Characterization of all second-order nonlinear-optical coefficients of organic N-benzyl-2-methyl-4-nitroaniline crystal

Full elements of second-order nonlinear optical (NLO) tensor can be completely characterized for an organic NLO crystal for the first time. As-grown bulk N-benzyl-2-methyl-4-nitroaniline (BNA) crystal was processed to expose (100) and (010) crystal orientations with fine optical surfaces by using precision lathe and diamond blade. Then, every five nonvanishing second-order NLO coefficient of BNA can be determined quantitatively using the precisely processed crystals based on 1st-kind Maker fringe measurements. Our method makes it possible to clarify uncertain NLO property of any organic materials and to accelerate application study via precise device fabrications even for fragile organic materials.

rms roughness typically. They found that there is no relation between processed surface roughness and processed crystal orientations. Then, Y. Namba et al., also processed organic DAST crystals using diamond turning 20 . By optimizing several conditions for processing, sub-nm rms surface roughness in 1 mm square area were obtained on the b-plane. Contrastively, they pointed out a relation between processed surface roughness and crystal orientations. In this way, technology to precisely process fragile organic materials has not been standardized yet and didn't result in actual application of organic NLO crystals. Besides, since LAP and DAST crystals have strong ionic bonding, processing is relatively easy compared to normal organic crystals bonded by only weak intermolecular forces. Therefore, processing for normal organic crystal such as BNA is still challenging and must be optimized one by one.
Another critical problem impeding the use of organic NLO crystals is the fact that many elements of their second-order NLO tensor remain still unknown. In principle, organic NLO crystals are designed so that single molecules possess large hyperpolarizability, β. Established strategies for enhancing β often include prolonging conjugated chains to generate a π-electron pool as well as introducing donors and acceptors between conjugated chains. However, such molecules tend to have large dipole moments and centrosymmetric crystal structures are mainly obtained. Non-centrosymmetric crystals are generally obtained when some partial molecular structures, such as bulky, hydrogen-bonding and/or chiral substituents, are effectively introduced. Since these organic NLO crystals have poor crystal symmetry, there are many nonvanishing elements in the second-order NLO tensor of the crystals. Nevertheless, complete characterizations of all second-order NLO coefficients have not been attained yet for any organic NLO crystals. For example, although organic DAST crystals have a total of ten nonvanishing elements in its second-order NLO tensor, only elements d 11 , d 12 , and d 26 have been characterized [21][22][23] . Since conventional as-grown DAST crystal has a routine morphology possessing dominant (001) facets, in which a-and b-axes lie, only d 11 , d 12 , and d 26 can be measured as long as one use as-grown DAST crystals. In other words, one cannot attempt to measure every second-order NLO tensor without proper crystal processing. Even in reported values for d 11 of DAST, there is big disagreement reaching 200% [21][22][23] . As for organic DSTMS and OH1 crystals, some second-order NLO tensors have been characterized using the Maker fringe technique 24,25 . However, since as-grown crystals without proper processing were used in the measurements, many elements of the second-order NLO tensors are still untouched. None of the second-order NLO tensors have been characterized yet for the organic HMQ-TMS crystal, although the β of a single molecule has been estimated 9 26 . However, there are nonnegligible discrepancies between the experimental Maker fringe data and theoretical fitting lines, which is likely attributed to imperfect crystal processing. In this way, magnitudes of second-order NLO tensors of organic NLO crystals remain ambiguous and there is no organic NLO crystal for which all second-order NLO coefficients are characterized. The complete characterization of them mandates the precise processing for fragile organic NLO crystals.
Herein, we report a precise processing technology for the organic NLO BNA crystal at the beginning. Then, we report characterization of all elements of second-order NLO tensor for the BNA crystal using precisely processed plane-parallel (100)-and (010)-slab crystals. This is the first accomplishment of measuring all elements of second-order NLO tensor completely for organic crystals.

Results
Ultra-precise processing using diamond blade for organic materials. There are several methods to evaluate second-order NLO properties of organic crystals. The powder method 27 is a qualitative or semiquantitative one, which is useful only for screening to find NLO-active crystals. Electric-field-induced second-harmonic generation 28 and hyper-Rayleigh scattering 29 can clarify β of molecules. However, in order to estimate second-order-NLO tensor, calculation according to the oriented-gas model 30 using the known crystal structure is necessary. Meanwhile, the Maker fringe technique including the rotation and wedge methods is the direct way to measure each element of the NLO tensor without using phase-matched conditions. This technique was first reported by Jerphagnon et al., for isotropic and uniaxial crystals 31 . The technique has been improved for biaxial crystals, where almost all organic NLO crystals are categorized 32,33 . The Maker fringe technique is based on the measurement of generated second harmonic fringe patterns caused by the perpendicular rotation of a plane-parallel crystals with respect to the pump beam axis 34 . Since coherence lengths of NLO crystals under non phase-matched conditions are typically less than several µm, thin plane-parallel crystal with smooth optical surfaces, which have roughness in the order of nm, should be prepared to obtain a decent Maker fringe pattern. The top and back surfaces of the thin plane crystal should be parallel enough to guarantee the same optical path length in the crystal for both edges of the pump beam. However, conventional technologies such as polishing using abrasive particles cannot satisfy the level of precision necessary for fragile organic NLO crystals because frictional heat melts the surface and abrasive particles are embedded into the surface. To overcome this shortcoming, we applied an ultrahigh-precision cutting process by employing a precisely-controlled lathe and a diamond blade 19,20 to organic as-grown BNA crystals. Because diamond has excellent thermal conductivity and dissipation, diamond cutting can avoid thermal damages on the surface and obtain high-grade optical surfaces. Cutting is one of the process to transfer the diamond-edge shape manufactured with extremely high smoothness and accuracy to target object. Its smoothness and accuracy can be directly transferred to cutting plane of organic crystals. Hence, ultra-precisely processing can be highly expected even for brittle organic crystals.
BNA usually crystallizes in point group mm2 of the orthorhombic system, which possesses five nonvanishing second-order NLO tensor elements, namely d 33 , d 32 , d 31 , d 24 , and d 15 . In this case, first-and second-kind Maker fringes are expected using (100)-, (010)-and (001)-BNA slabs. In general, first-kind Maker fringe gives less discrepancy between theory and experimental data 35 . Using two plane-parallel (100)-and (010)-BNA slabs, first-kind Maker fringe patterns for d 32 24 can be approved for NLO crystals belong to point group mm2. However, near the band-gap region, Kleinman symmetry is no longer validated. Therefore, each of the five second-order NLO tensors of BNA should be measured independently when the pump wavelength is 1064 nm. Moreover, since coherence lengths under non phase-matched conditions are typically very short, the thickness of the plane-parallel slab sample for the Maker fringe measurement should be very thin so that neighboring fringes can be clearly observed. Because of the hexagonal cylindrical shape of as-grown BNA crystals with the largest (010) facet in which <100> and <001> axes lie orthogonally, (100)-and (010)-BNA slabs must be made by cutting as-grown bulk BNA crystals perpendicularly to the principle <100> and <010> axes, respectively. To exclude differences of individual crystal quality in the determination of elements of the second-order NLO tensor, samples to make (100)-and (010)-BNA slabs were cutout from the same as-grown BNA single crystal using wire-saw firstly, as shown in Fig. 1(a). Then, thin plane-parallel (100)-and (010)-BNA slabs were precisely processed using ultrahigh-precision cutting. A photograph of processed (100)-BNA slab is shown in Fig. 1(b). The thickness of the precisely processed (100)-and (010)-BNA slabs are 303 and 305 µm, respectively. The roughnesses of their processed surfaces were measured using a 3D optical profiler, Zygo, which has pm-level displacement resolution. Figure 1(c) shows an example of measured profile of a processed (100)-BNA slab surface, and the variance of the surface roughness was several nm. This level of surface roughness on the sample is enough to obtain a decent Maker fringe pattern and similar levels of surface roughness can also be obtained for the (010)-BNA slabs. It is important to note that relations among processed surface roughness, cut direction, cut crystal plane, cleavage directions, rake angle of diamond blade, and so on are worthy research topics, but they are beyond the scope of the proposed paper and will be saved for future investigations.

Characterization of every second-order NLO tensor of BNA based on maker fringe measurement.
Maker fringe measurement system employs a Q-switched Nd:YAG laser with a 10 ns pulse width and wavelength of 1064 nm as a pump source for the BNA crystals. By applying a notch filter to the pump beam, only SHG waves generated in BNA crystals can be detected using the silicon pin-photodiode. A half-wave plate and polarizer are installed in front of the sample and the detector, respectively, to properly control polarization states of the pump beam and the SHG beam, depending on the target element of the second-order NLO tensor. Since the principle of the Maker fringe technique is based on relative measurements of SHG intensity, a well-known standard NLO crystal is necessary. Because the magnitude of d 33 of inorganic KTiOPO 4 (KTP) crystal, which belong to the same point group as BNA, is well characterized with reliable accuracy 37 , it is used as a standard reference to determine absolute values of second-order NLO tensors for BNA. Figure 2 exhibits a Maker fringe pattern produced by d 33 of Y-cut KTP crystal when the pulse energy of the pump beam is 150 μJ. The rotational axis of the KTP is its Z-axis, and the polarizations of the pump and detected SHG waves are parallel to the Z-axis. The amplitude of the fringe's envelope represents the magnitude of d 33 , and the spacing between fringes indicates coherence length. The red line shown in Fig. 2 represents the theoretical fitting line considering anisotropy of biaxial orthorhombic crystals 32 . Here two refractive indices n z@1064 , and n z@532 corresponds to the pump and SHG wavelengths as well as the amplitude coefficient A, containing d 33 are fitting parameters. The thickness of the KTP crystal was measured to be 800.6 µm, which is prior given in the fitting. Meanwhile, fitted refractive indices for the pump, n z@1064 , and SHG, n z@532 , are 1.828 and 1.888, respectively, both of which agree well with the values derived from a given Sellmeier equation 38 . The fitted value of the amplitude coefficient, A, is defined to be 1, as standard reference for d 33 = 14.7 pm/V of KTP 37 .
We then measured the Maker fringe patterns for organic BNA crystals. Figure 3(a) demonstrates a result for the d 33 element using a processed thin-parallel (010)-BNA slab. In this case, the rotational axis of the BNA is <001>, and the polarizations of both the pump and SHG are parallel to the <001> axis. The pump pulse energy of 150 μJ is maintained from the d 33 measurement of KTP and remains fixed for subsequent all experiments. As shown in Fig. 3(a), a favorable Maker fringe pattern without distortion, asymmetry, or nonzero-minima can be successfully obtained even for organic NLO crystal when it has been precisely processed. The fitted refractive indices n z@1064 for the pump wavelength and n z@532 for the SHG wavelength are 1.802 and 2.093, respectively. The fitted amplitude coefficient, A, for the fringe is 15.7. By comparing the values of A derived from BNA and KTP, the magnitude of d 33 of BNA can be characterized as 231 ± 5 pm/V. This value is significantly large, and its nonlinearity may be enhanced by charge transfer excitation resonance near the band-gap. Although previously reported values of d 33 of BNA are also large 25 , our Maker fringe pattern closely traces the theoretical fitting curve. This level of similarity can only be achieved with a precisely processed plane-parallel thin BNA slab and can drastically reduce the error-bars in determining the value of NLO coefficients. Employing the same processed (010)-BNA slab and resultant Maker fringe pattern, the value of d 15 is also characterized as shown in Fig. 3(b). In this case, the rotation axis is <100>, and the polarization of the detected SHG beam is parallel to the <100> axis. The polarization of the input pump beam is tilted 45 degrees with respect to the rotational axis <100> to generate equal pump amplitude for the <100> and <001> axes. The fitted refractive indices, n x@1064 , n y@1064 , n z@1064 , for the pump wavelength, and n x@532 for the SHG wavelength, are 1.568, 1.707, 1.808, and 1.631, respectively. From the fitted amplitude coefficient, A = 5.38, the magnitude of d 15 of BNA can be characterized as 77.6 ± 1.6 pm/V first time ever. This value is also large compared to off-diagonal elements of second-order NLO tensors of other NLO crystals and d 15 will be useful for Type-2 phase-matched NLO processes. The first-kind Maker fringe pattern for d 31 is also expected using the processed (010)-BNA slab; however, an explicit SHG signal cannot be observed in the experiment. This result is consistent with previous findings, which characterize d 31 of BNA as negligibly small 25 .
To characterize the remaining elements of the second-order NLO tensor of BNA, a processed plane-parallel thin (100)-BNA slab was used. Although d 33 of BNA was already characterized using the (010)-BNA slab, its characterization can be confirmed with the (100)-BNA slab, as exhibited in Fig. 3(c). The rotational axis of the BNA is <001>, and the polarizations of both the pump and SHG are parallel to the <001> axis in this case. A Maker fringe pattern similar to that of Fig. 3(a) can be observed because the thicknesses of the two processed slabs are almost the same. Based on fitting results for Fig. 3(c), d 33 can be characterized as 234 ± 5 pm/V, which supports the previous result obtained using the (010)-BNA slab. In this way, same NLO coefficient can be measured for two crystals with different facets by cutting them out from a single bulk crystal for the first time.
The two remaining elements, d 24 and d 32 , were also characterized using the (100)-BNA slab. In the case of d 24 , the rotational axis is <010>, while the detected SHG polarization is parallel to <010> and the input pump polarization is tilted 45 degrees with respect to <010>. The corresponding Maker fringe pattern is given in Fig. 3(d), and the fitted refractive indices n x@1064 , n y@1064 , n z@1064 for the pump wavelength, and n y@532 for the SHG wavelength are 1.538, 1.709, 1.796, and 1.784, respectively. Characterized magnitude of d 24 is 41.4 ± 0.8 pm/V. Finally, the Maker fringe measurement for d 32 was carried out, the result of which is given in Fig. 3(e). Herein, the rotational axis is <010>, and the polarizations of the pump and SHG are parallel and perpendicular to <010>, respectively. In this configuration, the SHG signal is relatively low and noisy compared to other Maker fringe data owing to the relatively short coherence length. The fitted refractive indices for pump wavelength, n y@1064 , and SHG wavelengths, n x@532 and n z@532 , are 1.720, 1.612 and 2.080, respectively. The magnitude of d 32 is characterized as 78.1 ± 1.6 pm/V based on the fitting result. www.nature.com/scientificreports www.nature.com/scientificreports/ The magnitudes of d 24 and d 32 of BNA were alternatively characterized based on the phase-matched Type-2 SHG method. These values were reported as 5.5 ± 0.2 39 and 15.6 ± 0.9 pm/V 25 , respectively, both of which differ significantly from our results. Although the cause of these discrepancies must be clarified scientifically, we hypothesize that the Maker fringe method may produce more reliable results because the phase-matched SHG power drastically changes with even slight changes in temperature, tuning angle and so on. Another possible explanation is our improved BNA crystal quality, which likely produces higher optical nonlinearity. As for the fitted refractive indices in our Maker fringe results, small disagreements are found with the refractive indices deduced from given Sellmeier equations 25,39 . However, because multiple refractive indices, thickness of sample and magnitude of second-order NLO coefficient simultaneously influence the shape of Maker fringes, such slight discrepancy as a result of least-square fitting can be inevitable. In addition, the given Sellmeier equations obtained www.nature.com/scientificreports www.nature.com/scientificreports/ for BNA are not very accurate to begin with, and actual differences between the refractive indices due to crystal quality or contamination by impurities might be observed.

Methods
In general, shapes of as-grown organic crystals cannot be suitably handled for processing and fixing on the turntable of a lathe. Therefore, BNA crystals are embedded in epoxy resin and aluminum (Al) ring for easier handling and reinforcement before processing, as shown in Fig. 4. The surrounding Al ring and resin are cut together with the BNA by a diamond blade during the processing. This structure prevents cracking and distortion of the thin organic crystals. Figure 5 displays a photograph of the system. The sample is mounted on the lathe's turntable with a vacuum chuck, and the lathe is rotated at a speed of 500 rpm. During the sample rotation, the tip of the single crystalline diamond blade contacts the surface of the sample very slowly from horizontal direction to cut the sample surface slightly. Diamond is the best blade from the viewpoints of smoothness of outline of the tip, its hardness and super thermal conductivity. During the cutting process, crystal chips are cleared from the sample surface by air blow to avoid surface damage due to scratching. To hold the sample despite friction between the sample and diamond blade, a stopper is also installed in the turning table; the height of the stopper can be controlled depending on the sample thickness. After one round-trip motion of the diamond blade along the horizontal axis, the blade approaches the sample with µm-step. This cutting process is repeated until the sample is cut to the desired thickness and then repeated for the other surface of the sample. An aerostatic bearing achieves stable rotation of the lathe without disturbing the sample, while feedback control using linear scale and precision ball-screw maintains 3D-axes scanning of the diamond blade with nm-level positioning resolution. This system enables fragile organic crystals to be processed very precisely, hence exposing any crystal facets with very smooth optical surfaces.

conclusion
We successfully characterized all elements of the second-order NLO tensors for organic BNA crystal for the first time by developing a method to produce thin plane-parallel (100)-and (010)-slab crystals with high-grade optical facets. Our technology enables us to not only characterize all of second-order NLO coefficients completely for any organic NLO crystals, but also fabricate new organic NLO devices for various applications.