are the metals with a high density of free conduction electrons. The Ag: Al₂O₃ composite material is a kind of promising material used in the photoelectric field for the high transparency of Al₂O₃ and the excellent electronic structure of Ag. Up to now, researchers have done a lot of study about optical properties on Ag: Al₂O₃ composite material fabricated by ion implantation. However, relevant measurements on the nonlinear refraction of this material are not sufficient. In this paper, efforts are made to study the nonlinear optical refraction of this Ag: Al₂O₃ composite material. The nonlinear refractive index of the sample was measured by Kerr-lens-autocorrelation method under the wave length of 800 nm [4].

2. Experiment

Colorless transparent synthetic sapphire crystals, 1 mm thick, were obtained from Shanghai Institute of Optics and Mechanics Chinese Academy of Science. Ag: Al₂O₃ composite materials were prepared by the ion implantation method with a metal vapor vacuum arc (MEVVA) implanter along <0001> orientation. The doped ion concentration is 1.2 × 10¹⁷ ions/cm². The acceleration voltage was 35 kV and the current density of the implantation was 25 μA/cm². The Ag: Al₂O₃ composite materials were annealed at 500 °C for 1 h in the Ar + H₂ gas after ion implantation to reduce damage in host matrix and to promote the formation of nanoparticles. Optical absorption spectrum of Ag: Al₂O₃ composite material was recorded by using the UV-vis dual–beam spectrophotometer in the wavelength interval from 1100 to 200 nm at the room temperature.

The supercontinuum spectrum of the Ag: Al₂O₃ sample was measured to show the nonlinear refraction. The 35 fs pulse centered at 800 nm with 1 KHz repetition was focused onto the sample. The peak intensity at the focus reached nearly 600 GW/cm². The transmission spectrum was measured by the Ocean Optics USB4000 Spectrometer.

The third-order nonlinear optical refractive index (n₂) of the Ag: Al₂O₃ sample was measured by the Kerr-lens autocorrelation (KLAC) technique [4]. The KLAC experimental equipment is listed in Fig. 1 and we can use it to measure the Kerr effect [5]. The excitation source is a mode-locked Nd:YAG laser (PY61-10,Continuum), with a pulse duration of 30 fs, a repetition frequency of 45.8 MHz, a wavelength of 800 nm and a power of 145 mW. In this experiment, the incident laser beam with a wavelength of 800 nm was divided into two pulses by the interferometer. With a converging lens of f = 5 cm, the radius of the Gaussian beam spot at focal waist ω₀ was about 13 μm. The Rayleigh length, Z₀, was calculated to be 0.66 mm. The far field transmittance of the beam through an aperture detected by the dual-channel energy meter (EPM2000) was analyzed to be a function of the delay between the two pulses. The delay (τ) between the two beams was adjusted by mounting one of the corner cubes of the interferometer on a loudspeaker driven by an 18 Hz signal generator. On the basis of Z-scan principle, the precision of the measurement is max when the sample is positioned at either a peak or a valley of the Z-scan transmittance profile [5]. For a thin sample and a partly closed aperture, these positions correspond to Z ≈ ± 0.85Z₀ [5]. For thick samples (i.e. when L > n₀Z₀), the empirical relationship ΔZpv ≈[(1.7Z₀)² + (L/n₀)²]^1/2 establishes the maximum sensitivity positions [6].

Fig. 1 The Kerr-lens autocorrelation (KLAC) arrangement.

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3. Results and discussion

The Al₂O₃ sample implanted by 1.2 × 10¹⁷Ag⁺ ions/cm² remains nearly transparent, which can be deduced from the optical absorption spectrum shown in Fig. 2. The spectrum ranges between 200 and 1100 nm. The formation of silver nanoparticles by ion implantation is proved by the presence of SPR absorption bands peaked at about 450 nm. This absorption band corresponds to the SPR of silver nanoparticles [7].

Fig. 2 Optical absorption spectrum of the Ag: Al₂O₃ sample.

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In order to display the n₂ of Ag: Al₂O₃ composite material, the supercontinuum spectrum of Ag: Al₂O₃ sample is obtained and shown in Fig. 3. The beam propagates along the c-axis.

Fig. 3 Supercontinuum spectra of Ag: Al₂O₃ sample compared to pump laser. The inserted shows profile of the beam throwing the Ag: Al₂O₃ sample in the far field.

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The frequency deviation due to the SPM effect can be described in the form [8]:

δ ω (τ) = - \frac{4 π n_{2} k z}{c} \times \frac{\partial I (τ)}{\partial τ}

Where

δ ω (τ)

is the frequency deviation varying with the pulse duration

τ

,

z

is the propagation distance of the pump beam in the medium,

I (τ)

is the instantaneous intensity [9].

It is clear that the frequency deviation is proportional to n₂ when other conditions are identical. It is illustrated in Fig. 3, the spectrum of Ag: Al₂O₃ sample is obviously wider than that of the pump laser, which demonstrates that this kind of sample has nonlinear refraction property.

The nonlinear refraction is expressed as n = n₀ + n₂I, where n₀ is the linear refractive index of the sample, n₂ is the nonlinear refractive index, and I denotes the intensity of the laser [10]. The third-order nonlinear refraction of the sample was detected by the KLAC technique. Table 1 depicts the characteristics of the Ag: Al₂O₃ composite material used in this experiment. The width of the sample is bigger than the size of the expression n₀Z₀, so the sample can be regarded as a thick one. Figure 4a depicts the KLAC trace of the Ag: Al₂O₃ composite material when positioned at the peak and valley of the Z-scan. The peak and valley positions are located by performing a Z-scan while monitoring rapid-scan KLAC traces on a digital oscilloscope [5]. The sign of the nonlinear refractive index of the sample is determined by the relative positions of the peak and valley. The absolute value of the third-order nonlinear refractive index for tested samples is calculated by the following equations:

Δ T_{p} (τ) = - Δ T_{v} (τ) ≅ 0.203 < Δ ϕ_{0} > [\frac{2 (1 + b^{2})}{{(1 + b)}^{2}} + \frac{8 b}{{(1 + b)}^{2}} U (τ)]

Where

Δ ϕ_{0}

is the average peak-on-axis phase shift,

U (τ) = \int f (t) f (t + τ) d t

is the intensity autocorrelation function (normalized to

U (0) = 1

),

b = I_{01} / I_{02}

is the power imbalance of the interferometer arms,

I_{01}

and

I_{02}

are the peak-on-axis irradiances inside the sample at the focus (

z

= 0). Normally,

b

= 1 (

I_{01} \approx I_{02}

), and then:

< Δ ϕ_{0} > = \frac{2 π}{λ_{0}} L_{e f f} n_{2} \frac{I_{01} + I_{02}}{2} A

Where

A

refers to the temporal averaging over the pulse profile and takes the value of

1 / \sqrt{2}

for Gaussian pulse.

L_{e f f}

is the effective propagation distance within the material, and it can be calculated by the following Eq. (4) [11]:

Table 1. The characteristics of the Ag: Al₂O₃ sample used in the KLAC experiments

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Fig. 4 a. Measured KLAC traces for Ag: Al₂O₃ sample when positioned at the peak and valley of the Z-scan. Figure 4(b). Measured Z-scan profile for a 2-mm-thick ZnS sample. The inserted is the KLAC trace with the sample positioned at the peak of the Z-scan.

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L_{e f f} = \frac{2.706 [{(L / n_{0} Z_{0} + 1)}^{1.44} - 1]}{{(L / n_{0} Z_{0})}^{1.44} + 3.924}

From the characteristics of the Ag: Al₂O₃ sample and the equations above, we obtain the value of n₂ of −1.1 × 10⁻¹⁵ cm²/W for the Ag: Al₂O₃ sample under the wavelength of 800 nm.To calibrate the pulse width and beam parameters of the laser, test the measurement accuracy of the KLAC technique, a 2 mm thick polycrystalline ZnS is used as the guide sample. Figure 4(b) depicts the measured KLAC trace with the sample positioned at the Z-scan peak. From Fig. 4(b), the pulse width ( $Δ τ$ = 30 fs, FWHM), Rayleigh range (Z₀ ≈0.66 mm) and focal spot size ( $ω_{0}$ ≈13 μm) are readily identified. The measured values of the parameters of the laser are consistent with the actual values. For other samples, the n₂ measurement can be performed only by recording the values of $Δ T_{p} (0)$ and $Δ T_{v} (0)$ .

Table 2 lists the comparison of our result and the literature. In [12], Ganeev et al. measured the nonlinear refractive index of Ag: Al₂O₃ composite material by RZ-scan. The absolute value of n₂ is ten thousand times larger than ours, which mainly because that the value of n₂ measured by RZ-scan depends on all of the contributions, however, during the KLAC measurement, n₂ is only affected by the Kerr effect. Besides, in [7], Ganeev et al. compared the absolute values and signs of nonlinear refractive indices of Al₂O₃ composite material doped with Ag, Cu and Au, and found the sign of n₂ can be determined by the effect of two-photon process on self-interaction properties of media. The absolute value of n₂ of our Ag: Al₂O₃ sample is about three times larger than the value of pure sapphire, so the magnitude can be widely increased by ion implantation [13]. Mota-Santiago et al. studied the nonlinear refraction of Au: Al₂O₃ material under the wavelength of 532 nm and 355 nm, found the value of n₂ strongly depended on the wavelength of the pulse, especially in the SPR range [14].

Table 2. Comparison between the literature and our result

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During the KLAC experiment, the nonlinear refraction mainly originates from the optical Kerr effect. The Kerr effect is often caused by the electronic response of metal nanoparticles and is associated with the presence of resonance transitions in a medium [12]. These electronic contributions of metal nanoparticles consist in intraband transition, interband transition and hot electron transition. In our experiment, the wavelength of the incident laser pulse is 800 nm, which is in the near infrared region. Therefore, the optical Kerr nonlinearity is certainly to be attributed to the intraband transition of electrons from the occupied state to unoccupied state.

In case of resonance transitions, the sign of n₂ is determined by the relative magnitude between the frequency of fundamental ( $ω_{10}$ ) or two-photon ( $ω_{20}$ ) frequencies and the resonance frequency of the material in question. In our experiment, the resonance frequency is the SPR frequency $ω_{p}$ of the nanoparticles. If two-photon transitions are enhanced around the frequency of the SPR, then there could be resonant contributions to n₂ that contains $ω_{20} = 2 ω_{10}$ . From [9], one can apply the following equation about n₂ which containing some terms that can strongly enhance the nonlinear refraction around the frequency of the SPR.

n_{2} (ω_{10}) \propto \frac{A}{(ω_{p} - ω_{10}) (ω_{p} - ω_{20})}

Where

A

is the independent constant.

As follows from the equation above, the sign of n₂ only relies on the frequency detuning of laser radiation from SPR of metal nanoparticles. For the Ag: Al₂O₃ composite material mentioned, the frequency $ω_{p}$ is 22222 cm⁻¹ (λ~450 nm, Fig. 1). In case of the two-photon process ( $ω_{20}$ = 25000 cm⁻¹, λ = 400 nm), the negative sign of n₂ can be obtained from Eq. (5), which agrees with our measurement. In this work, the two-photon process may exist during the KLAC measurement for the Ag: Al₂O₃ composite material under the wavelength of 800 nm.

4. Conclusion

In summary, Ag nanoparticles in Al₂O₃ have been formed by the ion implantation of Ag⁺ ions. The nonlinear optical refraction of this sample was studied by the KLAC technique. The n₂ measured at 800 nm is −1.1 × 10⁻¹⁵ cm²/W. The sign of nonlinear refractive index is discussed on the basis of the model which focused on the effect of two-photon process.

Acknowledgments

We thank Dr. Mansoor Sheik-Bahae and Dr. Zhou Yang for them help with the experiments. This work was supported by the National Natural Science Foundation of China under Grant No. 10805035 and No. 11375136.

References and links

1. R. A. Ganeev, G. S. Boltaev, R. I. Tugushev, and T. Usmanov, “Nonlinear optical absorption and refraction in Ru, Pd, and Au nanoparticle suspensions,” Appl. Phys. B 100(3), 571–576 (2010). [CrossRef]

2. S. M. Lee, K. C. Choi, D. H. Kim, and D. Y. Jeon, “Localized surface plasmon enhanced cathodoluminescence from Eu³⁺-doped phosphor near the nanoscaled sliver particles,” Opt. Express 19(14), 13209–13217 (2011). [CrossRef]

3. A. L. Stepanov, “Nonlinear optical properties of implanted metal nanoparticles in various transparent matrixes: A review,” Rev. Adv. Mater. Sci. 27, 115–145 (2011).

4. M. Sheik-Bahae, “Femtosecond Kerr-lens autocorrelation,” Opt. Lett. 22(6), 399–401 (1997). [CrossRef] [PubMed]

5. M. Sheik-Bahae and M. Ebrahimzadeh, “Measurements of nonlinear refraction in the second-order x ⁽²⁾ materials KTiOPO₄, KNbO₃, β-BaB₂O₄, and LiB₃O₅,” Opt. Commun. 142(4-6), 294–298 (1997). [CrossRef]

6. M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in “thick” media,” Opt. Eng. 30, 1228–1235 (1991). [CrossRef]

7. R. A. Ganeev, A. I. Ryasnyansky, A. L. Stepanov, C. Marques, R. C. da Silva, and E. Alves, “Application of RZ-scan technique for investigation of nonlinear refraction of sapphire doped with Ag, Cu, and nanoparticles,” Opt. Commun. 253(1-3), 205–213 (2005). [CrossRef]

8. V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media (or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003). [CrossRef]

9. J. J. Chen, X. F. Chen, A.H. Wu, H. J. Li, Y. L. Zheng, Y. Z. Ma, L. W. Jiang, and J. Xu, “Femtosecond Z-scan measurement of third-order nonlinear refractive indices of BaMgF4,” Appl. Phys. Lett. 98, 191102 (2011).

10. Q. Wan, T. H. Wang, and C. L. Lin, “Third-order optical nonlinearity and negative photoconductivity of Ge nanocrystals in Al₂O₃ dielectric,” Nanotechnology 14(11), L15–L17 (2003). [CrossRef]

11. E. W. Van Stryland and M. Sheik-Bahae, “Z-scan Technique for Materials Characterization,” Critical Reviews of Optical Science and Technology, CR69, 501, SPIE (1997).

12. R. A. Ganeev, A. I. Ryasnyansky, A. L. Stepanov, T. U. Usmanov, C. Marques, R. C. da Silva, and E. Alves, “Investigation of the Nonlinear Optical Characteristics of Composite Materials Based on Sapphire with Silver, Copper, and Gold Nanoparticles by the Reflection Z-scan Method,” Opt. Spectrosc+. 101(4), 615–622 (2006). [CrossRef]

13. D. N. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photon. 2(1), 60–200 (2010). [CrossRef]

14. P. E. Mota-Santiago, A. Crespo-Sosa, J. L. Jiménez-Hernández, O. Sánchez-Dena, R. C. Fernández-Hernández, J. A. Reyes-Esqueda, and A. Oliver, “Linear and non-linear optical properties of metallic nanocrystals in sapphire,” Proc. SPIE 8011, 80113V (2011). [CrossRef]

Samples	Excitation wavelength, nm	Current density, μA/cm²	Implantation energy, keV	Implantation dose, 10¹⁶ ion/cm²	Measurement method	Pulse duration	Repetition rate,Hz	Peak intensity, GWcm⁻²	n_2, cm²W⁻¹
Ag:Al₂O₃ [12]	1064	3	30	37.5	RZ-scan	55 ps	2	4.3	(3.4 ± 1.02) × 10⁻¹¹
Ag:Al₂O₃ [7]	1064	3	30	37.5	RZ-scan	55 ps	2	4.3	1.1 × 10⁻¹¹
Cu:Al₂O₃ [7]	1064	2.5	40	5.4	RZ-scan	55 ps	2	7.7	−1.3 × 10⁻¹¹
Au:Al₂O₃ [7]	1064	10	160	6	RZ-scan	55 ps	2	2.3	−9.4 × 10⁻¹¹
Al₂O₃ [13]	1064	none	none	none	Z-scan				0.31 × 10⁻¹⁵
Al₂O₃ [13]	532	none	none	none	Z-scan				0.33 × 10⁻¹⁵
Au:Al₂O₃ [14]	532	<10⁶	1500	2.5	TZ-scan	26 ps	1	3.1 × 10⁵	3.1 × 10⁻¹¹
Au:Al₂O₃ [14]	355	<10⁶	1500	2.5	TZ-scan	26 ps	1	3.36 × 10⁵	0
Ag:Al₂O₃	800	25	35	12	KLAC	30 fs	45.8 M	19.8	−1.1 × 10⁻¹⁵

Samples	Excitation wavelength, nm	Current density, μA/cm²	Implantation energy, keV	Implantation dose, 10¹⁶ ion/cm²	Measurement method	Pulse duration	Repetition rate,Hz	Peak intensity, GWcm⁻²	n_2, cm²W⁻¹
Ag:Al₂O₃ [12]	1064	3	30	37.5	RZ-scan	55 ps	2	4.3	(3.4 ± 1.02) × 10⁻¹¹
Ag:Al₂O₃ [7]	1064	3	30	37.5	RZ-scan	55 ps	2	4.3	1.1 × 10⁻¹¹
Cu:Al₂O₃ [7]	1064	2.5	40	5.4	RZ-scan	55 ps	2	7.7	−1.3 × 10⁻¹¹
Au:Al₂O₃ [7]	1064	10	160	6	RZ-scan	55 ps	2	2.3	−9.4 × 10⁻¹¹
Al₂O₃ [13]	1064	none	none	none	Z-scan				0.31 × 10⁻¹⁵
Al₂O₃ [13]	532	none	none	none	Z-scan				0.33 × 10⁻¹⁵
Au:Al₂O₃ [14]	532	<10⁶	1500	2.5	TZ-scan	26 ps	1	3.1 × 10⁵	3.1 × 10⁻¹¹
Au:Al₂O₃ [14]	355	<10⁶	1500	2.5	TZ-scan	26 ps	1	3.36 × 10⁵	0
Ag:Al₂O₃	800	25	35	12	KLAC	30 fs	45.8 M	19.8	−1.1 × 10⁻¹⁵

Measurement of nonlinear optical refraction of composite material based on sapphire with silver by Kerr-lens autocorrelation method

Abstract

1. Introduction

2. Experiment

3. Results and discussion

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (4)

Tables (2)

Equations (5)

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