Semiconductor nanowires (NWs) have been considered as basic components in optoelectronic nanodevices for tens of years. But only in the last decade, significant progresses were made by fast developments in NW fabrication and laser technologies. Nanolasers [1–3], frequency converters [4, 5] and logic elements in nanoscale optoelectronic circuitry [6–8] have been attracting worldwide attentions, in which the unique optical property of NWs plays a key role. As a result, great interests are focused on optical nonlinearity in semiconductor NWs including ZnO (II-VI), InP and GaAs (III-V) [9, 10]. Recently, results on two-photon excited fluorescence and second-harmonic generation (SHG) from ZnO/InP/GaAs NWs pumped by femtosecond (fs) laser were reported [11–14]. SHG signals were also generated in GaAs /GaP nanoneedles and nanopillars when excited by an 800-nm fs laser [15, 16]. However, sum frequency generation (SFG) in NWs is rarely investigated [17–19]. In this study, we demonstrate that pure zinc-blende GaAs NWs can remarkably generate SFG signals when excited by a tunable optical parametric oscillator (OPO) in the range from 1400 nm to 1800 nm and a femtosecond laser at 1048 nm. The SFG intensity does not change as greatly as GaAs bulk along with the angle between polarizations of two incident lasers. This is because although a large part of the SFG signal originates from the bulk structure of GaAs NWs, the large surface-to-volume ratio resulted from the nano-scale diameter of NWs induces weakly constrained dipoles in the NW surface that contribute to the SFG signal independence of that angle. Particularly, the SFG signal is quite sensitive to the temporal overlap of the two incident femtosecond laser pulses, which can work for measurement of laser pulse-width in near infrared region. These results strongly suggest that GaAs NWs are potentially excellent frequency mixers in optical nano-system.

Free-standing GaAs NW array in this study was grown by metal organic chemical vapor deposition on GaAs (111) B substrate [20]. The growth direction of NW was <111> and the zone axis was <110>. The length of NWs was around 5 μm and the average diameter was 160 nm. In experiments, those vertical NWs were put on a glass slide and the incident lasers were focused by an objective to illuminate the NWs facing lasers. The output of a homemade femtosecond laser at 1048 nm (pulse-width: 80 fs; repetition rate: 50 MHz) was split into two beams, one of which was used for pumping an OPO and then spatially combined with the other beam by a dichroic mirror (DM1). The OPO had an output range from 1400 nm to 4000 nm based on one MgO-doped periodically poled LiNbO₃ (PPLN) crystal [21]. These two beams were then reflected by another dichroic mirror (DM2) and focused onto the NWs by an objective (20X, NA = 0.40, Olympus). The setup is shown in Fig. 1. The total transmission efficiency of lasers propagating from DM1 to the sample was 35.9% at 1048 nm and 25.4% at 1508 nm. The diameter of the laser focus was around 3 μm, inside which there were around 10 ~15 NWs. The laser power density was at the level of 10⁵ W/cm² during experiments (the threshold for significant damage to the sample by the laser was around 10⁷ W/cm²), and the peak power density was at the level of 10¹⁰ W/cm². The SFG signal was collected by the same objective and analyzed by a spectrometer (Ocean Optics, SD2000).

 

Fig. 1 Setup diagram. The filter was used to remove all photons with wavelength below 1100 nm including SHG and SFG in the PPLN crystal by the pump laser and OPO output. Dichroic mirrors DM1 and DM2 reflect the wavelength above 1400 nm and 800 nm respectively. Two mirrors (box of dashed line) were used to tune the delay of the femtosecond laser at 1048 nm. Insert: side imaging of NWs by SEM.

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The OPO at first worked at 1508 nm which is in the typical wavelength band in present optical communication systems. The corresponding SHG signals of the two incident beams were easily detected at 524 nm and 755 nm respectively as shown in Fig. 2(a). The SFG signal was then expected at 618 nm as the sum of frequencies of incident beams as

 

Fig. 2 SFG signals. (a) The SHG and SFG signals from femtosecond lasers at 1048 nm and 1508 nm. (b) The power dependence of SFG signals to one beam is linear. The laser powers were measured after DM1.

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In experiment the SFG signal at 618 nm did appear when the pulses overlapped temporally by tuning the delay of 1048-nm femtosecond laser. The SFG efficiency should be enhanced in NW structure. First, the large surface-to-volume ratio of NWs breaks the crystal lattice to induce more dipoles (weaker constraint and higher surface activity) to oscillate with the incident electrical fields (E-field) more easily [19, 22]. In our previous experiment, it was also found that SHG in such GaAs NWs was greatly enhanced [14]. In this study, no SFG signal can be detected in GaAs bulk even at the power level of breaking samples (around 100 times of laser power for exciting SFG signals in NWs), which also indicates an enhancement effect in NWs. In addition, the NW spatial structure has confinement and surface-enhancement effects to the E-fields of incident lasers [23, 24], which is consistent with previous results [25, 26]. To be simple, the SFG intensity in NWs is still described by the following equation.

In our experiment, the intensity of SFG signals excited by two lasers at 1048 nm and 1508 nm was found linearly dependent on the incident power of one beam if keeping the other constant as shown in Fig. 2(b). The slopes of two according lines are different (1.52 and 0.31). This is because the 1048-nm laser and OPO were kept at 192 mW and 39 mW respectively when the power of the other was changed. Those results consist with Eq. (2) very well and further confirm that the process is SFG.

When considering the SFG to be a coherent process, the intensity should be dependent on the polarization of incident lasers. In our experiment, the polarization of the 1048-nm laser was tuned by a half-wave plate while the OPO beam at 1440 nm did not change. The SFG from the NW should follow the selection rules dictated by the $\overline{4}3m$ point group second-order susceptibility tensor. Therefore, considering the <111> direction of NWs, symmetry of GaAs lattice, and the E-field of incident lasers in the coordinate system, the SFG signal could be then expected by

 

Fig. 3 The SFG signal is dependent on the polarization direction of incident lasers. The polarizations of the lasers were at first both horizontal. Then the polarization of 1048-nm laser was tuned by a half-wave plate while keeping polarization of OPO as constant. Dashed line: fitted curve of ${\cos }^2\theta$.

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This theoretical result indicates that the minimum SFG intensity is only 2/3 of the maximum. The higher ratio acquired experimentally is probably related to the nano-scale structure of NWs. The SFG from GaAs NWs largely originates from the bulk while weaker constraint dipoles in the surface also have some contribution. Those dipoles can respond to the E-fields of incident lasers even though the polarizations of incident lasers are orthogonal to each other to contribute to the SFG signal. Therefore, the SFG in zinc-blende <111> GaAs NWs is more weakly dependent on the polarization directions of incident lasers. There might be some phase difference brought by the transverse propagation of SFG signal along the short axis of the NW to induce a little destructive interference. However, for the scales comparable with the wavelength, the contribution from particular microscopic structure would not be so significant.

We then furthered the investigation to test if the GaAs NWs could response to a broad spectral range to work for more potential applications in nano-scale optoelectronics. To this end, the OPO output was then tuned from 1416 nm to 1770 nm and again combined with the 1048-nm laser for SFG. It can be found in Fig. 4 that the NWs could respond well to lasers in this range to generate tunable SFG.

 

Fig. 4 The SFG signals generated by the 1048-nm femtosecond laser and tunable OPO from 1416 nm to 1770 nm.

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The intensity of SFG was very sensitive to the temporal overlap of pulses from the two lasers. In this regard, it could be used to measure pulse-width of femtosecond lasers by the cross correlation of them. To show this point, the OPO was at first tuned to work at 1440 nm with unknown pulse-width to be measured by the femtosecond laser at 1048 nm as reference with pulse-width of 152 fs (full width at half maximum (FWHM) measured after DM1). By tuning the delay of 1048-nm laser, the temporal overlap of pulses of the two lasers was changed and the cross correlation of them could be obtained as the SFG signal. As shown in Fig. 5(a), the SFG centered at 606 nm at different delays was detected. The corresponding FWHM duration of the SFG intensity versus delay was 240 fs as shown in Fig. 5(b). Assuming the pulses were in hyperbolic secant form, the pulse-width of the OPO beam could be then calculated as 160 fs according to [27]. We verified this result by using an autocorrelator to directly measure the pulse-width of it (after DM1) and found it to be 164 fs as shown in Fig. 5(c). The error was only 2.4% suggesting GaAs NWs to be good candidate for measurement of pulse-width of femtosecond lasers in the near infrared band. This method is especially applicable when it is used to measure weak signals that are quite difficult to generate enough SHG, since the weak signal can be amplified by using a large-power reference beam in SFG. It appears to be more attractive considering the limited wavelength measurement range offered by most commercial autocorrelators.

 

Fig. 5 Cross correlation of the 1048-nm femtosecond laser with the OPO beam at 1440 nm. (a) SFG signals at different delays. (b) The intensity of the SFG versus the temporal overlap of the laser and OPO pulses. The FWHM of this overlap is 240 fs. (c) Pulse-width of the 1048-nm laser and OPO measured by autocorrelator directly.

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In conclusion, we demonstrate that GaAs NWs can generate SFG signals across a broad spectral range by using a femtosecond laser at 1048 nm and a tunable OPO from 1416 nm to 1770 nm. The large surface-to-volume ratio resulted from nanoscale diameter of NWs breaks the crystal lattice in the surface and thus induces dipoles and enhances the responses to incident E-fields. As a result, the SFG shows weak polarization dependence with respect to the incident laser. In addition, GaAs NWs were found to be capable of measuring pulse-width by making the SFG as cross-correlation of incident lasers. Therefore, our results suggest GaAs NWs to be excellent frequency mixers in nano-optical systems.