Third harmonic generation (THG) is a nonlinear optical phenomenon which can be applied in diverse research areas including interfacial studies, sub-wavelength light manipulation, and high sensitivity bio-molecular detection. Most precedent studies on THG have focused on dielectric and metallic materials, including silicon, gold, and germanium, due to their high nonlinear susceptibility. Sapphire, a widely-used optical substrate, has not been studied in depth for its third harmonic characteristics, despite its excellent optical transmission in the UV-visible range, high thermal conductance, and superior physical and chemical stability. In this research, we comprehensively studied THG at thin air-dielectric interfaces of sapphire wafers by controlling the wafer cutting planes, focusing depth, incidence angle, laser intensity, and input polarization of the input laser beam. These findings can lead to broader use of third harmonics for high-precision sapphire characterization, such as surface quality inspection, crystallinity determination, interfacial studies, delamination check, and real-time monitoring of crack propagation.
© 2017 Optical Society of America
Nonlinear optical processes are phenomena that occur when intense light passes through an optical medium; as a result, new photons having different photon energies are generated while maintaining the coherence with the incident light. Two representative and simplest nonlinear processes are second harmonic generation (SHG) and third harmonic generation (THG) in which photons with doubled and tripled optical frequencies of the original light are generated . Because nonlinear optical processes are non-invasive, non-destructive, and highly sensitive to interfacial atomic structure and bonding status [2,3], they are regarded as the promising techniques for interfacial study , light manipulation at the nanoscale  and highly sensitive bio-molecular detection .
While SHG and other even-order nonlinear processes require intense light field on the target materials having noncentrosymmetric structures, THG and odd-order nonlinear processes are more general as the symmetry rules are relaxed for the most of the optical medium . THG processes have been investigated using different optical materials including bulk substrate , metal  and dielectric nanoparticles  and plasmonic metamaterials . Among those materials, silicon is the most widely used one due to its high third-order nonlinear susceptibility . However, the low transparency of silicon in the UV and visible range has limited its wider application in THG and higher order nonlinear optics . In contrast, sapphire is another good candidate as the nonlinear optical medium because of its high transparency in UV and visible range , high thermal conductivity for efficient heat dissipation [15,16], and good physical and chemical stability . Sapphire has been utilized as the supporting substrate material for the study of nonlinear optical processes of gold and silver nanoarrays [16,18,19] and quantum dots including CdSe and GaN [20,21]. Although the THG characteristics of silicon have been studied in depth, sapphire has not been characterized with THG to date. There are many factors that can affect THG on crystalline substrate such as crystal orientation , excitation depth , and incident angle . As a hexagonal crystalline material, sapphire can exhibit different crystal orientation when cut at different crystal planes. However, the effect of crystal orientation on THG at sapphire was not investigated. Besides, THG is believed to have a high conversion efficiency at the crystal-air interface  with a normal incidence but the detailed relationship between the excitation depth, incidence angle and THG intensity has not been also addressed. Therefore, a comprehensive characterization and understanding of THG on sapphire substrates is important for the optimization of nanostructure enhanced nonlinear optical processes and development of ultrafast short-wavelength light sources.
In this Letter, we characterized the sapphire as a nonlinear medium for THG by using near-infrared femtosecond light pulses with different input polarization, excitation depth, and incidence angles. Different crystal orientation modulated the THG intensity by ~20% for A, M and R-plane wafers. When the femtosecond laser pulses are focused with a 40 × objective lens, the skin depth for THG was measured to be a few tens of micrometers and the THG intensity approaches zero when the incidence angle was changed to 4.0 degrees. When THG was made at the top surface, the propagation direction of THG in the sapphire was different from that of the fundamental beam by refraction, while THG at the bottom surface within the skin depth made was no noticeable refraction or beam shift. These results suggest that THG can be applied to the precision characterization of sapphire wafers in the field of material science and nonlinear photonics as well as industrial applications for the mass production of semiconductors, flat panel displays, and light emitting diodes.
2. Nonlinear THG at crystalline sapphire: system configuration and sample preparation
The experimental setup for the THG is illustrated in Fig. 1(a). A near infrared (NIR) femtosecond laser with the central wavelength of 1.595 μm, repetition rate of 80 MHz and averaged power of 54 mW (Toptica FemtoFiber pro NIR) was used as the excitation light source. A half-wave plate (Thorlabs WPH10M-1550) was used to rotate the polarization state of the linearly polarized input beam. The excitation laser pulses pass through an 800 nm long-pass filter (Thorlabs FEL-800) installed before the focusing objective lens to remove the SHG and THG contributions generated in the Er-doped fiber pre-amplifier inside the laser system. The femtosecond laser pulses were then reflected by a set of mirrors and focused by a 40 × objective lens having a numerical aperture (NA) of 0.65. The focal spot size was 7.6 μm at a working distance of 600 μm, which corresponds to a peak power of 1.1 × 109 W/cm2. It is worth to note that the objective lens was installed on top of a 3-axis stage (Thorlabs RB13M) for adjusting the excitation depth and high-precision angular tilting mirrors were installed before the objective lens for testing the incidence angle effect. THG spectrum generated at sapphire wafers was then collected by a 20 × objective lens (Olympus UPlan 20 × ) installed at an inverted microscope and analyzed at a spectrometer (Andor’s Shamrock 193i) and an EMCCD (Andor’s IXon Ultra) as shown in Fig. 1(a). Single crystal sapphire wafers of a 430 μm thickness were used as the measurement specimen. The atomic structure of sapphire wafer and the excitation scheme for the in-depth characterization are shown in Fig. 1(b). The oxygen ions (shown as the blue spheres) take the form of closest hexagonal packing, and the alumina cations (shown as the gray spheres) lie in the octahedral hollows among the closely packed oxygen ions, filling two-thirds of these hollows . As a rhomboidal class 3m group hexagonal crystal, the sapphire can be cut along four different planes termed as A, C, M and R-planes; the different cutting plane results in different atomic structure along with the polarization state of the incident laser electric field. For example, C-plane sapphire is cut in perpendicular to the z-axis and has a hexagonal surface atomic structure; on the other hand, R-plane is defined as the plane where the non-occupied octahedral hollows are aligned. The surface atomic structure of R-plane is of rectangular shape . As a result, THG at the sapphires with different cut planes will differently respond to the input polarization, excitation depth, and incidence angle . In this investigation, we tested all the specimens with different cutting planes including A, C, M and R-planes.
3. THG characterization: spectral position, bandwidth, and conversion efficiency
The THG spectra from the sapphire wafers with different cutting planes are shown in Fig. 2(a). The incident beam was aligned perpendicular to the surface of sapphire wafers and focused onto the top surface. Clear THG peaks were observed at 531 nm for all cutting planes with negligible wavelength deviations, which is in a good agreement with one-third of the input laser wavelength. In order to identify the spectral bandwidth of THG, the bandwidth of the third harmonic was normalized here by dividing the photon energy spread by the harmonic order, 3, and overlapped with the bandwidth of the fundamental beam as shown in Fig. 2(c). The normalized spectral bandwidth of the THG was 0.005 eV in full-width-half-maximum (FWHM), which is relatively smaller than that of the fundamental beam, 0.008 eV in FWHM. The smaller normalized bandwidth of the THG is expected to come from the material dispersions from a series of optical components in the microscope system. Imperfect dispersion compensation broadens the pulse so different wavelength portions of the pulse arrive at the sample at different timing. This results in the spectral bandwidth reduction in generated third harmonic spectrum. All observed third harmonic peaks were in Gaussian shape shown in Fig. 2(a). The intensity dependence of the THG yield was tested for all cutting planes as shown in Fig. 2(b). The slopes were 3.09, 2.82, 2.93 and 2.76 with deviations of 0.016, 0.016, 0.036 and 0.040 in standard deviation for A, C, M and R-planes, respectively. These matches well with the power dependence law for nonlinear perturbative harmonic generation, ITHG ∝ Pn, where n is 3 in THG. The THG efficiency was estimated using a silicon wafer (non-doped, <100>, 280 μm in thickness) as the intermediate reference medium because THG was not easy to be directly detected by a conventional power meter due to the low power level. Firstly, the THG generated from a silicon wafer was absolutely measured using a photomultiplier tube (Thorlabs, PMT1001M); the THG efficiency of the silicon wafer was 9.92 × 10−8. Based on the linear power response of the EMCCD, the THG efficiencies of the sapphire wafers were estimated by using the relative power ratio between THGs at the sapphire and silicon wafers measured at the EMCCD. The resulting THG efficiencies are 2.83 × 10−9, 1.82 × 10−9, 2.12 × 10−9 and 1.22 × 10−9 for A, C, M and R-planes. Note that second harmonic was not detected in this experiment; the THG intensity was much higher than the SHG intensity at least by 105 times considering the EMCCD gain. This is because the sapphire lattice has a centrosymmetric structure in all cutting planes . When a sample excited by an external electric field (e.g. a laser pulse), the potential energy of the dipole in a centrosymmetric medium is in the form of even function without the directional sensitivity as shown in Fig. 2(d) . Since the dipole intensity corresponds to the integration of the dipole potential energy, it is comprised of the odd functions in centrosymmetric medium. Therefore, the nonlinear susceptibility, which is proportional to the dipole intensity, is also odd function, so the even order susceptibilities of the sapphire are zero (including the 2nd-order susceptibility required for SHG). Second harmonic can be generated at the sapphire surfaces where the centrosymmetric geometry is broken; however, the relative SHG intensity is still much lower compared to THG .
4. Polarization-dependent THG spectrum: study on crystallographic orientation dependence
The THG yield dependence on crystal orientation is shown in Fig. 3. Because the energy band varies with the electron oscillation direction, the harmonic generation process is also dependent on the crystalline structure [23,24]. Figure 3(a) shows a typical THG intensity spectrum from A-plane sapphire wafer excited by different input polarization states from 0 to 360°. Clear four-fold symmetry was observed for THG at 531 nm without any SHG signal at 775 nm for all polarization states. THG spectra at the sapphire wafers with different cutting planes are compared in Figs. 3(b)–3(e). Note that breaks are inserted into Figs. 3(b)–3(e) from 540 to 760 nm for a magnified view around THG and SHG. For A, M and R-planes, four-fold symmetries were clearly observed with ~20% modulation depth, which matched well with the symmetric crystal lattice structures of A, M, and R-plane sapphires . Meanwhile, C-plane sapphire has a six-fold symmetric lattice structure  but its THG spectrum did not show clear polarization dependency. The anisotropic nature of sapphire leads to a polarization dependent third order susceptibility, resulting in an angle dependent THG yield. However, for C-plane sapphire, the optical axis is normal to the surface, eliminating birefringence and consequently giving a weaker angle dependence compared to other planes [24, 26].
5. Surface and bulk THG: study on excitation depth dependence
THG is known to be more efficient at the interface between two materials with different refractive indices compared to the case generated inside the bulk medium [3, 8]. However, the detailed relationship between the excitation depth and THG yield from the sapphire wafers has not been explored. To identify the relationship, the excitation depth was controlled by adjusting the height of the focusing objective lens installed on a three-axis micrometer translation stage; the depth of focus was 29.3 μm. A schematic of the experimental system is shown in Fig. 4(a). Figures. 4(c)–4(f) shows the THG intensity distribution under different excitation depths for all sapphire wafers with different cutting planes. The polarization angle is chosen to be 70° for the optimization of THG intensity. The THG intensity is strong at the top surface of the air-sapphire interface and decreases to 0 inside the bulk volumetric part of the sapphire wafer. When the laser beam is focused on the bottom surface of another interface between air and sapphire, the THG intensity increases back. The lower THG intensity in the bulk part of the sapphire wafers before and after the laser focus can be explained by the Gouy phase shift which leads to the π/2 phase shift of generated THG beam ; as the result, the two THG beams, one THG beam generated before the focal point and the other generated after the focal point, interfere with each other in destructive way so cancel out the resultant intensity to zero . This phenomenon commonly occurs for all cutting planes, indicating no dependence on crystal orientation. Figure 4(b) shows the sectional THG intensity profiles at different focusing depth. The THG intensity decreases to 50% at 23.6, 14.0, 17.2 and 13.6 μm from the air-sapphire interface (top and bottom surfaces) for A, C, M and R-planes; the intensity decreases to 0 at 51.6 μm for all sapphires with different cutting directions. With a sapphire wafer thinner than 51.6 μm, THG at top and bottom surfaces can be excited at the same time, which possibly provides a stronger THG emission by making constructive interference with the aid of phase-matching scheme.
6. Sensitivity to incidence angle change; study on THG’s angle dependence and propagation vector
The THG intensity dependence to the incidence angle was investigated by tilting the mirror located before the focusing lens, as shown in Fig. 5(a). The input laser beam was tilted by 5.6° in 9 steps and the resulting THG intensity was measured for the sapphire wafers with different cutting planes. It is found that THG intensity decreases to 0 when the tilt angle is larger than 4° for all specimens with different cutting planes, as shown in Figs. 5(b) and 5(c). This decrease in THG intensity is mainly because of the weaker focused electric field on the sapphire surface to drive the atomic dipole in the horizontal plane of the crystal. This trend is similar at the bottom surface of the sapphire wafers.
The propagation directions of THGs in and out of the sapphire were finally tested. The position of the fundamental and THG beams were taken by a CCD camera with the tilt of the incidence angle and sapphire wafers. To visualize THG beam without the fundamental beam, a short-pass filter was installed in the illumination beam path. The resulting images of THG and fundamental beam on top and bottom surfaces of C-plane sapphire with different tilt angles from 0 to 1.8° are shown in Figs. 5(d) and 5(e). When the input beam was focused onto the bottom surface of the sapphire with a 1.8° tilt angle, both the fundamental and THG beams were shifted by ~15.6 μm, which meets well the theoretical value of 15.4 μm based on geometrical calculation. Meanwhile, when the input beam was focused onto the top surface, the optical refraction of the focused beam inside the sapphire induced an extra shift of the beams. As the result, both fundamental and THG beams were shifted by 18.3 μm with the same tilt angle of 1.8°, which is also close to the theoretical value of 19.3 μm. This shift was 26% larger than that of THG at the bottom surface. When the input beam was focused to the bottom surface, the third harmonic is generated in the shallow skin depth near to the bottom surface; therefore, the fundamental and THG beams were almost overlapped with each other without obvious chromatic beam split. On the contrary, when the input beam was focused onto the top surface of the sapphire, the fundamental and THG beams were separated by 1.7 μm at an incidence angle 1.8°, which is caused by the wavelength-dependent refractive indices (1.74 at fundamental and 1.78 at third harmonic wavelength) . The THG beam can be also steered by tilting the target specimen, the sapphire wafer, which is shown in Figs. 5(f) and 5(g). The global beam shift was 11.6 μm for an incident tilt angle of 3.6°, which is close to the calculated value of 11.5 μm; this is smaller than the case of tilting the input beam. The beam separation could not be clearly detected due to lower angular dependence. These results suggest that the fundamental and THG beams can be simply split or steered for a series of applications, such as multi-colour beam separation and combination in pump-probe experiment or THG efficiency improvement by angular phase-matching.
To conclude, we generated third harmonics at both the top and bottom air-dielectric interfaces of sapphire with different crystalline cutting planes by focusing intense near-infrared femtosecond laser pulses. The crystal orientation was found to affect the THG intensity by ~20% for A, M and R-plane wafer, while this orientation dependency was not clear for the C-plane. The THG intensity was highest at the top and bottom surface and decreased by half when focal depth was over 18 μm from the interface. This suggests that THG conversion efficiency can be improved by generating THG from the top and bottom interfaces at the same time by selecting the sapphire thickness to be less than 51.6 μm and phase-match the generated THGs. When THG was at the top surface, the propagation vectors of the fundamental beam and third harmonic beam were different by the refraction effect; which was not conceivable at the bottom surface when THG was generated within the shallow skin depth. The fundamental and THG beams were split by controlling the incidence angle; when the incident angle of the input beam was adjusted by 1.8°, the relative position shift was 15.6 μm, but when the sapphire wafer was tilted by 3.6°, the position shift was about 11.6 μm. These findings will enable simple and efficient in-depth characterization of sapphire wafers for monitoring surface quality, crystallinity, interfacial uniformity, inter-layer delamination, and crack propagation.
NRF Fellowship from Singapore National Research Foundation (NRF-NRFF2015-02); AcRF Tier 1 (RG85/15) from the Singapore Ministry of Education; National Research Foundation of the Republic of Korea (NRF-2012R1A3A1050386).
References and links
1. R. W. Boyd, Nonlinear Optics (Academic Press, 2008).
2. Y. R. Shen, “Surface properties probed by second-harmonic and sum-frequency generation,” Nature 337(6207), 519–525 (1989). [CrossRef]
3. P. N. Saeta and N. A. Miller, “Distinguishing surface and bulk contributions to third-harmonic generation in silicon,” Appl. Phys. Lett. 79(17), 2704–2706 (2001). [CrossRef]
5. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2012).
7. W. K. Burns and N. Bloembergen, “Third-harmonic generation in absorbing media of cubic or isotropic symmetry,” Phys. Rev. B 4(10), 3437–3450 (1971). [CrossRef]
9. G. Grinblat, Y. Li, M. P. Nielsen, R. F. Oulton, and S. A. Maier, “Enhanced third harmonic generation in single germanium nanodisks excited at the anapole mode,” Nano Lett. 16(7), 4635–4640 (2016). [CrossRef] [PubMed]
10. M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014). [CrossRef] [PubMed]
11. J. Reinhold, M. R. Shcherbakov, A. Chipouline, V. I. Panov, C. Helgert, T. Paul, C. Rockstuhl, F. Lederer, E. B. Kley, A. Tünnermann, A. A. Fedyanin, and T. Pertsch, “Contribution of the magnetic resonance to the third harmonic generation from a fishnet metamaterial,” Phys. Rev. B 86(11), 115401 (2012). [CrossRef]
12. A. S. Shorokhov, E. V. Melik-Gaykazyan, D. A. Smirnova, B. Hopkins, K. E. Chong, D. Y. Choi, M. R. Shcherbakov, A. E. Miroshnichenko, D. N. Neshev, A. A. Fedyanin, and Y. S. Kivshar, “Multifold enhancement of third-harmonic generation in dielectric nanoparticles driven by magnetic fano resonances,” Nano Lett. 16(8), 4857–4861 (2016). [CrossRef] [PubMed]
13. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).
14. V. Pishchik, E. R. Dobrovinskaya, and L. A. Lytvynov, Sapphire: Material, Manufacturing, Applications (Springer-Verlag US, 2009).
15. K. Zheng, F. Sun, J. Zhu, Y. Ma, X. Li, D. Tang, F. Wang, and X. Wang, “Enhancing the Thermal Conductance of Polymer and Sapphire Interface via Self-Assembled Monolayer,” ACS Nano 10(8), 7792–7798 (2016). [CrossRef] [PubMed]
17. V. Giordano, S. Grop, C. Fluhr, B. Dubois, Y. Kersalé, and E. Rubiola, “The autonomous cryocooled sapphire oscillator: a reference for frequency stability and phase noise measurements,” J. Phys. Conf. Ser. 723(1), 012030 (2016). [CrossRef]
18. K. Konishi, T. Higuchi, J. Li, J. Larsson, S. Ishii, and M. Kuwata-Gonokami, “Polarization-controlled circular second-harmonic generation from metal hole arrays with threefold rotational symmetry,” Phys. Rev. Lett. 112(13), 135502 (2014). [CrossRef] [PubMed]
19. V. Mondes, E. Antonsson, J. Plenge, C. Raschpichler, I. Halfpap, A. Menski, C. Graf, M. F. Kling, and E. Rühl, “Plasmonic electric near-field enhancement in self-organized gold nanoparticles in macroscopic arrays,” Appl. Phys. B 122(6), 155 (2016). [CrossRef]
20. A. Chowdhury, H. M. Ng, M. Bhardwaj, and N. G. Weimann, “Second-harmonic generation in periodically poled GaN,” Appl. Phys. Lett. 83(6), 1077–1079 (2003). [CrossRef]
21. M. Jacobsohn and U. Banin, “Size Dependence of Second Harmonic Generation in CdSe Nanocrystal Quantum Dots,” J. Phys. Chem. B 104(1), 1–5 (2000). [CrossRef]
22. H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, “High-harmonic generation from an atomically thin semiconductor,” Nat. Phys. 13(3), 262–265 (2017). [CrossRef]
23. T. Otobe, “First-principle description for the high-harmonic generation in a diamond by intense short laser pulse,” J. Appl. Phys. 111(9), 093112 (2012). [CrossRef]
24. G. Petrocelli, E. Pichini, F. Scudieri, and S. Martellucci, “Anisotropic effects in the third-harmonic-generation process in cubic crystals,” J. Opt. Soc. Am. B 10(5), 918–923 (1993). [CrossRef]
26. H. Yao and C. H. Yan, “Anisotropic optical responses of sapphire (α-Al2O3) single crystals,” J. Appl. Phys. 85(9), 6717–6722 (1999). [CrossRef]
27. L. V. D. Amitonova, A. A. Lanin, I. V. Fedotov, O. I. Ivashkina, M. A. Zots, A. B. Fedotov, K. V. Anokhin, and A. M. Zheltikov, “Dark-field third-harmonic imaging,” Appl. Phys. Lett. 103(9), 093701 (2013). [CrossRef]