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Abstract
Graphene has been considered as one of the best materials to implement mechanical resonators due to their excellent properties such as low mass, high quality factors and tunable resonant frequencies. Here we report the observation of phonon lasing induced by the photonthermal pressure in a few-layer graphene resonator at room temperature, where the graphene resonator and the silicon substrate form an optical cavity. A marked threshold in the oscillation amplitude and a narrowing linewidth of the vibration mode are observed, which confirms a phonon lasing process in the graphene resonator. Our findings will stimulate the studies on phononic phenomena, help to establish new functional devices based on graphene mechanical resonators, and might find potential applications in classical and quantum sensing fields, as well as in information processing.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Mechanical resonators have attracted various attentions in recent years because of their broad application prospects in both classical and quantum sensing fields [1]. Meanwhile, cavity optomechanics [2] associating mechanical resonators and radiation pressure has been a pioneering issue in optical research nowadays [3,4] and new physical phenomena have emerged in the field, among which phonon lasing has been a profound topic in a long time. A phonon is a quasiparticle in solids that represents an excited state of crystal lattice vibrations. The invention of the laser has greatly facilitated the development of technologies, ranging from metrology to sensing that has permeated all over our lives [5]. In view of the success of photon lasers and the common resemblance between the quanta of electromagnetic radiation (photon) and the quanta of mechanic vibration (phonon), a phonon laser has always been a tireless pursuit of scientists worldwide since the invention of the laser [6–13]. However, not until 2009, when Kerry J. Vahala reported a phonon laser with a $Mg^+$ ion pumped by a blue-detuned laser [14], did physicists achieve unprecedented leaps in the study on phonon lasers. The last decade has witnessed the great progress on studies in phonon lasers, observations of phonon lasing have been reported on magnesium ions [14,15], semiconductors [16], compound microcavity systems [17,18], electromechanical resonators [19], cavity opto-mechanics with membrane resonators [20,21], nanoparticles levitated by an optical tweezer [22] and so on, which are still proliferating throughout the world. Graphene has been picked up to implement mechanical resonators on demand to a shrink in dimensions due to its outstanding mechanical properties [23]. Graphene mechanical resonators have showed outstanding applications attained on the versatile two-dimensional material among the academic community [24–29]. Moreover, pioneering works in recent years have reported excellent phonon dynamical properties by using atomic thin graphene-based membrane resonators [30–33].
Here we present a phonon laser consisting of a few-layer graphene resonator. Although there is a large number of reports on phonon polaritons that could potentially achieve lasing at low threshold than phonon lasing [34,35], we have to clarify that phonon polaritons are electromagnetic waves coupled to lattice vibrational modes mediated through the electromagnetic dipoles, which is classified to the optical phonon phenomena [36], whereas our phonon lasing process is classified to the acoustic phonon phenomena induced by the photothermal pressure [37]. The mechanisms to achieve lasing on phonon polaritons and acoustic phonons are different from each other. We believe that studies on both kind of phonons are important for a fundamental understanding of phonons. The reported phonon laser is based on opto-mechanic cavity, where the graphene and the silicon substrate form an optical cavity and the graphene sheet is used as the coupling mirror as well as the mechanical resonator. The dissipation of the phonons decreases as the pumping laser power increases and vanishes when the pumping laser power is large enough. Then the phonons come to the state that known as stimulated emission in resemblance of a photon lasing process. As a result, a phonon laser is established. While R. D. Alba et al. have also demonstrated the amplification of mechanical motions (or the mechanical lasing) in a graphene resonator by inducing a parametric instability [30], our approach to establish phonon lasing induced by the photothermal pressure is more simplified, which only needs a simple lithography procedure to be implemented without auxiliary pumping circuits. What’s more, compared to former works reported on phonon lasers [14–22], our implementation is easy to be maintained and has potential to be fully integrated with a fiber system [29], hence helps to construct a portable phonon laser that could be applied in various situations. The established phonon laser will also greatly improve the sensitivity of a sensor, prompt studies in phononic functional devices based on graphene resonators [38], as well as other similar two-dimensional materials.
2. Experiment and results
The schematic experimental setups is shown in Fig. 1. Two lasers are used in the experiment, where a $633~nm$ continuous laser is used as the pump laser as well as to perform the measurement of the graphene resonator, and a $850~nm$ light from a power-stabilized laser is directed into the set-up through a $780~nm$ single mode fiber (SMF@780nm) and is used as an excitation to confirm the response of the graphene resonator. In order to align the lasers to be focused on the graphene resonator, a white light is used to illuminate the sample and the image of the resonator is detected by a camera (CCD). The sample image is inserted in the corner, where the light spot is the beam of the $633~nm$ laser, and the diameter of the spot is estimated to be around $1~\mu m$ which is the same within the whole experimental process. The spot of the $850~nm$ laser that is coincident with the $633~nm$ laser beam is not shown in the image. The half wave plates (HWP) and polarization beam splitters (PBS) are combined to couple the light sources as well as flexibly adjust the powers of the lasers directed to the sample. The $850~nm$ laser is modulated by an electro-optical modulator (EOM) to generate sinusoidal wave intensity laser power to excite the resonator. The quarter wave plate and the second PBS are combined to segregate the reflected pumping laser from the incident laser path. Then the reflected light is split into two parts by a beam splitter (BS): one is recorded by the CCD camera, and the other is first filtered by a filter (FL@633) and then detected by a photodiode (Pd). Finally, the signal from the Pd is either analysed by a frequency spectrometer to extract the vibration state of the graphene resonator or fed back to a vector network analyzer (VNA) to draw the response of the graphene resonator to the excitation. As shown in Fig. 1, the sample is placed on an electric displacement platform in a vacuum chamber. The phonon laser is operated under high vacuum with a chamber pressure around $1.0 \times 10^{-7}~mbar$ at room temperature (about $293~K$).
Fig. 1. Experimental setups. Two lasers are focused on the sample, where a graphene sheet covers over a silicon substrate with a microhole. The $633~nm$ laser is the pump laser, and the $850~nm$ laser is used to characterise the responsivity of the graphene resonator. A white light is used as the imaging light source to assist on tailing the laser beam to be focused on the sample. The image of the sample is inserted besides the CCD. SMF: single mode fiber, HWP: half-wave-plate, HR: high reflectivity mirror, PBS: polarization beam splitter, FC: fiber collimator, DS: dichromatic splitter, BB: beam block, QWP: quater-wave-plate, FL: filter, OL: objective lens, Pd: photodiode detector, CCD: camera, BS: beam splitter, VNA: vector network analyzer, EOM: electro-optical modulator.
The graphene resonator is fabricated with simple lithography procedure. First, a layer of photoresist is coated on the silicon substrate, and then the substrate is exposed to a contact ultraviolet lithography machine to form a photolithography pattern. After development, the photoresist irradiated by ultraviolet light is washed away, and the remaining part is attached to the silicon substrate to form a protective layer. Finally, the developed substrate is put into the inductively coupled plasma (ICP) machine and etched through the Bosch process to obtain a micro-hole structure. After that, a mechanically exfoliated graphene sheet is transferred to cover on the micro-holes to obtain a graphene resonator. In Fig. 2(a), we present an optical image (I) and a scanning electron microscope (SEM) image (II) of the sample. The depth of the micro-hole on the substrate is further measured through the SEM with a $45^\circ$ viewing angle, which is around $4.33~\mu m$. The spectra contrast of the optical image indicates that the thickness of the graphene sheet is around 10 layers [39]. The effective mass of the graphene resonator is estimated to be $m_{eff}=0.2695N \rho \pi r^2 \approx 4.0\times 10^{-17} ~kg$, where $N=10$ is the layers of the graphene sheet, $\rho =7.4\times 10^{-19} ~kg/\mu m^2$ is the surface mass density of the graphene sheet, $r=2.5~\mu m$ is the radius of the suspended graphene sheet [40,41].
Fig. 2. Basic characterizations of the graphene resonator (colored online). (a) An optical image of the sample (I) under the transfer system, and a scanning electron microscope (SEM) image of the graphene resonator (II). (b) A schematic diagram of the sample with a laser focused on the drumhead graphene resonator. (c) The reflectivity of the sample subject to the depth of the hole on the silicon substrate with a laser wavelength of $633~nm$. (d) The thermal vibration of the upper graphene resonator. The red line is a Lorentz fitting to the data and a quality factor $Q$ extracted from the fitting is signed besides the spectral peak. (e) and (f) Basic characterization of the graphene resonator through a vector network analyser (VNA).
In Fig. 2(b), we draw a schematic diagram of the sample with a laser focused on a drumhead graphene sheet. When the continuous wave laser at $633~nm$ is focused on the graphene resonator, the laser will be reflected for several times between the silicon substrate and the graphene sheet to form an optical cavity, where cavity opto-mechanics effects could occur. Figure 2(c) shows the normalized reflectivity of the graphene subject to the depth of the micro-hole on the substrate, where the reflectivity ratios of the silicon substrate and the graphene are taken as $0.3485$ and $0.171$ respectively. The inserts are the schematic diagram of the graphene resonator and a modulated reflectivity intensity due to the vibration of the graphene sheet. Then the modulated laser intensity is monitored by a photodiode and the vibration mode is extracted by a spectrometer [23]. Figure 2(d) shows a thermal vibration mode of the drumhead graphene resonator. In the measurement, the power of the $633~nm$ laser pumped in the sample is $500~\mu W$, and the power illuminated in the photodiode is around $30~\mu W$. We used the the approach introduced in Ref. [30] to estimate the displacement of the resonator, where the displacement measurement sensitivity of the laser interferometry is estimated to be around $G_x\approx 2.91 ~pm/\mu V$ with a measured photodiode gain of $4100~V/W$ and a measured depth of the micro-hole of $4.33~\mu m$. We have made a Lorentz fitting to the data, drawn a quality factor of $Q= 223.94$ and a center frequency of $18.66~MHz$, hence extracted a linewidth around $83.34~kHz$ (FWHM, full width at a half maximum). In order to characterise the response of the graphene resonator, we also use a vector network analyser (VNA) to draw the response of the graphene resonator to a sinusoidal wave intensity laser power at $850~nm$. We record the magnitude and phase over a large frequency span as is shown in Fig. 2(e) and 2(f), where both the peak in magnitude and the abrupt change in phase confirm the resonate response of the graphene resonator.
At finite temperatures, vibrations of a graphene sheet formally resembles motion of a Brownian particle. We consider the motion for the center-of-mass position $x$ of a graphene resonator, which could be described by the function below [42],
where $m$ is the effective mass of the resonator, $x$ is the instantaneous mechanical displacement, $\omega _0$ is the resonator frequency, $Q$ is the mechanical quality factor, $k_0$ is the linear spring constant and $F(t)$ is the forces exerted on the resonator. Considering the fact that photons exchange with kinematic momenta while being reflected or absorbed by a mirror, a certain force is applied to the mirror, which is known as the photothermal pressure (or radiation pressure) that could be calculated as [43] where $R$ and $A$ are the reflectivity and the absorption of the mirror, $T$ is the transmittance of the mirror, $P_{in}$ is the incident laser power, $R_0$ is the reflectivity of the other mirror consisting the cavity, $x$ is the length of the cavity, $\lambda$ is the laser wavelength and $c$ is the light speed. Considering the fact that the amplitude of vibrations of the graphene resonator is small compared to the depth of the micro-hole on the substrate, the radiation pressure could be reduced to the form where $F_0$ is the pressure at the equilibrium position. Then the motion equation of the resonator immersed in radiation pressure should be corrected as [37]Fig. 3. Phonon lasing. (a) The spectral envelopes of the graphene resonator versus the pumping optical power. (b) As the pump power increases, a marked lasing threshold is observed, and the phonon center frequency is also linearly increasing. (c) A narrowing spectral width (FWHM, full width at half maximum) extracted from (a) further confirms a stimulated emission of phonons.
3. Discussion and conclusion
In summary, for the first time we have experimentally demonstrated a phonon laser based on a few-layer graphene resonator under the photothermal pressure, which provides a promising platform to study phononic physics. From the analysis of optomechanics, the realization of the phonon laser reported in this work requires careful design of the microstructure: particularly the distance between the graphene film and the substrate. We measured two samples and each sample has four resonators. However, we cannot observe the lasing phenomenon in all resonators (typically, one out of four can success). Possible reasons might come from the errors from sample fabrications, the adhesive residues as well as the adsorption on the sample severely restrict the performances of the graphene mechanical resonators. In the future, it may be necessary to further design in-situ adjustable device structures to increase the success rate. We argue that this kind of phonon laser might be easier accessible compared to former implementations [14–22], which makes our structure to be an alternative to study phononic physics. In future studies, one can optimize the quality factor of graphene sheet to improve the performance of the phonon laser. Moreover, the dependence of the system performance, especially the limit of the oscillator linewidth, on temperature and properties of the graphene sheet are still some open questions and might be studied in further researches. Our discovery might find applications in sensing and information processing based on functional phononic devices [44,45]. What’s more, a delicate phonon laser maybe play critical roles in profound topics like chaos physics [21,46], pioneering in new physics phenomena and applications in the near future [2].
Funding
National Key Research and Development Program of China (2018YFA0306102, 2018YFA0307400, 2017YFA0304000); National Natural Science Foundation of China (91836102, 12074058, 61704164, 61604140, 61775025, 61705033, 61405030, 61308041); Sichuan Youth Science and Technology Foundation (2020YFG0289); Sichuan Province Science and Technology Support Program (2021YJ0089).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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