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We experimentally demonstrate enhanced third harmonic generation (THG) using a silicon metasurface, which is consist of symmetric spindle-shape nanoparticle array. Relying on the trapped mode supported by the high quality factor all-dielectric metasurface, the conversion efficiency of THG is about 300 times larger than that of bulk silicon slab. The maximum extinction ratio of the intensity of THG reaches about 25 dB by tuning the polarization of incident light. The simulation results agree with the experimental performances.
© 2016 Optical Society of America
1. Introduction
Driven by strong optical light, light-matter interactions lead to optical nonlinear processes such as four wave mixing [1], sum frequency generation [2], difference frequency generation [3], third harmonic generation (THG) [4], second harmonic generation [5] and so on, which are beneficial to the applications of high speed signal processing and all optical logic operation. The efficiency of nonlinear processes is mainly dependent on the nonlinear coefficients of material and the intensity of pump source. Besides of those, nonlinear processes should obey the law of energy and momentum conservations. Bulk optical materials are firstly applied to realize THG. However, the poor light-matter interaction results in requirement of strong pump source and long interactional length, which hampers the practical applications.
An alternative way to shrink the size of the device and lower the pump power is trapping light in a tiny region. The more energy is trapped, the stronger interaction between light and matter is obtained. Moreover, reduction of the effective modal volume within the interactional region is preferred, since the strength of the light-matter interaction is inversely proportional to the effective modal volume. Due to negligible phase matching in nanoscale films, the nth order harmonic generation is proportional to the integration of induced electric dipoles over the volume of a nanostructure unit cell [6],
where χ(n) is the intrinsic nth order nonlinear susceptibility of the nonlinear material, Eloc(r, ω) is the local electric field and V is the volume of a unit cell. For example, nanometallic structures capable of trapping the light can substantially enhance Eloc(r, ω) beyond the limit of rayleigh scattering by efficiently funneling light from the far field to a deep subwavelength scale. Single plasmonic nanoparticle was firstly used to realize THG for single-biomolecule tracking microscopy [7]. Many subsequent results of THG have been obtained by using metallic nanostructures such as plasmonic nanoantennas [8,9], plasmonic Fano structures [10], and plasmonic metamaterials [11–13]. The major disadvantage of metallic structures is deep-subwavelength confinement of the light accompanying with giant intrinsic absorption, which limits the conversion efficiency of THG.High index dielectric nanoparticles recently attract lots of attentions because of overcoming the critical issue of heat dissipation, in which silicon is a potential candidate. In silicon photonic platform, silicon-on-insulator wafers offer tight modal confinement and large third order nonlinearity. Mature CMOS processes enable precise fabrication for silicon nanostructures. Generally, silicon microcavities supporting high Q resonances is applied to strengthen the light-matter interaction, but suffer from poor far field coupling [14]. Coupled dielectric nanoresonators can overcome both inefficient far field coupling [15] and optical loss. Recently, Mie resonances of dielectric particles have been proposed for the engineering of magnetic resonances [16–21] to improve the nonlinear effect due to the enhancement of electric field. The first observation of enhanced THG driven by magnetic responses have been experimentally realized in silicon nanoparticles (SNPs) [22]. However, the leaky characteristics of the optical modes within the SNPs results in small enhancement for THG.
In this letter, we report THG enhancement in a Fano resonant silicon metasurface with high quality factor relying on trapped modes [23,24]. Comparing to other Fano resonant structures [6, 25–28], the individual unit cell of our metasurface is a symmetric configuration. By manipulating trapped modes, the locally enhanced electromagnetic fields give rise to third order nonlinear effects, leading to two orders of magnitude enhancement. The intensity of THG is sensitive to the polarization direction of the electric field, which can be used to determine the polarization of incident light.
2. Simulation
The proposed dielectric metasurface, shown in Fig. 1(a), consists of spindle-like SNPs resting on the SiO2 layer. The structure’s period and height are 960 nm and 220 nm, respectively. The yellow arrow represents the pump light while the blue-green arrow indicates the THG signal. The detailed configuration of the SNP is given in Fig. 1(b), of which the structural parameters are depicted in the caption of Fig. 1(b). The simulated transmission spectra, plotted in Fig. 1(c), are achieved by normal-incident plane beam with electric field oriented along the y axis (red curve) and x axis (blue curve), respectively. When the electric field is parallel to the y axis, an extreme sharp dip in the transmittance curve is observed using the method of Finite Difference Time Domain. The detailed illustration of the Fano resonance around a wavelength of 1475.4 nm is shown in Fig. 1(d), of which the quality factor is about 1.6 × 105. There is no Fano resonance in the transmission spectrum when the electric field is parallel to the x axis, which implies that the trapped energy is dependent on the orientation of the incident light. Further simulation results indicate that the Fano resonances shift towards longer wavelengths when the parameters a, b and r increase. And the quality factors of Fano resonances reduce significantly when the parameters a, b and r are changed a little away from the values present in Fig. 1.
Fig. 1 (a) Scheme of three-photon up conversion within the Fano resonant silicon metasurface; (b) Diagram of one unit cell of the metasurface. The geometrical parameters are a = 291 nm, b = 111 nm, and r = 268 nm, respectively; (c)Simulated transmittance spectra of the metasurface with the polarization direction parallel to the y axis (red) and x axis (blue); (d) Detailed resonant spectrum of the red curve in Fig. 1(c).
The formation of Fano resonance within the silicon metasurface is firstly depicted by characterization of the electromagnetic field distribution in the SNPs. In Fig. 2(a), the ratio of trapped electric field within the SNP and that of the incident light is given, in which the arrows present the directions of the trapped electric field in the x-y plane. At both sides of the SNP, unique circular displacement currents in opposite directions are shown, which can be treated as artificial magnetic dipoles in the optical frequencies. The field enhancement is almost five orders of magnitude. The maximum enhancement for the electric field is obtained in the central of SNP because of discontinuous distribution of the electric field at the interface of SNP. In addition, enhanced magnetic fields can also be obtained in the x-z plane due to the occurrence of magnetic dipoles, which is given in Fig. 2(b). When the incident light is off resonance, the magnetic dipoles are inaccessible according to Fig. 2(c). Therefore, the increment of the electric field is relatively small and only electric dipoles are shown at both sides of SNP. In the upper picture of Fig. 2(d), the electric field distribution in the SNP in the x-y plane significantly is reduced when the polarization of incident light aligns along the x axis. In the lower picture of Fig. 2(d), electric field distribution in x-z plane is presented. Although in this case, there exists weak circle displacement current, field radiation to BOX layer is significant.
Fig. 2 Simulated electric field in the x-y plane (a) and magnetic field in the x-z plane (b) at resonant wavelength of 1475.4 nm when incident light’s electric field is parallel to the y axis. (c) Simulated off-resonant electric field in the x-y plane when incident light’s electric field is parallel to the y axis. (d) Simulated electric field in the x-y plane when incident light’s electric field is parallel to the x axis at the resonant wavelength;
Figure 3(a) shows the quality factor of the silicon metasurface depending on the period variation. When the period ranges from 940 nm to 980 nm, the values of quality factor are all greater than 1 × 104, of which the maximum is about 1.6 × 105 when the period is around 960 nm. Figure 3(b) shows the electric field distribution both in x-y plane and x-z plane when the period of array is 860 nm, 960 nm and 1020 nm respectively. The electric field distribution with maximum quality factor is depicted in Fig. 3(b)(II). In Fig. 3(b)(I, III), although the magnetic resonances still remain, the corresponding electric field becomes small both in the x-z plane and x-y plane. In the x-y plane, the magnetic resonances take place in all three configurations. However, the field radiation to the BOX layer is clearly obtained in the x-z plane illustrated by Fig. 3(b)(I, III), which is probably the occurrence of smaller index difference between silicon and silicon dioxide than that between silicon and air. When suitable parameters are chosen, shown in Fig. 3(b)(II), the radiation of electric field is greatly inhibited resulting in giant increment of quality factor.
Fig. 3 (a) The extracted quality factors of the metasurface as a function of period. (b) The distribution of electric field in the x-z plane and x-y plane corresponding to the point I, II, and III marked in section (a). The choice of cut-plane is represented with the red dashed lines. The period of array is 860 nm, 960 nm, 1020 nm, respectively.
The origin of the unique strong electromagnetic enhancement in our structure can be traced to so-called “trapped modes” [23,24]. These electromagnetic modes can be weakly coupled to free space, which allow to achieve high quality resonances in very thin structures [29]. Figure 4(a) shows y-component of the displacement current distribution with the same excitation condition in Fig. 3(b)(II). Indicating by the white arrows in Fig. 4(a), the anti-phase oscillations are respectively generated close to the center and edge of the individual cell with almost equal-amplitude electric polarizations, resulting in anti-parallel displacement currents in the SNP. In Fig. 4(b), there exists induced displacement currents of x-component. Both of them contribute to the magnetic resonance due to electric coupling [30].
Fig. 4 (a) Magnitude of the y-component and of electric field distribution in the spindle-shape metasurface at resonance; (b) Magnitude of the x-component of electric field distribution in the spindle-shape metasurface at resonance.
3. Experimental
The device is fabricated on a SOI wafer with a 220 nm silicon layer and 3 μm buried oxide layer. A simple two-step fabrication process including electron-beam lithography (EBL) for mask formation and reactive-ion etching (RIE) is used. And suitable parameters of EBL are chosen, of which the beam current is about 10 nA, the exposure dose is 220 μC/cm2 and the resolution of electron beam lithography is 8 nm. A scanning electron microscope (SEM) image of the fabricated sample is shown in Fig. 5(a). At the upper right corner of Fig. 5(a), the individual cell is shown. Figure 5(b) is SEM of the detailed surface morphology, among which the individual cells aren’t in good uniformity due to fabrication error. In order to reduce optical losses, a large array is adopted (600 μm × 600 μm) to avoid strong scattering of light into free space and broadening of the resonance peak [28,31,32].
Fig. 5 (a, b) are top views of SEM images of the fabricated metasurface; (c) Schematic of the experimental setup for the investigation of the metasurface.
The experimental setup for THG measurement is showed in Fig. 5(c). A Ti-Sapphire laser (Coherent, Legend Elite HE + USP-1K-III) is coupled to an OPO (optical parametric oscillator) to provide a pump beam with wavelengths ranging from 0.8 μm to 2 μm and a tuning step of 20 nm. It has a pulse duration around 45 fs and a repetition rate of 1000 Hz. The laser power is controlled by a Glan-Taylor Polarizer. A half waveplate is inserted to change the polarization angle of pump beam. The residual visible light generated by OPO can be eliminated by a NIR Bandpass Filter (700 - 1650 nm). A circular aperture is used to reduce the beam size in order to match the silicon metasurface. The pump light is guided to backside of silicon metasurface, which offers following advantages: firstly, the generated THG signal within the visible range is directly coupled into the free space without silicon substrate’s absorption; secondly, the remained visible light in the pump light is further filtered by the silicon substrate. A UV/Visible Bandpass Filter (340 - 694.3 nm) is placed in front of the spectrometer (Ocean Optics Inc., QE65PRO (350nm-1100nm), NIRQUEST512-205 (900nm-2200nm)) to filter out the IR pump beam. The spectrometer is used to record the THG signal.
4. Results and discussion
Due to the imperfection of the fabricated sample and fixed tuning step of the source, the central wavelength of the femtosecond pulse laser is chosen around 1440 nm, of which the spectrum is given in Fig. 6(a). The spectrum of pump beam is not a rigorous Gaussian lineshap and its full width at half maximum is about 100nm. The main reasons may lie in chirp effect in the pump source, imperfection of filter and nonlinear absorptions of optical components within the experimental setup. When the pump light is incident normally to the silicon metasurface, the maximum THG signal is bright enough to be observed by naked eyes under ambient room light conditions as shown in Fig. 6(b), which is predicted in Fig. 2(a) due to the trapped mode. However, when the wavelength of pump beam is 100 nm away from 1440 nm, the THG signal is too weak to be observed. Figure 6(c) shows the THG spectrum normalized to the THG signal from the substrate away from the sample indicates a qualitatively different nonlinear response under the condition of different polarization angles. The maximum extinction ratio of the intensity of THG reaches 25 dB when the polarization changed from 0 degree to the 90 degrees. The enhancement of THG reaches more than 300 times around the wavelength of 482 nm due to Fano resonance of silicon metasurface. The pronounced reshaping of third-harmonic spectra might be mainly attributed to nonlinear interference between the resonance-induced THG from the sample and its back-radiated THG reflected from the SiO2/Si interface due to the extremely large refractive index contrast in the direction of the detector [33]. Due to the imperfection of fabricated sample, the enhancement of nonlinear performance isn’t as large as the numerical simulation prediction. In Fig. 6(d), the variation of the THG signal is experimentally recorded with red rhombus dots by changing the polarization of the pump light. Adopting the maximum electric field in the SNP, the simulation results agree with the result of the experiment. The theoretical fitting equation is
where κ is the constant related to the material’s nonlinear coefficient, E is the local electric field and θ is the polarization angle. When the intensity of THG with different polarization angles is normalized to the maximum intensity of THG, Eq. (2) can be written aswhich is shown by the theoretical fitting curve in the figure. It resembles a cosine-cubed function which agrees with Eq. (1).Fig. 6 (a) The spectrum of pump beam measured by spectrometer. (b) Photograph taken under ambient room light showing blue-green light emission with an incident wavelength of 1440 nm (peak pump intensity of 2 GW/cm2). (c) THG spectrum normalized to the THG signal from the substrate away from the sample indicates a qualitatively different nonlinear response with polarization angle ranging from 0 degree to 90 degrees; The inset gives the detailed information of the weak THG signal. The dashed line is based on the intensity of THG from the SOI substrate, which presents a baseline for THG comparison. (d) The measured normalized THG signals (red rhombus dots) fitted with simulation results (blue dashed line) and theoretical equation (black line).
5. Conclusion
In conclusion, we have experimentally demonstrated enhanced THG in a Fano resonant silicon metasurface due to the trapped mode. The efficiency of the IR-to-visible conversion is enhanced about 300 times with respect to the bulk silicon slab. The conversion efficiency of THG is dependent on both the wavelength and polarization angle of the pump light, which is confirmed by experimental results. The maximum extinction ratio of the intensity of THG signal reaches about 25 dB. The proposed silicon metasurface may open a new route toward the realization of ultracompact optical devices such as polarization sensors and multiphoton spectroscopy.
Funding
National Natural Science Foundation of China (NSFC) (60806016, 61177049, 11304365); National Basic Research Program of China (2012CB922103, 2013CB933303).
Acknowledgments
We thank all engineers in the Center of Micro-Fabrication and Characterization (CMCF) of Wuhan National Laboratory for Optoelectronics (WNLO) for the support in fabrication and Gong Cheng in Key Laboratory of Atomic Frequency Standards for providing calibrated light sources and useful discussions.
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