Summary of SHG results of ZnO NWs.
Second harmonic generation (SHG) is one of the most researched nonlinear material properties and finds applications in many fields ranging from laser projection to cancer detection to future optical switches for molecular devices. Studying SHG in ZnO nanostructures started few years ago and there is a long way to go to compete with the existing nonlinear crystals. Information gathered over the past few years in research on SHG of ZnO nanowires (NWs) is summarized in this chapter. Recent advancement in the growth techniques for various types of ZnO NWs used for SHG studies is also discussed. We present an extensive analysis and discussion on some key parameters that directly modify the efficiency of SHG in ZnO NWs. The key parameters considered for discussion are aspect ratio of NWs, doping, and external strain. At the end, current standing on the reported values of nonlinear coefficients and future outlook are presented.
- second harmonic generation
- sum frequency generation
- symmetry deviation
ZnO is a unique material with application prospects in areas ranging from medical to optoelectronic industry to astronomical radiation detection [1–5]. ZnO is a II–VI group wide-band gap semiconductor and is highly transparent in the visible region. In the hexagonal wurtzite phase of ZnO, each Zn ion is surrounded by a tetrahedron of four O ions and vice versa. This tetrahedral coordination results in a noncentrosymmetric crystal structure, which makes it a promising candidate to observe second harmonic generation (SHG) in ambient conditions. SHG is a second-order nonlinear coherent process in which two lower energy photons are up-converted to a single photon with frequency exactly twice the incident frequency. This interesting property of nonlinear materials has several important applications in various fields, e.g., probing the electronic and magnetic structure of crystals, cancer cell diagnostics, switches in molecular-scale memory devices, and many more [6–10]. It is a very sensitive all-optical and noninvasive technique that is compatible with bulk or surface detection under various circumstances.
Among the huge variety of ZnO nanostructures, nanorods and nanowires (NWs) have undoubtedly been the focus of most studies since their geometries allow the preparation of arrays of well-controlled uniformity and use as building blocks of many nanoscale devices. As well as for ZnO thinfilms, SHG from ZnO NWs grown by different methods has been widely investigated. Studying SHG in ZnO NWs started few years ago and lot of information/knowledge has been gathered over the years by the nanoscale research community. Previous studies reported efficient generation of SHG signal from various types of ZnO nanostructures, including NWs [11–20]. Therefore, with improvement in the fabrication technique for large area ZnO NWs, it can be widely used as one of the best SHG materials. It has been discovered that the magnitude of SHG is strongly influenced by crystal orientation, aspect ratio, crystal symmetry modification, and so on. Therefore, by controlling such parameters one can tune the SHG of ZnO NWs. However, effective implementation of the knowledge gathered over the past years to ZnO to get the best SHG performance is yet to be achieved. Strategies for raising the optical nonlinearities of materials are an active research theme with rich and broad implications/applications. Keeping this in mind, some previous studies attempted to improve the second-order nonlinearity of ZnO and developed some efficient methodologies. Very high values of susceptibility tensorial component of 22–30 pm/V were achieved by changing the crystallographic orientation or decorating the surface with metal nanoparticles followed by bicolor coherent treatment or doping-induced crystal symmetry deviation [20–23]. Recently, development of ZnO-based SHG microscopy has been successfully demonstrated [24, 25].
Presently there is no review article dedicated to SHG of ZnO NWs with extensive analysis of SHG parameters and up-to-date advancement in this field. In this chapter, we present an extensive review of recent advances in SHG from ZnO NWs including our own results. Following this brief introduction, crystal structure of ZnO and theoretical background of SHG from ZnO and nonvanishing second-order nonlinear tensorial components are presented in Section 2. Section 3 describes the methodology adopted to measure SHG and an extensive analysis of the associated susceptibility tensor components. Recent advancement in the growth techniques for various types of ZnO NWs used for SHG studies and their SHG characteristics is discussed in the next section. The effects of aspect ratio of NWs, doping, and external strain on SHG magnitude are extensively addressed in subsections. At the end, a summary of the current standing on the reported values of nonlinear coefficients and future outlook are presented.
2. Second harmonic generation
SHG is one of the most studied material properties since its discovery in the 1960s by Franken et al. . It is also known as the sum frequency generation because of the frequency doubling effect. When a strong primary radiation beam (frequency ω) is fed into the NLO crystal, along with the transmitted primary beam an additional light beam (frequency 2ω) appears from the crystal with frequency twice that of the primary beam. In other words, wavelength of the SHG signal is exactly half of the wavelength of the incident primary beam. Figure 1 depicts the schematic illustration of nonlinear optical process SHG. Most often, the polarization field is considered to be linearly related to the incident electric field
where the electrical susceptibility, χ is a second-rank tensor. While this consideration tends to be sufficient when relating incident fields at low field strengths, it is a simplified approximation. In reality, the polarization field is more complicated than the linear relation given above. If the variation is small under strong electric field, comparable to interatomic electric fields, the polarization can be exactly expressed with the help of Taylor series
where terms are summed over repeated indices. The first coefficient is the linear electric susceptibility component. The and are second-order and third-order nonlinear susceptibilities responsible for SHG and third harmonic generation phenomenon. The second-order susceptibility tensor is also expressed in terms of nonlinear optical coefficients, SHG arises only when the particular material has nonzero second-order susceptibility tensor, . The nonzero components exist only in the noncentrosymmetric crystal structure of the particular material. Furthermore, nanometer-sized centrosymmetric materials (nanostructures) also show weak SHG due to the breaking of space inversion symmetry at the boundary [27, 28].
The crystal structures shared by ZnO are wurtzite, zinc blende, and rocksalt; however, in ambient condition, only the wurtzite phase is thermodynamically stable. The wurtzite structure has a hexagonal unit cell with two lattice parameters,
As a consequence of noncentrosymmetric crystal structure, ZnO possess nonvanishing second-order susceptibility tensor. The
3. Measurement technique and methodology
Since its introduction, several experimental techniques have been developed to calculate the magnitude of nonvanishing macroscopic nonlinear coefficients. Out of several techniques, the Maker fringes technique  is widely used to determine the magnitude of second-order susceptibility tensor elements. In brief, an SHG signal transmitted through the nonlinear crystal was measured as a function of angle of incidence of the fundamental beam with respect to the sample plane. This method is based on analysis of variation of SHG magnitude by incidence angle of the fundamental beam and crystal thickness. A schematic block diagram of the standard Maker fringes-based SHG measurement setup is shown in Figure 3. To generate SHG signal, we used an 800 nm, mode-locked femtosecond pulse light source from Ti:sapphire laser as a primary radiation. The polarization state of the fundamental beam and SHG signal are selected by using a polarizer (λ/2 plate) before the sample and an analyzer after the sample. The laser beam is tightly focused on the sample using suitable mirrors and lens assembly. The variation of angle of incidence (θ) is achieved by placing the sample on a rotating stage. The generated SHG signal is analyzed using a monochromator and a highly sensitive detector. The angular dependence of SHG signal is measured either in P-in/P-out (
The original Maker fringes methodology was based on the assumption of 100% transparency of the material in the SHG wavelength region. It is perfectly applicable only to a 100% transparent crystal. However, none of the real crystals are perfectly transparent up to that level. The original Maker fringes methodology failed to correctly estimate magnitude of the second-order
are the Fresnel transmission coefficients of fundamental (
Therefore, at a monochromated fundamental beam of fixed wavelength (λ), the intensity of the SHG in Eq. (3) can be simplified as a function of θ only. After fitting Eq. (3) into the measured SHG profile as a function of angle of incidence, one can estimate the associated
where is the relative power of the primary beam at a particular wavelength, λ.
Alternative to Maker fringes experimental configuration, the reflective second harmonic generation (RSHG) scheme involves the measurement of the SHG signal in reflection mode, at a fixed incidence angle and as a function of the azimuthal angle, which is the angle between the incidence plane and the x-axis on the sample surface. In brief, the sample is rotated along its surface normal,
The RSHG is independent of azimuthal angle, if the direction of ZnO (0002) is along the z-axis. However, a tilt of the ZnO (0002) direction may cause a variation of the resulting SHG on the azimuthal polar plot.
4. Second harmonic generation in ZnO nanowires
As a consequence of noncentrosymmetric structure, ZnO is expected to possess nonzero second-order optical nonlinearity parameters and hence room temperature SHG is expected. SHG from ZnO nanostructures including NWs has been experimentally demonstrated by several groups. Many efforts have been made to quantitatively estimate the second-order nonlinear coefficients of single ZnO NWs or ZnO NW arrays. A theoretical study on the estimation of SHG intensity from ZnO nanostructures was done by Attaccalite et al. . The modified Maker fringes equation was employed by considering the dense NW arrays as a NW film. All the important experimental results on SHG of ZnO NWs are summarized in Table 1.
|Growth technique||Substrate||Laser source||Aspect ratio||Reference|
|Sonication and dispersion||Sapphire||fs Laser @800 nm||–||Wang et al. |
|Chemical vapor deposition||Sapphire||fs Laser @800 nm||–||= 5.5||Johnson et al. |
|Aqueous solution method||Glass||ns Laser @1064 nm||5.7
|Chan et al. |
|Low temperature chemical bath method||Glass||fs Laser @806 nm||23.2
|Das et al. |
|Aqueous solution method||–||fs Laser @810 nm||–||Green et al. |
|Chemical bath deposition||Glass||fs Laser @800 nm||8||Das et al. |
|Hydrothermal method||ITO coated glass||fs Laser @1034 nm||6.0
|Zhou et al. |
|Chemical vapor deposition||Si||fs Laser @800 nm||–||Liu et al. |
|Modified aqueous chemical method, Europium doping||Quartz||fs Laser @800 nm||–||Dhara et al. |
|Aqueous solution method||Glass||fs Laser @1044 nm||10.0||Liu et al. |
|Hydrothermal synthesis, Co doping||Glass||fs Laser @1044 nm||15.5||Liu et al. |
Chan et al.  show room temperature SHG from ZnO NWs with angular dependence exactly similar to thinfilms. Vertically aligned ZnO NWs were grown on the ZnO-seeded glass substrate by low temperature aqueous chemical solution method, which is shown in Figure 4(a). Following the reaction at 90°C, glass substrates were rinsed with de-ionized water to remove the residual salt on the surface, and then dried at 100°C. The average length of the ZnO NWs ranged from 50 to 700 nm. A Q-switched Nd:YAG laser was used as fundamental incident beam (λ = 1064 nm, 8 ns) at 10 Hz frequency. SHG signal from samples was detected by a photo-multiplier tube and then further processed with a signal-integrating oscilloscope. The variation of SHG intensity with the angle of incidence depicts periodic profile and obeys the Maker fringes methodology (Figure 4(b)). The second-order coefficients
The nonlinear second-order coefficients,
Our group used similar theoretical fitting method to retrieve the
The microscopic SHG mapping of a single ZnO NW was measured for the first time by near-field scanning optical microscopy (NSOM) . For NSOM studies, ZnO NWs were removed from the substrate by sonication and dispersed onto a flat sapphire substrate for NSOM studies. Near-field SHG wave was collected using a scanning fiber probe at an oblique angle (θ, angle between the surface normal and the fundamental beam k-vector) of 55°. A large nonlinear SHG response with asymmetric variation across the diameter of the NW was presented (Figure 6). Furthermore, a strong polarization dependence was evidenced by the SHG images, which is ascribed to the asymmetry of the nonlinear susceptibility. The NW shows relatively efficient SHG with a larger = 5.5 pm/V than a BBO crystal, ≈ 2.0 pm/V, a commonly used frequency doubling crystal. However, the estimated highest coefficient ( ) is considerably lower than the reported bulk value (14.3 pm/V) . One of the possible reasons for lower value is that the number of ZnO molecules probed for a single NW is less than those probed on a solid disk.
Studying SHG sometimes allows us to use a contactless surface as investigation tool to identify structural defects. Similar to thinfilms, if twin defects are present in the NWs, it can be experimentally investigated using SHG mapping to the individual rods . The ZnO rods were grown on fused quartz by the aqueous solution method. The rods (length of several microns and diameter of 100–250 nm) were grown horizontally to the substrate where the polar axes of rods are parallel to the surface of fused quartz, as shown in Figure 7(a) and (b). The SHG signal was generated using a mode-locked femtosecond pulse Ti:sapphire laser at approximately 810 nm. The transmitted SHG signals were measured under normal incidence with the polarization direction along the rod’s axis. The far-field scattering patterns of the transmitted SHG waves from single twinned rod were compared to the pattern arising from a twin-free ZnO rod to see if it is possible to differentiate between twinned and twin-free ZnO rods. Figure 7(c) and (d) shows typical SHG image for a single rod with twinned and twin-free structure, respectively. The images exhibit strong far-field scattering fringes resulting from the interferences of the SHG waves originating from different locations along the axis of the rod. Interestingly, a clear striking difference in the SHG fringes pattern was observed between SHG mapping images of twinned and twin-free rods. In particular, the zero-angle fringes highlight the different features of the two kinds of rods; a bright spot of SHG with a small dark gap for the twinned rod and very wide bright spot with no dark gap for the twin-free rods. A dark (bright) fringe at the 0° scattering angle was ascribed to destructive (constructive) interference of the SHG waves originating from each halve of the twinned (twin-free) rods. A small dark gap with low SHG efficiency (dark fringe) was observed only in the twinned rod, which indicates the existence of twin defects. Furthermore, use of polarization-dependent SHG microscopy to efficiently detect the lattice distortion in single-bent ZnO NWs has been demonstrated .
From SHG studies, it is found that SHG signal from bulk ZnO or even ZnO nanostructures is not so strong for application purpose. The reported value of an effective second-order tensorial component varies from 2 to 15 pm/V. However, it could be improved further by proper control of its crystal structure and disturbing crystal symmetry. Many studies have shown dependence of nonlinear parameters on various factors (internal or external to ZnO NWs) and also demonstrated several methods to improve the SHG further. Effects of some of the important parameters on the SHG are discussed in the following subsections. Recent advancement suggests that it is possible, in principle, for the researchers to identify the crystalline orientation, symmetry deviation, and polarities in more complicated ZnO nanostructures by the SHG patterns.
4.1. Wavelength dependence
When SHG was measured near the resonance region of ZnO, in most of the studies SHG signal was detected along with two-photon photoluminescence (2PL). Considering the different nonlinear mechanisms of both the process, final output intensities strongly depend on both pumping wavelength and light intensity. Competition between SHG and 2PL was observed and explained in several works [45–48]. Measuring emitted light as a function of fundamental beam wavelength is a useful way to distinguish the different contributions of SHG and 2PL to the emission spectrum. SHG wavelength changes according to the change in fundamental beam wavelength, while the wavelength of 2PL is fixed by the ZnO band gap energy. The competition between SHG and 2PL as a function of pump wavelength was described by Pedersen et al.  in randomly oriented ZnO NWs (Figure 8(a)). The monochromator was scanned over a broad region around SHG wavelength for a wide spectral range from 710 to 1000 nm. The contour plot that depicts the structure with highest intensity is the SHG signal at half the pump wavelength, while the weaker horizontal structure is multi-photon excited luminescence from the ZnO band gap. When the 2PL appears at shorter wavelengths than SHG (below the SHG line), it is presumably multiple-photon luminescence while the much stronger two-photon process is seen above the SHG line. The normalized
4.2. Dependence on aspect ratio
It is observed that the second-order nonlinear optical coefficients are strongly modified by dimensions of the NWs and aspect ratio. Chan et al.  and later Das et al.  demonstrated that changing of the aspect ratio of the ZnO nanorods could lead to a stronger SHG signal. ZnO NWs with different dimensions were grown by chemical method for different growth times, having diameter 10 to 62 nm and length 57 to 667 nm, respectively. Influence of aspect ratio on
4.3. The effect of doping
In order to improve the magnitude of the SHG in ZnO NWs, our group developed a technique to modify the crystal site symmetry of the ZnO crystal through rare earth element (Eu) doping . We were able to improve the SHG about four times higher than the undoped ZnO NWs. That was the first ever report that used crystal symmetry modification technique to improve SHG. In the first step, Eu-doped ZnO (Eu:ZnO) NWs were grown vertically on the ZnO-seeded quartz substrate by a modified low temperature aqueous chemical method, using europium nitrate doping precursor. To facilitate the incorporation of larger Eu ions than the Zn ions into the ZnO lattice, a modification was done in the standard aqueous chemical method [49–52]. Eu doping was performed in a controlled way and a set of samples were prepared for different concentrations of Eu ranging from 0.5 to 5.0 at.%. Incorporation of Eu inside the ZnO lattice causes modification in the crystal site symmetry by disturbing the internal lattice arrangement. Extensive structural analysis using XRD data and high-resolution lattice images reveals expansion of lattice spacing and existence of several lattice distortions, as shown in the inset in Figure 10. Due to the larger ionic radius of Eu ions and the charge imbalance, incorporation of Eu completely disturbed the inside lattice arrangement. It is expected that the existence of a “self-purification process”  may further disturb the lattice arrangement. As a result, the formation of several lattice distortions in the Eu:ZnO NWs and hence degradation of structural quality and modification of site symmetry around the doped ions are expected.
The SHG intensity is found to increase after Eu doping. A nonmonotonic enhancement in the SHG is observed with increase in europium concentration. Maximum SHG was obtained from the 1 at.% Eu:ZnO NWs with an enhancement factor of 4.5. The effective second-order nonlinear coefficient (
The effect of cobalt or thulium doping in ZnO NWs on the SHG characteristic was studied by other research group [40, 55]. Liu et al.  performed an SHG study after doping ZnO nanorods with cobalt. SHG was used to investigate bulk and surface structure quality of ZnO nanorods by measuring net dipole contribution for a different level of Co doping. Co-doped ZnO nanorods, Zn1-xCoxO [0 ≤ x ≤ 0.40, x is the weight (wt.) % of Co in the growth solution], were fabricated by hydrothermal synthesis on seeded glass substrate. The SHG experiment was performed by varying incident angles in transmission mode (P-in/P-out configuration) with a femtosecond laser (1044 nm) light source. Ratios of
4.4. External strain dependence
As we know, second harmonic generation depends on the nonzero second-order susceptibility tensor, which indeed depends on the crystal symmetry of that material. Now the question arises, can we modify the SHG in ZnO by applying external strain? To verify this, our group investigated external strain (tensile and compressive) dependent SHG in ZnO NWs after bending the NWs by applying external force . In the first step, ZnO NWs were transferred from substrate and dispersed into a PMMA solution. The solution mixture was spin coated on a thin steel substrate (thickness 0.5 mm) to prepare a thin layer (~200 nm) of PMMA with horizontally aligned ZnO NWs within it. The PMMA thinfilm was heated at ~60°C to remove residuals and get a continuous film. External force was applied at the center of the substrate (opposite side of the film) to bend it along the radius of curvature of the substrate. The bending of substrate led to bending of the attached ZnO NWs and it experienced a strain on the surface, as shown in the inset of Figure 11. The PMMA matrix was used to hold the ZnO NWs during bending of the substrate. Applied strain at the center of the substrate along the direction of the applied force was estimated according to the strain equation developed earlier [57, 58].
We measured RSHG at an angle of incidence of 45° using a
5. Conclusion and future outlook
In this chapter, an up-to-date summary of important studies and results by several research groups worldwide on the SHG of ZnO NWs/nanorods is demonstrated. We present an extensive analysis and discussion on some key parameters that directly modify the efficiency of SHG in ZnO NWs. The key parameters considered for discussion are aspect ratio of NWs, doping, and external strain. Sample growth techniques, SHG measurement parameters, and extracted values of the nonlinear second-order coefficients from all the important studies are tabulated in Table 1. Most SHG studies are conducted on ZnO NWs with
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