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Abstract
Focusing light down to subwavelength scales to enhance the light-matter interaction has been highly sought after, which has promoted significant researches and applications in nanophotonics. Plasmonic nanoantennae are a significant tool to achieve this goal since they can confine light into ultra-small volumes far below the diffraction limit. However, metallic materials have the property of central symmetry, resulting in weak second-order nonlinear effects. Here, we design plasmonic bowtie nanoantennae on thin-film lithium niobate (TFLN) for deep-subwavelength light confinement to boost the second-harmonic generation (SHG) in TFLN via the plasmonic hotspot enhancement. The SHG enhancement factor of about 20 times as compared to unpatterned TFLN is achieved in the experiment when resonantly excited by femtosecond laser. This work proposes a route for subwavelength nonlinear optics on the TFLN platform.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical nonlinearity lies in the core of modern photonics research and application, such as frequency conversion, detection, imaging, and quantum optics. However, the intrinsic nonlinear response of most materials is weak. Enhancing nonlinearity of weak light on the micro/nano scale is a major challenge for nonlinear optics. Plasmonic resonance, i.e., the collective oscillation of free-electron in metal with light, can confine light on the nanoscale and significantly enhance the light-matter interaction, i.e., increased (nonlinear) optical response [1–5]. The linear and third-order nonlinearity enhancement by plasmon has been well established. One seminal example is localized surface plasmon resonance (LSPR) or hotspot in resonant metallic nanostructures [1,6,7]. The plasmonic resonance results in strong localized electromagnetic fields in ultrasmall mode volumes far below the diffraction limit, which has been utilized for ultrasensitive sensing and detection. The sensitivity of LSPs enhanced Raman scattering or fluorescence has reached the single-molecule level [8–10].
Second-order nonlinearity on the other hand shows significant importance in photonics. And the second-order nonlinearity in small volumes is also particularly desirable. Metal is centrosymmetric; thus, the second-order nonlinearity must vanish in bulk and only exists at surfaces due to broken spatial inversion symmetry. Other ways to achieve SHG of metals is to break the symmetry in plasmonic nanostructures, such as metal nanocups [11,12], G-shaped antennae [13,14], split-ring resonators [15,16], and multi-resonant antennae [17–19]. Other ways to achieve plasmonics enhanced second-order nonlinearity includes the implementation of hybrid structures, like Au/Ag coated non-centrosymmetric dielectric/ferroelectric nanoparticles or non-centrosymmetric dielectric/ferroelectric crystal embedded at the plasmonic hotspot [20–22]. By leveraging the strong field enhancement, SHG in nanostructures features stability, tunability, coherence, fast response, and polarization sensitivity, which is highly powerful in frequency conversion, sensing, and quantum optics. In despite, the second order nonlinear conversion efficiency is still weak. Boosting SHG yield or nonlinear conversion efficiency on the subwavelength scale is still challenging yet a hot topic for nano-nonlinear optics.
The interplay of plasmonic resonance directly with second-order nonlinear materials is interesting and is expected to greatly boost SHG on the nanoscale. Second-order nonlinear effects are inherent in non-centrosymmetric materials like lithium niobate (LN) which has a large refractive index (${n_o} = 2.21$ and ${n_e} = 2.14$ at 1550 nm), strong second-order nonlinearity (${d_{33}} ={-} 27\; \textrm{pm}/\textrm{V}$, ${d_{31}} ={-} 4.5\; \textrm{pm}/\textrm{V}$) and electro-optic effect (${\gamma _{51}} = 32\; \textrm{pm}/\textrm{V}$). LN has been studied for decades in nonlinear optics for various types of nonlinear wave mixings. Recently, thin-film lithium niobate (TFLN) has emerged as a significantly promising integrated nonlinear photonic platform for micro-/nano-photonics with access to strong electro-optic and second-order nonlinear effects (LN) and strong light confinement (LN versus SiO2). Due to its excellent performance, TFLN nanostructures have been used for electro-optic modulators [23–25], frequency converters [26,27], entangled photons sources [28–30], and electro-optic/nonlinear metasurfaces [31–35]. To enhance the SHG conversion efficiency of LN nanostructures, mechanisms such as photonic crystal (PhC), bound states in the continuum (BIC) and guided-mode resonance (GMR) have been introduced and significantly increased the quality (Q) factor of the nanostructures [36–40]. Although the structures significantly enhance the Q factor, they are limited to the etching processing accuracy and the corresponding mode volume is still quite large as compared with plasmonics. Besides these researches, the investigation of plasmon on TFLN is still lacking.
Here, we experimentally demonstrate enhanced second-order nonlinear effect on TFLN by exploiting plasmonic hotpot in bowtie nanoantenna structures. About 20 times SHG enhancement is experimentally realized compared with unpatterned TFLN. The plasmon enhanced SHG signal in the TFLN is much stronger than that produced by the plasmonic structures via surface nonlinearity. The SH is high enough to be imaged by CCD (rather than using electron-multiplying CCD), and the latter can be neglected in our experiment. The normalized conversion efficiency is $1.3 \times {10^{ - 7}}$ under femtosecond laser pump at the telecom band. The plasmonic bowtie nanoantenna greatly reduces the mode volume to ∼$6 \times {10^{ - 6}}{({\lambda /n} )^3}$ and significantly enhances the interaction between light and matter, representing a new route for investigating subwavelength nonlinear optics on the TFLN platform.
2. Results and discussion
The plasmonic bowtie nanoantenna structure is fabricated on a 300-nm thick x-cut TFLN (NANOLN), bonded on a 2-µm thick silica buffering layer and a 500-µm thick silicon substrate. Both the plasmonic resonance and SHG is strongly dependent on the polarization of the optical field. The long axis of the Au bowtie nanoantenna is aligned along the z-axis of TFLN, to access the largest nonlinear coefficient ${d_{33}}$ or ${d_{zzz}}$ of LN when enhancement of the electric field in the gap of the triangle dimers is excited. The z-component nonlinear polarization ${P_z}({2\omega } )\; $ can be written as:
where $\omega$ is the frequency of incident pump $E_z$, $E_x$, and $E_y$ are the electric field components. The z-component electric field is greatly enhanced, resulting in a significant increase in the SHG. Figure 1(a) shows the schematic of the plasmonic bowtie nanoantenna structure on top of TFLN, converting the z-polarized fundamental harmonic (FH) pump to its second harmonic (SH) in the back-reflection configuration. The illustration of the plasmonic hotspot in the bowtie nanoantenna unit for SHG enhancement is shown in Fig. 1(b), which also shows the parameters defining the structure.
Fig. 1. Schematic of the plasmonic hotspot enhanced SHG on TFLN. (a) Schematic of Au bowtie nanoantenna array on TFLN for enhanced SHG. (b) Schematic of the bowtie nanoantenna unit. A, side length; G, gap; P, period. SEM images of (c) the plasmonic bowtie nanoantenna array and (d) the bowtie nanoantenna.
The periodic bowtie nanoantenna array is patterned using electron beam lithography (EBL). After lithography, a 3/50 nm thick Cr/Au layer is deposited via electron beam evaporation. The Au bowtie nanoantenna array is then obtained using the lift-off process. The bowtie nanoantenna consists of two tip-to-tip equilateral Au nanotriangles with a gap, G, varied from 25 nm to 95 nm and its side length $A = 310\; \textrm{nm}$. The period, P, of the bowtie nanoantenna array varies from 850 nm to 980 nm. The scanning electron microscopy (SEM) images of the periodic bowtie nanoantenna array and the unit structure are shown in Figs. 1(c) and 1(d), respectively. For comparison, we also designed the same plasmonic bowtie nanoantenna structures aligned along the y-axis of TFLN (not shown). The sample fabrication is conducted at the Center for Advanced Electronic Materials and Devices, Shanghai Jiao Tong University. More detailed processing process is given in Methods.
To analyze the optical resonance properties, the reflection spectra of the bowtie nanoantenna arrays is characterized within the wavelength range of 1450 nm to 1650 nm using a supercontinuum fiber laser, details of the measurement setup are given in Methods. Figure 2 gives the reflection spectra of z-oriented and y-oriented plasmonic bowtie nanoantenna under z-polarized and y-polarized illumination, respectively. In Figs. 2(a) and 2(b), the long axis of the Au bowtie nanoantenna is aligned along the z-axis and y-axis of TFLN, respectively. The pump polarized along the long axis leads to the dipole interaction of the plasmonic hotspot and the enhanced electric field is also along the long axis of the bowtie nanoantenna, thus, the z-oriented structures under z-polarized FH pump utilizing the largest nonlinear coefficient, ${d_{33}}$, of LN show a huge SHG enhancement. The y-oriented structures under y-polarized FH pump show no enhancement as compared with TFLN. Figure 2(c) [corresponding to Fig. 2(a)] shows the experimental reflection spectra for different $P$’s with $G = 25\textrm{nm}$. The central peak in the reflection spectrum corresponds to plasmonic resonance of the bowtie nanoantennae. This is verified by the absorption spectrum and the LSPR mode distribution from the simulation, see also Appendix A, as well as the enhanced SHG in the experiment. The resonance redshift with increased P, as predicted by the simulation in Fig. 2(e). The feature is exploited to match the plasmonic resonance with the pumping laser wavelength. The experimentally measured plasmonic resonance occurs at 1550 nm for $P = 910\textrm{nm}$. Figures 2(d) and 2(f) [corresponding to Fig. 2(b)] show the experimental and simulated reflection spectra for different $P$’s with $G = 25\textrm{nm}$. The results are similar to the z-oriented bowtie arrays. However, due to the birefringence effect of LN (${n_o} > {n_e}$), the resonance peak is redshifted for y-oriented bowtie arrays. The experimentally measured plasmonic resonance occurs at 1550 nm for $P = 890\textrm{nm}$.
Fig. 2. Reflection characterization. (a) Diagram of z-oriented bowtie nanoantenna under z-polarized illumination with SHG enhancement. (b) Diagram of z-oriented bowtie nanoantenna under y-polarized illumination without SHG enhancement. (c) Reflection spectra of z-oriented bowtie nanoantenna with different periods under z-polarized illumination. $G = 25\textrm{nm}$. (d) Reflection spectra of y-oriented bowtie nanoantenna with different periods under y-polarized illumination. $G = 25\textrm{nm}$. (e) Theoretical simulation corresponding to (c). (f) Theoretical simulation corresponding to (d).
In our study, plasmon resonance weakens as the gap increases. Figure 3(a) shows the experimental reflection spectra of z-oriented structures under z-polarized FH pump for different $G$’s with $P\; = 910\textrm{nm}$. A reflection peak is observed in the experiment and the simulated absorption spectra are shown in Appendix B. The reflection and absorption peaks redshift slightly and the reflection intensity is reduced as the gap decreases. Figure 3(c) shows the simulation results corresponding to Fig. 3(a). The approximately 80 nm deviation between the experimental and theoretical spectra arises from manufacturing errors. Figures 3(b) and 3(d) show the experimental and simulated reflection spectra of y-oriented structures under y-polarized FH pump for different $G$’s with $P\; = 890\textrm{nm}$. This orientation of the structure also induces plasmonic hotspot resonances, while the SHG utilizing the coefficient of LN is therefore much weaker (even weaker than TFLN under z-polarized FH pump). The SHG enhancement is not observed in our experiment.
Fig. 3. Reflection characterization. (a) Reflection spectra of z-oriented bowtie nanoantenna with different gaps under z-polarized illumination. $P = 910\textrm{nm}$. (b) Theoretical simulation corresponding to (a). (c) Reflection spectra of y-oriented bowtie nanoantenna with different gaps under y-polarized illumination. $P = 890\textrm{nm}$. (d) Theoretical simulation corresponding to (b).
The visualization of the local electromagnetic field is of interest to identify the modes of excitation and to assist in the design of plasmonic structures. Then, we analyze the electromagnetic field distribution of the designed bowtie nanoantenna arrays on TFLN. Figure 4(a) [Fig. 4(b)] shows the simulated reflection spectra of z-oriented (y-oriented) bowtie nanoantenna array under z-polarized (y-polarized) illumination. The inset is a cross-sectional view of the plasmon hotspot structure. The structural parameters, G and P, are engineered to make sure that their plasmonic resonance wavelength centers at around 1550 nm, to match that of the femtosecond laser in the experiment. Figure 4(c) [Fig. 4(d)] shows the distribution of the electric field enhancement factor ($|E |/|{{E_{\textrm{in}}}} |$) of the z-oriented (y-oriented) bowtie nanoantenna arrays at the nominal resonant wavelength at $x = 25\; \textrm{nm}$. The electric field is localized in the gap and the maximum enhancement factor is 73. Figure 4(e) [Fig. 4(f)] shows the distribution of the electric field enhancement factor of the z-oriented (y-oriented) bowtie nanoantenna arrays at the nominal resonant wavelength at $x = 0\; \textrm{nm}$. According to theoretical calculations, the electric field enhancement factor on the surface of TFLN at the resonant wavelength is even higher than that at the center of bowtie nanogap, because of the sharp edge of the bowtie bottom. Compared to unpatterned TFLN, the hotspot of z-oriented bowtie and have a maximum 180-fold field enhancement factor. Figure 4(g) [Fig. 4(h)] shows the distribution of the electric field enhancement factor of the z-oriented (y-oriented) bowtie nanoantenna arrays at the nominal resonant wavelength at $x ={-} 5\; \textrm{nm}$. Due to the strong electric field localization of the plasmon hotspot structure, there is still a 61-fold field enhancement inside LN. Although part of the electric field is localized in the air, there is still a high enhancement factor inside LN for SHG enhancement.
Fig. 4. Simulation of reflection and electric field enhancement in the bowtie nanoantenna. (a) Simulated reflection spectra of z-oriented bowtie nanoantenna under z-polarized illumination. $P = 972\textrm{nm},\textrm{}G = 25\textrm{nm}$. (b) Simulated reflection spectra of y-oriented bowtie nanoantenna under z-polarized illumination. $P = 960\textrm{nm},\textrm{}G = 25\textrm{nm}$. (c, e, g) Resonant electric field enhancement factor of z-oriented bowtie nanoantenna arrays under z-polarized illumination. $x=25, 0, -5\textrm{nm}$, respectively. (d, f, h) Resonant electric field enhancement factor of y-oriented bowtie nanoantenna arrays under y-polarized illumination. $x = 25,\textrm{}0,\textrm{} - 5$, respectively.
To quantitatively verify the performance of our designed plasmonic hotspot structure, we performed nonlinear tests using the fabricated samples using a home-built nonlinear microscope. The generated SH spectrum of a tightly focused z-polarized femtosecond laser (central wavelength 1560 nm, repetition rate 80 MHz, pulse duration 120 fs) is shown in Fig. 5(a). Details about the experimental setup is given in Methods. Figure 5(b) shows the SHG spectra of z-oriented (red line) bowtie nanoantenna arrays under z-polarized FH pump, y-oriented (blue line) bowtie nanoantenna arrays under y-polarized FH pump and unpatterned TFLN (black line) under z-polarized FH pump, respectively. An SHG enhancement from the z-oriented bowtie hotspot structure is obvious. The peak wavelength of SHG is $774.9\; \textrm{nm}$. About 20 times SHG enhancement is experimentally realized as compared with unpatterned TFLN while no enhancement is observed for the y-oriented bowtie structure under y-polarized FH pump. The measured maximum power for hotspot enhanced SHG is $0.26\; \textrm{nW}$ at the input FH power of $2.0\; \textrm{mW}$. The corresponding nonlinear conversion efficiency is $1.3 \times {10^{ - 7}}$. The calculation method is shown in the Appendix C, where a detailed comparison of our device's performance with typical reports is also shown in Table 1.
Fig. 5. Experimental result of SHG enhancement. (a) Spectrum of the FH femtosecond laser. (b) SH spectra from the z-oriented, y-oriented bowtie nanoantenna arrays with $P = 950\textrm{nm}$ and unpatterned TFLN. (c) Quadratic relationship between SH and FH power with different $G$’s. $P = 950\textrm{nm}$. (d) SHG enhancement factor varying with P and G.
The designed structure is more sensitive than Mie resonances [23] and resonant metasurfaces [38], with a comparable conversion efficiency. Rainbow metasurface [41] composed of multiple layers of metal structures has also been reported to enhance second-order nonlinear effects. Our plasmonic hotspot structure, utilizing a straightforward lift-off process, greatly reduces manufacturing expenses and decreasing mode volume. Metal-LN composite structures enhancing optical nonlinearity have been rarely reported. The SHG conversion efficiency of bowtie hotspot structures has surpassed that of LN gold nanoring structures [30].
Figure 5(c) shows the quadratic relationship of SHG with respect to the pump power for the bowtie nanoantenna array with different gaps, $G$’s, from 25 nm to 95 nm. The corresponding period, P, is $910\; \textrm{nm}$. Compared with unpatterned TFLN, enhanced SHG is achieved at the resonant wavelengths for different gaps and periods. The SHG signal is stronger as the gap decreases. Figure 5(d) shows the SHG enhancement factor of the plasmonic bowtie nanoantenna array with varied gaps, $G$’s, and periods, $P$’s, as compared to the unpatterned TFLN. As can be seen, the plasmonic enhancement is robust against the parameters as well as fabrication errors. It is worth noticing that the simulated mode volume is only ∼$6 \times {10^{ - 6}}{({\lambda /n} )^3}$ and n is the refractive index of LN, as defined by
The polarization dependence of the plasmon excitation and enhanced SHG is shown in Figs. 6(a) and 6(b) for the z- and y-orient bowtie nanoantenna array under z-polarized FH pump. About 6 times SHG enhancement is experimentally realized for the y-orient bowtie nanoantenna array under z-polarized FH pump as compared with unpatterned TFLN. Detailed results are shown in the Appendix C. The experimental results show the strong polarization sensitivity of the hotspot enhanced SHG, as both the plasmonic resonance and second-order nonlinearity is intrinsically polarization dependent. Figure 6(c) shows the SH spots of the y-oriented bowtie under z-polarized FH pump nanoantennae with $P = 920\; \textrm{nm}$ and $G = 35,\; 45,\; 55,\; 65,\; 75,\; 95\; \textrm{nm}$, respectively. The SHG arises from the enhancement from the LSPR of the Au triangles, rather than the hotspot in the nanogap. The strength of SHG signal gradually decreases as the gap increases. Besides, the y-oriented bowtie structures under y-polarized illumination in the resonant wavelength of 1560 nm utilize the smaller effective coefficient ${d_{31}}$ of LN. The SHG enhancement is not experimentally observed, indicating that the previously observed SHG signal arise from LN rather than Au. (The SHG from Au surface can be observed using more sensitive detectors like electron-multiplying CCD or photomultiplier tube.) Fig. 6(d) shows the SH spots of the z-oriented bowtie nanoantennae with $G = 25\; \textrm{nm}$ and $P = 870,\; 890,\; 910,\; 930,\; 950\; \textrm{nm}$, and unpatterned TFLN respectively. The diameter of the focused FH on the sample is ∼$5\; {\mathrm{\mu} \mathrm{m}}$. The utilized nonlinear coefficient of LN is ${d_{33}}$ for the z-polarized FH input. When P is small ($P = 870\; \textrm{nm}$), the coupling effect of different bowtie antennas in the array is strong, resulting in the weakening of the electric field in the hotspot. With the increase of P ($P = 910\; \textrm{nm}$), the coupling effect is weakened and the heat loss is reduced, resulting in the stronger electric field localization. When P ($P = 950\; \textrm{nm}$) increases further, the number of Bowtie antennas irradiated by incident pump light decreases, resulting in the weakening of the overall SHG signal.
Fig. 6. Experimental result of SHG enhancement. Dependence of SHG enhancement on the polarization of FH as the bowtie nanoantenna array is arranged in the (a) z direction and (b) y direction. (c) SH spots of the bowtie nanoantennae arranged in the y direction with $P = 960\textrm{nm}$ and $G = 95,\textrm{}85,\textrm{}75,\textrm{}65,\textrm{}55\textrm{}$ and $45\textrm{nm}$, respectively. (d) SH spots of the bowtie nanoantennae arranged in the z direction with $G = 25\textrm{nm}$, $P = 870,\textrm{}890,\textrm{}910,\textrm{}930,\textrm{}950\textrm{nm}$, and unpatterned TFLN respectively.
3. Conclusion
In summary, we theoretically and experimentally demonstrate plasmonic enhanced SHG on TFLN via resonance of bowtie nanoantenna structures on TFLN. The plasmonic bowtie nanoantenna greatly reduces the mode volume and significantly enhances the nonlinear interaction. About 20 times enhancement of SHG intensity is realized under resonant fs laser excitation and the SHG enhancement in metal hotspots is much larger than 20-fold. The achieved nonlinear conversion efficiency reaches $1.3 \times {10^{ - 7}}$. This work proposes a route for subwavelength nonlinear optics on the TFLN platform.
4. Methods
Device fabrication. The plasmonic bowtie nanoantenna array is fabricated on a 300-nm thick x-cut TFLN wafer on silicon hold. Firstly, a layer of polymethyl methacrylate (PMMA) photoresist is spin coated on the TFLN chip at a speed of 4000 rpm and baked at 180°C for 2 minutes. The thickness of the photoresist is approximately 220 nm. Next, a layer of photoresistive conductive adhesive (AR-PC 5090) is spin coated and baked at 120°C for $2$ minutes to increase the conductivity of the sample. Then, the mask for the bowtie nanoantenna array patterns is defined using electron beam lithography (EBL), with a spot size of 15 nm and beam current of 0.5 nA. After EBL, the conductive adhesive is removed in deionized water for $15$ seconds, and the PMMA photoresist is developed for 90 seconds in 1:3 MIBK/IPA developer and fixed with IPA for 1 minute. Then, a layer of 3/50 nm Cr/Au is deposited on the prepared photoresist pattern via electron beam evaporation. The Cr layer is used to strengthen the adhesiveness of Au to LN. Finally, the bowtie nanoantenna array structure is obtained after the lift-off process.
Optical characterization. The optical properties of the bowtie nanoantenna samples are characterized using a home-built nonlinear optical microscope. The input light is tightly focused on the sample by a NIR microscope objective (OptoSigma, 50×, NA = 0.67). The reflection light is collected by the same objective and reflected by a beam splitter (50:50, 600-1700nm). A flip mirror is added after the beam splitter to guide the beam into two arms. The transmitted light is coupled into a multimode fiber (the coupling efficiency is 70%) and recorded by a spectrometer (Anritsu, MS9740A). The reflected light is imaged using a NIR camera. The (linear) reflection spectra of the arrays covering the wavelength range of 1520 nm to 1650 nm is characterized using a supercontinuum fiber laser. For the nonlinear characterization, the SHG signal is achieved using a femtosecond laser (central wavelength 1560 nm, repetition rate 80 MHz, pulse duration 120 fs). The SHG spot is imaged using a visible camera before passing a short-pass filter.
Appendix A: numerical calculation
Figures 7(a) and 7(b) show the simulated absorption spectra of z-oriented structures under z-polarized FH pump and y-oriented structures under y-polarized FH pump when $P = 870,\; 890,\; 910,\; 930,\; 950,\; 970\; \textrm{nm}$. The Gap $G = 25\textrm{nm}$. With the increase of the period, the plasmon absorption peak gradually redshifts, and the plasmon resonance around 1560 nm can be realized. Figures 7(c) and 7(d) show the simulated absorption spectra of the bowtie nanoantenna arrays when $G = 25,\; 30,\; 35,\; 45,\; 55,\; 65,\; 75,\; 95\; \textrm{nm}$. The period $P = 910\; \textrm{nm}$. With the increase of the gap, the plasmon absorption peak only slightly blueshifts. The peak in the absorption spectra indicates the metallic loss at the condition of plasmonic resonance. It should be noted that there is an approximately 80 nm discrepancy between the experimental and theoretical resonance wavelength.
Fig. 7. Simulated absorption spectra of the bowtie nanoantenna arrays for different $P$’s and $G$’s. (a) and (c) Absorption spectra of the z-oriented bowtie nanoantenna arrays under z-polarized illumination. (b) and (d) Absorption spectra of the y-oriented bowtie nanoantenna arrays under y-polarized illumination.
The computational domains are covered with perfectly matched layers and periodic Bloch boundary conditions are used in the z- and y-direction. Figures 8(a) and 8(b) show the schematic of the bowtie nanoantenna unit and the enlarged schematic of the tip. To consider the fabrication errors, P and G are fixed at $980\; \textrm{nm}$ and $25\; \textrm{nm}$. Figures 8(c)-8(f) show the reflection spectra of the bowtie array with different $a$’s, $h$’s, ${r_1}$’s and ${r_2}$’s. The simulation results infer that for a sample with well-defined a and h, the errors introduced by the factors ${r_1}$and ${r_2}$ are small and have a negligible impact on the overall performance.
Fig. 8. Design and simulation of the bowtie nanoantenna array. (a) Schematic of the bowtie nanoantenna unit and (b) Enlarged view of the tip. Reflection spectra for different (c) $a$’s, (d) $h$’s, (e) ${r_1}$’s, and (f) ${r_2}$’s.
Appendix B: reflection spectrum measurement
Figure 9 shows the experimentally reflection spectra of z-oriented bowtie nanoantenna under y-polarized illumination and y-oriented bowtie nanoantenna under z-polarized illumination. The resonance redshift with increased P. The reflection peaks are deeper as the G increases indicates that z-oriented bowtie nanoantenna under y-polarized illumination and y-oriented bowtie nanoantenna under z-polarized illumination cannot excite hot spot resonance.
Fig. 9. (a) Diagram of z-oriented bowtie nanoantenna under y-polarized illumination. (b) Diagram of y-oriented bowtie nanoantenna under z-polarized illumination. (c) Experimental reflection spectra for the z-oriented bowtie nanoantennae with different periods under y-polarized illumination. G = 95 nm. (d) Experimental reflection spectra for the y-oriented bowtie nanoantennae with different periods under z-polarized illumination. G = 95 nm. (e) Experimental reflection spectra for the z-oriented bowtie nanoantennae with different gaps under y-polarized illumination. P = 880 nm. (f) Experimental reflection spectra for the y-oriented bowtie nanoantennae with different gaps under z-polarized illumination. P = 920 nm.
Appendix C: nonlinear experiments and SHG efficiency
The diagram of the SHG experimental setup is shown in Fig. 10(a). The white light source is used to image the bowtie antenna. The beam splitter (BS) before the white light source can be flipped to collinear with the femtosecond laser. The SHG signal is achieved using a femtosecond laser (central wavelength $1560\; \textrm{nm}$, repetition rate $80\; \textrm{MHz}$, pulse duration $120\; \textrm{fs}$). The femtosecond laser peak power calculated with the given parameters is $1.06\; G\textrm{W}/\textrm{c}{\textrm{m}^2}$. We focus the pump onto the sample using an objective lens (OptoSigma, 50×, NA = 0.67, $\textrm{WD} = 10\textrm{mm}$, $f = 4\; \textrm{mm}$). According to the Rayleigh criterion, $D = \frac{{2.44\lambda f}}{d}$, where d is the diameter of the incident femtosecond pump and D is the diameter of the spot. With $d = 3.4\; \textrm{mm},\textrm{}\lambda = 1550\; \textrm{nm},\; f = 4\; \textrm{mm},$ we can derive the theoretical spot size to be $4.45\; {\mathrm{\mu} \mathrm{m}}$. The experimental size is measured to be $5\; {\mathrm{\mu} \mathrm{m}}$.
Fig. 10. (a) Schematic of the SHG experimental setup. (b) SHG effect of z-oriented bowtie arrays under z-polarized illumination. (c) SHG effect of y-oriented bowtie arrays under z-polarized illumination.
Figures 10(b) and 10(c) show the SHG spectra of z-oriented bowtie arrays under z-polarized illumination and y-oriented bowtie arrays under z-polarized illumination, respectively. About 6 times SHG enhancement is experimentally realized for the y-orient bowtie nanoantenna array under z-polarized FH pump as compared with unpatterned TFLN. This result shows the superior electric field localization of plasmon hot spot resonance in x-cut TFLN.
The femtosecond pulsed laser is measured to calculate the SHG conversion efficiency, as shown in Fig. 5(a). In the SHG measurement setup, the power of the incident pump is about $52\; \textrm{mW}$. The transmission of the beam splitter cube is 42%. The transmission and reflection of the plate beam splitter are 33% and 64%. The transmission of the objective, short pass filter, and aspherical Lens are 69%, 92%, and 98%. The coupling efficiency of the multimode fiber is 70%. Therefore, the light that hits the sample is about $2\; \textrm{mW}$ and the SHG signal is 0.26 nW. The corresponding nonlinear conversion efficiency is$\; 1.3 \times {10^{ - 7}}$. Using a peak intensity of $1.06\; \textrm{GW}/\textrm{c}{\textrm{m}^2}$, the normalized SH conversion efficiency is $1.23 \times {10^{ - 7}}/({\textrm{GW}/\textrm{c}{\textrm{m}^2}} )$.
The finite element method is used to estimate the theoretical SHG conversion efficiency of the fabricated bowtie hotspots. We fix the intensity of the pump to be $1.06\; \textrm{GW}/\textrm{c}{\textrm{m}^2}$, the same as in the experiment. Using a peak intensity of the experiment, the peak power in each cell is 10.2 W. In the theoretical model, $P = 910\; \textrm{nm}$ and the gap $G = 25\textrm{nm}$. Firstly, the optical response of the structure at the FH is computed. The electric field ($E$) at the FH induces a nonlinear polarization P. Then, the components of P is calculated according to the second-order optical properties of LN, which also leads to the SH field distribution. Finally, an area integration of the reflected power flux is performance to get the SH power. The SHG conversion efficiency is calculated to be$\; 6 \times {10^{ - 6}}$. The comparison of efficiency to other literature of similar studies that explore SHG in nanostructured LN platforms is shown in Table 1.
Table 1. Comparison of SHG conversion efficiency
Funding
National Natural Science Foundation of China (12074252, 12192252, 62022058); National Key Research and Development Program of China (2022YFA1205101); Yangyang Development Fund.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding authors upon reasonable request.
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