Nonlinear optical properties of nanocrystalline diamond

Nonlinear optical properties of nanocrystalline diamond F. Trojánek,* K. Žídek, B. Dzurňák, M. Kozák, and P. Malý Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic *[email protected]

Abstract: We report on investigation of nonlinear optical phenomena in nanocrystalline diamond prepared by microwave plasma enhanced chemical vapour deposition. We observed the upconverted photoluminescence, the second and the third harmonic generation and Z-scan signal. The value of the third order nonlinear susceptibility was estimated. Our results show that nonlinear optical properties of nanocrystalline diamond have many features of the bulk diamond affected to some extent by the presence of grain boundaries. ©2010 Optical Society of America OCIS codes: (160.6000) Semiconductor materials; (160.4236) Nanomaterials; (190.2620) Harmonic generation and mixing; (190.3270) Kerr effect

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Received 4 Dec 2009; revised 5 Jan 2010; accepted 5 Jan 2010; published 12 Jan 2010

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1. Introduction Nanocrystalline diamond (NCD) attracts attention as a promising material for many applications that include electronics, photonics, medicine and biosensing [1–3]. The material is biocompatible, nontoxic, chemically inert, and environmentally benign. It is considered for advanced optical applications as adaptive microoptics [4], optical sensors [5] or material basis for quantum information processing and spintronics [6,7]. NCD has many unique properties of the bulk diamond which are however significantly modified by a presence of grain boundaries. These give rise to new energy states within the band-gap of the bulk diamond, which affects the properties of the material. The linear optical properties (mostly absorption in UV-VIS spectral intervals, photoluminescence) have been used routinely as a probe of NCD films properties [8]. However, the research of the nonlinear optical properties of NCD has been neglected. Only few papers deal with the nonlinear optics of bulk diamond [9–13] and diamond nanoparticles. In the bulk diamond, the research focused mainly on the optical #121002 - $15.00 USD

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nonlinearities connected with defect centres considered for quantum optical and information processing applications [14–16]; two photon absorption in the UV part of the spectrum was studied in [17,18]. For example, the multiphoton–excited photoluminescence from diamond nanoparticles was reported [19]. The nonlinear optical phenomena can be exploited in applications (e.g. generation of harmonic frequencies for the light wavelength transformations or Kerr-type nonlinearities for optical switching) but in some cases they can be considered as parasitic effect (e.g. optical losses due to multiple photon absorption). Investigation of nonlinear properties of NCD is important also from the fundamental physics viewpoint as it is connected with the microscopic processes both in the volume of diamond grains and on the grain boundaries. In this paper we report on optical nonlinearities in NCD prepared by microwave plasma enhanced chemical vapour deposition. The unique self-standing NCD membranes made it possible to study the nonlinear optical phenomena without the influence of a substrate. We observed and studied the up-converted photoluminescence (PL) (i.e. energetically above pump photon energy), the second and third harmonic generation, and the light-intensity dependence of index of refraction (optical Kerr nonlinearity). 2. Experimental details The sample of NCD film was grown on silicon (100) oriented substrate. The deposition was realized by microwave plasma enhanced chemical vapour deposition process [20]. A standard gas mixture of methane in hydrogen was used, microwave power was kept at 1300 W and the total gas pressure was 30 mbar. The NCD growth was provided at temperature from 600 to 850°C. The prepared film consisted of randomly oriented nanocrystals up to 100 nm in size. The typical surface roughness is about (rms) 40 nm. Using photolithography and KOH etching, windows were opened in the (100) silicon substrate masked with silicon nitride to get the self-supporting, transparent diamond membrane [21]. The thickness of the membranes studied was about 1 µm. In order to characterize the NCD membrane used for nonlinear optical measurements we show its SEM micrograph and Raman spectrum in Fig. 1. The Raman spectrum (excitation wavelength 325 nm, measured by Renishaw Raman spectrometer) is dominated by the 1332 cm−1 peak which corresponds to the diamond phase (sp3-bonded carbon) with good structural properties. A broad band around 1560 cm−1 corresponds to the non-diamond, sp2-bonded carbon atoms. Standard absorption was measured by a conventional spectrophotometer (Analytik Jena, Specord). The standard PL spectra were measured using the cw 325 nm line of HeCd laser. In nonlinear optical experiments, the excitation source was the Ti-sapphire laser system (Tsunami & Spitfire, Spectra Physics) with the output wavelength tuned by a parametric generator (Topas, Light Conversion). Parameters of femtosecond pulses were: pulse length 90 fs, repetition rate 1 kHz, maximal pulse energy ~20 µJ. The laser beam was focused to a spot with diameter from 70 µm (at 460 nm) to 200 µm (at 1055 nm) depending on the laser wavelength. The photoluminescence, photoluminescence excitation spectra (PLE) and spectra of the second- and third harmonics were obtained by a grating spectrograph (Oriel) and CCD (Andor) and corrected for the spectral sensitivity of the whole setup. The up-converted PL was detected under angle of 30 degrees. Detection of generated harmonics was done in a forward direction. Additional measurements were done under other angles. The nonlinear index of refraction was studied using the standard Z-scan setup [22]. A space-filtered Gaussian laser beam (diameter of 9 mm) was focused by the lens (13.3 D). The sample placed perpendicullary to the light beam was moved along the optical path by a computer driven precise motor. In case of the closed aperture measurements, an iris was inserted after the sample. The intensities of the input and transmitted beams were measured by silicon photodiodes. The ratio of both signals was recorded as a function of the sample position z. In all the experiments we used intense femtosecond pulses but we carefully limited their power so that the damage threshold was never exceeded. No permanent changes in the optical properties of the samples were observed. All the measurements were done at room temperature.

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Fig. 1. (a) SEM micrograph of NCD membrane; (b) Raman spectrum of NCD membrane.

3. Results and discussion 3.1 Linear optical properties of NCD membrane The linear optical properties of the nanodiamond membrane are illustrated in Fig. 2 where absorbance (–ln T, where T is the measured transmission) and photoluminescence spectra are shown. The transmission spectrum can be reproduced very well by the Fabry-Perot transmission function (red curve) which includes both the spectrally dependent extinction coefficient and index of refraction. The spectral positions of interference fringes in the model curve were obtained by using the dispersion relation of the index of refraction for the bulk diamond given in [23]. The geometrical thickness of the membrane used in the calculation was 1.01 µm. It is generally accepted that the transmission of nanocrystalline diamond is affected by both the light absorption and scattering [21,24]. The absorption in the spectral region energetically below the diamond band-gap (Eg = 5.50 eV at room temperature [23]) is interpreted usually by the presence of sp2 hybridized bonds, amorphous carbon at grain boundaries [25], or defects connected with nitrogen or other ad atoms [26]. The band tail

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absorption can also be a result of the distortion of bond lengths and bond angles at nanocrystal boundaries [27].

Fig. 2. Absorption and photoluminescence spectra of nanodiamond membrane. Red line – model (see text).

The energy states in the gap give rise also to PL which can be photoexcited by photons with energy smaller than the band gap. The PL spectra (see Fig. 2, where the spectrum of NCD membrane excited by cw He-Cd laser line at 325 nm is shown) consist typically of a broad or several overlapping bands and a narrower peak at 738 nm (1.68 eV) which is generally attributed to the defect centres linked with silicon – vacancy impurity in diamond [28–30]. The origin of the spectrally broad bands is still ambiguous [31–36]. For high quality NCD membranes the PL spectrum is strongly modulated by thin-film interference (peaks in Fig. 2; the interference fringes in the transmission and PL spectra differ due to the different measurement geometry in both cases). 3.2 Luminescence up-conversion The PL described above is a linear function of excitation for small excitation intensities (as by cw lasers). At high values of excitation light intensity, as with the intense femtosecond pulses, a nonlinear PL response can be observed. This can be due to the multiphonon absorption which leads to the PL at photon energies larger than that of exciting photons (so called upconverted PL). We have observed this nonlinear upconverted PL of NCD in the UV part of spectrum. This is illustrated in Fig. 3 where PL spectrum under 460 nm femtosecond excitation is shown. This sub-bandgap PL is a result of the two photon excitation across the band gap of the diamond. This follows from the measurement of PLE spectrum and from the PL pump intensity dependence. In the PLE spectrum shown in the inset (left) of Fig. 3 one can see clearly the onset of PL for photon energies greater than the half of the (indirect) band gap energy Eg/2 = 2.75 eV (which corresponds to 451 nm). The PL intensity is a quadratic function of the excitation intensity as can be seen in the inset (right) of Fig. 3.

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Fig. 3. Spectrum of upconverted PL of nanodiamond membrane excited by 460 nm femtosecond pulses. Inset (left): PLE spectrum of upconverted PL detected at 360 nm. Inset (right): dependence of PL intensity at 340 nm on excitation intensity at 460 nm. Solid line – the quadratic fit

2 I PL ∝ I exc .

3.3 Second harmonic generation In the PL spectrum shown in Fig. 3 the signal of second harmonics of 460 nm pulse can be seen in addition to upconverted PL. We observed the signal of second harmonics also for femtosecond pulses at other wavelengths – as shown in Fig. 4 (fundamental wavelengths of 460 nm, 505 nm, and 705 nm). As expected, the signal of second harmonics is a quadratic function of the incident light intensity, see the inset of Fig. 4 where the intensity dependence of the second harmonics of 460 nm light is shown. The observation of the second harmonic generation in NCD is somewhat surprising as this second order optical nonlinear process should not be observed in bulk diamond. Indeed, the second-order susceptibility χ(2) is essentially zero whenever the medium has inversion symmetry [37]. The observation of the second harmonics signal can be thus regarded as a probe of a symmetry perturbation (e.g. surface of the crystal) [9–12]. In NCD this is most likely due to the grain boundaries. The emitted light of the second harmonics has an omni-directional character, i.e. we have not observed an enhancement of the second harmonic intensity in any direction (including that of the input beam). This behaviour reflects random orientation of surfaces of nanocrystals in the NCD membrane. Omni-directional light scattering of frequency 2ω due to hyper-Rayleigh process was observed on molecules and inorganic nanocrystals [38,39]. Our further research will be devoted to the possible contribution of this scattering in NCD.

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Fig. 4. Second harmonic signal of labelled incident wavelengths from nanodiamond membrane. Inset: intensity dependence of second harmonics of 460 nm pulse. Solid line – a quadratic fit

I SH ∝ I 2 .

Fig. 5. The third harmonics of the input femtosecond pulses of labelled wavelengths from nanodiamond membrane. Inset: intensity dependence of the third harmonic signal for input pulse at 1055 nm. Solid line – a cubic fit I TH

∝ I3 .

3.4 Third harmonic generation The inversion symmetry of material does not restrict the third harmonic generation [37]. We indeed observed a strong third harmonic signal which was highly directional (in the input beam direction). Examples are shown (fundamental wavelengths of 820 nm, 1055 nm, and 1500 nm) in Fig. 5. The signal of the third harmonics should scale with the third power of the incident light intensity. This is really the case as illustrated in the Inset of Fig. 5. The nanocrystals in the membrane are randomly oriented; however, their size of about 100 nm is much smaller than the coherence length, so that third harmonics generation can occur

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without the fulfilment of the phasematching. The coherence length is given [37] l = λ0 ( 3n3ω − 3nω ) , where λ0 is the vacuum wavelength of the incident light. In our case the coherence length is actually greater than the thickness of the membrane (~1µm). Indeed, considering the index of refraction of the bulk diamond [23] one gets l ≈1.5 µm for λ0 = 820 nm and l ≈10.9 µm for λ0 = 1500 nm. From the measured efficiency of the third harmonic generation we can obtain the effective value of the real part of the third-order nonlinear susceptibility χ(3). From the plane-wave approximation of the coupled-wave equations for the third harmonics generation we receive

χ

(3)

=

2ε 0 c nω3 n3ω λω 0 3π lIω

η.

Under our experimental conditions the measured efficiency was η = 5.6 × 10−8, the fundamental wavelength λω0 = 1055 nm, the intensity Iω = 1.5 × 1011 W/cm2, the membrane thickness l = 1010 nm, and indexes of refraction were obtained from the dispersion formula of the bulk diamond [23]. We obtain the value of the real part of χ(3) = 5 × 10−22 m2/V2 = 0.4 × 10−13 esu. This value agrees very well with the values of χ(3) = 0.46 × 10−13 esu [13] and χ(3) = 1.5 × 10−13 esu [37] found in the bulk diamond. The agreement may be fortuitous due to uncertainty in estimation of the light intensity. However, this result indicates that the process of the third harmonics generation in NCD is dominated by the diamond phase and is not affected by presence of the grain boundaries. 3.5 Kerr optical nonlinearity We have investigated also the third order Kerr optical nonlinearities of NCD by a standard Zscan technique [22]. The measured curves were fitted by the normalized Z-scan function (see Eq. (11) in Ref. 22) that involves nonlinear refractive index and coefficient of nonlinear absorption. We obtained the values of nonlinear index of refraction. The maximum intensity of the beam at the focus plane was 2.5 × 1011 W/cm2 during the Z-scan measurement. The typical Z-scan data (for pulses tuned to 580 nm) are shown in Fig. 6. The closed aperture scan provides the value of nonlinear index of refraction. We verified that the observed optical nonlinearity is indeed of the third order (n2) by observation of the linear intensity dependence of the Z-scan signal. The obtained value of n2 = –2 × 10−17 m2/W (at 580 nm), which corresponds to Re χ(3)(– ω; ω, ω, –ω) = –4 × 10−19 m2/W = –3 × 10−11 esu, is negative and relatively high (compare with Re χ(3)(– 3ω; ω, ω, ω) = 0.4 × 10−13 esu from the third harmonics measurements for fundamental wavelength of 1055 nm). Under accuracy of our setup, we have not observed any modulation of the open aperture Z-scan signal, which indicates rather small value of the imaginary part of χ(3). By Z-scan measurements with selected wavelength we obtained the spectrum of nonlinear index of refraction which is shown in the Inset of Fig. 6. The absolute value of n2 is decreasing with wavelength and it is below the detection limit of our setup for wavelengths greater than ~730 nm. The thermal origin of the nonlinear index of refraction in the Z-scan measurements can be excluded due to a positive thermooptic coefficient of the bulk diamond (1.0 × 10−5 K−1) [40]. We interpret the origin of the nonlinear susceptibility χ(3)(– ω; ω, ω, –ω) in terms of the optical transitions related with the sub gap energy states of nanocrystalline diamond. Its much higher value in comparison with the value of Re χ(3)(– 3ω; ω, ω, ω) deduced from THG measurement can be explained by the presence of various resonance contributions in the relation between the elements of the third-order susceptibility tensor and the optical field frequency [41]. In particular, the tensor χ(3)(– ω; ω, ω, –ω) includes two-photon resonances which fall spectrally into the range of real shallow gap states. Indeed, the rising edge of n2 spectrum at ~600 nm agrees well with the rise of the absorption spectrum –ln T at ~300 nm (see Fig. 2).

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Fig. 6. The closed (solid squares) aperture Z-scan data for nanodiamond membrane at wavelength of 580 nm. The red curve is the fit described in the text. Inset: spectral dependence of nonlinear index of refraction (symbols).

4. Conclusion

We have observed several nonlinear optical phenomena in NCD: the upconverted photoluminescence excited by two-photon excitation, the second and the third harmonic generation. In spite of the inversion symmetry of the bulk diamond, NCD exhibits efficient omnidirectional second harmonic generation. It is a result of the presence of grain boundaries that perturb symmetry. We also estimated value of the real part of χ(3)(– 3ω; ω, ω, ω) = 0.4 × 10−13 esu (for fundamental wavelength of 1055 nm) that is nearly the same as in the bulk diamond. Finally we have measured χ(3) (– ω; ω, ω, –ω) by the Z-scan and we found a rather high value of its real part which we explain by two photon resonances related with the sub gap energy states of nanocrystalline diamond. Our results show that also nonlinear optical properties of nanocrystalline diamond membranes have many features of the bulk diamond affected by the presence of the grain boundaries. That is why the investigation of nonlinear optical phenomena in NCD can extend our knowledge of the properties of grain boundaries. On the other hand, the properties of the NCD membranes can be tailored by adjusting the parameters of the preparation [20] which makes it possible to tailor optical nonlinear properties for given application. Acknowledgements

We thank Dr. A. Kromka for providing the high quality NCD membranes, Dr. B. Rezek for valuable discussions, Dr. M. Ledinsky for measuring the Raman spectrum (Fig. 1(b)) and K. Hruska (all from Institute of Physics of the Academy of Sciences of the Czech Republic) for SEM micrograph (Fig. 1(a)) of the NCD membrane studied. This work was supported by Academy of Sciences of the Czech Republic (projects KAN400100701) and by Ministry of Education of the Czech Republic in the framework of the research plan MSM0021620834.

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