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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 22 — Oct. 25, 2010
  • pp: 22937–22943
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Phonon dynamics in γ-ray irradiated sapphire crystals studied by fs-CARS technique

Xin Du, Mingfu Zhang, Qingkun Meng, Yunfei Song, Xing He, Yanqiang Yang, and Jiecai Han  »View Author Affiliations


Optics Express, Vol. 18, Issue 22, pp. 22937-22943 (2010)
http://dx.doi.org/10.1364/OE.18.022937


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Abstract

We have studied the ultrafast dynamics of coherent phonons in sapphire crystals irradiated with 60Co γ-rays for three different doses by femtosecond time-resolved coherent anti-Stokes Raman scattering (fs-CARS) technique at room temperature. The obtained fs-CARS signals exhibit well-defined quantum beats, which are ascribed to the interference of the 645 and 750 cm−1 phonon modes. The dephasing times of the two modes both decrease with increasing irradiation dose, which is due to the scattering of coherent phonons by the defects introduced by γ-ray irradiation.

© 2010 OSA

1. Introduction

Sapphire has received great attention due to its excellent mechanical, physical and chemical properties [1

1. A. G. Lanin, E. L. Muravin, V. P. Popov, and V. N. Turchin, “Thermal shock resistance and thermal-mechanical processing of sapphire,” J. Eur. Ceram. Soc. 23(3), 455–468 (2003). [CrossRef]

3

3. G. G. Wang, M. F. Zhang, J. C. Han, X. D. He, H. B. Zuo, and X. H. Yang, “High-temperature infrared and dielectric properties of large sapphire crystal for seeker dome application,” Cryst. Res. Technol. 43(5), 531–536 (2008). [CrossRef]

]. 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

4. M. Hase, K. Ishioka, M. Kitajima, K. Ushida, and S. Hishita, “Dephasing of coherent phonons by lattice defects in bismuth films,” Appl. Phys. Lett. 76(10), 1258–1260 (2000). [CrossRef]

], graphite [5

5. K. Ishioka, M. Hase, M. Kitajima, and K. Ushida, “Ultrafast carrier and phonon dynamics in ion-irradiated graphite,” Appl. Phys. Lett. 78(25), 3965–3967 (2001). [CrossRef]

] and GaAs [6

6. M. Hase, K. Ishioka, M. Kitajima, and K. Ushida, “Ultrafast carrier and plasmon-phonon dynamics in ion-irradiated n-GaAs,” Appl. Phys. Lett. 82(21), 3668–3670 (2003). [CrossRef]

] 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

7. R. Leonhardt, W. Holzapfel, W. Zinth, and W. Kaiser, “Terahertz beats of vibrational modes studied by femtosecond coherent Raman spectroscopy,” Rev. Phys. Appl. (Paris) 22(12), 1735–1741 (1987). [CrossRef]

14

14. M. Karavitis, R. Zadoyan, and V. Ara Apkarian, “Time resolved coherent anti-Stokes Raman scattering of I2 isolated in matrix argon: Vibrational dynamics on the ground electronic state,” J. Chem. Phys. 114(9), 4131–4140 (2001). [CrossRef]

], 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

3. G. G. Wang, M. F. Zhang, J. C. Han, X. D. He, H. B. Zuo, and X. H. Yang, “High-temperature infrared and dielectric properties of large sapphire crystal for seeker dome application,” Cryst. Res. Technol. 43(5), 531–536 (2008). [CrossRef]

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

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

17. A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay,” Appl. Phys. Lett. 80(9), 1505–1507 (2002). [CrossRef]

,18

18. M. Cui, M. Joffre, J. Skodack, and J. P. Ogilvie, “Interferometric Fourier transform coherent antistokes Raman scattering,” Opt. Express 14(18), 8448–8458 (2006). [CrossRef] [PubMed]

]:

Sc(τ)+|Pc(3)(τ,t)|2dt
(1)

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

7. R. Leonhardt, W. Holzapfel, W. Zinth, and W. Kaiser, “Terahertz beats of vibrational modes studied by femtosecond coherent Raman spectroscopy,” Rev. Phys. Appl. (Paris) 22(12), 1735–1741 (1987). [CrossRef]

,18

18. M. Cui, M. Joffre, J. Skodack, and J. P. Ogilvie, “Interferometric Fourier transform coherent antistokes Raman scattering,” Opt. Express 14(18), 8448–8458 (2006). [CrossRef] [PubMed]

,19

19. D. S. Choi, S. C. Jeoung, and B. H. Chon, “Thickness dependent CARS measurement of polymeric thin films without depth-profiling,” Opt. Express 16(4), 2604–2613 (2008). [CrossRef] [PubMed]

]. 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 τ=300fs (see Fig. 3
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.
). The signals show the expected quantum beat phenomena. Such a beat signal is often observed in fs-CARS experiments [7

7. R. Leonhardt, W. Holzapfel, W. Zinth, and W. Kaiser, “Terahertz beats of vibrational modes studied by femtosecond coherent Raman spectroscopy,” Rev. Phys. Appl. (Paris) 22(12), 1735–1741 (1987). [CrossRef]

9

9. M. Heid, S. Schlücker, U. Schmitt, T. Chen, R. Schweitzer-Stenner, V. Engel, and W. Kiefer, “Two-dimensional probing of ground-state vibrational dynamics in porphyrin molecules by fs-CARS,” J. Raman Spectrosc. 32(9), 771–784 (2001). [CrossRef]

,11

11. H. Kano and H. Hamaguchi, “Femtosecond coherent anti-Stokes Raman scattering spectroscopy using supercontinuum generated from a photonic crystal fiber,” Appl. Phys. Lett. 85(19), 4298–4300 (2004). [CrossRef]

], 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.

The delay time dependence of the CARS signal is fitted with the following function [7

7. R. Leonhardt, W. Holzapfel, W. Zinth, and W. Kaiser, “Terahertz beats of vibrational modes studied by femtosecond coherent Raman spectroscopy,” Rev. Phys. Appl. (Paris) 22(12), 1735–1741 (1987). [CrossRef]

9

9. M. Heid, S. Schlücker, U. Schmitt, T. Chen, R. Schweitzer-Stenner, V. Engel, and W. Kiefer, “Two-dimensional probing of ground-state vibrational dynamics in porphyrin molecules by fs-CARS,” J. Raman Spectrosc. 32(9), 771–784 (2001). [CrossRef]

]:

Sc(τ)Q0a2exp(2τ/T2a)+Q0b2exp(2τ/T2b)+2Q0aQ0bexp(τ(T2a+T2b)/T2aT2b)cos(Δωτ+Δφ)
(2)

Here T2a and T2b represent the dephasing times of two excited phonon modes, respectively, Δω and Δφ are the frequency difference and the phase shift at τ=0between the two modes, Q0aandQ0bare the coherent amplitudes defined by the transition strengths and other experimental conditions.

For the three sapphire samples, the frequency differences Δω 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 T2aand T2b (shown in Table 1

Table 1. The values of T2a,T2b and Δφobtained from fitting the experimental data with the function of Eq. (2)

table-icon
View This Table
) 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

20. A. Laubereau and W. Kaiser, “Vibrational dynamics of liquids and solids investigated by picosecond light pulses,” Rev. Mod. Phys. 50(3), 607–665 (1978). [CrossRef]

], as well as the ratio of Q0aand Q0b [9

9. M. Heid, S. Schlücker, U. Schmitt, T. Chen, R. Schweitzer-Stenner, V. Engel, and W. Kiefer, “Two-dimensional probing of ground-state vibrational dynamics in porphyrin molecules by fs-CARS,” J. Raman Spectrosc. 32(9), 771–784 (2001). [CrossRef]

], we are able to assign the longer dephasing time T2ato 645 cm−1 mode and the shorter one T2bto 750 cm−1 mode.

The dephasing process (T2) of coherent phonons in crystals consists of energy relaxation (T1) and pure dephasing (T2) 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/T2=1/T1+1/T2 [4

4. M. Hase, K. Ishioka, M. Kitajima, K. Ushida, and S. Hishita, “Dephasing of coherent phonons by lattice defects in bismuth films,” Appl. Phys. Lett. 76(10), 1258–1260 (2000). [CrossRef]

,20

20. A. Laubereau and W. Kaiser, “Vibrational dynamics of liquids and solids investigated by picosecond light pulses,” Rev. Mod. Phys. 50(3), 607–665 (1978). [CrossRef]

,21

21. V. Chernyak, A. Piryatinski, and S. Mukamel, “Complete Determination of Relaxation Parameters from Two-Dimensional Raman Spectroscopy,” Laser Chem. 19(1–4), 109–116 (1999). [CrossRef]

]. 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.

The phase shift Δφ between the two phonon modes atτ=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

23. G. A. Garrett, T. F. Albrecht, J. F. Whitaker, and R. Merlin, “Coherent THz Phonons Driven by Light Pulses and the Sb Problem: What is the Mechanism?” Phys. Rev. Lett. 77(17), 3661–3664 (1996). [CrossRef] [PubMed]

,24

24. M. Hase, K. Mizoguchi, H. Harima, S. Nakashima, and K. Sakai, “Dynamics of coherent phonons in bismuth generated by ultrashort laser pulses,” Phys. Rev. B 58(9), 5448–5452 (1998). [CrossRef]

]. Accordingly, the phase shift Δφ between the vibrational modes will change. When γ-rays irradiation doses are different, the changes of Δφ 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, Δφ 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 A1g and 750 cm−1 Eg 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.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 20973050).

References and links

1.

A. G. Lanin, E. L. Muravin, V. P. Popov, and V. N. Turchin, “Thermal shock resistance and thermal-mechanical processing of sapphire,” J. Eur. Ceram. Soc. 23(3), 455–468 (2003). [CrossRef]

2.

T. Vodenitcharova, L. C. Zhang, I. Zarudi, Y. Yin, H. Domyo, T. Ho, and M. Sato, “The effect of anisotropy on the deformation and fracture of sapphire wafers subjected to thermal shocks,” J. Mater. Process. Technol. 194(1–3), 52–62 (2007). [CrossRef]

3.

G. G. Wang, M. F. Zhang, J. C. Han, X. D. He, H. B. Zuo, and X. H. Yang, “High-temperature infrared and dielectric properties of large sapphire crystal for seeker dome application,” Cryst. Res. Technol. 43(5), 531–536 (2008). [CrossRef]

4.

M. Hase, K. Ishioka, M. Kitajima, K. Ushida, and S. Hishita, “Dephasing of coherent phonons by lattice defects in bismuth films,” Appl. Phys. Lett. 76(10), 1258–1260 (2000). [CrossRef]

5.

K. Ishioka, M. Hase, M. Kitajima, and K. Ushida, “Ultrafast carrier and phonon dynamics in ion-irradiated graphite,” Appl. Phys. Lett. 78(25), 3965–3967 (2001). [CrossRef]

6.

M. Hase, K. Ishioka, M. Kitajima, and K. Ushida, “Ultrafast carrier and plasmon-phonon dynamics in ion-irradiated n-GaAs,” Appl. Phys. Lett. 82(21), 3668–3670 (2003). [CrossRef]

7.

R. Leonhardt, W. Holzapfel, W. Zinth, and W. Kaiser, “Terahertz beats of vibrational modes studied by femtosecond coherent Raman spectroscopy,” Rev. Phys. Appl. (Paris) 22(12), 1735–1741 (1987). [CrossRef]

8.

R. Leonhardt, W. Holzapfel, W. Zinth, and W. Kaiser, “Terahertz quantum beats in molecular liquids,” Chem. Phys. Lett. 133(5), 373–377 (1987). [CrossRef]

9.

M. Heid, S. Schlücker, U. Schmitt, T. Chen, R. Schweitzer-Stenner, V. Engel, and W. Kiefer, “Two-dimensional probing of ground-state vibrational dynamics in porphyrin molecules by fs-CARS,” J. Raman Spectrosc. 32(9), 771–784 (2001). [CrossRef]

10.

M. Heid, T. Chen, U. Schmitt, and W. Kiefer, “Spectrally resolved fs-CARS as a probe of the vibrational dynamics of a large polyatomic molecule: magnesium octaethylporphyrin,” Chem. Phys. Lett. 334(1–3), 119–126 (2001). [CrossRef]

11.

H. Kano and H. Hamaguchi, “Femtosecond coherent anti-Stokes Raman scattering spectroscopy using supercontinuum generated from a photonic crystal fiber,” Appl. Phys. Lett. 85(19), 4298–4300 (2004). [CrossRef]

12.

D. Pestov, M. C. Zhi, Z. E. Sariyanni, N. G. Kalugin, A. Kolomenskii, R. Murawski, Y. V. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, and M. O. Scully, “Femtosecond CARS of methanol–water mixtures,” J. Raman Spectrosc. 37(1–3), 392–396 (2006). [CrossRef]

13.

S. Meyer, M. Schmitt, A. Materny, W. Kiefer, and V. Engel, “A theoretical analysis of the time-resolved femtosecond CARS spectrum of I2,” Chem. Phys. Lett. 281(4–6), 332–336 (1997). [CrossRef]

14.

M. Karavitis, R. Zadoyan, and V. Ara Apkarian, “Time resolved coherent anti-Stokes Raman scattering of I2 isolated in matrix argon: Vibrational dynamics on the ground electronic state,” J. Chem. Phys. 114(9), 4131–4140 (2001). [CrossRef]

15.

Y. J. Lee, S. H. Parekh, Y. H. Kim, and M. T. Cicerone, “Optimized continuum from a photonic crystal fiber for broadband time-resolved coherent anti-Stokes Raman scattering,” Opt. Express 18(5), 4371–4379 (2010). [CrossRef] [PubMed]

16.

M. Kadleíková, J. Breza, and M. Veselý, “Raman spectra of synthetic sapphire,” Microelectron. J. 32(12), 955–958 (2001). [CrossRef]

17.

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay,” Appl. Phys. Lett. 80(9), 1505–1507 (2002). [CrossRef]

18.

M. Cui, M. Joffre, J. Skodack, and J. P. Ogilvie, “Interferometric Fourier transform coherent antistokes Raman scattering,” Opt. Express 14(18), 8448–8458 (2006). [CrossRef] [PubMed]

19.

D. S. Choi, S. C. Jeoung, and B. H. Chon, “Thickness dependent CARS measurement of polymeric thin films without depth-profiling,” Opt. Express 16(4), 2604–2613 (2008). [CrossRef] [PubMed]

20.

A. Laubereau and W. Kaiser, “Vibrational dynamics of liquids and solids investigated by picosecond light pulses,” Rev. Mod. Phys. 50(3), 607–665 (1978). [CrossRef]

21.

V. Chernyak, A. Piryatinski, and S. Mukamel, “Complete Determination of Relaxation Parameters from Two-Dimensional Raman Spectroscopy,” Laser Chem. 19(1–4), 109–116 (1999). [CrossRef]

22.

G. Q. Zhou, Y. J. Dong, J. Xu, H. J. Li, J. L. Si, X. B. Qian, and X. Q. Li, “Φ140 mm sapphire crystal growth by temperature gradient techniques and its color centers,” Mater. Lett. 60(7), 901–904 (2006). [CrossRef]

23.

G. A. Garrett, T. F. Albrecht, J. F. Whitaker, and R. Merlin, “Coherent THz Phonons Driven by Light Pulses and the Sb Problem: What is the Mechanism?” Phys. Rev. Lett. 77(17), 3661–3664 (1996). [CrossRef] [PubMed]

24.

M. Hase, K. Mizoguchi, H. Harima, S. Nakashima, and K. Sakai, “Dynamics of coherent phonons in bismuth generated by ultrashort laser pulses,” Phys. Rev. B 58(9), 5448–5452 (1998). [CrossRef]

OCIS Codes
(300.6230) Spectroscopy : Spectroscopy, coherent anti-Stokes Raman scattering
(300.6500) Spectroscopy : Spectroscopy, time-resolved
(300.6530) Spectroscopy : Spectroscopy, ultrafast

ToC Category:
Spectroscopy

History
Original Manuscript: July 28, 2010
Revised Manuscript: September 24, 2010
Manuscript Accepted: October 7, 2010
Published: October 14, 2010

Citation
Xin Du, Mingfu Zhang, Qingkun Meng, Yunfei Song, Xing He, Yanqiang Yang, and Jiecai Han, "Phonon dynamics in γ-ray irradiated sapphire crystals studied by fs-CARS technique," Opt. Express 18, 22937-22943 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-22-22937


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References

  1. A. G. Lanin, E. L. Muravin, V. P. Popov, and V. N. Turchin, “Thermal shock resistance and thermal-mechanical processing of sapphire,” J. Eur. Ceram. Soc. 23(3), 455–468 (2003). [CrossRef]
  2. T. Vodenitcharova, L. C. Zhang, I. Zarudi, Y. Yin, H. Domyo, T. Ho, and M. Sato, “The effect of anisotropy on the deformation and fracture of sapphire wafers subjected to thermal shocks,” J. Mater. Process. Technol. 194(1–3), 52–62 (2007). [CrossRef]
  3. G. G. Wang, M. F. Zhang, J. C. Han, X. D. He, H. B. Zuo, and X. H. Yang, “High-temperature infrared and dielectric properties of large sapphire crystal for seeker dome application,” Cryst. Res. Technol. 43(5), 531–536 (2008). [CrossRef]
  4. M. Hase, K. Ishioka, M. Kitajima, K. Ushida, and S. Hishita, “Dephasing of coherent phonons by lattice defects in bismuth films,” Appl. Phys. Lett. 76(10), 1258–1260 (2000). [CrossRef]
  5. K. Ishioka, M. Hase, M. Kitajima, and K. Ushida, “Ultrafast carrier and phonon dynamics in ion-irradiated graphite,” Appl. Phys. Lett. 78(25), 3965–3967 (2001). [CrossRef]
  6. M. Hase, K. Ishioka, M. Kitajima, and K. Ushida, “Ultrafast carrier and plasmon-phonon dynamics in ion-irradiated n-GaAs,” Appl. Phys. Lett. 82(21), 3668–3670 (2003). [CrossRef]
  7. R. Leonhardt, W. Holzapfel, W. Zinth, and W. Kaiser, “Terahertz beats of vibrational modes studied by femtosecond coherent Raman spectroscopy,” Rev. Phys. Appl. (Paris) 22(12), 1735–1741 (1987). [CrossRef]
  8. R. Leonhardt, W. Holzapfel, W. Zinth, and W. Kaiser, “Terahertz quantum beats in molecular liquids,” Chem. Phys. Lett. 133(5), 373–377 (1987). [CrossRef]
  9. M. Heid, S. Schlücker, U. Schmitt, T. Chen, R. Schweitzer-Stenner, V. Engel, and W. Kiefer, “Two-dimensional probing of ground-state vibrational dynamics in porphyrin molecules by fs-CARS,” J. Raman Spectrosc. 32(9), 771–784 (2001). [CrossRef]
  10. M. Heid, T. Chen, U. Schmitt, and W. Kiefer, “Spectrally resolved fs-CARS as a probe of the vibrational dynamics of a large polyatomic molecule: magnesium octaethylporphyrin,” Chem. Phys. Lett. 334(1–3), 119–126 (2001). [CrossRef]
  11. H. Kano and H. Hamaguchi, “Femtosecond coherent anti-Stokes Raman scattering spectroscopy using supercontinuum generated from a photonic crystal fiber,” Appl. Phys. Lett. 85(19), 4298–4300 (2004). [CrossRef]
  12. D. Pestov, M. C. Zhi, Z. E. Sariyanni, N. G. Kalugin, A. Kolomenskii, R. Murawski, Y. V. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, and M. O. Scully, “Femtosecond CARS of methanol–water mixtures,” J. Raman Spectrosc. 37(1–3), 392–396 (2006). [CrossRef]
  13. S. Meyer, M. Schmitt, A. Materny, W. Kiefer, and V. Engel, “A theoretical analysis of the time-resolved femtosecond CARS spectrum of I2,” Chem. Phys. Lett. 281(4–6), 332–336 (1997). [CrossRef]
  14. M. Karavitis, R. Zadoyan, and V. Ara Apkarian, “Time resolved coherent anti-Stokes Raman scattering of I2 isolated in matrix argon: Vibrational dynamics on the ground electronic state,” J. Chem. Phys. 114(9), 4131–4140 (2001). [CrossRef]
  15. Y. J. Lee, S. H. Parekh, Y. H. Kim, and M. T. Cicerone, “Optimized continuum from a photonic crystal fiber for broadband time-resolved coherent anti-Stokes Raman scattering,” Opt. Express 18(5), 4371–4379 (2010). [CrossRef] [PubMed]
  16. M. Kadleı́ková, J. Breza, and M. Veselý, “Raman spectra of synthetic sapphire,” Microelectron. J. 32(12), 955–958 (2001). [CrossRef]
  17. A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay,” Appl. Phys. Lett. 80(9), 1505–1507 (2002). [CrossRef]
  18. M. Cui, M. Joffre, J. Skodack, and J. P. Ogilvie, “Interferometric Fourier transform coherent antistokes Raman scattering,” Opt. Express 14(18), 8448–8458 (2006). [CrossRef] [PubMed]
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