Chaos in Atomic Force Microscopy

Hu, Shuiqing; Raman, Arvind

doi:10.1103/physrevlett.96.036107

Cited by 116 publications

(80 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…However, all of the previously studied capacitive metamaterial structures exhibited strong diamagnetic behavior that suppressed the relative magnetic permeability µ r in the low 3 frequency regime [10][11][12]. Hence, in all previous systems, the capability of increasing the refractive index n was very limited.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Three-Dimensional Metamaterials with an Ultrahigh Effective Refractive Index over a Broad Bandwidth

2009

View full text Add to dashboard Cite

show abstract

mentioning

confidence: 99%

“…In this structure, the enhancement of dielectric permittivity is also associated with a strong diamagnetic response that suppresses µ r . Such a strong diamagnetic response, in fact, holds true for all proposed metamaterial structures with a strong capacitative response [10][11][12] and limits the capability of index enhancement.…”

mentioning

confidence: 99%

Three-Dimensional Metamaterials with an Ultrahigh Effective Refractive Index over a Broad Bandwidth

2009

View full text Add to dashboard Cite

show abstract

“…It is defined as NL = 100r n /r s , where r s is the standard deviation of the signal and r n is the standard deviation of the minimal amount of noise that needs to be added to the signal to fully destroy its nonlinearity. This approach has been instrumental in inferring chaos in cardiac dynamics [30] and atomic force microscopy [31].…”

Section: Introductionmentioning

confidence: 99%

Detecting low-dimensional chaos by the “noise titration” technique: Possible problems and remedies

Gao¹,

Hu²,

Mao³

et al. 2012

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

a b s t r a c tDistinguishing low-dimensional chaos from noise is an important issue in time series analysis. Among the many methods proposed for this purpose is the noise titration technique, which quantifies the amount of noise that needs to be added to the signal to fully destroy its nonlinearity. Two groups of researchers recently have questioned the validity of the technique. In this paper, we report a broad range of situations where the noise titration technique fails, and offer solutions to fix the problems identified.

show abstract

“…The standard interpretation relates the measured phase lag to the energy dissipation resulting from the tip-sample interaction [2]. This interpretation is based on the assumption that the cantilever response is sinusoidal and only at the drive frequency, as in a linear approximation.More recently, the attention of the dynamic AFM community has focused on the nonlinear nature of the tipsample interaction [3,4,5,6]. It has been realized that the higher harmonics of the tip-motion carry valuable information about the tip-sample interaction.…”

mentioning

confidence: 99%

Phase imaging with intermodulation atomic force microscopy

et al. 2010

View full text Add to dashboard Cite

Intermodulation atomic force microscopy (IMAFM) is a dynamic mode of atomic force microscopy (AFM) with two-tone excitation. The oscillating AFM cantilever in close proximity to a surface experiences the nonlinear tip-sample force which mixes the drive tones and generates new frequency components in the cantilever response known as intermodulation products (IMPs). We present a procedure for extracting the phase at each IMP and demonstrate phase images made by recording this phase while scanning. Amplitude and phase images at intermodulation frequencies exhibit enhanced topographic and material contrast.Key words: atomic force microscopy, intermodulation, multifrequency AFM, phase imaging IntoductionSince its invention by Binnig et al. [1], the atomic force microscope (AFM) has become one of the most widely used tools in nanoscience. In the first applications of AFM only the sample topography was measured by monitoring the static deflection of the AFM cantilever. The introduction of dynamic AFM with an oscillating cantilever brought various improvements, such as much lower measurement back action which greatly reduced damage to soft samples while imaging. In addition, the ability to measure the phase lag between the cantilever response and the exciting force, opened a new information channel to record while scanning. These "phase images" enabled compositional mapping of surfaces with dynamic AFM. The standard interpretation relates the measured phase lag to the energy dissipation resulting from the tip-sample interaction [2]. This interpretation is based on the assumption that the cantilever response is sinusoidal and only at the drive frequency, as in a linear approximation.More recently, the attention of the dynamic AFM community has focused on the nonlinear nature of the tipsample interaction [3,4,5,6]. It has been realized that the higher harmonics of the tip-motion carry valuable information about the tip-sample interaction. Each higher harmonic represents two new information channels (amplitude and phase) that can be recorded while scanning. Higher harmonic amplitudes and phases have been used for imaging both under ambient conditions and in liquids [7,8,9]. With a sufficient number of these information channels, a quantitative reconstruction of the tip-sample force is possible without measuring amplitude-distance curves [10,11]. * Corresponding author Email address: haviland@kth.se (David B. Haviland) However, the signal-to-noise ratio (SNR) for higher harmonics measurements is usually very poor because the harmonics are in general not located at a cantilever resonance. Various efforts have been made to improve the signal detection, for example by modifying the cantilever design [12]. Other approaches to increase the information acquired while scanning involve multifrequency excitations like bimodal AFM [13] or band excitation [14]. With bimodal AFM, two excitation tones are applied at the first two flexural eigenmodes of the cantilever. In this driving scheme the amplitude and phase at both dri...

show abstract

Chaos in Atomic Force Microscopy

Cited by 116 publications

References 16 publications

Three-Dimensional Metamaterials with an Ultrahigh Effective Refractive Index over a Broad Bandwidth

Three-Dimensional Metamaterials with an Ultrahigh Effective Refractive Index over a Broad Bandwidth

Detecting low-dimensional chaos by the “noise titration” technique: Possible problems and remedies

Phase imaging with intermodulation atomic force microscopy

Contact Info

Product

Resources

About