1. Introduction

Sapphire has received great attention due to its excellent mechanical, physical and chemical properties [1–3]. It is widely used for optical windows in aerospace and military affairs fields. During the serving of sapphire windows, the creation of crystal defects by cosmic ray and particle radiation will degrade the service performance of the windows. Developing non-destructive detection approaches capable of estimating the amount of defects is necessary to predict the damage degree of optical windows. Because of the significant influence of defects on phonon dynamics, it is very important to study the phonon dynamics in defective sapphire. The development of ultrashort pulse laser allows a direct time-resolved study of phonon dynamics. The effect of defects on coherent phonon dynamics has been studied in bismuth films [4], graphite [5] and GaAs [6] by femtosecond pump-probe reflectivity measurements. However, this excellent method is suitable for the study of low-frequency vibrational modes and requires that the femtosecond laser pulse duration should be much shorter than the period of the excited coherent vibrations. Instead, femtosecond time-resolved coherent anti-Stokes Raman scattering (fs-CARS) technique is a powerful tool to study high-frequency vibrational modes, it has been widely employed in liquid phase and gas phase materials [7–14], but scarcely in bulk crystals due to the difficulties in experimental operation. Especially, it is very difficult to obtain the fs-CARS signals of phonon modes in crystals at room temperature. Here, we present fs-CARS investigation of effect of defects on the phonon dynamics in sapphire crystals. In the fs-CARS measurements of three sapphire samples irradiated with ⁶⁰Co γ-rays for different doses, we observed well-defined quantum beat signals, which are ascribed to the interference of the 645 and 750 cm⁻¹ phonon modes. By fitting the experimental data, we are able to simultaneously give the dephasing times of the two modes, both of them decrease with increasing irradiation dose, which is due to the scattering of coherent phonons by the defects introduced by γ-ray irradiation. This work offers the possibility of developing a new non-destructive detection approach to predict the damage degree of crystals.

CARS is a four-wave mixing process. The sample is first subjected to two time-coincident pump and Stokes pulses. If the frequency difference of the two pulses matches the frequency of a specific phonon mode, this mode will be excited coherently. The temporal evolution of the coherent phonons is probed by the third time-delayed probe pulse, giving rise to a CARS signal. The signal intensity is recorded as a function of the delay time τ between the probe pulse and the simultaneous pump and Stokes pulses. Obviously, the fs-CARS technique is perfectly suitable for the selective excitation of phonon modes by adjusting the frequency difference between the pump and Stokes pulses. In this work, we use a white-light continuum (WLC) for the Stokes pulse. Due to the chirp characteristics of the ultrabroadband WLC, no complicated laser system is required for the wavelength tuning of the Stokes pulse.

2. Experiment

Large-sized high-quality sapphire crystals were grown by SAPMAC (sapphire growth technique with micro-pulling and shoulder-expanding at cooled center) method [3]. The three samples were prepared by cutting the as-grown sapphire crystal perpendicularly to the c-axis into small pieces with the size of Φ36 mm × 2 mm and final both-sides polished, and were irradiated with ⁶⁰Co γ-rays at doses of 1 × 10⁷, 1 × 10⁸ and 5 × 10⁸ rad, respectively.

The fs-CARS measurements are performed at room temperature. The schematic diagram of experimental setup is shown in Fig. 1(a) . The laser pulse from a regenerative amplifier (1 kHz, Spectra-Physics, Spitfire) with a center wavelength of 800 nm, single pulse energy of 500 μJ, and pulse duration of 110 fs is split into three parts. Two of them are used as the pump (ω _p, k _p) and probe (ω _pr = ω _p, k _pr) pulses, and the third one is focused into a 4 mm thick Al₂O₃ crystal to produce a WLC used for the Stokes pulse (ω _s, k _s). Two delay lines are employed. The Stokes pulse defines an arbitrary temporal zero point. The delay time between the pump and Stokes pulse and that between the probe and Stokes pulse can be varied. Figure 1(b) displays the energy diagram. A folded BOXCARS configuration [see Fig. 1(c)] with properly chosen angles (less than 2 degrees) between the beams, determined by the phase matching condition, is used. The CARS signal is collected by a silica fibre, dispersed in a spectrometer (Bruker Optics 500 IS/SM) and detected by a CCD detector (Andor DU440-BU2).

 

Fig. 1 (a) Experimental setup of the fs-CARS; BS: Beam splitter; L: Lens; Pol: polarizer, (b)energy diagram, and (c) folded BOXCARS configuration.

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The WLC has an ultrabroadband spectral profile, ranging from 300 to 1100 nm. Based on the temporal chirp characteristics of the WLC, the frequency difference between the pump and Stokes pulses can be tuned by changing the delay time between the pump and WLC pulses, the selective excitation of a wide range of phonon modes can be accomplished [11,15]. Figure 2 shows the measured Raman spectrum of the non-irradiated sapphire at room temperature. There are seven active phonon modes located at 379, 418, 431, 450, 577, 645 and 750 cm⁻¹, which are consistent with the results reported in publications [16]. Compared to the non-irradiated sapphire, there is no detectable change in the Raman spectra of the three irradiated samples. We concentrate on the 645 and 750 cm⁻¹ modes, corresponding to the $A_{1g}$ and $E_g$ phonons, respectively. The two modes are related to the stretching vibrations of [AlO₆] group, and the 645 cm⁻¹ mode is due to the Al-O symmetric stretching vibration. In order to suppress the excitation of the other modes and the generation of the degenerate four-wave mixing process, the WLC is spectrally filtered using a filter to cut off the components of wavelength less than 830 nm. The large spectral bandwidth of the femtosecond laser pulses and the two close vibrational levels provide the opportunity to observe the quantum beat phenomena on a terahertz scale. The pump, Stokes, and probe pulses are focused on the samples to a diameter of about 300 μm using a lens with a focal length of 300 mm. The length of the spatial overlap of all the three laser beams is about 10 mm and can cover well the thickness of the samples (2 mm). The single pulse energies at the samples are 30 μJ for the pump and probe pulses, and 2 μJ for the Stokes pulse. The polarizations of the three pulses are set to be parallel to each other. The temporal overlap between the pump and Stokes pulses is properly adjusted to accomplish selective excitation of phonon modes.

 

Fig. 2 Raman spectrum of the sapphire at room temperature.

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3. Results and discussion

The detected wavelength of the fs-CARS signals for the sapphire samples irradiated with ⁶⁰Co γ-rays at doses of 1 × 10⁷, 1 × 10⁸ and 5 × 10⁸ rad is set at 758 nm, corresponding to an excitation wavenumber of 693 cm⁻¹. This is approximately the mean wavenumber value of the 645 and 750 cm⁻¹ modes. The time-integrated CARS signal intensity can be written as [17,18]:

The nonlinear polarization P _c ⁽³⁾ consists of two contributions: the fast nonresonant part due to the response of the electronic system and the slow resonant part due to the response of the coherent phonons [7,18,19]. The rapidly decaying nonresonant part does not provide any information on the phonon modes. To avoid the intense nonresonant contribution in the determination of the dephasing time of the coherent phonons, we analyze the fs-CARS signals starting from the delay time $\tau =300$fs (see Fig. 3 ). The signals show the expected quantum beat phenomena. Such a beat signal is often observed in fs-CARS experiments [7–9,11], and is due to the different vibrational modes are excited simultaneously because of the large spectral bandwidth of the femtosecond laser pulses. The observed well-defined quantum beats with the period times of ~333 fs agree well with the frequency difference (105 cm⁻¹) of the 645 and 750 cm⁻¹ modes.

 

Fig. 3 Fs-CARS signals for sapphire samples irradiated with ⁶⁰Co γ-rays at doses of (a) 1 × 10⁷ rad, (b) 1 × 10⁸ rad, and (c) 5 × 10⁸ rad. Solid circle: experimental data; solid line: fitting curves.

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The delay time dependence of the CARS signal is fitted with the following function [7–9]:

Here $T_{2a}$ and $T_{2b}$ represent the dephasing times of two excited phonon modes, respectively, $\Delta \omega$ and $\Delta \phi$ are the frequency difference and the phase shift at $\tau =0$between the two modes, $Q_{0a}$and$Q_{0b}$are the coherent amplitudes defined by the transition strengths and other experimental conditions.

For the three sapphire samples, the frequency differences $\Delta \omega$ are all around 100 cm⁻¹, which are consistent with the difference between the 645 and 750 cm⁻¹ modes. We confirm that the 645 and 750 cm⁻¹ modes are coherently excited at the same time, and the beat signals are ascribed to the interference of the two modes. It should be noted that the dephasing times $T_{2a}$and $T_{2b}$ (shown in Table 1 ) exhibit a dose-dependent behavior, both of them decrease with increasing γ-rays irradiation dose. According to the relationship between the dephasing time of the coherently excited vibrations and linewidth of Raman peak [20], as well as the ratio of $Q_{0a}$and $Q_{0b}$ [9], we are able to assign the longer dephasing time $T_{2a}$to 645 cm⁻¹ mode and the shorter one $T_{2b}$to 750 cm⁻¹ mode.

Table 1. The values of $T_{2a}$,$T_{2b}$ and $\Delta \phi$obtained from fitting the experimental data with the function of Eq. (2)

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The dephasing process ($T_2$) of coherent phonons in crystals consists of energy relaxation ($T_1$) and pure dephasing ($T_2^{\ast }$) contributions. The overall value for the phonon dephasing rate is described as a sum of the anharmonic decay rate and the pure dephasing rate, $1/T_2=1/T_1+1/T_2^{\ast }$ [4,20,21]. In good-quality crystals, the pure dephasing process induced by lattice spatial disorder plays a minor role and the phonon dephasing is mostly due to phonon–phonon interaction caused by the intrinsic anharmonicity of the lattice potential. When defects are introduced into the crystals, the pure dephasing process of coherent phonons is accelerated due to the scattering of coherent phonons by the defects.

F and F⁺ color centers are the main defects in γ-ray irradiated sapphire crystals. The defect density is related with many factors, such as crystal growth method, irradiation condition and the purity of the samples. There exists a relation between the number density N (cm⁻³) of color centers per unit volume and the parameters of the absorption bands of the crystal, which is expressed by the formula of Smakula [22]:

The phase shift $\Delta \phi$ between the two phonon modes at$\tau =0$ also exhibits a dose-dependent behavior (shown in Table 1). In sapphire crystals, charge excitation is the main effect of γ-ray irradiation. This kind of excitation will quasi-instantaneously (on the time scale of laser pulse duration) change the electron-ion potential, and therefore a new equilibrium separation is established. This will set an oscillatory motion of the ions around the new equilibrium position [23,24]. Accordingly, the phase shift $\Delta \phi$ between the vibrational modes will change. When γ-rays irradiation doses are different, the changes of $\Delta \phi$ are different. In fact, further study is being performed in our laboratory, despite the quite complex relation between the phase shift and the irradiation dose. With the increase of the irradiation dose, $\Delta \phi$ may experience a periodical change.

4. Conclusion

In conclusion, we have studied the dynamics of coherent phonons in ⁶⁰Co γ-ray irradiated sapphire crystals by fs-CARS technique at room temperature, in spite of the difficulties in experimental operation. We use the ultrabroadband WLC for the Stokes pulse. Due to the chirp characteristics of the WLC, we have achieved the selective excitation of the phonon modes without requiring complicated laser system for the wavelength tuning of the Stokes pulse. The observed well-defined quantum beat signals are ascribed to the interference of the 645 cm⁻¹ $A_{1g}$ and 750 cm⁻¹ $E_g$ phonon modes. The dephasing times of the two modes both decrease with increasing γ-ray irradiation dose, which is due to that the dephasing processes of coherent phonons are accelerated because of the scattering of phonons by the defects introduced by γ-ray irradiation. This investigation indicates that fs-CARS technique is a powerful tool to study the effect of defects on the dynamics of coherent phonons, and it provides the possibility of developing a new non-destructive detection approach to predict the damage degree of crystals.