Enhancing higher-order modal response in multifrequency atomic force microscopy with a coupled cantilever system

• Wendong Sun,
• Jianqiang Qian,
• Yingzi Li,
• Yanan Chen,
• Zhipeng Dou,
• Rui Lin,
• Peng Cheng,
• Xiaodong Gao,
• Quan Yuan and
• Yifan Hu

Beilstein J. Nanotechnol. 2024, 15, 694–703, doi:10.3762/bjnano.15.57

• , including increasing the modal frequency of the original cantilever and generating additional resonance peaks, demonstrating the significant potential of the coupled system in various fields of AFM. Keywords: atomic force microscopy; coupled system; higher-order modes; macroscale; multifrequency AFM

• effect of higher-order modes has not been compared with traditional cantilever beams. Therefore, further simulation analyses and experiments are required to validate the practical application of this model. In this work, all research is based on an enlarged macroscale cantilever, which was proportionally

• the higher-order modal response of the coupled system gradually increases, which will improve the sensitivity of the detection and promote the development of multifrequency AFM utilizing higher-order modes of the cantilever to image sample properties. Finite element analysis Model size and simulation

Observation of multiple bulk bound states in the continuum modes in a photonic crystal cavity

• Rui Chen,
• Yi Zheng,
• Xingyu Huang,
• Qiaoling Lin,
• Chaochao Ye,
• Meng Xiong,
• Martijn Wubs,
• Yungui Ma,
• Minhao Pu and
• Sanshui Xiao

Beilstein J. Nanotechnol. 2023, 14, 544–551, doi:10.3762/bjnano.14.45

• . Light blocking by region B could be easily observed for the lower-order modes whose indices are lower than (3,3). For higher-order modes, large mode profiles need a larger size in region B to build a higher potential barrier to confine the light. Due to C4 symmetry of the structure, all Mpq and Mqp

• eigenwavelengths than the low-order modes. This trend is well followed by the low-order mode in Figure 4b and the higher-order modes in Figure 4c. However, the resonances in Figure 4c show, counterintuitively, higher Q factors for the resonances at longer wavelength. This might be due to a different influence of

Numerical analysis of vibration modes of a qPlus sensor with a long tip

• Kebei Chen,
• Zhenghui Liu,
• Yuchen Xie,
• Chunyu Zhang,
• Gengzhao Xu,
• Wentao Song and
• Ke Xu

Beilstein J. Nanotechnol. 2021, 12, 82–92, doi:10.3762/bjnano.12.7

• tuning fork and the wiring in the liquid, a longer tip is required. By keeping the nodes of the tip in the higher-order modes close to the liquid surface, the frequency drift of the sensor can be effectively limited, maintaining a high Q factor [16][17]. By using a qPlus sensor with a long tip, atomic

Electromagnetic analysis of the lasing thresholds of hybrid plasmon modes of a silver tube nanolaser with active core and active shell

• Denys M. Natarov,
• Trevor M. Benson and
• Alexander I. Nosich

Beilstein J. Nanotechnol. 2019, 10, 294–304, doi:10.3762/bjnano.10.28

• highest red-shift, followed by the higher-order modes of the same type, and etc. If the tube gets thicker, each of the emission wavelengths of these modes moves closer to the value of 359 nm (from the red side) that is the accumulation point for the modes of the solid circular silver nanowire placed in

• selected as the working mode. This is because it has a relatively low threshold gain (around γ = 0.1 if h = 10 nm) and emits light in the yellow or green parts of the visible spectrum. It is well separated from the higher-order modes of the same type, and which are significantly shifted to the blue range

Two-dimensional photonic crystals increasing vertical light emission from Si nanocrystal-rich thin layers

• Lukáš Ondič,
• Marian Varga,
• Ivan Pelant,
• Alexander Kromka,
• Karel Hruška and
• Robert G. Elliman

Beilstein J. Nanotechnol. 2018, 9, 2287–2296, doi:10.3762/bjnano.9.213

• secure coupling of light emitted from SiNCs only into the fundamental mode with Gaussian-like energy profile and thus prevent leakage of light into higher-order modes that would be extracted into other directions. However, if the contrast in refractive index was too low the mode would be extended into

• . Further, we can see a higher-order mode becoming visible from around 20° to higher detection angles for both directions of the square lattice. The crossing of one of these higher-order modes in the Γ–X direction with the fundamental mode is visible at around 45°. The results of the angle-resolved PL

Optimization of the optical coupling in nanowire-based integrated photonic platforms by FDTD simulation

• Nan Guan,
• Andrey Babichev,
• Martin Foldyna,
• Dmitry Denisov,
• François H. Julien and
• Maria Tchernycheva

Beilstein J. Nanotechnol. 2018, 9, 2248–2254, doi:10.3762/bjnano.9.209

• photodetector; (b) Front-view cross-section schematic illustration with refractive indices for materials used in the simulations given; (c) The fundamental mode and three higher order modes of a hexagonal GaN NW with a diameter of 1 µm for the wavelength of 400 nm. The fundamental mode was used for the FDTD

• applied to the geometry optimized using 2D simulations and also to the initial geometry from [30]. We note that for the typical NW dimensions used in experiments, the LED and the photodetector NWs themselves behave as multimode waveguides. Figure 1c illustrates the fundamental and several higher order

• modes in a GaN nanowire with hexagonal shape calculated using COMSOL [32] mode solver at a wavelength of 400 nm. It is difficult to estimate precisely which modes are excited in an operating core/shell LED. For light propagation simulations, we simulate the light generation in the LED nanowire by

Valley-selective directional emission from a transition-metal dichalcogenide monolayer mediated by a plasmonic nanoantenna

• Haitao Chen,
• Mingkai Liu,
• Lei Xu and
• Dragomir N. Neshev

Beilstein J. Nanotechnol. 2018, 9, 780–788, doi:10.3762/bjnano.9.71

• plasmonic modes are excited [29][30][31]. In particular, localized emitters could effectively excite the higher-order modes of the nanoantenna, which are usually only weakly coupled to free-space plane waves [32][33] but can dramatically modify the radiation of the emitters. Importantly, the near-field and

• weaker than for the azimuthal component because of contributions from higher order modes excited in the long bar. Since the valley polarization of the monolayer TMDCs (corresponding to the chirality of the point-dipole emitters) depends on the polarization states of the pumping laser, we could easily

• structures have more geometric parameters and more higher-order modes when excited by point-dipole emitters, hence the process to optimize the geometry is difficult and time-consuming. Moreover, any complex plasmonic structures requires more demanding fabrication efforts in practice. In contrast, the

3D continuum phonon model for group-IV 2D materials

• Morten Willatzen,
• Lok C. Lew Yan Voon,
• Appala Naidu Gandi and
• Udo Schwingenschlögl

Beilstein J. Nanotechnol. 2017, 8, 1345–1356, doi:10.3762/bjnano.8.136

• values εxx = 4.4ε0 and εzz = 1.3ε0. In Figure 2, we show the frequency vs wavenumber (ω–kx) dispersion in the vicinity of the Γ point (ky = 0). Evidently, one mode shows a parabolic dispersion and one mode is linear. There are two higher-order modes originating from the boundary conditions along the z

Multimodal cantilevers with novel piezoelectric layer topology for sensitivity enhancement

• Steven Ian Moore,
• Michael G. Ruppert and
• Yuen Kuan Yong

Beilstein J. Nanotechnol. 2017, 8, 358–371, doi:10.3762/bjnano.8.38

• of the transducer layout on the cantilever for higher order modes has not been addressed. To fully utilize an integrated piezoelectric transducer, this work alters the layout of the piezoelectric layer to maximize both the deflection of the cantilever and measured piezoelectric charge response for a

• multifrequency AFM and has the potential to provide higher resolution imaging on higher order modes. Keywords: atomic force microscopy; multifrequency AFM; multimodal AFM; piezoelectric cantilever, self-sensing; Introduction The invention of the atomic force microscope (AFM) [1] provided for the observation of

• with multiple frequencies has led to vast improvements in the nanomechanical characterization of the sample beyond it’s topography [16]. For these multifrequency AFM (MF-AFM) methods, higher order modes provide enhanced imaging properties such as higher modal stiffnesses and faster response times. It

Precise in situ etch depth control of multilayered III−V semiconductor samples with reflectance anisotropy spectroscopy (RAS) equipment

• Ann-Kathrin Kleinschmidt,
• Lars Barzen,
• Johannes Strassner,
• Christoph Doering,
• Henning Fouckhardt,
• Wolfgang Bock,
• Michael Wahl and
• Michael Kopnarski

Beilstein J. Nanotechnol. 2016, 7, 1783–1793, doi:10.3762/bjnano.7.171

• (BAL) have the advantage of high output powers. Nevertheless, a serious drawback is the multi-transverse-mode operation [30][31][32][33][34]. To achieve operation in the fundamental transverse mode only, the higher order modes have to be suppressed. This can be realized by monolithically integrating a

Electromagnetic enhancement of ordered silver nanorod arrays evaluated by discrete dipole approximation

• Guoke Wei,
• Jinliang Wang and
• Yu Chen

Beilstein J. Nanotechnol. 2015, 6, 686–696, doi:10.3762/bjnano.6.69

• plasmon resonances. For AgNRs of large sizes, however, higher order modes of plasmon resonances can be excited [20]. As the target units investigated in the arrays consist of tilted rods, it is expected that both transverse and longitudinal modes can be excited when they are illuminated under normal

Hollow plasmonic antennas for broadband SERS spectroscopy

• Gabriele C. Messina,
• Mario Malerba,
• Pierfrancesco Zilio,
• Ermanno Miele,
• Michele Dipalo,
• Lorenzo Ferrara and
• Francesco De Angelis

Beilstein J. Nanotechnol. 2015, 6, 492–498, doi:10.3762/bjnano.6.50

• incident field [23]. It is worth noting that the obtained absorption and enhancement values are particularly high considering that they originate from a single antenna. This can be attributed to the complex three-dimensional geometry of the system. The efficient excitation of higher order modes leads to

Dye-doped spheres with plasmonic semi-shells: Lasing modes and scattering at realistic gain levels

• Nikita Arnold,
• Boyang Ding,
• Calin Hrelescu and
• Thomas A. Klar

Beilstein J. Nanotechnol. 2013, 4, 974–987, doi:10.3762/bjnano.4.110

• those in commercially available dye-doped spheres. However, commercially available concentrations are already apt to achieve negative absorption, and to narrow and enhance scattering by higher order modes. Narrowing of the plasmonic modes by gain also makes visible higher order modes, which are normally

k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy

• Martin Esmann,
• Simon F. Becker,
• Bernard B. da Cunha,
• Jens H. Brauer,
• Ralf Vogelgesang,
• Petra Groß and
• Christoph Lienau

Beilstein J. Nanotechnol. 2013, 4, 603–610, doi:10.3762/bjnano.4.67

• generation of strongly enhanced near-field signals. Higher-order modes are coupled into the far field at finite distances from the apex. Here, we demonstrate experimentally how to distinguish and separate between the lowest and higher-order eigenmodes of such a metallic taper by filtering in the spatial

• critically upon the exact shape of the tip and the incoming phase front. Theoretical studies have shown that only the lowest, rotationally symmetric eigenmode is nanofocused down to the very apex of the tip [13] where it gets highly confined. In contrast, higher order modes radiate into the far-field while

• wire for smaller radii. The same is true for all higher order modes. As a consequence, only the n = 0 and n = 1 eigenmodes of the wire are expected to contribute to near-fields in the vicinity of the taper apex. When scattered into the far-field, the contributions of those two modes cannot be

Mapping of plasmonic resonances in nanotriangles

• Simon Dickreuter,
• Julia Gleixner,
• Andreas Kolloch,
• Johannes Boneberg,
• Elke Scheer and
• Paul Leiderer

Beilstein J. Nanotechnol. 2013, 4, 588–602, doi:10.3762/bjnano.4.66

• recent investigations [1][24][25][26], because they have sharp tips where the localization of the field enhancement can be particularly pronounced. The size of these triangles was relatively large, so that not a simple dipole mode, but higher order modes were excited by the incident light, demonstrating

Multiple regimes of operation in bimodal AFM: understanding the energy of cantilever eigenmodes

• Daniel Kiracofe,
• Arvind Raman and
• Dalia Yablon

Beilstein J. Nanotechnol. 2013, 4, 385–393, doi:10.3762/bjnano.4.45

• with various higher order modes on the ternary blend sample are shown in Figure 1. The cantilever parameters were k1 = 4 N/m, Q1 = 212 (remaining parameters given in Table 1). Two different scans are compared. The first scan is a bimodal image using the 1st and 2nd eigenmodes (left column (a,c,e)), and