Investigations on the optical forces from three mainstream optical resonances in all-dielectric nanostructure arrays

• Guangdong Wang and
• Zhanghua Han

Beilstein J. Nanotechnol. 2023, 14, 674–682, doi:10.3762/bjnano.14.53

• remains spatially localized while the frequency co-exists within a continuum of radiations. Although this concept was first proposed in the field of quantum mechanics [11], it has also attracted much attention in recent years in photonics [12] due to its ability to achieve high-quality (Q) factor

• resonance and the associated high-field enhancement. The ideal BIC has an infinite Q-factor and zero resonance linewidth, so it can only exist as a mathematical quantity and cannot be excited by free-space radiations. However, with some intentional perturbations in the geometry or objective loss channels

• , such as surface roughness, a BIC will turn into a quasi-BIC mode with both the Q-factor and resonant bandwidth becoming limited. Many applications of quasi-BICs have been reported, including ultrasensitive sensing [13], ultra-narrow bandwidth filters [14], and enhanced nonlinear effects [15]. The BICs

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

• devices, suitable topological constellations can ensure low radiation in the vertical direction, while infinite periods ensure vanishing transverse leakage, leading theoretically to an infinite Q factor. However, realistic devices inevitably have only a finite size, which introduces lateral leakage at the

• outgoing boundary. Consequently, BIC modes with infinite Q factor turn into quasi-BICs that are accessible from the radiative continuum [27][28]. In addition to the degradation of the Q factor, the finite-size effect also turns the continuous photonic bands of the infinite device into discrete energy

• . Such a periodic nanostructure array supports a BIC around 1.56 μm and has an infinite Q factor at the Г point, as shown in Figure 1b and Figure 1c, respectively. The electric field (E field) distribution of the eigenmode is shown in the inset of Figure 1b, and the white arrows indicate the in-plane E

Quasi-guided modes resulting from the band folding effect in a photonic crystal slab for enhanced interactions of matters with free-space radiations

• Kaili Sun,
• Yangjian Cai,
• Uriel Levy and
• Zhanghua Han

Beilstein J. Nanotechnol. 2023, 14, 322–328, doi:10.3762/bjnano.14.27

• guided modes, which do not interact with external radiation, will appear with the dispersion curves above the light cone. Our results show that ultrahigh Q-factor resonances with large operating bandwidth can be achieved. Interestingly, the perturbation in only one direction of the photonic lattice will

• optical applications where multiple or spectrally tunable inputs are required simultaneously. Consequently, new mechanisms are still explored to realize novel photonic components with additional advantages besides a high Q-factor. These are, for example, phase gradient metasurfaces and spatial beam

• the kx direction, which is the same as for the GMs. The total Q-factor (Qtotal) of a resonance observed in the far-field spectrum is determined by the Q-factors of radiation (Qrad) and absorption (Qabs) [26]: Because the absorption loss of materials is not considered here, that is, Qabs is infinite

Intermodal coupling spectroscopy of mechanical modes in microcantilevers

• Ioan Ignat,
• Bernhard Schuster,
• Jonas Hafner,
• MinHee Kwon,
• Daniel Platz and
• Ulrich Schmid

Beilstein J. Nanotechnol. 2023, 14, 123–132, doi:10.3762/bjnano.14.13

• Q-factor of the fundamental mode. Intermodal coupling requires a strong drive tone, referred to as a pump, at either the frequency difference between or the sum of two cantilever eigenmodes of interest. Using the difference, also known as a red sideband or anti-Stokes pump, leads to sideband cooling

• ) Measurements of the first mode coupled with the second. Increasing the pump amplitude presents both a shift in the frequency and a reduction in effective temperature. Inset: Effective temperature and Q factor as functions of the pump amplitude. (b) Data of the second mode under different pump settings. Mode

Double-layer symmetric gratings with bound states in the continuum for dual-band high-Q optical sensing

• Chaoying Shi,
• Jinhua Hu,
• Xiuhong Liu,
• Junfang Liang,
• Jijun Zhao,
• Haiyan Han and
• Qiaofen Zhu

Beilstein J. Nanotechnol. 2022, 13, 1408–1417, doi:10.3762/bjnano.13.116

• , Hebei 056038, P. R. China 10.3762/bjnano.13.116 Abstract Herein, we theoretically demonstrate that a double-layer symmetric gratings (DLSG) resonator consisting of a low-refractive-index layer sandwiched between two high-contrast gratings (HCG) layers, can host dual-band high-quality (Q) factor

• optical field; nonlinear optics; optical sensing; Introduction High quality (Q) factor resonance in nanophotonics has attracted considerable attention in the past decades due to its wide applications in narrow-band filters [1], nonlinear optics [2], optical sensors [3] and lasers [4]. To date, most

• Neumann and Wigner first proposed the BIC theory shortly after the advent of quantum mechanics [20], which was then extended to acoustics, electromagnetism, and other fields [21][22][23][24]. A true BIC has an infinite Q-factor and vanishing resonant linewidth, and this can only exist in an ideal lossless

Analytical and numerical design of a hybrid Fabry–Perot plano-concave microcavity for hexagonal boron nitride

• Felipe Ortiz-Huerta and
• Karina Garay-Palmett

Beilstein J. Nanotechnol. 2022, 13, 1030–1037, doi:10.3762/bjnano.13.90

• was achieved for the TEM mode at the DBR center wavelength. A Q-factor of Q = 731.4 ± 102.7 was also calculated in our simulations where the resonant modes of the microcavity (Figure 8) are shown in good agreement (Table 1) with the resultant modes from the analytical model (Figure 7). Conclusion We

Tunable high-quality-factor absorption in a graphene monolayer based on quasi-bound states in the continuum

• Jun Wu,
• Yasong Sun,
• Feng Wu,
• Biyuan Wu and
• Xiaohu Wu

Beilstein J. Nanotechnol. 2022, 13, 675–681, doi:10.3762/bjnano.13.59

• shift as the background refractive index changes [14]. Narrow-band absorbers have attracted attention in practical applications due to the absorption with high quality factor (Q-factor), which is beneficial to improve the sensing performance. Up to now, many strategies for improving the Q-factor have

• perfect light confinement and giant field enhancement [25][26][27][28][29]. Hence, quasi-BICs can be utilized to design narrow-band absorbers with high Q-factor. Tunable absorption is interesting regarding many potential applications. There are generally two ways to achieve tunable absorption. One is to

• . The absorption at the resonant wavelength is about 54.13%. The enhanced absorption at this wavelength is attributed to the excitation of quasi-BICs, which will be verified in the following. Moreover, the corresponding Q-factor is about 37657, which yields an ultrasharp absorption profile. Here, the Q

The patterning toolbox FIB-o-mat: Exploiting the full potential of focused helium ions for nanofabrication

• Victor Deinhart,
• Lisa-Marie Kern,
• Jan N. Kirchhof,
• Sabrina Juergensen,
• Joris Sturm,
• Enno Krauss,
• Thorsten Feichtner,
• Sviatoslav Kovalchuk,
• Michael Schneider,
• Dieter Engel,
• Bastian Pfau,
• Bert Hecht,
• Kirill I. Bolotin,
• Stephanie Reich and
• Katja Höflich

Beilstein J. Nanotechnol. 2021, 12, 304–318, doi:10.3762/bjnano.12.25

• resonance is significantly broadened for the lithographically defined tetramer. Interestingly, the highest Q factor (Q = ωres/δω with the resonance frequency Q = ωres and the resonance width δω) was achieved for the tetramers obtained by pure Ga patterning, even though the monomer shape is not perfectly

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

• temperature range [1]. In addition, quartz tuning forks have a high elastic constant, a high quality factor (Q factor), and are self-sensing due to the piezoelectric effect [1]. Therefore, a quartz tuning fork can be used as a force sensor. The central part of the “qPlus sensor” is a quartz tuning fork of

• 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

• . Here, we report a numerical study of the vibration modes of qPlus sensors. Eigenfrequencies, tip amplitudes, ratios between vertical and lateral amplitude components, output currents, and Q factor values as functions of the tip size of the qPlus sensor are systematically analyzed. Eventually, the

Atomic defect classification of the H–Si(100) surface through multi-mode scanning probe microscopy

• Jeremiah Croshaw,
• Thomas Dienel,
• Taleana Huff and
• Robert Wolkow

Beilstein J. Nanotechnol. 2020, 11, 1346–1360, doi:10.3762/bjnano.11.119

• using a field ion microscope (FIM) [90]. AFM tips used the third-generation Giessibl tuning forks with a FIB mounted tungsten tip (f0 ≈ 28 kHz, Q-factor ≈ 16k–22k) [91]. The tip was cleaned and sharpened in vacuum using a FIM [90]. In situ tip conditioning was done by executing controlled contact on a

An atomic force microscope integrated with a helium ion microscope for correlative nanoscale characterization

• Santiago H. Andany,
• Gregor Hlawacek,
• Stefan Hummel,
• Charlène Brillard,
• Mustafa Kangül and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2020, 11, 1272–1279, doi:10.3762/bjnano.11.111

• ][27]. Operating in ORT mode instead of amplitude-modulation AFM (AM-AFM) is particularly advantageous in vacuum, where the Q-factor of the cantilever is about one order of magnitude higher than in air. Indeed, AM-AFM imaging bandwidth is inversely proportional to the Q-factor [28] and is therefore

• very slow in vacuum [29]. In ORT, the tapping rate is a least one order of magnitude below the first resonance of the cantilever and hence the enhancement of the Q-factor in vacuum is less detrimental to the achievable scan speed. Results The system has been experimentally tested on a variety of sample

Integration of sharp silicon nitride tips into high-speed SU8 cantilevers in a batch fabrication process

• Nahid Hosseini,
• Matthias Neuenschwander,
• Oliver Peric,
• Santiago H. Andany,
• Jonathan D. Adams and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2019, 10, 2357–2363, doi:10.3762/bjnano.10.226

• amplitude modulation AFM (HS-AM-AFM) enhanced by up to one order of magnitude due to their low mechanical quality factor (Q-factor) and hence their high mechanical bandwidth [23]. A tip made of SU8 or other structural polymers can be integrated into a polymer cantilever by moulding. Such tips have been

• and to increase the detection speed and sensitivity. The detection speed in amplitude-modulation mode is determined by the amplitude response time of the cantilever. The tapping-mode bandwidth is given by BW = πf0/Q, where f0 is the resonance frequency and Q is the Q-factor [32]. The resonance

• resulting in a low Q-factor. This low Q-factor however comes at the price of a low mechanical excitation efficiency when shaking the cantilever at resonance with a dither piezo. Hence the drive amplitude for these cantilevers has to be higher than that of traditional cantilevers. This gives rise to

Nanoscale spatial mapping of mechanical properties through dynamic atomic force microscopy

• Zahra Abooalizadeh,
• Leszek Josef Sudak and
• Philip Egberts

Beilstein J. Nanotechnol. 2019, 10, 1332–1347, doi:10.3762/bjnano.10.132

• contaminants on the surface when measuring the mechanical properties of atomic-sized defects [15][16][17]. Furthermore, the high quality factor of the AFM cantilever that is achieved under UHV conditions can be very beneficial in dynamic AFM modes, as the Q-factor is inversely proportional to the force

Time-resolved universal temperature measurements using NaYF₄:Er³⁺,Yb³⁺ upconverting nanoparticles in an electrospray jet

• Kristina Shrestha,
• Arwa A. Alaulamie,
• Ali Rafiei Miandashti and
• Hugh H. Richardson

Beilstein J. Nanotechnol. 2018, 9, 2916–2924, doi:10.3762/bjnano.9.270

• permittivity and permeability of water, l is an integer, and a is the radius of the WGM cavity [39][40]. The plot of wavenumbers of WGM peaks vs as a function of l + 1/2 is shown in Figure 6B. The slope from a linear fit is used to calculate the cavity radius of 2.87 ± 0.02 μm. The Q-factor of the WGM cavity

• can be calculated using where ν0 is the wavenumber of the peak center and Δν0 is the FWHM of the peak [40]. The inset in Figure 6A shows the peak and fit for the three peaks near 425 nm. The Q-factor is found to be 165 ± 20. The water velocity changes inside the Taylor cone with the highest velocity

• excitation at the tip of the Taylor cone sets up a WGM cavity increasing the optical path length by the Q-factor of the cavity [39]. The increased path length results in more light absorption at the tip of the Taylor cone and an increased instead of a decreased temperature as expected. This change of path

Quantitative comparison of wideband low-latency phase-locked loop circuit designs for high-speed frequency modulation atomic force microscopy

• Kazuki Miyata and
• Takeshi Fukuma

Beilstein J. Nanotechnol. 2018, 9, 1844–1855, doi:10.3762/bjnano.9.176

• cantilever thermal vibrations nth. These values were calculated using the following equation [1][33]: where kB, T, k, and A denote Boltzmann's constant, the absolute temperature, the cantilever spring constant, and the cantilever vibration amplitude, respectively. Qd* represents the apparent Q-factor in the

Electrostatically actuated encased cantilevers

• Benoit X. E. Desbiolles,
• Gabriela Furlan,
• Adam M. Schwartzberg,
• Paul D. Ashby and
• Dominik Ziegler

Beilstein J. Nanotechnol. 2018, 9, 1381–1389, doi:10.3762/bjnano.9.130

• excitation gives a clean resonance peak at f0 = 347.530 kHz, with a phase transition from 0° to 180°, and no spurious peaks over the entire frequency range (0 to 500 kHz). c) By fitting a simple harmonic oscillator model to the thermal power spectral density, one calculates resonance frequency, Q-factor and

Design of photonic microcavities in hexagonal boron nitride

• Sejeong Kim,
• Milos Toth and
• Igor Aharonovich

Beilstein J. Nanotechnol. 2018, 9, 102–108, doi:10.3762/bjnano.9.12

• -resonators such as a high chemical stability and an excellent thermal conductivity [22][23]. In this work, we propose to use hBN for the fabrication of photonic crystal cavities (PCCs). We design two dimensional (2D) PCCs and show that they have high quality-factor (Q-factor) resonances in the visible

• spectral range, which overlap with the ZPLs of SPEs in hBN [24]. We further optimize the structures and model 1D nanobeam photonic crystals that exhibit a Q-factor in excess of ≈20,000. In the light of recent progress in direct-write etching of hBN [25], our results are promising for realization of high Q

• cavities and monolithic coupled systems made from this material. Results and Discussion We begin with a 2D photonic crystal that contains a line defect cavity. The L3 cavity has been widely investigated because it was the first to exceed an experimental Q-factor of 10,000 [26][27]. In this study, we used a

A robust AFM-based method for locally measuring the elasticity of samples

• Alexandre Bubendorf,
• Stefan Walheim,
• Thomas Schimmel and
• Ernst Meyer

Beilstein J. Nanotechnol. 2018, 9, 1–10, doi:10.3762/bjnano.9.1

• = 13.1 N·m−1, Q2 = 208, where Qi is the Q factor of the i-th flexural mode in free space. The force constants were computed for k1 from the theoretical formula k1 = (Ewt3)/(4l3) [22], where E, t, w and l are, respectively, Young’s modulus, thickness, width and length of the cantilever beam, and for k2 by

Near-field surface plasmon field enhancement induced by rippled surfaces

• Mario D’Acunto,
• Francesco Fuso,
• Ruggero Micheletto,
• Makoto Naruse,
• Francesco Tantussi and
• Maria Allegrini

Beilstein J. Nanotechnol. 2017, 8, 956–967, doi:10.3762/bjnano.8.97

• –metal (MIM) cavities characterized by the cavity Q-factor and the effective mode volume Veff, so that a large Q/Veff ratio results in enhanced light–matter interaction, as typically quantified by the LDOS. Let us consider a one-dimensional array of coupled QNMs, where the QNMs are exponentially

Functional dependence of resonant harmonics on nanomechanical parameters in dynamic mode atomic force microscopy

• Federico Gramazio,
• Matteo Lorenzoni,
• Francesc Pérez-Murano,
• Enrique Rull Trinidad,
• Urs Staufer and
• Jordi Fraxedas

Beilstein J. Nanotechnol. 2017, 8, 883–891, doi:10.3762/bjnano.8.90

• silicon cantilever with a resonant frequency f0 = 300 kHz and a Q factor of 400. The threshold of the repulsive region (φ > 0 degrees) is represented by a vertical discontinuous grey line. Figure 1c displays the A6 approach curves corresponding to the parameters used in Figure 1a and Figure 1b (continuous

• ]. This expression is valid for Q >> 1. In order to obtain an approximate manageable expression of the functional dependence of A6 on kc we have used the nominal geometrical and resonance frequency values of different commercial rectangular cantilevers, as provided by the manufacturers and Q factor values

Optimizing qPlus sensor assemblies for simultaneous scanning tunneling and noncontact atomic force microscopy operation based on finite element method analysis

• Omur E. Dagdeviren and
• Udo D. Schwarz

Beilstein J. Nanotechnol. 2017, 8, 657–666, doi:10.3762/bjnano.8.70

• considerable experience. As a result, personal skills have often a major impact on the sensing characteristics of the completed device. To help minimizing the related problems, this work investigates the influence of different tip mounting options on the spring constant, Q-factor, resonance frequency, and

• , we find that spring constant, Q-factor, and eigenfrequency are attenuated for tip-holder setups that feature an increasing degree of asymmetry. This effect is, however, modest if compared to the effect of an asymmetric wire connection, as they are frequently added to collect a tunneling current for

Flexible photonic crystal membranes with nanoparticle high refractive index layers

• Torben Karrock,
• Moritz Paulsen and
• Martina Gerken

Beilstein J. Nanotechnol. 2017, 8, 203–209, doi:10.3762/bjnano.8.22

• directions. The sample holder allows for an adjustable strain of up to 20%. neff and Q-factor values with respect to the concentration of TiO2 nanoparticles in the spincoat solution. neff is calculated with Equation 2 and Q is calculated with Equation 3.

Noise in NC-AFM measurements with significant tip–sample interaction

• Jannis Lübbe,
• Matthias Temmen,
• Philipp Rahe and
• Michael Reichling

Beilstein J. Nanotechnol. 2016, 7, 1885–1904, doi:10.3762/bjnano.7.181

• : amplitude noise; cantilever stiffness; closed loop; detection system noise; frequency shift noise; non-contact atomic force microscopy (NC-AFM); Q-factor; spectral analysis; thermal noise; tip–sample interaction; Introduction Non-contact atomic force microscopy (NC-AFM) [1][2] is an unmatched surface

• experimental data obtained under realistic measurement conditions. We find excellent agreement between simulated and experimental results for noise in a cantilever-based NC-AFM with optical beam-deflection and measurements performed in an ultra-high vacuum environment, where the cantilever Q-factor is close to

Signal enhancement in cantilever magnetometry based on a co-resonantly coupled sensor

• Julia Körner,
• Christopher F. Reiche,
• Thomas Gemming,
• Bernd Büchner,
• Gerald Gerlach and
• Thomas Mühl

Beilstein J. Nanotechnol. 2016, 7, 1033–1043, doi:10.3762/bjnano.7.96

• presented here but we want to stick to our existing experimental system and have taken the mechanical properties of the CNT as measured. From Table 3 we see that the cantilever has a lower minimal detectable frequency shift (due to its better Q-factor and smaller resonance frequency) compared to the

Understanding interferometry for micro-cantilever displacement detection

• Alexander von Schmidsfeld,
• Tobias Nörenberg,
• Matthias Temmen and
• Michael Reichling

Beilstein J. Nanotechnol. 2016, 7, 841–851, doi:10.3762/bjnano.7.76

• deflection. To further optimize the signal, we introduce a method for positioning the fiber precisely in the optimal lateral position and examine the importance of this positioning. Finally, we investigate the impact of the interferometric signal on the effective modal spring constant and the modal Q-factor

• expected from our previous studies [8]. For small amplitudes and a negative fringe, the Q-factor is up to 6% larger than for the positive fringe. Although, this variation is significant within the statistical error, it is much less than the typical tolerance of commercial cantilevers and the impact of the

• P = 400 μW measured for cantilever 3. The inset shows the noise floor for positive and negative fringes at d = 18 μm as a function of the light power P. Effective modal Q-factor , effective modal cantilever stiffness and noise floor for the positive and negative fringe for 400 μW under conditions