Continuous wave second harmonic generation enabled by quasi-bound-states in the continuum on gallium phosphide metasurfaces
Aravind P. Anthur, Haizhong Zhang, Ramon Paniagua-Dominguez, Dmitry Kalashnikov, Son Tung Ha, Tobias Wilhelm Wolfgang Mass, Arseniy I. Kuznetsov, Leonid Krivitsky
aa r X i v : . [ phy s i c s . op ti c s ] F e b Continuous wave second harmonic generationenabled by quasi-bound-states in thecontinuum on gallium phosphide metasurfaces
Aravind P. Anthur, † , ‡ Haizhong Zhang, † , ‡ Ramon Paniagua-Dominguez, † , ‡ DmitryKalashnikov, † Son Tung Ha, † Tobias Wilhelm Wolfgang Mass, † Arseniy I.Kuznetsov, ∗ , † and Leonid Krivitsky ∗ , † † Institute of Materials Research and Engineering, A*STAR (Agency for Science,Technology and Research) Research Entities, 2 Fusionopolis Way, ‡ Equal contribution. [Version submitted to Nano Letters.Revised version: https: // doi. org/ 10. 1021/ acs. nanolett. 0c03601 ] E-mail: [email protected]; [email protected]
Abstract
Resonant metasurfaces are an attractive platform for enhancing the non-linear op-tical processes, such as second harmonic generation (SHG), since they can generatevery large local electromagnetic fields while relaxing the phase-matching requirements.Here, we take this platform a step closer to the practical applications by demonstrat-ing visible range, continuous wave (CW) SHG. We do so by combining the attractivematerial properties of gallium phosphide with engineered, high quality-factor photonicmodes enabled by bound states in the continuum. For the optimum case, we obtainefficiencies around 5e-5 % W − when the system is pumped at 1200 nm wavelength ith CW intensities of 1 kW/cm . Moreover, we measure external efficiencies as highas 0.1 % W − with pump intensities of only 10 MW/cm for pulsed irradiation. Thisefficiency is higher than the values previously reported for dielectric metasurfaces, butachieved here with pump intensities that are two orders of magnitude lower. Nonlinear optical processes like second harmonic generation (SHG) has attracted theinterests of researchers for more than sixty years.
SHG is utilized for a broad range ofapplications including lasers, quantum optics, spectroscopy, imaging and pulse-width mea-surement, to name a few.
One of the fundamental goals for any practical use of SHGis to achieve efficient conversion of the fundamental frequency pump to the second har-monic signal. Several materials and device designs have been proposed and demonstratedto enhance the efficiency. These, however, come at the price of several constraints related tothe operational wavelength ranges, necessary pump intensities, phase-matching requirementsand/or the size of these devices. Towards reducing the device dimensions and overcomingthe phase matching constraints, there are ongoing efforts in utilizing metasurfaces, arrays ofnanostructures that exploit resonant enhancement of the pump.
Using this concept, highefficiency has been achieved, for example, in plasmonic metasurfaces.
While leading tovery high local field, plasmonic metasurfaces have the disadvantage of having intrinsic dissi-pative losses, which result in relatively low damage thresholds for this kind of devices. As analternative, dielectric and semiconductor metasurfaces have recently emerged as a promis-ing platform.
They offer lower intrinsic material losses and higher damage thresholds,as well as, potentially, high non-linear coefficients. Using materials that lack the inversionsymmetry of the crystal lattice allows SHG in the volume, rather than at the surface (asis the case of metals). In this regard, semiconductor metasurfaces with multiple quantumwells are among those with the largest non-linear coefficients, and have been used to achievehigh conversion efficiencies.
The main limitation of this approach, however, is that theSHG signal in these structures saturates at relatively low pump intensities, limiting the totalamount of power that can be converted in the device. Resonant dielectric and semiconductor2etasurfaces using volumetric SHG, and having higher damage and saturation thresholds,have been used to demonstrate very high SHG efficiencies utilizing cleverly engineered opticalmodes.
In this regard, a novel design strategy of dielectric nanoantennae and metasurfaces basedon the concept of bound-states in the continuum (BIC) have recently attracted interest inthe community.
The main reason is that it allows to achieve very high quality factor (Q)modes, which can be easily tuned by varying the device geometry, enabling highly efficientnonlinear optical processes.
Despite the advances in the optical mode and materialengineering, all nanoantenna- and metasurface-based SHG devices demonstrated so far havebeen realized in the high-intensity, pulsed regime (typically involving femtosecond lasers),which hinders their use in many practical applications that work in the low intensity CWregime. This also creates an additional limitation due to a limited overlap of the short-pulse laser spectrum with the narrow-band resonances of high-Q metasurface, which furtherlimits the conversion efficiency. In this work, we combine an emerging material platformfor non-linear applications, namely gallium phosphide (GaP), and a metasurface designsupporting a high-Q quasi-BIC mode that exploits the symmetries of the non-linear tensor, togenerate continuous wave (CW) SHG at low pumping intensities with reasonable conversionefficiencies. We also show that, in the pulsed regime, we achieve external efficiencies thatare higher than the results reported in the literature for dielectric metasurfaces to the bestof our knowledge, despite using two orders of magnitude lower pumping intensities.Our metasurface consists of a square array of nano-dimers comprising two GaP cylinderswith elliptical cross section, as shown in Fig. 1(a). They have period of Λ =700 nm, minoraxis length of D =200 nm, major axis length of D =460 nm, height of 150 nm and center-to-center distance of d=340 nm. When the major axes of these cylinders are perfectly parallelto each other,the system supports a perfect BIC at the gamma point for the selected pumpwavelength ( λ ≈ This BIC stems from the excitation of an in-plane electricquadrupole mode, Q exy , and an out-of-plane magnetic dipole mode, m z , in each dimer, which3igure 1: (a) Schematic of the metasurface, comprising a square lattice (periods, Λ = 700nm) of dimers formed by two elliptical cylinders (with minor and major axes D and D ,respectively, height of 150 nm and center-to-center separation of d = 340 nm) with a relativetilting by an angle θ between their major axes. (b) Schematic representation of origin ofthe quasi-BIC. A single in-plane electric dipole is induced in each particle in the dimer,containing x- and y-components ( p i ( x,y ) ). These, when summed up, give origin to an out-of-plane magnetic dipole ( m z ) and in-plane electric quadrupole (Q exy ), and an x-orientedelectric dipole ( p x ), whose amplitude can be controlled by θ . Of these, only p x can couple tonormally incident, x-polarized plane waves. (c) Simulated transmission spectra of x-polarizednormally incident plane waves traveling through the metasurface with θ = 0 ◦ (red) and θ = 5 ◦ (black). (d) Amplitude of the electric near-field distribution at the quasi-BIC resonance inthe xy-plane passing through the center of the particles. (e) Measured transmission spectraof x-polarized, normally incident light traveling through the fabricated metasurfaces with θ = 0 ◦ (red) and θ = 5 ◦ (black). (f) SEM image of the fabricated sample with θ = 5 ◦ withscale bar of 1 um.in turn result from individual electric dipoles excited in each nanocylider, as shown in Fig.1(b). Due to the symmetry of the waves radiated from these modes, they cannot couple toplane waves emerging from the system at normal incidence and the system becomes decoupledfrom the radiation continuum. A simple way to visualize the emergence of this BIC is thefollowing. Each unit cell, comprising a dimer, radiates according to the sum of the in-planeelectric quadrupole and the out-of-plane magnetic dipole. Since each of these two modes hasvanishing radiation intensity in the direction normal to the metasurface, their sum obviouslyalso has so. Now, when all the unit-cells oscillate in phase, a situation corresponding to4he gamma point, and when the lattice period is sub-diffractive, this normal direction is theonly direction in which the system is allowed to radiate. However, when radiation from eachunit cell vanishes in the normal direction, as is the case of these dimers, overall radiation isforbidden from the system and the modes become bounded to the system (hence the nameBIC). By reciprocity, this also implies that no energy can be coupled into these modes fromnormally incident plane waves. In order to be able to do so, a certain radiation leakagechannel is necessary. In this system, an easy way to open such a channel is by symmetrybreaking, realized via tilting of the ellipses in opposite directions around the z-axis by acertain angle θ , as shown in Fig. 1(a). In such situation, the system might support anadditional in-plane, x-oriented electric dipole moment, p x (see Fig. 1(b)) that opens thepossibility to couple power in and out of the system, when illuminated by a normally-incident x-polarized plane wave (see Fig. 1(a)). This effectively transforms the perfect BIC,characterized in the lossless case for having Q → ∞ , into the quasi-BIC, with large but finiteQ. The amplitude of p x , which can be controlled by the angle θ , determines the amount ofleakage and, thus, the Q of the mode. We use this quasi-BIC mode to couple power into the system and achieve enhancement ofthe pump intensity, thereby achieving highly efficient SHG. Figure 1(c) shows the simulatedtransmission spectra for two different metasurfaces, one supporting a perfect BIC ( θ = 0 ◦ )and one supporting a quasi-BIC ( θ = 5 ◦ ). As can be seen, a spectrally narrow resonance at ∼ θ = 5 ◦ , corresponding to the excitation of thequasi-BIC. The Q factor is estimated to be more than 4000, obtained through a fitting ofthe curve to the Fano formula. As expected, this dip is not present for the case in whichthe perfect BIC is formed ( θ = 0 ◦ ), as the mode becomes uncoupled from external radiationand, thus, cannot be excited by the pump. In Fig. S1, we plot the evolution of this mode asa function of θ , from which the narrowing and amplitude decrease of the resonance as theangle reduces becomes clearly apparent, as expected for a mode evolving towards a perfectBIC. Note that this behaviour is not observed for the broad resonance excited at shorter5avelengths, which has its origin in a simple, in plane electric dipole ( p x ) that is almostinsensitive to the tilting angle. Figure 1(d) shows the simulated enhancement of the electricnear-field amplitude at the quasi-BIC excitation condition. The result indicates that insidethe structures, field enhancements above 50 can be obtained, corresponding to intensityenhancement of more than 2500. While, theoretically, arbitrarily high values of Q factorsare possible by simply reducing θ , in practice they are limited by the size of the array, thematerial losses and any fabrication imperfections. In our experiments, the minimum anglefor which we observed the quasi-BIC mode is θ = 5 ◦ , and is therefore the case presentedhere. A detailed analysis of the multipolar moments supported by this system is presentedin Fig. S2, corroborating the interpretation of the quasi-BIC origin given above.We choose GaP for fabricating our devices because it combines all key features that makean attractive platform for non-linear processes at the nanoscale. First, it has a large second-order nonlinear coefficient (d ≈
70 pm/V for λ ≈ Second, it has a relativelylarge band gap that pushes the cut-off wavelength down to λ ≈
550 nm, together with ahigh refractive index, n ≈ λ ≈ And last but not the least, nanofabricationof GaP is well established in the semiconductor industry. Since the GaP crystal has zinc-blende structure, it is critical to know and utilize the nonlinear tensor appropriately toachieve high SHG efficiency. For that, we first analyze the crystal axis orientation of ourwafer, which turns out to be tilted with respect to the surface normal. Then we fabricateour metasurfaces with an orientation that maximizes the SHG. We do so using electronbeam lithography (EBL) followed by reactive ion etching (RIE). Both crystal orientationand fabrication details are provided in the supporting information. The fabricated samplesare of high quality, as indicated by the good agreement between the measured transmissionspectra (Fig. 1(e)) with the simulated ones (Fig. 1(c)), as well as the scanning electronmicroscopy (SEM) images of the sample (see Fig. 1(f) for the θ = 5 ◦ case and Fig. S3for all the cases measured). Despite the slight blueshift in the measured position of thetransmission dip with respect to the simulated one, both spectra are in good agreement,6btaining a quality factor of approximately 2000 for the experimental quasi-BIC structure.For these transmission measurements, the sample was illuminated using an x-polarized broadband halogen light source (see supporting information).The simulated and measured transmission spectra of metasurfaces with different angle θ ,spanning from ◦ to ◦ , are given in Figs. 2(a) and 2(b), respectively, with the correspondingSEM images given in Fig. 2(c). As expected, the Q factor experiences a dramatic increaseas θ reduces, while the resonance wavelength redshifts. Simulations and experiments are ina very good agreement with respect to the relative spectral position of the resonance fordifferent cases and the Q factors (see Fig. 2(f) for a direct comparison). The overall slightblueshift ( ∼
20 nm) of the experimental spectra with respect to the theoretical ones can beattributed to a slight deviation in the height of the structures. The quasi-BIC resonantwavelengths are designed to be around 1200 nm so that the SHG wavelength is above thecut-off wavelength of the GaP. It should be noted that all the spectra are measured underx-polarized illumination, and that no resonances are observed for y-polarized light.We now use the near field enhancement inside the structures enabled by the quasi-BICresonances to obtain SHG and study its efficiency as a function of the angle θ . We first pumpthe metasurfaces using a pulsed laser from an optical parametric oscillator (APE) with apulse duration of around 200 fs and wavelength that is tunable from 1100 nm to 1400 nm.The light is focused onto the sample with a plano-convex lens with a focal length of 25.4mm. The forward generated second harmonic light is collected using an objective lens witha numerical aperture (NA) of 0.95 in air. The SHG signal is filtered using a bandpass filterand analyzed (see supporting information and Fig. S4 for more details on the experimentalsystem).In Figs. 2(d) and 2(e), we show as solid lines, respectively, the simulated and measuredSHG spectra obtained when the central wavelength of the pulsed pump is tuned to give themaximum SH signal. In our simulations, we assume that the pump pulse has a Gaussianshape, with 5 nm full-width at half maximum (FWHM). In Fig. 2(d), we also show as7igure 2: (a) Simulated and (b) measured transmission spectra near the quasi-BIC resonanceof x-polarized, normally incident light traveling through metasurfaces with varying θ , from30 ◦ to 5 ◦ . (c) SEM images of the fabricated samples. (d) Simulated and (e) measured SHGspectra when the metasurfaces in (a) and (b) are illuminated by a pulsed pump (FWHMaround 5 nm) centered at the wavelength giving maximum SHG (solid lines). In (d), we alsoshow as shaded area the SHG spectra computed assuming an infinitely narrow pump, whosefrequency is scanned in the range shown. (f) Quality factor (Q) retrieved from simulatedand measured transmission spectra through a fitting to the Fano formula.a shaded area the simulated SHG assuming a single frequency pump, scanned over therange of wavelengths. All simulated results are computed in two steps. First, the electricfield distribution ( E ( ω F F )) inside the nanostructures at the fundamental frequency ( ω F F )is computed. Then, it is used to calculate the non-linear polarization density, which servesas the source for a second simulation at the second harmonic frequency, using the relation P (2 ω F F )=2 ǫ χ (2) E ( ω F F ). Here, ǫ is the vacuum permittivity and χ (2) is the appropriatenon-linear susceptibility tensor in the laboratory frame, which takes into account the crystalaxis orientation in the experiment, as explained in the supporting information. Figure 2(e) ismeasured using a spectrometer (Ocean Optics, USB4000) with a spectral resolution of ∼ ◦ and 5 ◦ have similar spectral widths. From Figs.2(d) and (e) one can see that the wavelength of maximum SHG signal exactly corresponds tothe quasi-BIC condition. Moreover, a noticeable narrowing of the SHG spectra is observedwhen the pump is tuned to the resonant wavelength of the metasurface; its FWHM evolvingfrom that of the pump to being determined by the resonance itself. In the experimentaldata, this narrowing saturates when it hits the resolution limit of our spectrometer.Figure 3(a) shows the measured SHG power in the forward direction as a function ofthe input pump power for the four cases shown in Fig. 2(e). The input pump power isvaried using a variable neutral density filter at the input. The SHG power is measuredusing a power meter for the pulsed pump and using a lock-in amplifier system with anamplified photo detector (APD) for the CW pump (see supporting information and Fig.S4 for details). Fitting the curve to a function with the shape P SHG = aP bpump , we foundthe nearly quadratic dependence expected for SHG. As can be seen from Fig. 3(a), theaverage collected SHG power for θ = 5 ◦ is around 1.44 µ W for 37 mW of average inputpump power. This corresponds to an external SHG efficiency of 4e-5 ( P SHG / P pump ) and 0.1 % W − ( P SHG / P pump ), for a pump intensity of approximately 10 MW/cm . This level ofefficiency, to the best of our knowledge, is better than previously reported results in theliterature, despite being obtained here using 100 times lower intensities (see Table S1). It isworth noting that, for this input power, the SHG power is not saturated. We also note theevident impact of the narrowing of the quasi-BIC resonance on the SHG as the angle variesfrom θ = 30 ◦ to θ = 5 ◦ . As expected, the increase in Q factor has an associated increase ofthe SHG, reaching values for the θ = 5 ◦ that is 2.5 times larger than the θ = 30 ◦ case. Thisvalue is lower than what would be expected if one simply considers the Q factor increase.This is attributed to the fact that the width of resonance becomes significantly narrowerthan the pump at small angles ( θ ), and thus only a part of the femtosecond pump spectrais used for the generation of the SH signal. This finally leads to a limited enhancement inthe SHG for the 5 degree compared to the 30 degree and inspires us to pursue CW SHG in9 deg.10 deg.20 deg.30 deg.0 deg. S H i n t e n s i t y ( a . u ) S H i n t e n s i t y ( a . u ) -1.0-0.50.00.5 k / k y k / k x 0 -1.0 -0.5 0.0 0.5 1.0 Figure 3: (a) Measured SHG power as a function of the average pulsed pump power. Foreach angle, the pulsed central wavelength is tuned to the wavelength giving the maximumSHG. Fits to the equation P SHG = aP bpump , are shown as dotted lines, while experimentalpoints are shown as circles. The exponent values obtained from the fits are 2, 1.97, 1.93, and2.1 for 30 ◦ , 20 ◦ , 10 ◦ and 5 ◦ respectively. The R-squared values are ∼
1. (b) Simulated (redsolid line) and measured (black circles) SHG power as a function of the pump polarization(0 ◦ corresponding to the polarization parallel to the x-axis, i.e. with the axis of the dimer)for the metasurface with θ = 5 ◦ . (c) Simulated and (d) measured SHG back-focal plane10mages at the maximum of SHG for the metasurface with θ = 5 ◦ . (e) Simulated and (f)measured SHG spectra when the central frequency of the pulsed pump is scanned aroundthe quasi-BIC condition.this system.Before that, we corroborate the quasi-BIC origin of the observed SHG by analyzing itsdependence on the polarization of the pump. As mentioned before, the quasi-BIC resonancecan only be excited when the normally incident wave has its electric field polarized along theaxis of the dimer (x-axis). The perpendicular, y-oriented polarization, cannot couple to theelectric quadrupole Q exy , nor to the out-of-plane magnetic dipole mode, m z , as it follows fromthe symmetry considerations. Therefore, we expect significant SHG only when the incidentelectric field is oriented along the x-axis. In the experiment, the polarization of the pump isrotated using a half wave plate and the power of the SHG at the output is measured withoutany polarizer (either at the input or the output of the sample). The measurement resultsare plotted as circles in Fig. 3(b), together with the simulation predictions, representedas solid lines. As expected, the SHG power is highest for x-polarized pump, while for thefully y-polarized pump it is below the detection limit of our measurement system, involvingamplified photodetector and lock-in amplifier. For completeness, the simulated and measuredback-focal plane images of the far-field SHG radiation pattern in the forward direction aregiven in Figs. 3(c) and 3(d), respectively, for the θ = 5 ◦ sample. The measured back-focalplane image uses an objective with an NA of 0.95 to collect the SHG signal. As can be seenfrom Fig. 3(d), five spots are observed, corresponding to the direct forward emission andthe SHG coupling into the four diffraction orders opened at the SH frequency, 2 ω F F . Two ofthe five spots are more intense than the other three, in good agreement with the simulations(Fig. 3(c)). Since the crystal axis is rotated by an angle of 15 ◦ with respect to the normal tothe wafer, we observe the beam along the direction of propagation at 0 ◦ angle, which wouldotherwise be zero due to the nonlinear tensor for GaP if the axis of the crystal would beparallel to the normal. 11inally, we sweep the central frequency of the pulsed pump in a range of wavelengthsaround the (quasi-)BIC for all samples, from θ = 30 ◦ to θ = 0 ◦ , and plot the simulated andmeasured normalized SHG intensity spectra in Figs. 3(e) and 3(f), respectively. As can beseen, maximum SHG is obtained when the central wavelength corresponds to the resonant dipobserved in the transmission spectra of Figs. 2(a) and 2(b). Also, as expected, the FWHMof the curves gets narrower for decreasing angle, but becomes limited by the convolutionwith pump pulse width. In fact, as mentioned before, the mismatch between the (narrower)spectral width of the quasi-BIC resonance for small angles and the (broader) pulsed pumpimplies that part of the incident power is not coupled to the mode and, therefore, to the SHGprocess (the quasi-BIC acting effectively as a filter). Thus, we move on to study the samplesunder narrow-band CW pump instead, for which the whole input power can be efficientlyused in the SHG.In Fig. 4(a), we show the optical spectra of the maximum SHG obtained when thedifferent samples are excited with a tunable CW laser (see supporting information for details).As an inset in that figure, we show the spectra of the pump used to obtain the SHG. We notethat maximum SHG is observed when the CW pump is tuned to the corresponding resonanttransmission dip of each of the metasurface arrays. Notably, we observed and measured SHGusing ∼ kW/cm levels of intensity in all the arrays, with angles ranging from θ = 30 ◦ to θ = 5 ◦ . As before, SHG is not observed for the case of parallel ellipses, i.e. for θ = 0 ◦ .The variation of the SHG power as a function of the input power of the CW pump isshown in Fig. 4(b). As expected, one can observe an increase in the SHG power (and thusthe efficiency) as θ decreases from ◦ to ◦ . In our experiments, the maximum SHG poweris observed for the θ = 5 ◦ case, reaching values around 70 nW for 360 mW of input pumppower. This translates into an external SHG efficiency of 2e-7 ( P SHG / P pump ) and 5e-5 % W − ( P SHG / P pump ), for a pump intensity as low as 1 kW/cm . As compared to the pulsedcase, since the CW linewidth is less than 1 MHz, the narrowing of the resonance (or increaseof the Q factor) does not cut any incident power, and thus the enhancement is not limited12hen θ decreases. Therefore, in Fig. , the impact of the increase in Q factor is more clearlyobserved in the SHG, which is almost two orders of magnitude larger for θ =5 ◦ than it is for θ = 30 ◦ , compared to only 2.5 times increase in the pulsed case.
580 600 620 6400.20.40.60.81.0
30 deg.20 deg.10 deg.5 deg. (b)
Wavelength (nm) N o r m a li z e d p o w e r ( a . u ) (a) S H G p o w e r ( n W )
200 300 40010
30 deg.20 deg.10 deg.5 deg.
CW input pump power (mW)
Wavelength (nm)
Figure 4: (a) Spectra of the SHG when the CW pump is tuned to the resonance of 30 ◦ , 20 ◦ ,10 ◦ and 5 ◦ samples, and the corresponding pump spectra given in the inset. (b) The SHGpower as a function of input CW pump power for various angles of the dimer. Fits to theequation P SHG = aP bpump , are shown as dotted lines, while experimental points are shown ascircles. The exponent values obtained from the fits are 1.9, 2.3, 1.91, and 2.1 for 30 ◦ , 20 ◦ ,10 ◦ and 5 ◦ respectively. The R-squared values for the fit are ∼ onclusion In conclusion, we have demonstrated high efficiency second harmonic generation (SHG) fromGaP metasurfaces with sub-wavelength thicknesses ( ∼ λ /8). This is achieved by combiningthe emerging material platform of GaP, offering high non-linearity, high refractive index, lowloss and ease of fabrication, with high-Q optical resonances enabled by quasi bound-states inthe continuum (BIC). We achieve these quasi-BIC resonances by breaking the metasurfaceunit-cell symmetry, that controllably opens a leaky channel in the normal direction. Openingof leaky channel allows the coupling of radiation in-and-out of the otherwise perfect BIC,formed by in-plane electric quadrupole and out-of-plane magnetic dipole modes. We observea dramatic increase of the Q factor of the resonance as the asymmetry parameter decreases,which translates into increased SHG efficiency, P SHG / P pump ( P SHG / P pump ), reaching valuesof 0.1 % W − (4e-5) for pulsed pumps with intensities of approximately 10 MW/cm . Thislevel of external efficiency is obtained without reaching saturation and is higher than thevalues previously reported in the literature, to the best of our knowledge, but achieved hereusing 100 times lower intensities. We also demonstrated SHG in these metasurfaces usinga continuous wave (CW) pump. We generated CW SHG using pump with intensities of 1kW/cm , and achieved conversion efficiencies of 5e-5 % W − (2e-7) in the metasurface withthe highest Q factor. We believe that our work shows that the combination of suitable mate-rial platforms and properly engineered optical resonances might push SHG in metasurfacesto levels closer to those required for practical applications, including those that demandcontinuous wave, second harmonic generation. Acknowledgement
We acknowledge the support of the Quantum Technologies for Engineering (QTE) programof A*STAR, IET A F Harvey Engineering Research Prize 2016 and A*STAR SERC Pharosprogram, Grant No. 152 73 00025 (Singapore).14 uthor contributions
R. P.-D. proposed and simulated the structures. H. Z. Z. fabricated the samples. A. P. A.constructed and performed the optical characterization measurements. S. T. H. performedthe transmission measurements. T. W. W. M. simulated the back-focal plane images. D. K.helped in the optical characterization. A. P. A wrote the first draft of the manuscript, withinputs from R. P.-D. and H. Z. Z. A. I. K. and L. K. conceived the idea and supervised theproject. All authors contributed to the final version of the manuscript
Competing interests
The authors declare no competing financial interest.
Supporting Information Available
The following files are available free of charge.• Supplementary material contain the details of simulation, fabrication and experimen-tal measurement system. Supplementary material also contains the following figuresand table. Colour map representing the metasurface transmission as a function ofwavelength and angle of tiling ( θ ) of the elliptical cylinders forming the dimers in themetasurface. Multipolar decomposition of one unit-cell of the metasurface supporting aquasi-BIC with θ = 5 ◦ . Scanning electron microscope images of the different fabricatedmetasurfaces. Schematic of the experimental setup. Comparison of the state-of-the-artperformances of SHG in dielectric metasurfaces.15 upplementary material: continuous wave second harmonicgeneration enabled by quasi-bound-states in the contin-uum on gallium phosphide metasurfaces Simulations
Simulations of SHG were carried out using the Finite Element Method in a commercialsoftware package (COMSOL Multiphysics). The simulations consist of two steps. In thefirst one, the transmission spectra and the near-fields inside the nanostructures comprisingthe metasurface, E ( ω F F ), are computed at the fundamental frequency, ω F F . For that, wesimulate the infinite periodic system by using Periodic Boundary Conditions in the x- andy-directions (transverse to the incident wave propagation). Periodic ports are used at thetop and bottom to excite the system and record the transmitted and reflected fields. TheGaP material parameters are taken from the software database, which in turn are takenfrom the literature. A homogeneous surrounding environment with refractive index 1.46 istaken. In the second step, the near-fields recorded in the first one are used to compute thenon-linear dipole moment density, which is used as the excitation source in the simulations.This non-linear dipole moment density is computed through the expression: P (2 ω F F ) = 2 ǫ χ (2) E ( ω F F ) , (1)where ǫ is the vacuum permittivity and χ (2) is the non-linear susceptibility tensor ofthe crystal in the laboratory frame. To obtain the correct results, one should note that,in our GaP wafers, the material is grown such that the crystal axis subtends an angle of15 ◦ with respect to the normal to the wafer surface. Thus, we first need to express thenear-fields, as obtained in the first simulation, in the crystal frame, in which the non-linearsusceptibility tensor has only off-diagonal components and they are all equal (d = d =d ≈
70 pm/V). This can be achieved simply using the appropriate rotation matrix. Once16he fields in the crystal frame are known, we compute the non-linear dipole moment in thisframe using expression in Eq. 1. This is brought back again to the laboratory frame bythe inverse rotation matrix, to perform the simulations. In the simulation, we use againPeriodic Boundary Conditions in the transverse directions but substitute the Periodic Portsby Perfectly Matched Layers in the z-directions (top and bottom of the simulation). Forthe computation of the far-field pattern given in Fig. 3(c), a homemade implementation ofStratton-Chu formulas is used. For that, the complex electromagnetic fields in one unit-cellare recorded in a plane at distance of 500 nm from the structures. These are used to generatea finite array of 50 x 50 periods, which is then rigorously propagated to the far-field.
Fabrication
The GaP active layer ( ∼
400 nm) is first grown on a gallium arsenide (GaAs) substrate withan AlGaInP buffer layer by metal-organic chemical vapor deposition (MOCVD) to reduce thelattice mismatch between the GaAs substrate and GaP layer. Then this structure is directlybonded to the sapphire substrate after depositing ∼ SiO layer on top of both the surfaces.The AlGaInP/GaAs substrate is then removed by wet etching. The fabrication of the GaPnanostructures start with a standard wafer cleaning procedure (acetone, iso-propyl alcoholand deionized water in that sequence under sonication), followed by O and hexamethyldisilizane (HMDS) priming in order to increase the adhesion between GaP and the subsequentspin-coated electron-beam lithography (EBL) resist of hydrogen silsesquioxane (HSQ). Afterspin-coating of HSQ layer with a thickness of ∼
540 nm, EBL and development in 25 % tetra-methyl ammonium hydroxide (TMAH) are carried out to define the nanostructuresin HSQ resist. Inductively-coupled plasma reactive ion etching (ICP-RIE) with N andCl is then used to transfer the HSQ patterns to the GaP layer. Finally, ∼ µ m SiO cladding layer is deposited on top of the structures by ICP-CVD. For optical measurements,an additional layer of polydimethylsiloxane (PDMS) is placed on top of the cladding layerto avoid Fabry-Perot resonances. The structures fabricated are 100 µ m × µ m in size.17 xperimental setup The schematic of the experimental setup is given in the Fig. S4. The laser light from anoptical parameteric oscillator (OPO) is passed through a dichroic beam splitter cutting-offshorter wavelength components. The pulsed pump is obtained from a Coherent APE OPOtunable from 1100 nm to 1300 nm, pumped by a Ti:Sapphire laser at a wavelength of 830nm. The CW OPO is a Hubner CWave laser pumped by a 532 nm laser, that is tunablefrom 900 nm to 1330 nm. The pump light then passes through a variable optical neutraldensity filter, quarter-wave plate (QWP) and half-wave plate (HWP). The variable neutraldensity filter is used for varying the pump power levels. The QWP and HWP are jointly usedfor varying the pump polarization at the input. A polarization extinction of approximately100 is achieved for the pump light at the input of the sample, as given in Fig. S4(b). Apolarizer is used for the power measurements and polarization analysis of the input pump.For Fig. 3(b), no polarizer is used at the input. All the other measurement results given inFigs. 1, 2, 3 and 4 use a polarizer at the input of the sample. Lens, L1, is a plano-convexlens with a focal length of 25.4 mm, to achieve a beam waist diameter of approximately100 um for the pulsed and CW pump. The beam width measurement is carried out usingknife edge and the results are given in Fig. S4(c). The lens, L2, is an objective with an NAof 0.95. At the output, a flipping mirror is used to image the far-field beam pattern andthe sample. A 4f imaging system (L3-L6) with a charged coupled device (CCD) camera isused to image the back-focal plane of the objective, to obtain Fig. 3(d). After this imagingsystem, there is a filter centered at 650 nm and having a spectral width of 150 nm (Semrock).The output of the filter is directed through a chopper to an amplified photo-detector (APD)to measure the SHG power for CW pump and a power meter (PM) calibrated to the APDis used for the pulsed pump. The P SHG is the average measured SHG power after the filterand P pump is the average measured pump power before L1. The transmission spectrum inFig. 2(b) is obtained using the same experimental system pumped by a broad band super-continuum source (Leukos) and coupling the light output through the sample, immediately18fter L2 using a flip mirror, to a high resolution optical spectrum analyzer (OSA, Yokogawa)through a single mode fiber, and taking the ratio of the transmitted signal through thesample with and without the nanostructured array. This fiber coupling system is also usedfor capturing the spectra of the SHG generated from the metasurface using the spectrometer(Ocean Optics, USB4000). 19igure S1: Colour map representing the metasurface transmission as a function of wavelengthand angle of tilting ( θ ) of the elliptical cylinders forming the dimers in the metasurface, asshown in Figure 1 in the main text. As seen, the resonance corresponding to the excitation ofthe quasi-BIC mode experiences a strong narrowing of the linewidth, as well as a decrease inthe amplitude, when θ decreases and the mode evolves towards the perfect BIC. The broadresonance observed at shorter wavelengths, corresponds to the excitation of an in-plane,electric dipole directed along the incident polarization ( p x ), and is almost insensitive to thetilting angle. 20 x z ! xye (cid:127) y (cid:127) x " % " % (a)(a) (b) Figure S2: Multipolar decomposition of one unit-cell of the metasurface supporting a quasi-BIC with θ = 5 ◦ . (a) Non-negligible multipole moments when applying the multipole de-composition, only, to the fields of one of the cylinders comprising the dimer. The originof coordinates is taken at the center of the cylinder. As can be seen, the only significantmultipole moment is a tilted electric dipole moment (as indicated by the presence by bothx- and y- components). (b) Non-negligible multipole moments when applying the multipoledecomposition to the whole dimer. The origin of coordinates is taken at the center of thedimer. As can be seen, there are three significant multipole moments: an out-of-plane mag-netic dipole moment (m z ), an in-plane electric quadrupole moment (Q exy =Q eyx ) and, withmuch lower amplitude, an in-plane electric dipole (with only x-component, double of thatof the single cylinder in (a)). The origin of these multipolar components is detailed in themain text, in connection with Fig. 1(b). 21igure S3: Scanning electron microscope images of the different fabricated metasurfacesstudied in this work, comprising elliptical cylinder dimers with relative tilting: (a) θ = 0 ◦ ,(b) θ = 2 ◦ (for which we were not able to observe the quasi-BIC), (c) θ = 5 ◦ , (d) θ = 10 ◦ ,(e) θ = 20 ◦ and (f) θ = 30 ◦ . The scale bar is the same for all the images.22igure S4: (a) Schematic of the experimental setup used to capture the back focal planeimage of the objective, measure the SHG power levels as a function of pump power andpump polarization, and collect the transmission characteristics of the devices. (b) Measuredpump power at the output of the polarizer as a function of the HWP rotation angle beforeL1. (c) Beam radius with respect to the sample position measured using a knife edge.23able S1: Comparison of performances of SHG in dielectric metasurfaces. Efficiency isdefined as P SHG /P pump , where the power levels are average values. Platform Pump intensity(GW/cm ) Pump wave-length (nm) Efficiency ReferenceGaP 10e-3 1200 4e-5 This work(Pulse)GaP 1e-6 1200 2e-7 This work(CW) AlGaAs 0.22 1570 1.2e-5 AlGaAs 7 1550 8e-6 AlGaAs 1.72 1556 9e-6
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