Letter pubs.acs.org/NanoLett
Modal Engineering of Second-Harmonic Generation in Single GaP Nanopillars Reza Sanatinia,† Srinivasan Anand,† and Marcin Swillo*,‡ †
School of Information and Communication Technology, KTH Royal Institute of Technology, Electrum 229, S-164 40 Kista, Sweden School of Engineering Sciences, KTH Royal Institute of Technology, S-106 91 Stockholm, Sweden
‡
S Supporting Information *
ABSTRACT: We report on modal dispersion engineering for second-harmonic generation (SHG) from single vertical GaP nanopillars/nanowaveguides, fabricated by a top-down approach, using optical modal overlap between the pump (830 nm) and SHG (415 nm). We present a modal analysis for the SHG process in GaP nanopillars and demonstrate efficient utilization of the longitudinal component of the nonlinear polarization density. Our SHG measurements show quantitatively the presented model. We experimentally demonstrate that polarization beam shaping and field distribution modification of the radiated SHG light, at nanometer scale, can be achieved by tuning the pillar diameter and linear pump polarization. SHG from single pillars can be used as femtosecond nanoscopic light sources at visible wavelengths applicable for single cell/molecular imaging and interesting for future integrated nanophotonics components. While this work focuses on GaP nanopillars, the results are applicable to other semiconductor nanowire materials and synthesis methods. KEYWORDS: Nanopillar, second-harmonic generation, modal dispersion, polarization, nanowaveguide, gallium phosphide
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semiconductor NWs/NPs enables efficient guiding of light through water and other liquid media, which is very important for biological and biochemical analysis.7 Recently, SHG-form NWs has been proposed as an ultracompact optical correlator,4 while more functions and applications are expected to emerge in the future for integrated nanophotonic components.4,7 Among semiconductor materials, zincblende GaP, which belongs to the 4̅3m space group, with its high second order nonlinear coefficient,29 broad transparency range, low optical absorption,30 and high thermal conductivity is an excellent candidate for SHG. GaP NWs have also been demonstrated to be biocompatible.31,32 Although 4̅3m semiconductors lack birefringence, efficient SHG can be achieved at the macroscopic scale, by satisfying momentum conservation of optical waves, using different forms of phase matching methods.33−36 At the nanoscopic scale, alternative approaches can be employed. In the case of NWs/NPs, the distinctive optical resonances of these structures can also enhance the pumping electric field at certain wavelengths.6,37 Plasmon-enhanced generation, using metallic plasmonic resonances, has also been suggested to enhance the electric field and therefore increase the second harmonic signal.22,38 Previous reports on SHG in NWs/NPs can be broadly divided in two categories: (1) SHG from NWs lying on a substrate where the pump is illuminated
onlinear optical properties of semiconductor nanostructures, very recently, have attracted a lot of research interest both for better understanding of light-matter interaction at the nanoscale and for potential applications using sum, difference, and higher harmonic generation.1−3 The main drive for applications has been in two categories: obtaining smaller footprint for nonlinear elements in nanophotonic devices4,5 and novel applications1,6−8 using the unique optical properties of these nanostructures. Second-harmonic generation (SHG) is the lowest order of nonlinear optical phenomena and the most widely studied. In the SHG process, two photons with fundamental angular frequency (ω) convert into one photon at an angular frequency 2ω, which satisfies energy conservation. SHG is of great importance in many applications including generation of visible coherent light sources,1 probing surfaces,9,10 quantum information science,11,12 identification of crystal structure,13,14 photodynamic therapy,15 imaging in scattering media,16,17 and nonlinear microscopy,18 to name a few. In this respect, nanowires(NW)/ nanopillars(NP) of noncentrosymmetric semiconductors have accounted for a large part of recent studies on SHG in semiconductor nanostructures.1,2,4,10,14,19−22 Because of the large surface to volume ratios and the relatively high dielectric constants, semiconductor NWs/NPs have been used as nanoscopic light sources for highly localized excitation,18,23 in vivo imaging,24 and nanoendoscopy.25 Additionally, NWs/NPs in vertical geometries can serve as scaffolds for growth of cells and neural networks.26−28 The large refractive index of © 2014 American Chemical Society
Received: July 4, 2014 Revised: August 11, 2014 Published: August 26, 2014 5376
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Figure 1. (a−e) Electric field profiles for the different guided modes in a 250 nm diameter GaP nanopillar: pump (a,b) with 830 nm wavelength and the SHG at 415 nm (c,d,e). x, y and z correspond to the crystallographic axes of GaP. (a) Ex of the fundamental mode (HE11) for pump. (b) Ez of the fundamental mode (HE11) for pump. The intensity of the electric field, Ez, is normalized to the maximum intensity of Ex in panel a. (c,d) A possible superposition of TM01 and HE21 modes and of TE01 and HE21 modes, respectively. The arrows in (c) and (d) indicate the final polarization given by the superposition. (e) Ez component of TM01 mode.
COMSOL 4.3b. Figure 1a,b shows the profiles of Ex and longitudinal (Ez) components of the electric field, respectively, for the fundamental guided mode (HE11) in a 250 nm diameter GaP NP. This is the only mode in a cylindrical dielectric waveguide, which does not have a cutoff, and thus can propagate at any waveguide diameter.47 This is the guided mode for the pump, and has Ex and Ez as the dominant electric field components. The extinction ratio between the Ex and Ey polarizations is larger than 20 dB. For GaP, and all the 4̅3m crystals, the only nonzero components of second-order nonlinear susceptibility tensor are d14 = d25 = d36 = d. Hence, the second order nonlinear polarizations, along the crystallographic axes are as follows
perpendicular to the wire axis where the wires are treated as Mie scatterers6,14 and (2) vertical NWs where the pump is parallel to the axis and waveguiding has been taken into account.10,22 For many of the aforementioned applications, vertical geometry of NWs/NPs would be beneficial. In this Letter, we demonstrate a novel way to efficiently employ the tight confinement of light, using pump polarization and pillar (waveguide) geometry for modal engineering in single vertical GaP NPs, to generate second harmonic light. The longitudinal component of the nonlinear polarization density in GaP nanowaveguides adds an extra mechanism for SHG. While this method is directly applicable to all semiconductor NWs/NPs with similar 4̅3m space group, for example, zincblende crystals, it can be extended to other materials such as z-cut LiNbO3. We also demonstrate that it is possible to produce second-harmonic radiation from single GaP NPs with desired polarization beam pattern, for example, doughnut-shaped and two-lobe pattern, by tuning the pillar geometry and linear pump polarization. While the focus of this work is to employ bulk nonlinearly to generate SHG, it is possible to effectively use the surface contribution to SHG, in NPs with smaller diameters, to enhance the SHG light even further.10 We characterized polarization of the emitted SHG from individual NPs with different diameters, using a 100 fs pulsed laser at 830 nm wavelength as the pump. In an optimized configuration, we demonstrate enhancement of SHG due to the strong confinement of the guided pump. We develop an optical model for SHG in single GaP NPs based on modal analysis, which quantitatively explains the observed results. Our findings are also applicable for epitaxially grown nanowires,39−44 especially with zincblende crystal structure,39,40,43 where several micron long wires can in principle be obtained and thus increasing the interaction length. In the following, we present an analysis of the guided modes for the pump and SHG in the GaP NPs together with their polarization properties. Here we use the conventional nomenclature for optical modes in a cylindrical dielectric waveguide.45,46 The electric field mode profiles in the pillars with different diameters for both pump (830 nm) and the SHG light (415 nm) were calculated by finite element method using
Px(2) = 2dEy ·Ez = 2dET ·Ez sin θ P(2) y = 2dEx · Ez = 2dET · Ez cos θ Pz(2) = 2dEx ·Ey = d(ET )2 sin 2θ
(1)
where ET and Ez are the transverse (x−y plane) and longitudinal electric fields of the guided pump (830 nm), respectively; and θ is the angle between the pump polarization and x-axis in the x−y plane. Now, we consider two cases: (i) When the pump polarization is along x-axis, θ = 0°, and therefore the guided mode consists of Ex and Ez. In this case, (2) P(2) = 2dEx·Ez and P(2) = 0. (ii) When the pump x = 0, Py z polarization is oriented at θ = 45°. In this case, the transverse component of the nonlinear polarization according to eq 1 can (2) be written as PT,45° = 2dET·Ez, while the longitudinal 2 component of the nonlinear polarization is P(2) z,45° = d(ET) . Considering the symmetry of the transverse and longitudinal components of the electric field for the guided pump in the fundamental mode HE11, (Figure 1a,b), the nonlinear polarization density can excite four modes at the SHG wavelength. These modes, based on the effective refractive index in descending order, are the TE01, the two degenerate modes of HE21, and TM 01 (Supporting Information, S1).46 The degeneracy in the HE21 mode results from the circular geometry of the waveguide. Because of the crystal symmetry and waveguide geometry, second-harmonic light will be guided 5377
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in the superposition of TE01 + HE21 or TM01 + HE21 modes (Figure 1 c,d), depending on the pump polarization. As indicated in eq 1 for a linear pump polarization along x-axis (θ = 0°), the only nonzero nonlinear polarization is P(2) y which has the best projection on TE01+ HE21 due to similar symmetry. On the other hand, for the pump polarization at θ = 45° both nonlinear polarization densities, the transverse P(2) T,45° and the (2) longitudinal P(2) , should be considered. P has the best z,45° T,45° (2) projection on TM01+ HE21, whereas Pz,45° has a similar symmetry as the longitudinal electric field component of TM 01 mode (Figure 1e). The TM 01 mode, can be constructively excited only by the electric field of second harmonic wavelength, E(2ω), generated at a certain angle α, corresponding to the wavevector for that mode (Supporting Information, S2). The E(2ω) field is generated at the angle α due (2) to the nonlinear polarization Pz,45° ·sin α. Since energy is carried by the transverse component of the electric field, E(2ω) = E(2ω)· x (2) (2) cos α, we consider projection of Pα = Pz,45°·sin α·cos α on the transverse electric field distribution of the TM01 mode. As we applied the nondepleted pump approximation, generation of second harmonic light in each guided mode can be treated independently. Therefore, the final polarization of SHG at the end of the NP is defined by the electric field overlap, absorption and modal dispersion. For pillars with large diameters above 400 nm (Supporting Information, S3), the effective refractive indices of the SHG (at wavelength 415 nm) guided modes converge, which indicates preservation of polarization. On the contrary, for smaller diameters the dispersion relation suggests that the polarization of SHG at the output depends on the propagation length (NP length). However, at the SHG wavelength, which is above the bandgap of GaP,30 absorption loss has also to be considered. By introducing loss, it is found that the modal dispersion has a much smaller influence on the polarization of SHG (Supporting Information, S4). We should note that the loss is sufficiently small, which allows us to still use the slowly varying amplitude approximation for SHG simulation. The calculated electric field profiles were used to determine the second order nonlinear polarization (using the electric field profile at the pump wavelength, eq 1). Subsequently, the inner product between the amplitude of nonlinear polarization and the corresponding guided modes at the second-harmonic wavelength is obtained and is shown in Figure 2a. The inner (2) product values of P(2) y and TE01 + HE21, and of PT,45° and TM01 + HE21 are near unity for pillars with diameters above 400 nm. These values drop for smaller diameters due to the leakage of the electric field outside the NP while the nonlinear polarization is only inside the pillar. The inner product between P(2) and TM01 has a peak value around the NP α diameter of 200 nm, which is an indication of the strong longitudinal component of the electric field. Therefore, it significantly contributes to SHG for the pump polarization at 45° for which the maximum intensity of SHG is also expected. The amplitude of the SHG light in each mode at the end of NP is obtained by integrating the inner product of the nonlinear polarization and the corresponding guided mode over the length of the NP. The superposition of all the excited modes at the end of NP defines the final polarization and intensity of SHG. Figure 2b shows the ratio between the SHG intensity for pump polarizations at θ = 45° to that along x-axis, θ = 0°, at the beginning of the pillar. As it can be seen, the SHG intensity is always larger for the pump polarization along 45°. Here we
Figure 2. (a) Inner product of the amplitude of the nonlinear polarization profiles along different directions and the corresponding guided modes in GaP nanopillars as a function of pillar diameter. The pump wavelength is 830 nm and its polarization is indicated according to the crystallographic axes. (b) The curve shows the ratio of SHG intensity for pump polarization at θ = 45° (45° to the crystallographic axis) to that at θ = 0° for different pillar diameters. For the pillar diameters below 200 nm (shaded area) surface contribution to the SHG should also be taken into account.
note that for pillars with diameters smaller than 200 nm the surface contribution should be taken into account.10 As seen above, the polarization and intensity of SHG in a single NP can be controlled by engineering the excitation of different modes, namely TE01 + HE21, TM01 + HE21, and TM01. To validate this experimentally, we fabricated the GaP NPs using undoped (100) GaP substrates by dry etching. The details of fabrication are given in the Supporting Information, S5. The NPs were etched by inductively coupled plasma reactive ion etching (ICP-RIE) using CH4/H2/Cl2 chemistry.48 The etch parameters were optimized to obtain near-cylindrical profiles of the NPs. Representative SEM images of the fabricated GaP NPs are shown in Figure 3a,b. The pillar diameters ranged from 170 to 400 nm; their heights were ∼0.9 μm. The fabricated pillars are either isolated or in arrays with large spatial distance and are optically uncoupled. A Ti:Sapphire laser with 100 fs pulses and a central wavelength of 830 nm at 82 MHz repetition rate was used as the pump for SHG measurements in a transmission configuration setup. We used a rotatable half-wave plate to change the linear polarization of the pump. The laser beam with the average power of 30 mW was focused on individual GaP NPs using an infinity corrected 5× microscope objective with a numerical aperture of 0.15. In the focal region of the lens, the spot size of the pump is approximately 10 μm, which is much larger than the NP diameters (
