- Email: [email protected]
Ultrafast dynamics of carriers and nonlinear refractive index in bulk polycrystalline diamond
Accepted Manuscript Title: Ultrafast dynamics of carriers and nonlinear refractive index in bulk polycrystalline diamond Author: Ben Zhang Shenye Liu Xingzhi Wu Tao Yi Yu Fang Jian Zhang Quanjie Zhong Xiaoshi Peng Xiangming Liu Yinglin Song PII: DOI: Reference:
S0030-4026(16)31444-9 http://dx.doi.org/doi:10.1016/j.ijleo.2016.11.107 IJLEO 58523
To appear in: Received date: Accepted date:
29-9-2016 23-11-2016
Please cite this article as: Ben Zhang, Shenye Liu, Xingzhi Wu, Tao Yi, Yu Fang, Jian Zhang, Quanjie Zhong, Xiaoshi Peng, Xiangming Liu, Yinglin Song, Ultrafast dynamics of carriers and nonlinear refractive index in bulk polycrystalline diamond, Optik - International Journal for Light and Electron Optics http://dx.doi.org/10.1016/j.ijleo.2016.11.107 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Ultrafast dynamics of carriers and nonlinear refractive index in bulk polycrystalline diamond
Ben Zhang a, Shenye Liu a,*, Xingzhi Wu b, Tao Yi a, Yu Fang b, Jian Zhang a, Quanjie Zhong a, Xiaoshi Peng a, Xiangming Liu a, and Yinglin Song b
a
Research Center of Laser Fusion, China Academy of Engineering Physics,
Mianyang 621900, China b
School of Physical Science and Technology, Soochow University, Suzhou 215006,
China
*Correspondence author: Shenye Liu, [email protected]
Abstract The free-carrier dynamics and nonlinear refractive index in bulk polycrystalline diamond are investigated using a femtosecond ultraviolet-pump-optical-probe technique with a phase object. Normalized transmittances under open-aperture and closed-aperture
1
conditions are simultaneously measured to determine the dynamics of nonlinear absorption and refraction in the sample. In the dynamics of nonlinear absorption, three processes are clearly observed: nondegenerate two-photon absorption, fast and slower decay components of the free-carrier dynamics. The lifetimes of the free carriers are precisely measured. In the dynamics of nonlinear refraction, we obtain the nonlinear refractive coefficient and find that the results obtained under the femtosecond regime differ from those of other semiconducting materials previously measured under the picosecond regime.
Keywords: optical nonlinear dynamics; diamond; free carriers; pump-probe technique; phase object
2
1. Introduction
As the hardest known material, diamond plays an important role in scientific research [1]. After the appearance of the laser in 1960 [2], the optical properties of diamond have been of significant interest. In particular, the nonlinear optical properties of single-crystal diamond [3–8] and nanocrystalline diamond membranes [9–12] under high-intensity laser irradiation have been studied. Meanwhile, diamond Raman lasers with continuous-wave [13] and ultrashort-pulses [14,15] have also been reported. In studies of inertial confinement fusion (ICF), diamond is often used as the window material of the optical diagnostic apparatus on account of its strength and high transmittance in the UV-VIS spectral regime [16]. Furthermore, in the development of the chemical vapor deposition (CVD) technique, optical-grade CVD polycrystalline diamond has been used instead of single-crystal diamond because of its lower cost. In ICF experiments, the high-intensity drive laser and laser-plasma-induced X-ray can change the optical properties of the window materials which leads to changes in the strength and phase of the probe beam in diagnostic apparatuses. This process can lead to inaccuracies of the measurement results. Therefore, it is important to investigate the
3
ultrafast dynamics of carriers and nonlinear optical properties in bulk polycrystalline diamond. Pump-probe techniques have been used widely to study ultrafast dynamics in various materials [17–20]. According to this technique, the laser source is split into two beams (pump beam and probe beam). These two beams are then focused on the sample with a certain time delay. The ultrafast dynamics in the sample can then be investigated by recording the intensity of the probe beam under different time delays. Recently, the phase object (PO) has been applied to the pump-probe scheme in order to increase the precision of measurements [21–23]. The PO is used to shift the phase of the central part of probe beam and then enhance the interference in the probe beam. Therefore the intensity of probe beam measured by energy detectors is modulated which results in improvements in the measurement accuracy. Moreover, by using this approach, the dynamics of nonlinear absorption and nonlinear refraction can be measured simultaneously. In this paper, we report on the ultrafast dynamics of nonlinear optical phenomena in bulk polycrystalline diamond using a femtosecond nondegenerate pump-probe technique with a phase object.
2. Experimental setup
4
A two-color pump-probe scheme with a PO was built, as shown in Fig. 1. Laser pulses with a wavelength of 515 nm, a full width at half maximum (FWHM) of 190 fs, and a repetition rate of 20 Hz were generated using a Yb:KGW laser amplifier (made by Light Conversion, and the second harmonic of the output was used). The pulses were split into two beams that acted as the sources of the pump and probe beams, respectively. An optical parametric amplification system (OPA) was used to change the wavelength of the pump pulses to 351 nm because this wavelength has usually been chosen to be the wavelength of drive laser in ICF experiments. The duration of the pump pulse that is obtained from the OPA was measured to be 200 fs. A time-delay stage was placed in the pump beam. All the optical elements were precisely arranged to ensure that the pump and probe beams were stable during the movement of the time-delay stage. The probe beam was spatially filtered by L1, L2 and a pinhole to obtain a near Gaussian beam. An optical-grade CVD diamond, which is fabricated by Element Six and had dimensions of 33 mm × 12 mm × 0.7 mm, was used as the sample. The sample had a band gap of 5.5 eV [3]. The photon energies of the pump and probe beams were 3.54 eV and 2.41 eV, respectively. The probe beam was too weak to generate any nonlinear
5
optical phenomena in the sample. When there was no pump, the transmittance of the probe beam through the sample was 70% because of the reflection on the surfaces and the scattering in the sample. A PO was placed in the optical path of the probe beam. The PO, which consisted of a glass plate and a transparent dielectric disc (radius of 0.5 mm) deposited on the plate, did not absorb the probe beam. However, the phase of the incident light through the disc was retarded relative to the light that was not incident on the disc. The interference between these two parts of the probe beam was enhanced, and the intensity of the beam was modulated after passing through the sample. In this way, changes in the absorption and refraction of the sample can be determined by the energy detectors D1 and D2. The pump and probe beams were focused on the same point of the sample at a small angle (about 5°) with respect to each other. The diameters of the focal points of the pump and probe beams were 220 μm and 30 μm, respectively. After the sample, the probe beam was split into two beams. The energy detectors (D1, D2) were used to measure the energy of these two beams, respectively. An aperture was placed before D2; its radius was accurately adjusted to be equal to the radius of the diffraction of the light through the disc of the PO. The two-photon absorption (TPA) coefficient, free-carrier absorption cross-section, Kerr refractive index, free-carrier refractive index, and
6
free-carrier lifetime of the sample can be calculated using the normalized transmittance of the probe beam under open-aperture and closed-aperture conditions, as measured by D1, D2, and D3. The theories for bound electric and free-carrier nonlinearity of semiconductors in the PO pump-probe system have been described [21] and adapted [23] before, and therefore it is not necessary to repeat the theories here in this paper. All experiments were carried out at room temperature.
3. Results and discussion
The open-aperture result of the sample is shown in Fig. 2. The energy density of the pump pulse is 4.5 mJ/cm2 (pulse energy: 1.7 μJ). In the dynamics of nonlinear absorption, we can observe an abrupt reduction in the normalized transmittance of the probe beam at zero time delay, along with a relatively slow recovery after zero time delay. When the pump and probe pulses are synchronized and focused on the sample, a pump photon and a probe photon can be absorbed simultaneously to excite an electron from the valance band to the conduction band. Therefore, the transmittance of the probe beam decreases; this process is known as nondegenerate two-photon absorption (ND-TPA). In addition, two pump photons can also be absorbed simultaneously by the
7
sample and subsequently excite an electron; this process is known as degenerate TPA. At this stage, a reduction of the probe beam’s transmittance can be observed because of the interactions between photons and excited electrons. Therefore, the dynamics of free carriers can be detected by scanning the relative retardation between the pump and probe beams. Investigation of carrier recombination and diffusivity in bulk microcrystalline CVD diamonds has been reported [30]. They observed the very fast (80ps) and slower (3–8ns) decay components of the free-carrier dynamics. These two components have also been observed in polycrystalline diamond. The variation of the normalized transmittance can be described as follows: ∆Ttotal = ∆TND−TPA + ∆Te1 + ∆Te2
(1)
The ND-TPA process occurs only when the pump and probe pulses are temporally overlapped. As shown in the inset of Fig. 2, the FWHM of this process is 0.3 ps, which is consistent with the temporal width of the pump and probe pulses, considering the temporal broadening of the pulses induced by the optical elements. As the time delay between the pump and probe beams increases, the ND-TPA process quickly disappears. At the same time, the nonlinear absorption caused by free carriers decays exponentially. In other words, ∆Te1 = A1 e−t/τ1
8
(2)
∆Te2 = A2 e−t/τ2
(3)
From the measurement shown in Fig. 2, we have τ1 = 85 ps (±4 ps) and τ2 = 2324 ps (±38 ps), which represent the lifetimes of fast and slower decay components of the free-carrier dynamics, respectively. The nonlinear absorption dynamics with the pump pulse energy densities of 10.1 mJ/cm2 and 14.6 mJ/cm2 have also been measured, as shown in Fig. 3(a) and Fig. 3(b) respectively. The lifetimes of free carriers with different pump pulse energy densities are listed in Table 1.
Pump and probe technique with two-photon excitation has also been applied to monocrystalline diamond in recent years [26,27]. In Ref. 26, the infrared probe photons were used to measure the free-carrier absorption. Because of the different experimental setup, it is not proper [28,29] to use the Drude model to compare the experiments on polycrystalline diamond here and the experiments on monocrystalline diamond in Ref. 26. The nonlinear refraction dynamics of the sample within the femtosecond regime can be determined using D2 (closed-aperture conditions), as shown in Fig. 4. The phase variation of the probe beam can be obtained by fitting the experimental data of D2 according to the theory of Fresnel diffraction. In Fig. 4, the closed-aperture result is
9
shown and fitted. The energy density of the pump pulse is 0.60 mJ/cm2 (pulse energy: 0.23 μJ), which is 7.5 times smaller than what is used in Fig. 2. Under this pump intensity, the dynamics of nonlinear absorption detected by D1 (open-aperture conditions) is almost negligible. As a result of the very weak pump intensity, the nonlinear refractive index originating from free carriers is too weak to be detected. But the resulting free carriers constitute a cluster of plasma, and plasma dispersion will produce a decrease in the refractive index of the material. The free carriers have a lifeime of about a hundred picoseconds, as shown in Tab. 1. Therefore, the opposite sign of the fast and slow components of the refractive index can be apparently seen from Fig. 4. In order to make the measurement of nonlinear refractive coefficient more precise, the nonlinear refraction dynamics of the sample has been measured and fitted using different pump pulse energy densities (0.47 mJ/cm2, 0.60 mJ/cm2, and 0.91 mJ/cm2), as shown in Fig. 5. The corresponding open-aperture results have been used to separate the nonlinear absorption out from the closed-aperture data. The refractive index of the sample can be described by the following equation: n = n0 + n2 I
10
(4)
where n0 represents the refractive index in the absence of a pump pulse, I represents the intensity of the pump pulse, and n2 is the nonlinear refractive coefficient. By analyzing the experimental data shown in Fig. 4, we measure n2 to be (1.4±0.2)×10−15 cm2/W. The third order nonlinear susceptibility χ(3) which correspond to the measured n2 has been calculated to be 2.7×10-21 m2/V2. The third-order nonlinear optical coefficients of various materials have been listed by Boyd in Ref. [25], where the nonlinear refractive coefficient of diamond is 1.3×10−15 cm2/W. There are three possible causes of the difference between the measured n2 of polycrystalline diamond and the nonlinear refractive coefficient of single crystal diamond listed in Ref. [25]. First, In Ref. [25], only the third-order nonlinear process (which is due to the response of bound electrons) was considered to calculate and measure the nonlinear optical coefficient. While in our nondegenerate PO pump-probe regime, the measured n2 also contains the nonlinear refractive index caused by ND-TPA processes according to the Kramers-Kronig relations. Second, the grain boundaries may also generate an additional nonlinear refractive index in polycrystalline diamond. Third, we measured n2 to be (1.4±0.2)×10−15 cm2/W. Therefore, the difference may also be caused by the measurement error. Further researches and more accurate experiments should be done to clearly understand this difference.
11
It is worth noting that the closed-aperture results of the sample are different from those of other semiconducting materials, such as GaN [21], CdS [22], and ZnS [23]. This can be explained by the fact that, in those experiments, the nonlinear refractive index originating from TPA processes is much smaller than that caused by free carriers. By way of contrast, in our results, the nonlinear refractive index caused by free carriers is almost negligible in comparison with that due to ND-TPA processes. In other words, the free-carrier process was the main source of the nonlinear refractive index of the materials in the picosecond PO pump-probe experiments. While in our femtosecond PO pump-probe experiments, the ND-TPA process was the main source of the nonlinear refractive index of the sample. This is because we used the femtosecond regime instead of the picosecond regime; as a result, the intensity of beams is higher and the bound electric effect is stronger. In addition, the sensitivity of the pump-probe system could be improved when a PO was introduced into the system [21-23]. The experiments on polycrystalline diamond illustrated this point again. As we see, the nonlinear refractive index has been detected at a lower fluence.
4. Conclusion
12
The femtosecond ultraviolet pump-optical-probe regime technique (with the use of a PO) has been used to investigate the ultrafast dynamics of free carriers and the nonlinear refractive index in bulk polycrystalline diamond. Three processes were observed in the nonlinear absorption dynamics: the ND-TPA process, fast and slower decay components of the free-carrier dynamics. The lifetimes of the free carriers were precisely measured. Contrary to the results concerning other semiconducting materials previously measured under the picosecond regime, our results for diamond under the femtosecond regime show that the nonlinear refractive index caused by free carriers is very small in comparison to that due to the ND-TPA process. The nonlinear refractive coefficient n2 (caused by the nondegenerate bound electric Kerr effect) has been measured to be 1.4×10−15 cm2/W which is a little larger than that of a single crystal diamond (1.3×10−15 cm2/W). This means that when we use a polycrystalline diamond instead of a single crystal diamond as the window material, the nonlinear refractive index would become a little larger. This phenomenon should be considered along with the cost to choose the suitable window material. In addition, the measured n2 can be used to evaluate the inaccuracies of the measurement results when a polycrystalline diamond has been chosen to be the window material in a specific ICF experiment. This work can help in improving the measurement accuracy of diagnostic apparatuses in ICF
13
experiments and facilitate our understanding of the ultrafast dynamics of carriers and the nonlinear refractive index in diamond.
Acknowledgements
We gratefully acknowledge the Project Funded by National Natural Science Foundation of China (Grant Nos. 11575166 and 51581140).
References [1] M. I. Eremets, I. A. Trojan, P. Gwaze, J. Huth, R. Boehler, and V. D. Blank, The strength of diamond, Appl. Phys. Lett. 87 (2005) 141902. [2] T. H. Maiman, Stimulated optical radiation in ruby, Nature 187 (1960) 493-494. [3] L. S. Pan, D. R. Kania, P. Pianetta, and O. L. Landen, Carrier density dependent photoconductivity in diamond, Appl. Phys. Lett. 57 (1990) 623-625.
14
[4] D. H. Reitze, H. Ahn, and M. C. Downer, Optical properties of liquid carbon measured by femtosecond spectroscopy, Phys. Rev. B 45 (1992) 2677-2693. [5] S. Preuss, and M. Stuke, Subpicosecond ultraviolet laser ablation of diamond: Nonlinear properties at 248 nm and time-resolved characterization of ablation dynamics, Appl. Phys. Lett. 67 (1995) 338-340. [6] N. Naka, T. Kitamura, J. Omachi, and M. Kuwata-Gonokami, Low-temperature excitons produced by two-photon excitation in high-purity diamond crystals, Phys. Stat. Sol. B 245 (2008) 2676-2679. [7] N. Naka, J. Omachi, H. Sumiya, K. Tamasaku, T. Ishikawa, and M. Kuwata-Gonokami, Density-dependent exciton kinetics in synthetic diamond crystals, Phys. Rev. B 80 (2009) 035201. [8] M. Kozák, F. Trojánek, and P. Malý, Large prolongation of free-exciton photoluminescence decay in diamond by two-photon excitation, Opt. Lett. 37 (2012) 2049-2051. [9] K. Murayama, Y. Sakamoto, T. Fujisaki, S. Yamasaki, and H. Okushi, Free-exciton luminescence spectrum broadening due to excitonic complex in diamond, Diamond Related Materials 16 (2007) 958-961.
15
[10] P. Němec, J. Preclíková, A. Kromka, B. Rezek, F. Trojánek, and P. Malý, Ultrafast dynamics of photoexcited charge carriers in nanocrystalline diamond, Appl. Phys. Lett. 93 (2008) 083102. [11] F. Trojánek, K. Žídek, B. Dzurňák, M. Kozák, and P. Malý, Nonlinear optical properties of nanocrystalline diamond, Opt. Express 18 (2010) 1349-1357. [12] J. Preclíková, A. Kromka, B. Rezek, and P. Malý, Laser-induced refractive index changes in nanocrystalline diamond membranes, Opt. Lett. 35 (2010) 577-579. [13] W. Lubeigt, G. M. Bonner, J. E. Hastie, M. D. Dawson, D. Burns, and A. J. Kemp, Continuous-wave diamond Raman laser, Opt. Lett. 35 (2010) 2994-2996. [14] D. J. Spence, E. Granados, and R. P. Mildren, Mode-locked picoseconds diamond Raman laser, Opt. Lett. 35 (2010) 556-558. [15] M. Murtagh, J. Lin, R. P. Mildren, and D. J. Spence, Ti:sapphire-pumped diamond Raman laser with sub-100-fs pulse duration, Opt. Lett. 39 (2014) 2975-2978. [16] W. Theobald, J. E. Miller, T. R. Boehly, E. Vianello, D. D. Meyerhofer, T. C. Sangster, J. Eggert, and P. M. Celliers, X-ray preheating of window materials in direct-drive shock-wave timing experiments, Phys. Plasmas 13 (2006) 122702. [17] W. Wu, and Y. Wang, Ultrafast carrier dynamics and coherent acoustic phonons in bulk CdSe, Opt. Lett. 40 (2015) 64-67.
16
[18] G. Batignani, D. Bossini, N. Di Palo, C. Ferrante, E. Pontecorvo, G. Cerullo, A. Kimel, and T. Scopigno, Probing ultrafast photo-induced dynamics of the exchange energy in a Heisenberg antiferromagnet, Nat. Photon. 9 (2015) 506-510. [19] S. M. Durbin, T. Clevenger, T. Graber, and R. Henning, X-ray pump optical probe cross-correlation study of GaAs, Nat. Photon. 6 (2012) 111-114. [20] O. Krupin, M. Trigo, W. F. Schlotter, M. Beye, F. Sorgenfrei, J. J. Turner, D. A. Reis, N. Gerken, S. Lee, W. S. Lee, G. Hays, Y. Acremann, B. Abbey, R. Coffee, M. Messerschmidt, S. P. Hau-Riege, G. Lapertot, J. Lüning, P. Heimann, R. Soufli, M. Fernández-Perea, M. Rowen, M. Holmes, S. L. Molodtsov, A. Föhlisch, and W. Wurth, Temporal cross-correlation of x-ray free electron and optical lasers using soft x-ray pulse induced transient reflectivity, Opt. Express 20 (2012) 11396-11406. [21] Y. Fang, X. Z. Wu, F. Ye, X. Y. Chu, Z. G. Li, J. Y. Yang, and Y. L. Song, Dynamics of optical nonlinearities in GaN, J. Appl. Phys. 114 (2013) 103507. [22] M. Shui, X. Jin, Z. G. Li, J. Y. Yang, G. Shi, Z. Q. Nie, X. Z. Wu, Y. X. Wang, K. Yang, X. R. Zhang, and Y. L. Song, Investigation of nonlinear dynamics in CdS by time-resolved nondegenerate pump-probe system with phase object, J. Mod. Opt. 58 (2011) 973-977.
17
[23] M. Shui, Z. G. Li, X. Jin, J. Y. Yang, Z. Q. Nie, G. Shi, X. Z. Wu, K. Yang, X. R. Zhang, Y. X. Wang, and Y. L. Song, Measurement of dynamics of nondegenerate optical nonlinearity in ZnS with pulses from optical parameter generation, Opt. Commun. 285 (2012) 1940-1944. [24] W. Saslow, T. K. Bergstresser, and M. L. Cohen, Band structure and optical properties of diamond, Phys. Rev. Lett. 16 (1966) 354-356. [25] R. W. Boyd, Nonlinear Optics, (Academic Press, Singapore, 2009), p.212. [26] M. Kozák, F. Trojánek, T. Popelář, and P. Malý, Dynamics of electron-hole liquid condensation in CVD diamond studied by femtosecond pump and probe spectroscopy, Diamond & Related Materials 34 (2013) 13-18. [27] P. Šcajev, V. Gudelis, E. Ivakin, and K. Jarašiūnas, Nonequilibrium carrier dynamics in bulk HPHT diamond at two-photon carrier generation, Phys. Status Solidi A 208 (2011) 2067-2072. [28] J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, Time-resolved Z-scan measurements of optical nonlinearities, J. Opt. Soc. Am. B 11 (1994) 1009-1017.
18
[29] Y. Li, G. Pan, K. Yang, X. Zhang, Y. Wang, T. Wei, and Y. Song, Time-resolved pump-probe system based on a nonlinear imaging technique with phase object, Opt. Express 16 (2008) 6251-6259. [30] P. Šcajev, V. Gudelis, K. Jarašiūnas, I. Kisialiou, E. Ivakin, M. Nesládek, and K. Haenen, Carrier recombination and diffusivity in microcrystalline CVD-grown and single-crystalline HPHT diamonds, Phys. Status Solidi A 209 (2012) 1744-1749
19
Figure Captions Fig. 1. Ultraviolet-pump-optical-probe scheme with a phase object. M1 and M2: mirrors. P1 and P2: polarizers. BS1–BS3: beam splitters. L1–L6: lenses. D1–D3: energy detectors.
Fig. 2. Nonlinear absorption dynamics of diamond (open-aperture conditions). Inset: experimental data and theoretical curve near zero time delay.
20
Fig. 3. Nonlinear absorption dynamics of diamond with pump pulse energy density of (a) 10.1 mJ/cm2, and (b) 14.6 mJ/cm2.
21
Fig. 4. Nonlinear refraction dynamics of diamond (closed-aperture conditions). Inset: experimental data and theoretical curve near zero time delay.
22
Fig. 5. Nonlinear refraction dynamics of diamond with different pump pulse energy densities.
23
24
Table 1: Parameters obtained from the nonlinear absorption dynamics of the sample with different pump pulse energy densities.
τ1 (ps)
A1
τ2 (ps)
A2
4.5
85±4
-0.00690±0.00011
2324±38
-0.02797±0.00006
10.1
134±10
-0.00848±0.00028
963±29
-0.03148±0.00022
14.6
76±3
-0.03283±0.00031
1548±24
-0.12856±0.00011
Pump pulse energy density (mJ/cm2)
25
S0030-4026(16)31444-9 http://dx.doi.org/doi:10.1016/j.ijleo.2016.11.107 IJLEO 58523
To appear in: Received date: Accepted date:
29-9-2016 23-11-2016
Please cite this article as: Ben Zhang, Shenye Liu, Xingzhi Wu, Tao Yi, Yu Fang, Jian Zhang, Quanjie Zhong, Xiaoshi Peng, Xiangming Liu, Yinglin Song, Ultrafast dynamics of carriers and nonlinear refractive index in bulk polycrystalline diamond, Optik - International Journal for Light and Electron Optics http://dx.doi.org/10.1016/j.ijleo.2016.11.107 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Ultrafast dynamics of carriers and nonlinear refractive index in bulk polycrystalline diamond
Ben Zhang a, Shenye Liu a,*, Xingzhi Wu b, Tao Yi a, Yu Fang b, Jian Zhang a, Quanjie Zhong a, Xiaoshi Peng a, Xiangming Liu a, and Yinglin Song b
a
Research Center of Laser Fusion, China Academy of Engineering Physics,
Mianyang 621900, China b
School of Physical Science and Technology, Soochow University, Suzhou 215006,
China
*Correspondence author: Shenye Liu, [email protected]
Abstract The free-carrier dynamics and nonlinear refractive index in bulk polycrystalline diamond are investigated using a femtosecond ultraviolet-pump-optical-probe technique with a phase object. Normalized transmittances under open-aperture and closed-aperture
1
conditions are simultaneously measured to determine the dynamics of nonlinear absorption and refraction in the sample. In the dynamics of nonlinear absorption, three processes are clearly observed: nondegenerate two-photon absorption, fast and slower decay components of the free-carrier dynamics. The lifetimes of the free carriers are precisely measured. In the dynamics of nonlinear refraction, we obtain the nonlinear refractive coefficient and find that the results obtained under the femtosecond regime differ from those of other semiconducting materials previously measured under the picosecond regime.
Keywords: optical nonlinear dynamics; diamond; free carriers; pump-probe technique; phase object
2
1. Introduction
As the hardest known material, diamond plays an important role in scientific research [1]. After the appearance of the laser in 1960 [2], the optical properties of diamond have been of significant interest. In particular, the nonlinear optical properties of single-crystal diamond [3–8] and nanocrystalline diamond membranes [9–12] under high-intensity laser irradiation have been studied. Meanwhile, diamond Raman lasers with continuous-wave [13] and ultrashort-pulses [14,15] have also been reported. In studies of inertial confinement fusion (ICF), diamond is often used as the window material of the optical diagnostic apparatus on account of its strength and high transmittance in the UV-VIS spectral regime [16]. Furthermore, in the development of the chemical vapor deposition (CVD) technique, optical-grade CVD polycrystalline diamond has been used instead of single-crystal diamond because of its lower cost. In ICF experiments, the high-intensity drive laser and laser-plasma-induced X-ray can change the optical properties of the window materials which leads to changes in the strength and phase of the probe beam in diagnostic apparatuses. This process can lead to inaccuracies of the measurement results. Therefore, it is important to investigate the
3
ultrafast dynamics of carriers and nonlinear optical properties in bulk polycrystalline diamond. Pump-probe techniques have been used widely to study ultrafast dynamics in various materials [17–20]. According to this technique, the laser source is split into two beams (pump beam and probe beam). These two beams are then focused on the sample with a certain time delay. The ultrafast dynamics in the sample can then be investigated by recording the intensity of the probe beam under different time delays. Recently, the phase object (PO) has been applied to the pump-probe scheme in order to increase the precision of measurements [21–23]. The PO is used to shift the phase of the central part of probe beam and then enhance the interference in the probe beam. Therefore the intensity of probe beam measured by energy detectors is modulated which results in improvements in the measurement accuracy. Moreover, by using this approach, the dynamics of nonlinear absorption and nonlinear refraction can be measured simultaneously. In this paper, we report on the ultrafast dynamics of nonlinear optical phenomena in bulk polycrystalline diamond using a femtosecond nondegenerate pump-probe technique with a phase object.
2. Experimental setup
4
A two-color pump-probe scheme with a PO was built, as shown in Fig. 1. Laser pulses with a wavelength of 515 nm, a full width at half maximum (FWHM) of 190 fs, and a repetition rate of 20 Hz were generated using a Yb:KGW laser amplifier (made by Light Conversion, and the second harmonic of the output was used). The pulses were split into two beams that acted as the sources of the pump and probe beams, respectively. An optical parametric amplification system (OPA) was used to change the wavelength of the pump pulses to 351 nm because this wavelength has usually been chosen to be the wavelength of drive laser in ICF experiments. The duration of the pump pulse that is obtained from the OPA was measured to be 200 fs. A time-delay stage was placed in the pump beam. All the optical elements were precisely arranged to ensure that the pump and probe beams were stable during the movement of the time-delay stage. The probe beam was spatially filtered by L1, L2 and a pinhole to obtain a near Gaussian beam. An optical-grade CVD diamond, which is fabricated by Element Six and had dimensions of 33 mm × 12 mm × 0.7 mm, was used as the sample. The sample had a band gap of 5.5 eV [3]. The photon energies of the pump and probe beams were 3.54 eV and 2.41 eV, respectively. The probe beam was too weak to generate any nonlinear
5
optical phenomena in the sample. When there was no pump, the transmittance of the probe beam through the sample was 70% because of the reflection on the surfaces and the scattering in the sample. A PO was placed in the optical path of the probe beam. The PO, which consisted of a glass plate and a transparent dielectric disc (radius of 0.5 mm) deposited on the plate, did not absorb the probe beam. However, the phase of the incident light through the disc was retarded relative to the light that was not incident on the disc. The interference between these two parts of the probe beam was enhanced, and the intensity of the beam was modulated after passing through the sample. In this way, changes in the absorption and refraction of the sample can be determined by the energy detectors D1 and D2. The pump and probe beams were focused on the same point of the sample at a small angle (about 5°) with respect to each other. The diameters of the focal points of the pump and probe beams were 220 μm and 30 μm, respectively. After the sample, the probe beam was split into two beams. The energy detectors (D1, D2) were used to measure the energy of these two beams, respectively. An aperture was placed before D2; its radius was accurately adjusted to be equal to the radius of the diffraction of the light through the disc of the PO. The two-photon absorption (TPA) coefficient, free-carrier absorption cross-section, Kerr refractive index, free-carrier refractive index, and
6
free-carrier lifetime of the sample can be calculated using the normalized transmittance of the probe beam under open-aperture and closed-aperture conditions, as measured by D1, D2, and D3. The theories for bound electric and free-carrier nonlinearity of semiconductors in the PO pump-probe system have been described [21] and adapted [23] before, and therefore it is not necessary to repeat the theories here in this paper. All experiments were carried out at room temperature.
3. Results and discussion
The open-aperture result of the sample is shown in Fig. 2. The energy density of the pump pulse is 4.5 mJ/cm2 (pulse energy: 1.7 μJ). In the dynamics of nonlinear absorption, we can observe an abrupt reduction in the normalized transmittance of the probe beam at zero time delay, along with a relatively slow recovery after zero time delay. When the pump and probe pulses are synchronized and focused on the sample, a pump photon and a probe photon can be absorbed simultaneously to excite an electron from the valance band to the conduction band. Therefore, the transmittance of the probe beam decreases; this process is known as nondegenerate two-photon absorption (ND-TPA). In addition, two pump photons can also be absorbed simultaneously by the
7
sample and subsequently excite an electron; this process is known as degenerate TPA. At this stage, a reduction of the probe beam’s transmittance can be observed because of the interactions between photons and excited electrons. Therefore, the dynamics of free carriers can be detected by scanning the relative retardation between the pump and probe beams. Investigation of carrier recombination and diffusivity in bulk microcrystalline CVD diamonds has been reported [30]. They observed the very fast (80ps) and slower (3–8ns) decay components of the free-carrier dynamics. These two components have also been observed in polycrystalline diamond. The variation of the normalized transmittance can be described as follows: ∆Ttotal = ∆TND−TPA + ∆Te1 + ∆Te2
(1)
The ND-TPA process occurs only when the pump and probe pulses are temporally overlapped. As shown in the inset of Fig. 2, the FWHM of this process is 0.3 ps, which is consistent with the temporal width of the pump and probe pulses, considering the temporal broadening of the pulses induced by the optical elements. As the time delay between the pump and probe beams increases, the ND-TPA process quickly disappears. At the same time, the nonlinear absorption caused by free carriers decays exponentially. In other words, ∆Te1 = A1 e−t/τ1
8
(2)
∆Te2 = A2 e−t/τ2
(3)
From the measurement shown in Fig. 2, we have τ1 = 85 ps (±4 ps) and τ2 = 2324 ps (±38 ps), which represent the lifetimes of fast and slower decay components of the free-carrier dynamics, respectively. The nonlinear absorption dynamics with the pump pulse energy densities of 10.1 mJ/cm2 and 14.6 mJ/cm2 have also been measured, as shown in Fig. 3(a) and Fig. 3(b) respectively. The lifetimes of free carriers with different pump pulse energy densities are listed in Table 1.
Pump and probe technique with two-photon excitation has also been applied to monocrystalline diamond in recent years [26,27]. In Ref. 26, the infrared probe photons were used to measure the free-carrier absorption. Because of the different experimental setup, it is not proper [28,29] to use the Drude model to compare the experiments on polycrystalline diamond here and the experiments on monocrystalline diamond in Ref. 26. The nonlinear refraction dynamics of the sample within the femtosecond regime can be determined using D2 (closed-aperture conditions), as shown in Fig. 4. The phase variation of the probe beam can be obtained by fitting the experimental data of D2 according to the theory of Fresnel diffraction. In Fig. 4, the closed-aperture result is
9
shown and fitted. The energy density of the pump pulse is 0.60 mJ/cm2 (pulse energy: 0.23 μJ), which is 7.5 times smaller than what is used in Fig. 2. Under this pump intensity, the dynamics of nonlinear absorption detected by D1 (open-aperture conditions) is almost negligible. As a result of the very weak pump intensity, the nonlinear refractive index originating from free carriers is too weak to be detected. But the resulting free carriers constitute a cluster of plasma, and plasma dispersion will produce a decrease in the refractive index of the material. The free carriers have a lifeime of about a hundred picoseconds, as shown in Tab. 1. Therefore, the opposite sign of the fast and slow components of the refractive index can be apparently seen from Fig. 4. In order to make the measurement of nonlinear refractive coefficient more precise, the nonlinear refraction dynamics of the sample has been measured and fitted using different pump pulse energy densities (0.47 mJ/cm2, 0.60 mJ/cm2, and 0.91 mJ/cm2), as shown in Fig. 5. The corresponding open-aperture results have been used to separate the nonlinear absorption out from the closed-aperture data. The refractive index of the sample can be described by the following equation: n = n0 + n2 I
10
(4)
where n0 represents the refractive index in the absence of a pump pulse, I represents the intensity of the pump pulse, and n2 is the nonlinear refractive coefficient. By analyzing the experimental data shown in Fig. 4, we measure n2 to be (1.4±0.2)×10−15 cm2/W. The third order nonlinear susceptibility χ(3) which correspond to the measured n2 has been calculated to be 2.7×10-21 m2/V2. The third-order nonlinear optical coefficients of various materials have been listed by Boyd in Ref. [25], where the nonlinear refractive coefficient of diamond is 1.3×10−15 cm2/W. There are three possible causes of the difference between the measured n2 of polycrystalline diamond and the nonlinear refractive coefficient of single crystal diamond listed in Ref. [25]. First, In Ref. [25], only the third-order nonlinear process (which is due to the response of bound electrons) was considered to calculate and measure the nonlinear optical coefficient. While in our nondegenerate PO pump-probe regime, the measured n2 also contains the nonlinear refractive index caused by ND-TPA processes according to the Kramers-Kronig relations. Second, the grain boundaries may also generate an additional nonlinear refractive index in polycrystalline diamond. Third, we measured n2 to be (1.4±0.2)×10−15 cm2/W. Therefore, the difference may also be caused by the measurement error. Further researches and more accurate experiments should be done to clearly understand this difference.
11
It is worth noting that the closed-aperture results of the sample are different from those of other semiconducting materials, such as GaN [21], CdS [22], and ZnS [23]. This can be explained by the fact that, in those experiments, the nonlinear refractive index originating from TPA processes is much smaller than that caused by free carriers. By way of contrast, in our results, the nonlinear refractive index caused by free carriers is almost negligible in comparison with that due to ND-TPA processes. In other words, the free-carrier process was the main source of the nonlinear refractive index of the materials in the picosecond PO pump-probe experiments. While in our femtosecond PO pump-probe experiments, the ND-TPA process was the main source of the nonlinear refractive index of the sample. This is because we used the femtosecond regime instead of the picosecond regime; as a result, the intensity of beams is higher and the bound electric effect is stronger. In addition, the sensitivity of the pump-probe system could be improved when a PO was introduced into the system [21-23]. The experiments on polycrystalline diamond illustrated this point again. As we see, the nonlinear refractive index has been detected at a lower fluence.
4. Conclusion
12
The femtosecond ultraviolet pump-optical-probe regime technique (with the use of a PO) has been used to investigate the ultrafast dynamics of free carriers and the nonlinear refractive index in bulk polycrystalline diamond. Three processes were observed in the nonlinear absorption dynamics: the ND-TPA process, fast and slower decay components of the free-carrier dynamics. The lifetimes of the free carriers were precisely measured. Contrary to the results concerning other semiconducting materials previously measured under the picosecond regime, our results for diamond under the femtosecond regime show that the nonlinear refractive index caused by free carriers is very small in comparison to that due to the ND-TPA process. The nonlinear refractive coefficient n2 (caused by the nondegenerate bound electric Kerr effect) has been measured to be 1.4×10−15 cm2/W which is a little larger than that of a single crystal diamond (1.3×10−15 cm2/W). This means that when we use a polycrystalline diamond instead of a single crystal diamond as the window material, the nonlinear refractive index would become a little larger. This phenomenon should be considered along with the cost to choose the suitable window material. In addition, the measured n2 can be used to evaluate the inaccuracies of the measurement results when a polycrystalline diamond has been chosen to be the window material in a specific ICF experiment. This work can help in improving the measurement accuracy of diagnostic apparatuses in ICF
13
experiments and facilitate our understanding of the ultrafast dynamics of carriers and the nonlinear refractive index in diamond.
Acknowledgements
We gratefully acknowledge the Project Funded by National Natural Science Foundation of China (Grant Nos. 11575166 and 51581140).
References [1] M. I. Eremets, I. A. Trojan, P. Gwaze, J. Huth, R. Boehler, and V. D. Blank, The strength of diamond, Appl. Phys. Lett. 87 (2005) 141902. [2] T. H. Maiman, Stimulated optical radiation in ruby, Nature 187 (1960) 493-494. [3] L. S. Pan, D. R. Kania, P. Pianetta, and O. L. Landen, Carrier density dependent photoconductivity in diamond, Appl. Phys. Lett. 57 (1990) 623-625.
14
[4] D. H. Reitze, H. Ahn, and M. C. Downer, Optical properties of liquid carbon measured by femtosecond spectroscopy, Phys. Rev. B 45 (1992) 2677-2693. [5] S. Preuss, and M. Stuke, Subpicosecond ultraviolet laser ablation of diamond: Nonlinear properties at 248 nm and time-resolved characterization of ablation dynamics, Appl. Phys. Lett. 67 (1995) 338-340. [6] N. Naka, T. Kitamura, J. Omachi, and M. Kuwata-Gonokami, Low-temperature excitons produced by two-photon excitation in high-purity diamond crystals, Phys. Stat. Sol. B 245 (2008) 2676-2679. [7] N. Naka, J. Omachi, H. Sumiya, K. Tamasaku, T. Ishikawa, and M. Kuwata-Gonokami, Density-dependent exciton kinetics in synthetic diamond crystals, Phys. Rev. B 80 (2009) 035201. [8] M. Kozák, F. Trojánek, and P. Malý, Large prolongation of free-exciton photoluminescence decay in diamond by two-photon excitation, Opt. Lett. 37 (2012) 2049-2051. [9] K. Murayama, Y. Sakamoto, T. Fujisaki, S. Yamasaki, and H. Okushi, Free-exciton luminescence spectrum broadening due to excitonic complex in diamond, Diamond Related Materials 16 (2007) 958-961.
15
[10] P. Němec, J. Preclíková, A. Kromka, B. Rezek, F. Trojánek, and P. Malý, Ultrafast dynamics of photoexcited charge carriers in nanocrystalline diamond, Appl. Phys. Lett. 93 (2008) 083102. [11] F. Trojánek, K. Žídek, B. Dzurňák, M. Kozák, and P. Malý, Nonlinear optical properties of nanocrystalline diamond, Opt. Express 18 (2010) 1349-1357. [12] J. Preclíková, A. Kromka, B. Rezek, and P. Malý, Laser-induced refractive index changes in nanocrystalline diamond membranes, Opt. Lett. 35 (2010) 577-579. [13] W. Lubeigt, G. M. Bonner, J. E. Hastie, M. D. Dawson, D. Burns, and A. J. Kemp, Continuous-wave diamond Raman laser, Opt. Lett. 35 (2010) 2994-2996. [14] D. J. Spence, E. Granados, and R. P. Mildren, Mode-locked picoseconds diamond Raman laser, Opt. Lett. 35 (2010) 556-558. [15] M. Murtagh, J. Lin, R. P. Mildren, and D. J. Spence, Ti:sapphire-pumped diamond Raman laser with sub-100-fs pulse duration, Opt. Lett. 39 (2014) 2975-2978. [16] W. Theobald, J. E. Miller, T. R. Boehly, E. Vianello, D. D. Meyerhofer, T. C. Sangster, J. Eggert, and P. M. Celliers, X-ray preheating of window materials in direct-drive shock-wave timing experiments, Phys. Plasmas 13 (2006) 122702. [17] W. Wu, and Y. Wang, Ultrafast carrier dynamics and coherent acoustic phonons in bulk CdSe, Opt. Lett. 40 (2015) 64-67.
16
[18] G. Batignani, D. Bossini, N. Di Palo, C. Ferrante, E. Pontecorvo, G. Cerullo, A. Kimel, and T. Scopigno, Probing ultrafast photo-induced dynamics of the exchange energy in a Heisenberg antiferromagnet, Nat. Photon. 9 (2015) 506-510. [19] S. M. Durbin, T. Clevenger, T. Graber, and R. Henning, X-ray pump optical probe cross-correlation study of GaAs, Nat. Photon. 6 (2012) 111-114. [20] O. Krupin, M. Trigo, W. F. Schlotter, M. Beye, F. Sorgenfrei, J. J. Turner, D. A. Reis, N. Gerken, S. Lee, W. S. Lee, G. Hays, Y. Acremann, B. Abbey, R. Coffee, M. Messerschmidt, S. P. Hau-Riege, G. Lapertot, J. Lüning, P. Heimann, R. Soufli, M. Fernández-Perea, M. Rowen, M. Holmes, S. L. Molodtsov, A. Föhlisch, and W. Wurth, Temporal cross-correlation of x-ray free electron and optical lasers using soft x-ray pulse induced transient reflectivity, Opt. Express 20 (2012) 11396-11406. [21] Y. Fang, X. Z. Wu, F. Ye, X. Y. Chu, Z. G. Li, J. Y. Yang, and Y. L. Song, Dynamics of optical nonlinearities in GaN, J. Appl. Phys. 114 (2013) 103507. [22] M. Shui, X. Jin, Z. G. Li, J. Y. Yang, G. Shi, Z. Q. Nie, X. Z. Wu, Y. X. Wang, K. Yang, X. R. Zhang, and Y. L. Song, Investigation of nonlinear dynamics in CdS by time-resolved nondegenerate pump-probe system with phase object, J. Mod. Opt. 58 (2011) 973-977.
17
[23] M. Shui, Z. G. Li, X. Jin, J. Y. Yang, Z. Q. Nie, G. Shi, X. Z. Wu, K. Yang, X. R. Zhang, Y. X. Wang, and Y. L. Song, Measurement of dynamics of nondegenerate optical nonlinearity in ZnS with pulses from optical parameter generation, Opt. Commun. 285 (2012) 1940-1944. [24] W. Saslow, T. K. Bergstresser, and M. L. Cohen, Band structure and optical properties of diamond, Phys. Rev. Lett. 16 (1966) 354-356. [25] R. W. Boyd, Nonlinear Optics, (Academic Press, Singapore, 2009), p.212. [26] M. Kozák, F. Trojánek, T. Popelář, and P. Malý, Dynamics of electron-hole liquid condensation in CVD diamond studied by femtosecond pump and probe spectroscopy, Diamond & Related Materials 34 (2013) 13-18. [27] P. Šcajev, V. Gudelis, E. Ivakin, and K. Jarašiūnas, Nonequilibrium carrier dynamics in bulk HPHT diamond at two-photon carrier generation, Phys. Status Solidi A 208 (2011) 2067-2072. [28] J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, Time-resolved Z-scan measurements of optical nonlinearities, J. Opt. Soc. Am. B 11 (1994) 1009-1017.
18
[29] Y. Li, G. Pan, K. Yang, X. Zhang, Y. Wang, T. Wei, and Y. Song, Time-resolved pump-probe system based on a nonlinear imaging technique with phase object, Opt. Express 16 (2008) 6251-6259. [30] P. Šcajev, V. Gudelis, K. Jarašiūnas, I. Kisialiou, E. Ivakin, M. Nesládek, and K. Haenen, Carrier recombination and diffusivity in microcrystalline CVD-grown and single-crystalline HPHT diamonds, Phys. Status Solidi A 209 (2012) 1744-1749
19
Figure Captions Fig. 1. Ultraviolet-pump-optical-probe scheme with a phase object. M1 and M2: mirrors. P1 and P2: polarizers. BS1–BS3: beam splitters. L1–L6: lenses. D1–D3: energy detectors.
Fig. 2. Nonlinear absorption dynamics of diamond (open-aperture conditions). Inset: experimental data and theoretical curve near zero time delay.
20
Fig. 3. Nonlinear absorption dynamics of diamond with pump pulse energy density of (a) 10.1 mJ/cm2, and (b) 14.6 mJ/cm2.
21
Fig. 4. Nonlinear refraction dynamics of diamond (closed-aperture conditions). Inset: experimental data and theoretical curve near zero time delay.
22
Fig. 5. Nonlinear refraction dynamics of diamond with different pump pulse energy densities.
23
24
Table 1: Parameters obtained from the nonlinear absorption dynamics of the sample with different pump pulse energy densities.
τ1 (ps)
A1
τ2 (ps)
A2
4.5
85±4
-0.00690±0.00011
2324±38
-0.02797±0.00006
10.1
134±10
-0.00848±0.00028
963±29
-0.03148±0.00022
14.6
76±3
-0.03283±0.00031
1548±24
-0.12856±0.00011
Pump pulse energy density (mJ/cm2)
25