Nonlinear PB phase elements with CP pump. a) Phases of the nonlinear harmonic waves generated from a C1 (1-fold symmetry) plasmonic antenna. Simulation and experiment results of linear absorption spectra of the nonlinear metasurface for SHG (a) and THG (b). Scanning electron microscope (SEM) images of metasurfaces. a) Top view of the C3 structure for SHG and (b) the C4 structure for THG.
Introduction
- Surface Plasmon Polaritons
- Intersubband Transitions from Quantized Energy Band in MQW
- Nonlinear Photonic Metasurface
- Spin Angular Momentum Control
- Overview of the Thesis
The transition energy can be tuned by changing the doping level, width and depth of the quantum well. In nonlinear photonics, due to mixing of the pump wave, the nonlinear polarization of the material acts as a source of new frequency. Nonlinear photonic metasurfaces have attracted much attention due to their ability to control the local amplitude, phase of the nonlinear response using the PB phase at the subwavelength scale.28-33.
In linear optical PB phase, the phase factor of circularly polarized incident beam, expressed as 𝑒𝑖2𝜙𝜎 where 𝜙 is the rotation angle of the meta-atom and 𝜎 is '+' or '-' sign indicating that the light's spin state (right circular) polarization respectively (RCP) and left circular polarization (LCP).27, 36 Such a PB phase in the nonlinear material polarization can be understood in a coordinate transformation process. After transformation, the expression for the nonlinear dipole moment is Ρ𝜃,𝜎𝑛𝜔= Ρ𝜃,𝐿,𝜎𝑛𝜔 𝑒−𝑖𝜎𝜃∝ 𝑒(𝑛𝃜1) 1.4.2) The nonlinear polarizability of the plasmonic antenna can be written as Therefore, by choosing a meta-atom with m-fold (𝑚 ≥ 3) rotational symmetry, we can control the spin state of the nonlinear signal (Figure 1.4.2).
The order of the nonlinear process and the rotational symmetry metaatoms (C1 to C4) determine the phase of the nonlinear wave during harmonic generation processes. In Chapter 2, I designed a three- and four-fold (C3 and C4) metaatom with rotational symmetry to control the spin state of the nonlinear signal from harmonic generation and achieve a giant nonlinear response of both SHG and THG.
Spin-controlled Nonlinear Harmonic Generations
Introduction
Design of Nonlinear Metasurface
- Design of MQW and Metasurface
- Simulation and Calculation of Nonlinear Response
One period MQW conduction band diagram with a coupled In0.53Ga0.47As/Al0.48In0.52As triple quantum well structure designed for 2nd and 3rd order giant nonlinear responses. Zij and Eij Zij are the element of the dipole moment and the transition energy of intersubband transitions between electronic subbands i and j, respectively. 2.1.2), where ω denotes the input frequency, 𝜂0 is 1/𝜀0𝑐, 𝜀0 is the transmittance in vacuum, 𝑐 denotes the speed of light in vacuum, 𝐼𝜔 denotes the intensity of the input beam, L denotes the thickness of the MQW layer, and 𝜒𝑒𝑓𝑓 is the effective nonlinear susceptibility expressed as 10, 44.
Vunit and VMQW are the volumes of the MQW region of the meta-atom before and after etching, respectively. Nonlinear susceptibility of the MQW structure as a function of the input pump wavelength (a) second order nonlinear susceptibility for SHG. b) third order non-linear susceptibility to THG. And Figure S2 c and d shows the normalized Ez field enhancement distribution induced in the meta-atom with 4-fold rotational symmetry, at FF and third harmonic (TH, λTH ~3.5 μm) frequency, respectively.
Cross section in plan view at the (a) FF and (b) SH frequency for the C3 meta-atom and at the (c) FF and (d) TH frequency for the C4 meta-atom. Simulation and experiment results of linear absorption spectra of the nonlinear metasurface for SHG (C3 structure) (a) and THG (C4 structure) (b).
Fabrication
In this case, I used a special composition of two materials, In0.53Ga0.47As / Al0.48In0.52As, where the lattice constants of the layers practically match well to the InP substrate. In our case, gold-gold thermo-compression wafer bonding was used for MQW layer transfer to a metal ground plane. To improve the adhesion of metal layer on the wafer and remove the oxidation layer, the MQW wafer was cleaned using Reactive Ion Etching (RIE) ((FAB star, O2 100sccm, 40mTorr, RF 100W, for 60 sec.) and by setting BOE ( buffered oxide i) etchant) for 10 seconds.
Metal layers of 10 nm titanium, 50 nm platinum, and 150 nm gold were deposited onto the MQW layer and. After bonding the wafers, the InP substrate, layer and In0.53Ga0.47As layer were removed by selective wet etching. After wet etching, to remove surface oxidation and improve adhesion of the metal layer, the MQW layer was cleaned with oxygen RIE (FAB star, O2 100 sccm, 40 mTorr, RF 100 W, 60 seconds).
To make a nanoresonator array, 5nm thick layer of titanium for adhesion layer and a 50nm thick Au for nanoresonator were evaporated on the MQW layer. For etching a metal layer and MQW layer, the patterned SiN layer was used as a dry etching mask.
Experiment
- Intersubband absorption measurment
- Nonlinear Optical Characterization
- Nonlinear Beam-steering Experiment
The dielectric constant of the MQW for the in-plane E-field polarization ( ) can be expressed by. Nonlinear optical measurements of the metasurface were measured via the nonlinear optical measurement setup shown in Figure. Nonlinear power conversion efficiencies for SHG (black dot) and THG (red dot) as functions of FF peak power or intensity.
In this measurement, the linearly polarized input beam from the CO2 laser is converted to RCP via a QWP located in front of the CO2 laser, and the RCP input beam is focused onto the metasurface via a ZnSe lens and a harmonic signal is generated on the metasurface. . The meta atom has a spatial change of the orientation angle ( , ) x y and the local phase changes of the nonlinear susceptibility are expressed as 𝜒𝑅𝑅𝑅(2)𝑒𝑓𝑓(𝑥, 𝑦) = 𝜒𝑅𝑅𝑅(2)𝑒 𝑓𝑓𝑒𝑖3𝜑(𝑥,𝑦 ) and 𝜒𝑅𝑅𝑅(3) 𝑥, 𝑦) = 𝜒𝑅𝑅𝑅𝑅(3)𝑒𝑓𝑓𝑒𝑖4𝜑(𝑥,𝑦) for SHG and THG respectively. The spatial variation of the orientation of the nanostructures is shown in the form of the angle 𝜑.
In this measurement, the linearly polarized input beam from the CO2 laser is converted to RCP by the QWP located in front of the CO2 laser, and the RCP input beam is focused on metasurface via ZnSe lens and a harmonic signal is generated. The RCP and LCP harmonic signals were selectively measured based on the adjustment of the polarizer as I mentioned before. As shown in Figure 2.4.9, the beam steering angles of the harmonic signals were measured based on the measurement of the lateral shifts of the detector (ddetector).
According to the basic reflective array theory, the beam steering angle with RCP component in the case of the RCP input pump can be expressed as.
Conclusion
The beam steering angles of the RCP output signals with both SHG and the THG generated from the C3 and C4 meta-atom based gradient metasurfaces, respectively, were in very good agreement with the theoretically calculated beam steering angles indicated above. The harmonic LCP output signals were almost equal to zero and some peaks are generated due to the active wavelength of QWP (input wavelength: 10.6 μm, SHG: 5.3 μm, THG: 3.5 μm and active wavelength of QWP : 9 μm, 5 μm, 3 μm) and manufacturing defect. Far-field beam steering profiles of the SHG (a) and THG (b) output of the phase gradient nonlinear metasurfaces with equal to 20° and 30° for SHG, and 15° and 30° for THG in the case of the RCP input pump.
The black line represents an LCP output and the red line represents an RCP output for each harmonic signal. I have experimentally demonstrated one chip system with spin-controlled SHG and THG and non-linear beam steering, as shown in Figure 2.5.1. The proposed approach will provide an efficient design platform for future applications based on nonlinear metasurfaces, such as nonlinear metasurface holography, nonlinear spectroscopy, nonlinear optical switching and modulation, and nonlinear information processing.
Schematic view of the concept of one chip system with spin-controlled SHG and THG and non-linear beam steering. Red, green, and blue beams indicate a fundamental frequency (FF) input pump beam, an SHG beam, and a THG beam, respectively.
Outlook
The Ez field distributions were monitored in the MQW layer (below 100 nm in the Au layer) using LCP input pump and RCP input pump (wavelength: 10.5 m) as input sources. In the case of the RCP input pump, as shown in Figure 3.1.2, the FF Ez field and the HF Ez field overlap well (simulated overlap factor: 1.33352, simulated by FDTD simulation). However, in the case of LCP input, the HF Ez fields marked by black circles in Figure 3.1.3 are weaker than in the case of RCP input.
Therefore, the FF Ez field and the HF Ez field do not overlap well (Simulated overlap factor simulated by FDTD simulation). SH, TH peak power ∝ (overlap factor)2. 3.1.1) Therefore, in this case, the peak harmonic power with the RCP input is 400 orders of magnitude higher than the peak harmonic power with the LCP input. As shown in Figure 3.1.3, the measured SHG-CD agrees well with the simulation result, however the measured THG-CD does not agree well with the simulation result.
I will aim to optimize C4-chiral plasmonic nanostructure and fabricate nonlinear beam steering using nonlinear gradient metasurface with C3-chiral and C4-chiral plasmonic nanostructure. SHG circular dichroism (CD) (a) and THG-CD (b) simulation and measurement results from C3-chiral and C4-chiral plasmonic nanostructures.
Conclusion
Summary
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