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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 16 — Aug. 12, 2013
  • pp: 19012–19021
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Second-harmonic generation in lithium niobate nanowires for local fluorescence excitation

Anton Sergeyev, Reinhard Geiss, Alexander S. Solntsev, Andrea Steinbrück, Frank Schrempel, Ernst-Bernhard Kley, Thomas Pertsch, and Rachel Grange  »View Author Affiliations


Optics Express, Vol. 21, Issue 16, pp. 19012-19021 (2013)
http://dx.doi.org/10.1364/OE.21.019012


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Abstract

We study the nonlinear optical properties of lithium niobate (LiNbO3) nanowires (NWs) fabricated by a top-down ion beam enhanced etching method. First, we demonstrate generation and propagation of the second-harmonic (SH) light in LiNbO3 NWs of typical rectangular cross-sections of 400 x 600 nm2 and length from 10 to 50 μm. Then, we show local fluorescent excitation of 4',6-diamidino-2-phenylindole (DAPI) dye with the propagated SH signal in standard concentrations as for biological applications. By measuring the detected average power of the propagated fundamental harmonic (FH) and the SH signal at the output of the NWs, we directly prove the dominating role of the SH signal over possible two-photon excitation processes with the FH in the DAPI dye. We estimate that 63 ± 6 pW of the propagated SH average power is required for detectable dye excitation. Finally, we model the waveguiding of the SH light to determine the smallest NW cross-section (around 40x60 nm2) which is potentially able to excite fluorescence with a FH intensity below the cell damage threshold.

© 2013 OSA

1. Introduction

Owing to their specific shape, nanowires (NW) are invaluable building blocks for various nanodevices and important components for future applications [1

1. R. Yan, D. Gargas, and P. Yang, “Nanowire photonics,” Nat. Photonics 3(10), 569–576 (2009). [CrossRef]

3

3. C. J. Barrelet, A. B. Greytak, and C. M. Lieber, “Nanowire photonic circuit elements,” Nano Lett. 4(10), 1981–1985 (2004). [CrossRef]

]. For instance, NWs are demonstrated to be useful for nanolasing [4

4. X. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature 421(6920), 241–245 (2003). [CrossRef] [PubMed]

] or light transportation [5

5. T. Voss, G. T. Svacha, E. Mazur, S. Müller, C. Ronning, D. Konjhodzic, and F. Marlow, “High-order waveguide modes in ZnO nanowires,” Nano Lett. 7(12), 3675–3680 (2007). [CrossRef] [PubMed]

]. More recently, a very interesting approach has been suggested which uses NWs in biological studies for performing localized imaging inside cells [6

6. P. Yang, R. Yan, and M. Fardy, “Semiconductor nanowire: what’s next?” Nano Lett. 10(5), 1529–1536 (2010). [CrossRef] [PubMed]

]. For this purpose, a NW has to be inserted into a cell which contains fluorescent material. Then, laser light is coupled into the NW and excites fluorescent material either with evanescent waves along the NW [7

7. C. Xie, L. Hanson, Y. Cui, and B. Cui, “Vertical nanopillars for highly localized fluorescence imaging,” Proc. Natl. Acad. Sci. U.S.A. 108(10), 3894–3899 (2011). [CrossRef] [PubMed]

] or with the delivered light at the NW’s opposite side [8

8. R. Yan, J.-H. Park, Y. Choi, C.-J. Heo, S.-M. Yang, L. P. Lee, and P. Yang, “Nanowire-based single-cell endoscopy,” Nat. Nanotechnol. 7(3), 191–196 (2011). [CrossRef] [PubMed]

]. Both of these demonstrated applications use linear optical excitations with visible light and still suffer from the illumination of the surrounding tissue.

For a convenient discrimination of the incident light, nonlinear optical effects are widely exploited phenomena like in two-photon fluorescence microscopy [9

9. W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990). [CrossRef] [PubMed]

], second-harmonic generation (SHG) imaging [10

10. P. J. Campagnola and L. M. Loew, “Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms,” Nat. Biotechnol. 21(11), 1356–1360 (2003). [CrossRef] [PubMed]

] or coherent anti-Stokes Raman scattering techniques (CARS) [11

11. C. L. Evans and X. S. Xie, “Coherent anti-stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Ann. Rev Anal Chem (Palo Alto Calif) 1(1), 883–909 (2008). [CrossRef] [PubMed]

]. Indeed, the contrast mechanism relies on converting the near infrared (NIR) incident laser wavelength into a different wavelength due to the nonlinear properties of the used materials. Moreover, NIR wavelengths provide an increase of the penetration distance by a decrease of the laser beam scattering in water and living tissue [12

12. F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198(4323), 1264–1267 (1977). [CrossRef] [PubMed]

].

Combining nonlinear effects and NWs has been demonstrated in semiconductor NWs as GaN [13

13. J. P. Long, B. S. Simpkins, D. J. Rowenhorst, and P. E. Pehrsson, “Far-field imaging of optical second-harmonic generation in single GaN nanowires,” Nano Lett. 7(3), 831–836 (2007). [CrossRef] [PubMed]

], ZnO [14

14. J. C. Johnson, H. Q. Yan, R. D. Schaller, P. B. Petersen, P. D. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2(4), 279–283 (2002). [CrossRef]

16

16. A. Kachynski, A. N. Kuzmin, M. Nyk, I. Roy, and P. N. Prasad, “Zinc oxide nanocrystals for nonresonant nonlinear optical microscopy in biology and medicine,” J. Phys. Chem. C 112(29), 10721–10724 (2008). [CrossRef]

], GaAs [17

17. R. Chen, S. Crankshaw, T. Tran, L. C. Chuang, M. Moewe, and C. Chang-Hasnain, “Second-harmonic generation from a single wurtzite GaAs nanoneedle,” Appl. Phys. Lett. 96(5), 051110 (2010). [CrossRef]

,18

18. R. Grange, G. Brönstrup, M. Kiometzis, A. Sergeyev, J. Richter, C. Leiterer, W. Fritzsche, C. Gutsche, A. Lysov, W. Prost, F.-J. Tegude, T. Pertsch, A. Tünnermann, and S. Christiansen, “Far-field imaging for direct visualization of light interferences in GaAs nanowires,” Nano Lett. 12(10), 5412–5417 (2012). [CrossRef] [PubMed]

], AlN [19

19. W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012). [CrossRef]

], InP [20

20. F. Wang, P. J. Reece, S. Paiman, Q. Gao, H. H. Tan, and C. Jagadish, “Nonlinear optical processes in optically trapped InP nanowires,” Nano Lett. 11(10), 4149–4153 (2011). [CrossRef] [PubMed]

], ZnSe [21

21. V. Barzda, R. Cisek, T. L. Spencer, and U. Philipose, “Giant anisotropy of second harmonic generation for a single ZnSe nanowire,” Appl. Phys. Lett. 92, 113111 – 113111–3 (2008). [CrossRef]

] and GaP [22

22. R. Sanatinia, M. Swillo, and S. Anand, “Surface second-harmonic generation from vertical GaP nanopillars,” Nano Lett. 12(2), 820–826 (2012). [CrossRef] [PubMed]

], since they show noncentrosymmetric crystal structures needed for second-order nonlinear effects such as SHG, which combines two photons of a defined wavelength into a single photon with half the wavelength. Niobate NWs (K-, Li-, NaNbO3) are also promising candidates since they have already been shown both to maintain SHG properties at nanoscale size [23

23. R. Grange, J.-W. Choi, C.-L. Hsieh, Y. Pu, A. Magrez, R. Smajda, L. Forró, and D. Psaltis, “Lithium niobate nanowires synthesis, optical properties, and manipulation,” Appl. Phys. Lett. 95(14), 143105 (2009). [CrossRef]

,24

24. B. Knabe, K. Buse, W. Assenmacher, and W. Mader, “Spontaneous polarization in ultrasmall lithium niobate nanocrystals revealed by second harmonic generation,” Phys. Rev. B 86(19), 195428 (2012). [CrossRef]

] and to propagate the second-harmonic (SH) signal [25

25. F. Dutto, C. Raillon, K. Schenk, and A. Radenovic, “Nonlinear optical response in single alkaline niobate nanowires,” Nano Lett. 11(6), 2517–2521 (2011). [CrossRef] [PubMed]

]. However, no data are available to quantify the amount of the propagated SH signal and whether this signal is strong enough for further fluorescent dyes excitation at standard concentrations.

Furthermore, up to now, only chemically synthesized niobate NWs have been studied for the SH propagation [25

25. F. Dutto, C. Raillon, K. Schenk, and A. Radenovic, “Nonlinear optical response in single alkaline niobate nanowires,” Nano Lett. 11(6), 2517–2521 (2011). [CrossRef] [PubMed]

,26

26. Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447(7148), 1098–1101 (2007). [CrossRef] [PubMed]

]. However, this chemical approach faces several challenges. The non-perfect crystal structure and the random crystal orientation of these NWs limit their SHG properties. In this work, we study the SHG properties of LiNbO3 NWs because of the relatively high second-order nonlinear susceptibilities [27

27. R. W. Boyd, Nonlinear Optics, 2nd ed. (Amsterdam: Academic Press, 2003).

] and the biocompatibility of the crystal [28

28. D. Staedler, T. Magouroux, R. Hadji, C. Joulaud, J. Extermann, S. Schwung, S. Passemard, C. Kasparian, G. Clarke, M. Gerrmann, R. Le Dantec, Y. Mugnier, D. Rytz, D. Ciepielewski, C. Galez, S. Gerber-Lemaire, L. Juillerat-Jeanneret, L. Bonacina, and J. P. Wolf, “Harmonic nanocrystals for biolabeling: a survey of optical properties and biocompatibility,” ACS Nano 6(3), 2542–2549 (2012). [CrossRef] [PubMed]

]. The LiNbO3 NWs are fabricated with Ion Beam Enhanced Etching (IBEE) method [29

29. H. Hartung, E.-B. Kley, T. Gischkat, F. Schrempel, W. Wesch, and A. Tünnermann, “Ultra thin high index contrast photonic crystal slabs in lithium niobate,” Opt. Mater. 33(1), 19–21 (2010). [CrossRef]

]. This method provides a better control over the design and the crystal orientation of the NWs and allows fabrication of longer NWs (up to 100 µm).

We demonstrate the generation and propagation of the SH in the LiNbO3 NWs. We show fluorescence excitation with the propagated SH signal in standard dye concentration solutions. We experimentally investigate the limits of the SH signal needed for sufficient detection of fluorescent emission in typical dye concentration. Finally, we model generation and waveguiding of the SH in the LiNbO3 NWs to find the smallest possible NW cross-section, which still offers enough propagated SH signal to further excite fluorophores.

2. Sample preparation

The LiNbO3 NWs are fabricated following the top-down IBEE method described in details elsewhere [29

29. H. Hartung, E.-B. Kley, T. Gischkat, F. Schrempel, W. Wesch, and A. Tünnermann, “Ultra thin high index contrast photonic crystal slabs in lithium niobate,” Opt. Mater. 33(1), 19–21 (2010). [CrossRef]

]. IBEE is based on the reduced chemical stability of LiNbO3 after ion-beam irradiation. For the patterning of the NWs, a mask containing the nanoscale waveguides is written with electron beam lithography. A series of high energy argon ions (600 keV with a fluence of 7.2e14 cm−2 and 350, 150, 60 keV at 1.38e14 cm−2) is used to transfer this mask in the substrate. After removing the masking layer, a second irradiation with helium ions (285 keV at 5e16 cm−2) damages a layer localized under the surface. The irradiated regions are subsequently removed by chemical wet etching in hydrofluoric acid forming free-standing LiNbO3 NWs with typical rectangular cross-section between 400 and 600 nm.

The NWs are oriented on the LiNbO3 substrate so that the crystal axes X and Z are parallel to the height and width of NWs, respectively. Since the substrate can generate unwanted background SH signals, the NWs are detached by ultrasonication in ethanol. Thus, we obtain a solution of LiNbO3 NWs with various lengths, usually from 10 up to 50 μm, depending on where the NWs break.

The samples for the experiment are prepared by dropping several microliters of NWs-ethanol solution onto a glass slide. The glass slide has a numbered pattern so that the position of a NW can be identified and the same NW can be studied repeatedly. Figures 1(a)
Fig. 1 SEM images of a NW (a) and its facet (b). The inset in (b) shows the crystal structure of the NW. The width, the height and the length of the presented NW are 460 ± 20 nm, 610 ± 20 nm and 48.9 ± 0.4 µm, respectively.
and 1(b) shows a scanning electron microscopy (SEM) picture of a typical LiNbO3 NW on a glass substrate.

Depending on the experiment, we drop 10 µl of either water (for the SH measurements) or dyes solution (for the fluorescence measurements) onto the dried NW sample. In order to prevent evaporation, we seal the sample with a cover slip.

The dyes solution is prepared by mixing water and 4',6-diamidino-2-phenylindole (DAPI, Sigma-Aldrich) at different concentrations. We have chosen DAPI dye because it is widely used in biology for staining nuclei and membranes of cells [30

30. K. G. Porter and Y. S. Feig, “The use of DAPI for identifying aquatic microflora,” Limnol. Oceanogr. 25(5), 943–948 (1980). [CrossRef]

,31

31. F. Otto, “DAPI staining of fixed cells for high-resolution flow cytometry of nuclear DNA,” Methods Cell Biol. 33, 105–110 (1990). [CrossRef] [PubMed]

]. Owing to the broad peak of the DAPI absorption spectrum centered at 340 nm, the dye can be easily excited with the SH light which is generated with the fundamental wavelength (760 nm) from a Ti:Sapphire oscillator. In addition, the DAPI dye’s emission wavelength is centered at 488 nm and is therefore well distinct from the excitation [32

32. 4’,6-Diamidino-2-phenylindole (D9542, D8417, D9564) - product information sheet,” http://www.sigmaaldrich.com/etc/medialib/docs/Sigma/Product_Information_Sheet/d9542pis.Par.0001.File.tmp/d9542pis.pdf.

].

3. Experimental setup

For the SH and the fluorescence imaging experiments, we use a home-built transmission optical microscope [18

18. R. Grange, G. Brönstrup, M. Kiometzis, A. Sergeyev, J. Richter, C. Leiterer, W. Fritzsche, C. Gutsche, A. Lysov, W. Prost, F.-J. Tegude, T. Pertsch, A. Tünnermann, and S. Christiansen, “Far-field imaging for direct visualization of light interferences in GaAs nanowires,” Nano Lett. 12(10), 5412–5417 (2012). [CrossRef] [PubMed]

]. A Ti:Sapphire laser with a 283-fs pulsed beam at wavelength of 760 nm wavelength and 80 MHz repetition rate is focused with a 10x objective onto a sample with NWs to a beam spot of 4 µm. The slightly focused laser beam is used to relax the condition on the position of the NW and to ensure reproducible and stable coupling configuration. The NW lies on a glass substrate and the focused laser beam falls perpendicularly in respect to the sample and illuminates one of the NW ends. The SH and fluorescence signals are collected from the sample by a 100x objective and focused with a 250-mm lens onto a cooled electron-multiplied charge-coupled device (EMCCD) camera.

The crystal structure of the LiNbO3 NWs requires certain polarization of the incident light to take advantage of the largest susceptibility tensor components of the material [27

27. R. W. Boyd, Nonlinear Optics, 2nd ed. (Amsterdam: Academic Press, 2003).

] and as a result to achieve the maximal amount of the SH. Therefore, we use a half-wave plate at the entrance of the experimental setup to optimize the polarization of the incident laser beam.

Depending on the spectral range of the studied signals, we use corresponding filters in front of the EMCCD. Thus, we employ a band-pass filter to suppress the infrared beam and to observe the SH signal. A long-pass filter is added to remove the SH signal when the fluorescence signal is to be detected. In addition, the collecting objective is mounted on a miniature translation stage. It allows changing the distance between the collecting objective and the sample and therefore to compensate the change of the objective’s focal length due to the wavelength tuning.

4. Experimental results and discussion

4.1. Propagation of the fundamental harmonic (FH) and SH signals in LiNbO3 NWs

First, we demonstrate the propagation of the FH and SH signals through a NW. For the experiment, we prepare a sample with NWs in water with a sealed cover slip. After we couple the FH signal at 760 nm into a NW by illuminating one of its ends with a focused laser beam, we observe the same wavelength at the opposite end of the NW.

If we block the FH with a band-pass filter centered at 470 nm with a bandwidth of ± 110 nm at the camera input, we observe a strong signal at the NW input and a weaker signal at the output. Both signals disappear when the NW is moved out of the laser beam spot. Figure 2(a)
Fig. 2 (a) White light image of the studied NW. The dashed circle indicates the illumination area of the FH incident beam spot. (b) SH light at the NW input and propagated SH light at the NW output. The average power of the output SH signal is found to be 347 ± 40 pW. The width, the height and the length of the studied NW are 460 ± 20 nm, 610 ± 20 nm and 48.9 ± 0.4 µm, respectively. The dash-and-dot line indicates the position of the NW. (c) The dependence of the SH signal at the NW output on the incident laser beam power. The dots correspond to the experimental results and the solid line corresponds to the quadratic fit. The error bars show uncertainty of choosing the signal pixels for integration.
shows the white-light image of one of the studied NWs and Fig. 2(b) displays the signals which are observed at both NW ends when we bring the band-pass filter into the setup. In order to clear the nature of the observed signal, we measure the power dependence of the detected signal while varying the incident laser beam power. The power is calculated by integrating the signal from each pixel of the taken image and by taking into account the setup’s transmissivity, the camera’s sensitivity and acquisition parameters. In Fig. 2(c), we plot the dependence of the output signal on the incident laser beam power. The good correspondence to the quadratic fit proves that the observed signal is indeed a second-order nonlinear effect such as SHG. In our setup configuration, we detect the portions of the total propagated FH and SH signals that are scattered towards the camera at the NW output facet. Besides the signals at the NW ends, we also detect a weak SH light along the NW. We refer it to a result of scattering of the propagating SH by the NW surface roughness [19

19. W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012). [CrossRef]

,33

33. L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]

].

The performed experiments show that LiNbO3 NWs can be used not only for guiding the FH signal but also for generating and guiding the SH. However, it is not clear which process stands behind this observation. The propagation process is probably a combination of waveguiding and scattering which are affected by the input facet and the surface roughness of the NW. Therefore, since we do not know the propagation process, the field distribution inside the NW is unknown. Identification of the dominating mechanism may help optimise the NW design for generating and propagating stronger SH signal and is currently under investigation in our group.

We have measured the average power values of the detected FH and SH signals at the outputs of several NWs at the same average power of the laser beam (85 ± 3 mW). Prior to the measurements, the laser beam polarization is set for each NW so that the maximum SH signal at the NW output is achieved. The incident laser beam polarization at which the maximum of the propagated SH signal is achieved varies for each NW. Indeed, it depends on the NW facets design and the crystal structure orientation in space with respect to the incident beam. Both influence the coupling of the IR into the NW and consequently the generated and propagated SH. Note that the NW crystal structure may have two possible orientations in space with respect to the laser beam propagation direction. Depending on the side that touches the substrate, the Z-axis of the crystal is either perpendicular or parallel to the laser beam propagation direction. Due to the setup configuration with a wide laser beam (4 µm diameter) impinging perpendicularly on the NWs end (400 to 650 nm width), the coupling is quite inefficient. The average power of the FH transported by the studied NWs varies between 90 ± 10 nW and 441 ± 44 nW at the outputs of several NW. We explain this large variation by various scattering processes at the facets that may strongly influence the in- and out-coupling. Furthermore, the propagated SH is affected by the amount of the coupled FH light and varies from infinitely low values up to 2.57 ± 0.26 nW.

Besides the low coupling, the SH signal is also expected to depend on the NW design. Firstly, the SH signal is expected to vary periodically along the NW according to the undepleted pump approximation as the NW is longer than the coherence length of the SH process (for example, according to the waveguiding modeling we discuss in Subsection 4.5, the coherence length in the above-studied NW varies between 0.45 and 0.53 µm) and the FH signal is considerably higher than the generated SH signal [27

27. R. W. Boyd, Nonlinear Optics, 2nd ed. (Amsterdam: Academic Press, 2003).

]. Secondly, the cross-section design is expected to have an influence on the conversion efficiency between the FH and SH signals which propagate inside a NW [34

34. A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, R. Iliew, R. Geiss, T. Pertsch, and Y. S. Kivshar, “Cascaded third harmonic generation in lithium niobate nanowaveguides,” Appl. Phys. Lett. 98(23), 231110 (2011). [CrossRef]

].

4.2. Observation of the fluorescent dye excitation

In Figs. 3(a)
Fig. 3 Images of the fluorescence signal in DAPI dye solution with concentrations of 1 µg/ml (a) and 50 ng/ml (b). The collected fluorescence signals at the NW output are found to be 17.6 ± 1.9 fW and 2.4 ± 1.2 fW in DAPI dye solutions with concentrations of 1 µg/ml and 50 ng/ml, respectively. The dashed and the dotted circles indicate the illumination area of the incident beam spot and the fluorescence signal at the NW output, respectively. The dash-and-dot line indicates the position of the NW.
and 3(b), we demonstrate the detection of 17.6 ± 1.9 fW and 2.4 ± 1.2 fW of the fluorescence signal at the output of the NW in dye solutions with concentration of 1 µg/ml and 50 ng/ml, respectively. We also detect signals at the illumination area and along the NW. The detected signal at the illumination area is a mixture of the laser beam light leaked through the filters and the fluorescence signal excited with the SH signals that is generated at the NW input. The weak fluorescence signal along the NW is most probably excited with the propagated SH signal which is scattered by the surface roughness of the NW [19

19. W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012). [CrossRef]

,33

33. L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]

].

By repeating the measurement after a defined period of time, we have noticed an increase of the fluorescence signal. For instance, the fluorescence signal for one of our samples has increased 28 times after keeping a NW in 1 µg/ml dye solution for two weeks. We explain this counter-intuitive effect by settling of the dye on NWs. In other words, the dye tends to deposit on the NW and the concentration must therefore increase dramatically. Therefore, all results which are presented in this paper are obtained with fresh samples to avoid dyes accumulation on the NWs.

It is worth noticing that both used dye concentrations belong to a concentration range which is usually used for cell staining [35

35. K. Morikawa and M. Yanagida, “Visualization of individual DNA molecules in solution by light microscopy: DAPI staining method,” J. Biochem. 89(2), 693–696 (1981). [PubMed]

,36

36. S. Hamada and S. Fujita, “DAPI staining improved for quantitative cytofluorometry,” Histochemistry 79(2), 219–226 (1983). [CrossRef] [PubMed]

]. Thus, the use of a NW for fluorescence excitation does not require higher dye concentration and can be applied for cell studies.

4.3. Contribution of the propagated FH and the SH signals to the dye excitation

As we have shown above, the NWs transport not only the SH but also the FH light. As a result, both propagated signals may contribute to the excitation of the fluorescence through the single-photon absorption (SPA) or the two-photon absorption (TPA) processes, respectively. In order to clear out, which process is dominant, we employ rate equations for the SPA and TPA processes [37

37. M. Bass, Handbook of Optics Volume I, 2nd ed. (McGraw-Hill, 1994).

] and estimate the contributions of the SH and FH signals to the fluorescence excitation in a 1 µg/ml DAPI dye solution following the absorption laws described in Table 1

Table 1. Rate Equations for the SPA and TPA Processes and Their Contribution to Fluorescence Excitationa

table-icon
View This Table
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.

For the calculation, we use quantum efficiency, SPA and two-photon emission (TPE) cross-sections of the DAPI dye molecules q = 1.7% [38

38. G. Cosa, K. S. Focsaneanu, J. R. McLean, J. P. McNamee, and J. C. Scaiano, “Photophysical properties of fluorescent DNA-dyes bound to single- and double-stranded DNA in aqueous buffered solution,” Photochem. Photobiol. 73(6), 585–599 (2001). [CrossRef] [PubMed]

], σA = 64.6·10−18 cm−2 [39

39. J. M. Dixon, M. Taniguchi, and J. S. Lindsey, “PhotochemCAD 2: a refined program with accompanying spectral databases for photochemical calculations,” Photochem. Photobiol. 81(1), 212–213 (2005). [CrossRef] [PubMed]

] and βE = 0.16·10−50 cm4·s/photon [40

40. C. Xu and W. W. Webb, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm,” J. Opt. Soc. Am. B 13(3), 481–491 (1996). [CrossRef]

], respectively. The constant c stands for the dye molecule concentration and βA denotes TPA cross-section. The initial intensity values I0 are calculated by assuming the NW cross-section to be 500x500 nm and the propagated FH signal to keep the pulse duration of the incident laser beam. The layer thickness of the DAPI dye solution x = 20 µm is estimated by dividing the used volume of the dye solution by the area of the cover slip.

The calculations show that though NWs deliver more FH signal than SH, the FH light has a negligible contribution to the fluorescence excitation in comparison with the SH signal. For the comparison, we take the values of the FH and SH signals which are detected at the output of one of the NWs we have discussed in Subsection 4.1. Thus, 441 ± 44 nW of the FH signal do not excite any fluorescence photons, whereas 2.57 ± 0.26 nW of the SH are expected to excite 1.028 ± 0.104 pW of the fluorescence signal. As a result, the SH signal has an overwhelming impact onto the fluorescence signal excitation.

4.4 Quantification of the SH power limits for the dye excitation

In order for a NW to excite detectable fluorescence signal, the propagated SH light has to surpass a certain threshold value. This threshold value depends on the dye concentration, the irradiation wavelength and the sensitivity of the camera.

As discussed above, NWs provide a variation of the propagated SH power depending on the SHG conversion efficiency. Thus, some NWs may require illumination of higher beam power in order to propagate enough SH signal and to excite detectable fluorescence signal. Nevertheless, the illuminated laser beam power itself should not exceed a certain power above which an irradiated cell may get damaged [41

41. K. König, P. T. So, W. W. Mantulin, and E. Gratton, “Cellular response to near-infrared femtosecond laser pulses in two-photon microscopes,” Opt. Lett. 22(2), 135–136 (1997). [CrossRef] [PubMed]

]. As a result, some NWs may possess too low efficiency for safe study of cells.

In order to sort low-efficient NWs and NWs which can be applied for the dye excitation experiments, one has to know the threshold value for the propagated SH power in a defined dye concentration. Here, we experimentally determine the minimal value of the SH power at which we achieve detectable fluorescence in 1 µg/ml DAPI dye concentration.

For this task, we perform two experiments. In the first one, we measure the detected power of the propagated SH signal in a NW sample. In the second one, we estimate the power of the fluorescence signal. As only 0.0004% (See Subsection 4.3) of the SH signal is expected to be absorbed in our dyes sample, we perform both the SH and fluorescence measurements in the sample with the DAPI dye solution. It enables us to keep the same coupling conditions, polarization and power of the incident laser beam while performing the SH and fluorescence measurements.

In Fig. 4(a)
Fig. 4 (a) SH and fluorescence signals versus FH laser beam power. The squares correspond to the propagated SH signal power and the circles correspond to the fluorescence signal power. The error bars show uncertainty of choosing the signal pixels for integration. (b) The SNR of the fluorescence signal versus the average power of the propagated SH signal. The width, the height and the length of the studied NW are 671.35 ± 53.48 nm, 503.9 ± 39.87 nm and 38.8 ± 0.3 µm, respectively. The red dashed line shows the limiting value of the SNR equal to 5 at which the features of the image can be unambiguously identified according to the Rose criterion. The error bars show uncertainty of choosing the signal pixels for integration.
, one can see the SH and fluorescence power values for one of the NWs at various values of the average power of the incident laser beam.

In order to find the limiting power of the propagated SH signal for the detectable dye excitation, we calculate the signal-to-noise ratio (SNR) for the excited fluorescence signal at various values of the propagated SH signal and show the SNR values in Fig. 4(b). The SNR is estimated by averaging the pixels with the fluorescence signal and dividing the achieved value by the standard deviation of the image noise. According to the Rose criterion, the image features can be unambiguously identified only for the images with the SNR above 5 [42

42. J. T. Bushberg, J. A. Seibert, E. M. Leidholdt, Jr., and J. M. Boone, The Essential Physics of Medical Imaging (Lippincott Williams & Wilkins, 2002).

]. As one can see in Fig. 4(b), the fluorescence signal shows SNR below 5 for the average power of the SH signal below 63 ± 6 pW. As a result, we conclude that the average power of the propagated SH power above 63 ± 6 pW allows performing of the fluorescence imaging with a 1 µg/ml DAPI concentration.

4.5 Modeling of the SH waveguiding

Though we propose to apply the LiNbO3 NWs for cell studies, their cross-sections are relatively large for safe cell penetration. As a consequence, NWs with decreased cross-sections have to be used. However, thinner NWs may lead to a weaker SHG effect due to its volume dependence. Furthermore, a smaller NW cross-section may result in lower SH power than it is required for detectable dye excitation. Here, we perform simulations to check whether the NWs with smaller cross-section are potentially able to provide enough SH power for dye excitation.

The simulations assume the waveguiding process and undepleted pump approximation [27

27. R. W. Boyd, Nonlinear Optics, 2nd ed. (Amsterdam: Academic Press, 2003).

] and use COMSOL RF module and a semianalytical model [34

34. A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, R. Iliew, R. Geiss, T. Pertsch, and Y. S. Kivshar, “Cascaded third harmonic generation in lithium niobate nanowaveguides,” Appl. Phys. Lett. 98(23), 231110 (2011). [CrossRef]

]. The RF module finds the FH and SH modes which are supported by a certain NW cross-section. The semianalytical model is employed to find the contribution dynamics of the FH modes to the SHG process. As a result, for each cross-section, we find the most efficient FH mode which gives the highest contribution to the SHG.

Finally, we estimate the amount of the SH signal to be delivered by a NW of a defined cross-section by assuming only the most efficient FH mode to propagate inside the NW and to carry the highest power which does not cause death of the cell. For the parameters of the used laser, the highest allowed average power is estimated to be 18.5 mW [41

41. K. König, P. T. So, W. W. Mantulin, and E. Gratton, “Cellular response to near-infrared femtosecond laser pulses in two-photon microscopes,” Opt. Lett. 22(2), 135–136 (1997). [CrossRef] [PubMed]

]. In the modeling, we also assume that the propagated FH signal keeps the pulse duration of the incident laser beam τ and the propagated SH signal has a pulse duration of τ/1.41 [43

43. G. Valiulis, V. Jukna, O. Jedrkiewicz, M. Clerici, E. Rubino, and P. DiTrapani, “Propagation dynamics and X-pulse formation in phase-mismatched second-harmonic generation,” Phys. Rev. A 83(4), 043834 (2011). [CrossRef]

].

In the model, we vary the NW width and height from 30 up to 100 nm with steps of 10 nm. The modeling is performed for six possible crystal structures varying the crystal axes parallel to the NW width, height and length. Having performed the simulations for each crystal structure, we find the smallest cross-section at which the NW provides enough SH signal for detectable dye excitation. For this goal, we compare the simulation results with the above-defined threshold of the SH average power for detectable dye excitation (63 ± 6 pW).

The simulations show that only NWs possessing three out of the six studied crystal structures are potentially able to provide an average power of the propagated SH signal above the set threshold value for the NW cross-section size below 100x100 nm2. For the NWs with these three crystal structures, we summarize the simulation results of the limiting cross-section size and the corresponding predicted average power of the propagated SH signal in Table 2

Table 2. Smallest NW Height and Width for Various NW Crystal Structures at which the NW Provides a Propagated SH Average Power above 63 ± 6 pW and the Predicted Average Power of the SH Signala

table-icon
View This Table
| View All Tables
.

As a result, the LiNbO3 NWs with certain crystal structure and with cross-sections below 100x100 nm2 provide enough SH signal for detectable dye excitation. In addition, the modeling results show that the NW with crystal axes X and Z parallel to the height and width, respectively, are expected to show the highest conversion efficiency.

Note that with cross-sections as small as mentioned in Table 2, a considerably bigger fraction of the guided modes propagates outside the NWs. However, this should not disturb the potential for dye excitation since all the SH power is delivered to the NW tip, where the dye is only expected to be.

We like to note that since minimization of the NW cross-sections leads to the increase of the mode fraction propagating outside the NW and to the decrease of the NW volume, the SH signal from the surface may start to play a role and to contribute to the total SH light [22

22. R. Sanatinia, M. Swillo, and S. Anand, “Surface second-harmonic generation from vertical GaP nanopillars,” Nano Lett. 12(2), 820–826 (2012). [CrossRef] [PubMed]

,44

44. J. I. Dadap, “Optical second-harmonic scattering from cyllindrical particles,” Phys. Rev. B 78(20), 121–1098 (2008). [CrossRef]

]. Nevertheless, we have not considered this effect in our model.

Consequently, the modeling proves that the LiNbO3 NWs can potentially be used for DAPI dye excitation. Thus, there are two main challenges arising. First, the limits of the fabrication method have to be studied and pushed to produce the NWs with the cross-sections below 100x100 nm2. Second, the coupling efficiency of the FH laser beam has to be increased in order to couple a larger part of the incident laser beam power into a NW and to achieve higher power of the FH signal in NWs. Possible ways to achieve this goal include modification of the input facet profile [45

45. H. Choo, M. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal-insulator-metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012). [CrossRef]

,46

46. C. J. Barrelet, H.-S. Ee, S.-H. Kwon, and H.-G. Park, “Nonlinear mixing in nanowire subwavelength waveguides,” Nano Lett. 11(7), 3022–3025 (2011). [CrossRef] [PubMed]

] and change of the coupling method [8

8. R. Yan, J.-H. Park, Y. Choi, C.-J. Heo, S.-M. Yang, L. P. Lee, and P. Yang, “Nanowire-based single-cell endoscopy,” Nat. Nanotechnol. 7(3), 191–196 (2011). [CrossRef] [PubMed]

].

5. Conclusion

We have demonstrated the generation and propagation of the SH signal in LiNbO3 NWs with the measurements of the detected average output power. We have also shown fluorescent dye excitation with the propagated signal. As the fluorescence is obtained in standard concentrations of the DAPI dye solution, the frequency conversion is efficient enough in such NWs.

Unlike other works dedicated to the SHG in NWs, we have quantified the detected power of the propagated FH and SH signals and, therefore, we have unambiguously proved that the fluorescence signal is mostly excited by the propagated SH signal and not by the two-photon absorption of the FH light.

We have also defined the range of the SH signal required for achieving detectable dye fluorescence signal. Knowing this range, we have modeled generation and waveguiding of the SH light in a NW and we have found the smallest NW cross-section, at which a NW is potentially able to provide enough SH light for detectable dye excitation. Such design below 100x100 nm2 in cross-section sizes will require demanding fabrication process that we are currently exploring.

The ways of increasing the amount of the propagated SH signal is also to be explored. For example, one can increase the amount of the propagated FH light by optimizing the coupling efficiency. In addition, one can synthesize a gold nanoshell around the NW surfaces to achieve enhancement of the SH signal by localized surface plasmon-polariton resonances in the near infrared spectral range [47

47. R. Grange, F. Dutto, and A. Radenovic, “Niobates nanowires: synthesis, characterization and applications,” in Nanowires - Implementations and Applications, D. A. Hashim, ed. (InTech, 2011).

,48

48. J. Richter, A. Steinbrück, T. Pertsch, A. Tünnermann, and R. Grange, “Plasmonic core–shell nanowires for enhanced second-harmonic generation,” Plasmonics 8(1), 115–120 (2013). [CrossRef] [PubMed]

].

As a result, we have shown that LiNbO3 NWs have great potential in localized delivery of light. In addition, the NWs can be applied not only for bringing light at a certain location but also for collecting it [8

8. R. Yan, J.-H. Park, Y. Choi, C.-J. Heo, S.-M. Yang, L. P. Lee, and P. Yang, “Nanowire-based single-cell endoscopy,” Nat. Nanotechnol. 7(3), 191–196 (2011). [CrossRef] [PubMed]

]. Thus, the LiNbO3 NWs are very promising types of nanomaterials in various future applications for both biological and non-biological purposes.

Acknowledgments

We thank Andrey Sukhorukov and Dragomir Neshev for useful discussions. This work was financially supported by the Carl Zeiss Foundation, by the German Research Foundation (Project numbers: KL 1199/2-2, PE1524/5-1) and by the Australian Research Council (Discovery project number: DP130100135).

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C. Xie, L. Hanson, Y. Cui, and B. Cui, “Vertical nanopillars for highly localized fluorescence imaging,” Proc. Natl. Acad. Sci. U.S.A. 108(10), 3894–3899 (2011). [CrossRef] [PubMed]

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R. Yan, J.-H. Park, Y. Choi, C.-J. Heo, S.-M. Yang, L. P. Lee, and P. Yang, “Nanowire-based single-cell endoscopy,” Nat. Nanotechnol. 7(3), 191–196 (2011). [CrossRef] [PubMed]

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W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990). [CrossRef] [PubMed]

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S. W. Chan, R. Barille, J. M. Nunzi, K. H. Tam, Y. H. Leung, W. K. Chan, and A. B. Djurisic, “Second harmonic generation in zinc oxide nanorods,” Appl. Phys. B 84(1-2), 351–355 (2006). [CrossRef]

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R. Chen, S. Crankshaw, T. Tran, L. C. Chuang, M. Moewe, and C. Chang-Hasnain, “Second-harmonic generation from a single wurtzite GaAs nanoneedle,” Appl. Phys. Lett. 96(5), 051110 (2010). [CrossRef]

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R. Grange, G. Brönstrup, M. Kiometzis, A. Sergeyev, J. Richter, C. Leiterer, W. Fritzsche, C. Gutsche, A. Lysov, W. Prost, F.-J. Tegude, T. Pertsch, A. Tünnermann, and S. Christiansen, “Far-field imaging for direct visualization of light interferences in GaAs nanowires,” Nano Lett. 12(10), 5412–5417 (2012). [CrossRef] [PubMed]

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W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012). [CrossRef]

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F. Wang, P. J. Reece, S. Paiman, Q. Gao, H. H. Tan, and C. Jagadish, “Nonlinear optical processes in optically trapped InP nanowires,” Nano Lett. 11(10), 4149–4153 (2011). [CrossRef] [PubMed]

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V. Barzda, R. Cisek, T. L. Spencer, and U. Philipose, “Giant anisotropy of second harmonic generation for a single ZnSe nanowire,” Appl. Phys. Lett. 92, 113111 – 113111–3 (2008). [CrossRef]

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R. Sanatinia, M. Swillo, and S. Anand, “Surface second-harmonic generation from vertical GaP nanopillars,” Nano Lett. 12(2), 820–826 (2012). [CrossRef] [PubMed]

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R. Grange, J.-W. Choi, C.-L. Hsieh, Y. Pu, A. Magrez, R. Smajda, L. Forró, and D. Psaltis, “Lithium niobate nanowires synthesis, optical properties, and manipulation,” Appl. Phys. Lett. 95(14), 143105 (2009). [CrossRef]

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B. Knabe, K. Buse, W. Assenmacher, and W. Mader, “Spontaneous polarization in ultrasmall lithium niobate nanocrystals revealed by second harmonic generation,” Phys. Rev. B 86(19), 195428 (2012). [CrossRef]

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42.

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43.

G. Valiulis, V. Jukna, O. Jedrkiewicz, M. Clerici, E. Rubino, and P. DiTrapani, “Propagation dynamics and X-pulse formation in phase-mismatched second-harmonic generation,” Phys. Rev. A 83(4), 043834 (2011). [CrossRef]

44.

J. I. Dadap, “Optical second-harmonic scattering from cyllindrical particles,” Phys. Rev. B 78(20), 121–1098 (2008). [CrossRef]

45.

H. Choo, M. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal-insulator-metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012). [CrossRef]

46.

C. J. Barrelet, H.-S. Ee, S.-H. Kwon, and H.-G. Park, “Nonlinear mixing in nanowire subwavelength waveguides,” Nano Lett. 11(7), 3022–3025 (2011). [CrossRef] [PubMed]

47.

R. Grange, F. Dutto, and A. Radenovic, “Niobates nanowires: synthesis, characterization and applications,” in Nanowires - Implementations and Applications, D. A. Hashim, ed. (InTech, 2011).

48.

J. Richter, A. Steinbrück, T. Pertsch, A. Tünnermann, and R. Grange, “Plasmonic core–shell nanowires for enhanced second-harmonic generation,” Plasmonics 8(1), 115–120 (2013). [CrossRef] [PubMed]

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4180) Nonlinear optics : Multiphoton processes
(230.7370) Optical devices : Waveguides
(260.2510) Physical optics : Fluorescence

ToC Category:
Nonlinear Optics

History
Original Manuscript: May 21, 2013
Revised Manuscript: July 11, 2013
Manuscript Accepted: July 11, 2013
Published: August 2, 2013

Virtual Issues
Vol. 8, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Anton Sergeyev, Reinhard Geiss, Alexander S. Solntsev, Andrea Steinbrück, Frank Schrempel, Ernst-Bernhard Kley, Thomas Pertsch, and Rachel Grange, "Second-harmonic generation in lithium niobate nanowires for local fluorescence excitation," Opt. Express 21, 19012-19021 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-16-19012


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References

  1. R. Yan, D. Gargas, and P. Yang, “Nanowire photonics,” Nat. Photonics3(10), 569–576 (2009). [CrossRef]
  2. P. Yang, “Semiconductor nanowire building blocks: From flux line pinning to artificial photosynthesis,” MRS Bull.37(09), 806–813 (2012). [CrossRef]
  3. C. J. Barrelet, A. B. Greytak, and C. M. Lieber, “Nanowire photonic circuit elements,” Nano Lett.4(10), 1981–1985 (2004). [CrossRef]
  4. X. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature421(6920), 241–245 (2003). [CrossRef] [PubMed]
  5. T. Voss, G. T. Svacha, E. Mazur, S. Müller, C. Ronning, D. Konjhodzic, and F. Marlow, “High-order waveguide modes in ZnO nanowires,” Nano Lett.7(12), 3675–3680 (2007). [CrossRef] [PubMed]
  6. P. Yang, R. Yan, and M. Fardy, “Semiconductor nanowire: what’s next?” Nano Lett.10(5), 1529–1536 (2010). [CrossRef] [PubMed]
  7. C. Xie, L. Hanson, Y. Cui, and B. Cui, “Vertical nanopillars for highly localized fluorescence imaging,” Proc. Natl. Acad. Sci. U.S.A.108(10), 3894–3899 (2011). [CrossRef] [PubMed]
  8. R. Yan, J.-H. Park, Y. Choi, C.-J. Heo, S.-M. Yang, L. P. Lee, and P. Yang, “Nanowire-based single-cell endoscopy,” Nat. Nanotechnol.7(3), 191–196 (2011). [CrossRef] [PubMed]
  9. W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science248(4951), 73–76 (1990). [CrossRef] [PubMed]
  10. P. J. Campagnola and L. M. Loew, “Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms,” Nat. Biotechnol.21(11), 1356–1360 (2003). [CrossRef] [PubMed]
  11. C. L. Evans and X. S. Xie, “Coherent anti-stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Ann. Rev Anal Chem (Palo Alto Calif)1(1), 883–909 (2008). [CrossRef] [PubMed]
  12. F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science198(4323), 1264–1267 (1977). [CrossRef] [PubMed]
  13. J. P. Long, B. S. Simpkins, D. J. Rowenhorst, and P. E. Pehrsson, “Far-field imaging of optical second-harmonic generation in single GaN nanowires,” Nano Lett.7(3), 831–836 (2007). [CrossRef] [PubMed]
  14. J. C. Johnson, H. Q. Yan, R. D. Schaller, P. B. Petersen, P. D. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett.2(4), 279–283 (2002). [CrossRef]
  15. S. W. Chan, R. Barille, J. M. Nunzi, K. H. Tam, Y. H. Leung, W. K. Chan, and A. B. Djurisic, “Second harmonic generation in zinc oxide nanorods,” Appl. Phys. B84(1-2), 351–355 (2006). [CrossRef]
  16. A. Kachynski, A. N. Kuzmin, M. Nyk, I. Roy, and P. N. Prasad, “Zinc oxide nanocrystals for nonresonant nonlinear optical microscopy in biology and medicine,” J. Phys. Chem. C112(29), 10721–10724 (2008). [CrossRef]
  17. R. Chen, S. Crankshaw, T. Tran, L. C. Chuang, M. Moewe, and C. Chang-Hasnain, “Second-harmonic generation from a single wurtzite GaAs nanoneedle,” Appl. Phys. Lett.96(5), 051110 (2010). [CrossRef]
  18. R. Grange, G. Brönstrup, M. Kiometzis, A. Sergeyev, J. Richter, C. Leiterer, W. Fritzsche, C. Gutsche, A. Lysov, W. Prost, F.-J. Tegude, T. Pertsch, A. Tünnermann, and S. Christiansen, “Far-field imaging for direct visualization of light interferences in GaAs nanowires,” Nano Lett.12(10), 5412–5417 (2012). [CrossRef] [PubMed]
  19. W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett.100(22), 223501 (2012). [CrossRef]
  20. F. Wang, P. J. Reece, S. Paiman, Q. Gao, H. H. Tan, and C. Jagadish, “Nonlinear optical processes in optically trapped InP nanowires,” Nano Lett.11(10), 4149–4153 (2011). [CrossRef] [PubMed]
  21. V. Barzda, R. Cisek, T. L. Spencer, and U. Philipose, “Giant anisotropy of second harmonic generation for a single ZnSe nanowire,” Appl. Phys. Lett. 92, 113111 – 113111–3 (2008). [CrossRef]
  22. R. Sanatinia, M. Swillo, and S. Anand, “Surface second-harmonic generation from vertical GaP nanopillars,” Nano Lett.12(2), 820–826 (2012). [CrossRef] [PubMed]
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