Subharmonic Resonant Optical Excitation of Confined Acoustic Modes in a Free-Standing Semiconductor Membrane at GHz Frequencies with a High-Repetition-Rate Femtosecond Laser

Abstract

We propose sub-harmonic resonant optical excitation with femtosecond lasers as a new method for the characterization of phononic and nanomechanical systems in the gigahertz to terahertz frequency range. This method is applied for the investigation of confined acoustic modes in a free-standing semiconductor membrane. By tuning the repetition rate of a femtosecond laser through a subharmonic of a mechanical resonance we amplify the mechanical amplitude, directly measure the linewidth with megahertz resolution, infer the lifetime of the coherently excited vibrational states, accurately determine the system's quality factor, and determine the amplitude of the mechanical motion with femtometer resolution.In recent years, nanophononic and nanomechanical systems have emerged as intriguing subjects for studying mechanics, heat transfer and opto-mechanical coupling on a nanometer scale [1][2][3]. From a fundamental point of view, they provide a route to study mechanical excitations and their interactions with other elementary excitations [1,4]. ¿From an applied perspective they have opened a pathway for high sensitivity sensors in the zeptogram mass range and in the attonewton force range [5,6]. In established experimental methods these systems are driven electrically, magnetically, thermoelastically [7], via radiation pressure from continuous wave lasers [8], or via other optical non-radiation-pressurebased schemes [9,10]. The frequencies of typical systems investigated so far are in the megahertz to gigahertz frequency range [7]. The investigation of higher frequencies is strongly restricted by the driving and detection methods. Here, we report a new method for the investigation of a vibrational system by sub-harmonic resonant excitation with a high-repetition rate femtosecond laser. This excitation scheme can be regarded as tuning the separation of modes of the frequency comb of a femtosecond laser [11] to a commensurable of the frequency of the phononic system. By sweeping the comb spacing of the femtosecond laser, resonant impulsive excitation of the mechanical oscillator can be achieved, which allows the determination of its quality factor in the gigahertz to terahertz frequency range with femtometer sensitivity for the mechanical amplitude. We demonstrate the amplification of the fundamental eigenmode of a free-standing silicon membrane at 19 GHz by a factor of 20 compared to the off-resonant case and determine its quality factor.The dynamical properties of the free-standing silicon membranes were investigated by performing fs resolution pump-probe experiments using the recently developed high-speed asynchronous optical sampling (ASOPS) method [12,13]. This method is based on two asynchronously linked femtosecond Ti:sapphire ring lasers of repetition rate f R ∼ 1 GHz. One laser provides the pump beam and the second laser the probe beam. In this technique the time delay between pump-/probepulse pairs of the two pulse trains is realized through an actively stabilized 10 kHz repetition-rate-offset ∆f R between the tw...

Study of confined coherent acoustic phonon modes in a free-standing cubic GaN membrane by femtosecond spectroscopy

“…Time-resolved pump-probe spectroscopy has been applied to study ultrafast carrier dynamics and phononic properties of various semiconductors, such as GaN, [1][2][3][4] GaAs, [5][6][7] and Si. [8][9][10][11] Among these, GaN is of great importance in optoelectronic and short-wavelength devices because of its widebandgap. [12][13][14] GaN has two crystal structures: wurtzite (hexagonal) and zinc-blende (cubic).…”

Time-resolved detection of propagating Lamb waves in thin silicon membranes with frequencies up to 197 GHz

“…7 Recently, femtosecond lasers have been successfully applied to generate and detect longitudinal acoustic modes in free-standing silicon (Si) membranes with frequencies up to 500 GHz corresponding to 20 nm wavelengths. [8][9][10] As the dispersion relations of propagating Lamb waves are emerging from standing wave resonances, 11 these experiments indicate that propagating Lamb waves in membranes at similarly high frequencies could be monitored all-optically as well, if the conditions for their effective generation and detection are achieved. Recently, Rayleigh waves with wavelengths down to 45 nm (Refs.…”

“…Rayleigh waves are surface acoustic waves on a semi-infinite substrate. 14 Here, we combine the femtosecond pump-probe technique applied earlier to the monitoring of standing wave resonances [8][9][10] and of Rayleigh waves 12 with nanostructuring of the surface 12,13,15 in order to achieve the generation and detection of propagating Lamb waves at frequencies up to 197 GHz and wavelengths down to 50 nm in thin semiconductor membranes. Those high frequencies can be generated because for the same wave vectors the dispersion relations of Lamb waves contain modes of much higher frequencies than those of Rayleigh waves.…”

Coherent Control of GHz Resonant Modes by an Integrated Acoustic Etalon

“…In free-standing membrane structures recently considered for high-frequency (10+ GHz) acoustic resonator applications, this spectral width is large enough to simultaneously excite the membrane's resonant longitudinal acoustic modes up to the 15 th harmonic (285 GHz) [12,13].…”