Parametric Excitation of Optomechanical Resonators by ... - MDPI

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Parametric Excitation of Optomechanical Resonators by Periodical Modulation Jianguo Huang 1,2 , Muhammad Faeyz Karim 2 , Jiuhui Wu 1 , Tianning Chen 1 and Aiqun Liu 2, * 1 2

*

School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China; [email protected] (J.H.); [email protected] (J.W.); [email protected] (T.C.) School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore; [email protected] Correspondence: [email protected]; Tel.: +65-6790-4336

Received: 26 February 2018; Accepted: 17 April 2018; Published: 18 April 2018

Abstract: Optical excitation of mechanical resonators has long been a research interest, since it has great applications in the physical and engineering field. Previous optomechanical methods rely on the wavelength-dependent, optical anti-damping effects, with the working range limited to the blue-detuning range. In this study, we experimentally demonstrated the excitation of optomechanical resonators by periodical modulation. The wavelength working range was extended from the blue-detuning to red-detuning range. This demonstration will provide a new way to excite mechanical resonators and benefit practical applications, such as optical mass sensors and gyroscopes with an extended working range. Keywords: optomechanics; extended working range; periodical modulation

1. Introduction The ability to optically control mechanical resonators is the key requirement of many technological and fundamental advances in physical and engineering field [1–4]. The recent development of optomechanics—which utilizes the photon-phonon coupling in nanoscale photonic structures—has provided a new means to manipulate and measure mechanical resonators [5–8]. The retarded optical force within an optical cavity can be used to cool the mechanical resonators into quantum ground state or to amplify the mechanical resonators into self-oscillation. Recently, several groups have cooled the mechanical motion close to the quantum ground state both in the microwave domain [9] and in the optical domain [10]. For practical applications, optomechanical excitation is attracting more and more attention due to its great technological value. Nowadays, plenty of promising applications have been demonstrated, such as radiofrequency optomechanical resonators [11], nonvolatile optical memory [12], wavelength routing [13], optomechanical sensing [14], and so on. Conventional excitation of optomechanical resonators relies on passive backaction between mechanical resonators and optical cavities [15] or active feedback control [16], which are shown in Figure 1a,b. The optical anti-damping effect is used in the passive backaction method, in which the optical anti-damping is large enough to compensate the intrinsic mechanical damping to excite mechanical resonators [14]. Due to optical anti-damping depending on input optical wavelength, the working range is limited in the blue-detuning range, in which the input wavelength is smaller than the cavity resonance wavelength. Complex off-chip control systems are needed in the active feedback control method, although it can work in the red-detuning range [17–19]. From the aspects of device applications, it is desirable to extend the working range in a single chip without complex control systems. Even though manipulating the optomechanical system by an amplitude-modulated

Micromachines 2018, 9, 193; doi:10.3390/mi9040193

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light has been proposed both in theory and experiments [20–23], the parametric excitation not has been proposed both in theory and experiments [20–23], the parametric excitation has nothas been been demonstrated. demonstrated. In this study, excitation of of optomechanical optomechanicalresonators resonatorsby byperiodically periodicallymodulating modulatingoptical opticalspring spring at twice twice the thenatural naturalfrequency frequency was experimentally demonstrated, which is shown in Figure was experimentally demonstrated, which is shown in Figure 1c. This1c. method is achieved by utilizing optical spring rather than optical anti-damping effects. It can break This method is achieved by utilizing optical spring rather than optical anti-damping effects. It can break the wavelength limit by by extending extendingthe theworking workingwavelength wavelengthfrom fromthe theblue-detuning blue-detuningtotored-detuning red-detuning Thisdemonstration demonstrationwill willprovide provide a new to excite mechanical resonators and benefit range. This a new wayway to excite mechanical resonators and benefit practical practical applications, such as optical mass sensors and gyroscopes with an extended working range applications, such as optical mass sensors and gyroscopes with an extended working range [24–27]. [24–27].

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(c) Figure 1. Schematic of different methods for excitation of optomechanical resonators. (a) Passive Figure 1. Schematic of different methods for excitation of optomechanical resonators. (a) Passive backaction between cavity and mechanical cantilever by direct current (DC) light using optical antibackaction between cavity and mechanical cantilever by direct current (DC) light using optical damping effect; (b) active feedback control by DC light using optical anti-damping effect; (c) anti-damping effect; (b) active feedback control by DC light using optical anti-damping effect; modulated light at twice the mechanical frequency using optical spring effect. (c) modulated light at twice the mechanical frequency using optical spring effect.

The proposed excitation of optomechanical resonator by periodical modulation consists of a The proposed excitation of optical optomechanical mechanical cantilever, a racetrack cavity, andresonator a curved by busperiodical waveguidemodulation as shown in consists Figure 2.of aMechanical mechanicalcantilever cantilever, a racetrack optical cavity, and a curved bus waveguide as shown in is located at the side of the racetrack optical cavity with a gap of 200 Figure nm to 2. Mechanical is locatedcantilever at the side of the with a gapcantilever of 200 nmisto build opticalcantilever coupling between beam andracetrack racetrackoptical cavity.cavity The mechanical build optical between beam racetrack mechanical cantilever is released fromcoupling the substrate with cantilever a gap of 500 nm and can vibratecavity. in the The x-direction and z-direction, released from the substrate with a gap of 500 nm and can vibrate in the x-direction and z-direction, corresponding to fundamental and second mechanical modes. The mechanical cantilever consists of corresponding to fundamental and second mechanical modes. mechanical consists two parts: one part has a cross-section of 200 nm × 340 nm with The a length of 6 µmcantilever and the other partof two one partofhas cross-section of 200 nm × of 340 lengthbus of 6waveguide µm and the part has aparts: cross-section 450a nm × 340 nm with a length 12nm µm.with Theacurved is other coupled has a cross-section of 450 nm × 340anm a length to the racetrack optical cavity with gapwith of 200 nm. of 12 µm. The curved bus waveguide is coupled to the racetrack optical cavity with a gap of 200 nm.


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Figure Figure 2. 2. (a) (a) The The schematic schematic illustration illustration of of modulated modulated method method by by alternating alternating current current (AC) (AC) light light using using optical spring effect for mechanical excitation; (b) the size of mechanical cantilever. optical spring effect for mechanical excitation; (b) the size of mechanical cantilever.

When the pump light is coupled into the racetrack optical cavity through the bus waveguide, When the pump light is coupled into the racetrack optical cavity through the bus waveguide, optical force due to the evanescent wave overlapping is generated between the mechanical cantilever optical force due to the evanescent wave overlapping is generated between the mechanical cantilever and racetrack optical cavity. When the pump light is amplitude modulated at twice the mechanical and racetrack optical cavity. When the pump light is amplitude modulated at twice the mechanical frequency, the alternating optical force will drive the mechanical cantilever and amplify the frequency, the alternating optical force will drive the mechanical cantilever and amplify the mechanical mechanical vibrations, which are known as parametric excitations. vibrations, which are known as parametric excitations. The pump light was amplitude modulated in the experiment, resulting in the periodical The pump light was amplitude modulated in the experiment, resulting in the periodical modulation of optical light in the cavity. The intracavity mode amplitude a and the coupled modulation of optical light in the cavity. The intracavity mode amplitude a and the coupled mechanical mechanical resonator are described as resonator are described as a(t )  i(   gom x)   / 2  a(t )   √ n 2 (1) . (1) a(t) = (i (∆ − gom x ) − κ/2) a(t) + κ n/2 meff x  meff  m x  meff m02 x  gom a*a (2) .. . me f f x + me f f γm x + me f f ωm0 2 x = } gom a∗ a (2) where Δ = ω0 − ω is the frequency detuning, ω is the driving laser frequency, ω 0 is the optical cavity where ∆ = frequency, ω 0 − ω is the detuning, ω iscoupling, the driving laser ω 0 is thenoptical cavity resonance gomfrequency is the optomechanical κ is thefrequency, cavity linewidth, is the cavity 2 resonance frequency, gom is the optomechanical coupling, κ is the cavity linewidth, n is the cavity photon number when the detuning is zero n  4Pin e  2 , κe is the external cavity linewidth and photon number when the detuning is zero n = 4Pin κe /κ }ω, κ e is the external cavity linewidth and P0 P P+ cos(2 t ) is the optical input with static power P0 and Pac ,Pωacm0 power in = PPin P0 alternating and alternating power , ωism0the is 0 ac Pac cosm(02ωm0 t ) is the optical input with static power the mechanical frequency, m is the effective mechanical mass, γ is the mechanical damping factor,  mechanical frequency, meff iseff the effective mechanical mass, m is the m mechanical damping factor, x is x is displacement the displacement of mechanical resonator. the of mechanical resonator. To simulate can be be generalized To simulate the the response response of of the the coupled coupled Equations Equations (1) (1) and and (2), (2), the the equations equations can generalized and reduced to q and reduced to . e − geom xe) − κe/2)e e a(et) = (i (∆ a(et) + κe 1 + ε cos(2et)/2 (3) a(t )  i(   gom x )   2  a(t )   1   cos(2t ) 2 (3) .. . em xe + xe = Je xe + γ a*e a∗ (4) x   m x  x  Jaa (4) √ where the frequencies are normalized by ωm0 , et = ωm0 t, xe = gom x/ωm0 , e a = a/ n0 , 2 e x  g x  t    t e e e n0the  4modulation P0 e  2  , n0 = 4P 1, κ m=  aPac /P n0 0, is where the are∆/ω normalized ,m = γ e /κ }ω, ∆ = m , gom = by 0 κfrequencies omm /ωmm0 0 , εa = m 0, γ 0 , κ/ωm0 strength, and J = 4}n0 gom 2 /me f f ωm0 3 is the normalized optomechanical coupling strength.    m , gom  1 ,    m0 ,  m   m m0 ,   Pac P0 is the modulation strength, and To get the physical insight of this model and simplify the simulation complexity, the parameters are 2 3 J  4 n g m  is the normalized strength. −3optomechanical e 0 om eff m 0 e eom coupling set as ∆ = −3, κe = 25, γ = 1. By setting ε = 0, Equations (3) and (4) m = 1.2 × 10 , J = 0.22, g are reduced to the conventional optomechanical coupled oscillators. The simulated response of the To get the physical insight of this model and simplify the simulation complexity, the parameters mechanical oscillators is shown in Figure 3 3a, in which the mechanical oscillator is not excited. However, are set as   3 ,   25 ,  m  1.2 10 , J  0.22 , gom  1 . By setting   0 , Equations (3) and (4) are the mechanical oscillator is excited into self-oscillation by setting ε = 1 with other parameters the reduced to the conventional optomechanical The simulated response of the same, which is shown in Figure 3b. It can becoupled seen thatoscillators. the modulation can effectively excite the mechanical oscillators is shown in Figure 3a, in which the mechanical oscillator is not excited. mechanical resonators into self-oscillation even though the passive feedback is too small. However, the mechanical oscillator is excited into self-oscillation by setting   1 with other

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parameters the same, which is shown in Figure 3b. It can be seen that the modulation can effectively excite thesteady mechanical resonators self-oscillation even though the passive feedback isstrength too small.is The response of the into mechanical amplitudes as a function of modulation The steady response of the mechanical amplitudes as a function of modulation strength is shown shown in Figure 3c. When the modulation strength is smaller than ε = 0.25, the mechanical in Figure 3c. the modulation strength is smaller than ε> 0.25, themechanical mechanicaloscillators oscillatorsare are 0.25 ,the oscillators areWhen not excited. Above a certain threshold power not excited. Above a certain threshold power , the mechanical oscillators are excited into self  0.25 excited into self-oscillation and the amplitudes increase approximately linearly with the modulation oscillation and the linearly with are the excited modulation strength. This strength. This can beamplitudes explained asincrease follows:approximately as the mechanical oscillation into self-oscillation, canamplitudes be explained as follows: the mechanical oscillation are excited into self-oscillation, the the are saturated andasincrease linearly with the power. amplitudes are saturated and increase linearly with the power.

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Figure 3. The theoretical simulation of the normalized mechanical response under the periodical Figure 3. The theoretical simulation of the normalized mechanical response under the periodical modulation. (a) The mechanical oscillator is not excited at ε = 0; (b) the mechanical oscillator is excited modulation. (a) The mechanical oscillator is not excited at ε = 0; (b) the mechanical oscillator is excited at ε = 1; (c) the steady amplitudes as a function of the modulation strength. at ε = 1; (c) the steady amplitudes as a function of the modulation strength.

2. Fabrication and Experimental Setup 2. Fabrication and Experimental Setup The fabrication process of the optomechanical resonators is described in this section, which is The fabrication process of the optomechanical resonators is described in this section, which is based on the silicon nanophotonic processes [28,29]. The racetrack optical cavity had a footprint of 25 based on the silicon nanophotonic processes [28,29]. The racetrack optical cavity had a footprint of µ m × 20 µm and was fabricated in the silicon-on-Insulator (SOI) wafer, which had a 2 µm box layer 25 µm × 20 µm and was fabricated in the silicon-on-Insulator (SOI) wafer, which had a 2 µm box layer between the 340 nm silicon structure layer and substrate. The optomechanical resonator was between the 340 nm silicon structure layer and substrate. The optomechanical resonator was patterned patterned by deep-ultraviolet lithography and followed by plasma dry etching. Note that a hard by deep-ultraviolet lithography and followed by plasma dry etching. Note that a hard mask process mask process was adopted to ensure accurate etching because the photoresist is too thick to withstand was adopted to ensure accurate etching because the photoresist is too thick to withstand reactive ion reactive ion etching [30]. When the etching depth is above 100 nm, the hard mask can help to protect etching [30]. When the etching depth is above 100 nm, the hard mask can help to protect the etching the etching profiles in order to ensure the linewidth and sidewall surface roughness. profiles in order to ensure the linewidth and sidewall surface roughness. A hard mask made from a 70 nm thin layer of SiO2 was deposited on the surface of wafer by A hard mask made from a 70 nm thin layer of SiO2 was deposited on the surface of wafer by low-temperature plasma-enhanced chemical vapor deposition (PECVD). Subsequently, a 90 nm low-temperature plasma-enhanced chemical vapor deposition (PECVD). Subsequently, a 90 nm bottom bottom anti-reflective coating (BARC) and 700 nm photoresist (PR) was dispensed on the surface of anti-reflective coating (BARC) and 700 nm photoresist (PR) was dispensed on the surface of the hard the hard mask. The bottom anti-reflective coating is also a must to reduce the standing wave effect mask. The bottom anti-reflective coating is also a must to reduce the standing wave effect from the from the lithography to ensure the linewidth. Another important issue is the hydrogen fluorider lithography to ensure the linewidth. Another important issue is the hydrogen fluorider release process, release process, which is used to make the silicon structures movable in the desired directions. The which is used to make the silicon structures movable in the desired directions. The hydrogen fluorider hydrogen fluorider vapor is good choice to release the structures because it only reacts with SiO2 but vapor is good choice to release the structures because it only reacts with SiO2 but not with silicon not with silicon waveguide. These unique characters can leave the etched waveguide with a good waveguide. These unique characters can leave the etched waveguide with a good profile and a smooth profile and a smooth surface without causing the stiction problems. More importantly, the gap surface without causing the stiction problems. More importantly, the gap between the silicon and between the silicon and substrate can be controlled by choosing different etching times. The etching substrate can be controlled by choosing different etching times. The etching rate is estimated as rate is estimated as 30 nm/min in our structures. A scanning electron microscope (SEM) image of the 30 nm/min in our structures. A scanning electron microscope (SEM) image of the fabricated device fabricated device is shown in Figure 4a,b. It should be noted that the estimated width of the fabricated is shown in Figure 4a,b. It should be noted that the estimated width of the fabricated mechanical mechanical cantilever is 100 nm, which is smaller than the original design of 200 nm. This is due to cantilever is 100 nm, which is smaller than the original design of 200 nm. This is due to imperfect imperfect fabrication, such as lithography or etching, in which an unwanted deviation can occur. fabrication, such as lithography or etching, in which an unwanted deviation can occur.

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Figure 4. 4. (a) scanning scanning electron microscope microscope (SEM) image image of the the fabricated device; device; (b) zoom-in zoom-in view Figure Figure 4. (a) (a) scanning electron electron microscope (SEM) (SEM) image of of the fabricated fabricated device; (b) (b) zoom-in view view with the width labeled. with the width labeled. with the width labeled.

The experimental setup is shown in Figure 5. In the experiment, the probe light was used to Figure 5. 5. In the experiment, the probe light was used to The experimental setup is shown in Figure measure the mechanical cantilever in the racetrack optical cavity and pumped in a different direction measure the mechanical cantilever in the racetrack optical cavity and pumped in a different direction from the pump light to avoid influencing the pump light. The transmission spectrum of the optical avoid influencing influencing the the pump pump light. light. The transmission transmission spectrum of the optical from the pump light to avoid cavity was firstly measured by a broadband light from a 12 dBm ASE light source (Amonics ALS-CLcavity ASE light source (Amonics ALS-CL-13, cavity was was firstly firstlymeasured measuredby byaabroadband broadbandlight lightfrom froma a1212dBm dBm ASE light source (Amonics ALS-CL13, Kowloon, Hong Kong, China) and then detected by an optical spectrum analyzer (OSA) 13, Kowloon, anddetected then detected by an optical analyzer spectrum(OSA) analyzer (OSA) Kowloon, HongHong Kong,Kong, China)China) and then by an optical spectrum (AQ6370D, (AQ6370D, Yokogawa Test & Measurement Corporation, Tokyo, Japan) by switching S1 and S3. The (AQ6370D,Test Yokogawa Test & Measurement Japan) by switching S1resolution and S3. The Yokogawa & Measurement Corporation,Corporation, Tokyo, Japan)Tokyo, by switching S1 and S3. The of resolution of the OSA was 0.02 nm. By switching S2 and S4, the mechanical response was measured. resolution of 0.02 the OSA was 0.02 nm.S2 Byand switching S2 and S4, the mechanical response The waspump measured. the OSA was nm. By switching S4, the mechanical response was measured. light The pump light from a tunable laser (Santec TSL 510, Hackensack, NJ, USA) was modulated by an The pump lightlaser from(Santec a tunable TSL 510, NJ, USA)by was by an from a tunable TSLlaser 510, (Santec Hackensack, NJ, Hackensack, USA) was modulated anmodulated electrical-optical electrical-optical modulator and the frequency was controlled by a programmable function generator electrical-optical modulator frequency controlled byfunction a programmable generator modulator and the frequencyand wasthe controlled bywas a programmable generatorfunction (PM 5193, Philips, (PM 5193, Philips, Amsterdam, The Netherlands). The power of the probe light from a tunable laser (PM 5193, Philips, Amsterdam, The power the aprobe light from a tunable Amsterdam, The Netherlands). TheNetherlands). power of the The probe light of from tunable laser (Santec TSLlaser 510, (Santec TSL 510, Hackensack, NJ, USA) was controlled by the variable optical attenuator. The probe (Santec TSL 510, Hackensack, NJ, USA) controlled by the variable The optical attenuator. probe Hackensack, NJ, USA) was controlled by was the variable optical attenuator. probe light wasThe separated light was separated from the pump light by the bandpass filter and was received by the photodetector light was separated thebandpass pump light by the filter by andthe was received by the photodetector from the pump lightfrom by the filter andbandpass was received photodetector (FPD 510, Menlo (FPD 510, Menlo Systems GmbH, Planegg, Germany), in which the power spectral density of the (FPD 510, MenloPlanegg, SystemsGermany), GmbH, Planegg, in whichdensity the power density of the Systems GmbH, in whichGermany), the power spectral of thespectral mechanical oscillation mechanical oscillation in the frequency domain and time domain was shown in the oscilloscope mechanical oscillation inand the time frequency domain and time domain was shown in the oscilloscope in the frequency domain domain was shown in the oscilloscope (MDO4104B-3, Tektronix, (MDO4104B-3, Tektronix, Inc., Beaverton, OR, USA). The device was measured under a high-vacuum (MDO4104B-3, USA). under The device was measured under(2a× high-vacuum Inc., Beaverton,Tektronix, OR, USA).Inc., The Beaverton, device was OR, measured a high-vacuum chamber 10−6 mBar). chamber (2 × 10−6 mBar). chamber (2 × 10−6 mBar).

Figure 5. The schematic of the experimental setup. Abbreviations: EOM, electro-optical modulator; Figure 5. 5. The The schematic schematic of of the the experimental experimental setup. setup. Abbreviations: Abbreviations: EOM, EOM, electro-optical modulator; modulator; Figure CL, optical circulator; VOA, variable optical attenuator; BF, bandpass filter;electro-optical PD, photon detector; OS, CL, optical VOA, optical attenuator; BF, bandpass filter; PD,PD, photon detector; OS, CL, optical circulator; circulator; VOA,variable variable optical attenuator; bandpass detector; oscilloscope; ASE, amplified spontaneous emission light;BF, OSA, opticalfilter; spectrum photon analyzer; S1–S4, oscilloscope; ASE, amplified spontaneous emission light; OSA, optical spectrum analyzer; S1–S4, OS, oscilloscope; optical switch. ASE, amplified spontaneous emission light; OSA, optical spectrum analyzer; S1–S4, optical switch. switch. optical

3. Experimental Results and Discussions 3. Experimental Results and Discussions 3. Experimental Results and Discussions 3.1. Optical Characterization of the Racetrack Optical Cavity 3.1. Optical Characterization of of the the Racetrack Racetrack Optical Optical Cavity Cavity 3.1. Optical Characterization In the experiment, the transmission spectrum of the racetrack resonator was firstly characterized In the the experiment, the transmission spectrum of the racetrack resonator was firstly characterized experiment, the transmission racetrack firstly characterized by a In low-power broadband light. Figure spectrum 6a shows of thethe output lightresonator from the was grating coupler. by a low-power broadband light. Figure 6a shows the output light from the grating coupler. by a low-power light. Figurewas 6a shows the output from therange grating coupler. The optical broadband resonance wavelength separated by the light free spectral (FSR) with a range The optical resonance wavelength was separated by the free spectral range (FSR) with a range of 5.34 nm. In order to separate the pump and probe light, resonance wavelength at 1571.86 nm was of 5.34 nm. In order to separate the pump and probe light, resonance wavelength at 1571.86 nm was

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The optical resonance wavelength was separated by the free spectral range (FSR) with a range Micromachines 2018, 8, x 6 of 10 of 5.34 nm. In order to separate the pump and probe light, resonance wavelength at 1571.86 nm was used asthe thepump pump channel resonance wavelength at 1587.94 used as the Micromachines 2018, 8, xlight 6 ofprobe 10 used as light channel andand resonance wavelength at 1587.94 nm was nm usedwas as the probe light lightchannel. channel.The The transmission spectrum at 1571.86 nmawith a Lorenz transmission spectrum at 1571.86 nm with Lorenz fitting isfitting shownisinshown Figure in 6b.Figure The 6b. 4 with used as the pump light and wavelength The optical quality factor 8.4 ×4 10 20 dB. at 1587.94 nm was used as the probe light optical quality factor is is 8.4channel × 10 with aresonance dipaofdip 20 of dB. channel. The transmission spectrum at 1571.86 nm with a Lorenz fitting is shown in Figure 6b. The optical quality factor is 8.4 × 104 with a dip of 20 dB.

Figure 6. Transmission (a) Transmission spectrumof of the the optical optical racetrack showing resonance at different Figure 6. (a) spectrum racetrackcavity cavity showing resonance at different optical wavelengths. Resonance wavelength at 1571.86 nm was used as the pump light channel and optical wavelengths. Resonance wavelength at 1571.86 nm was used as the pump light channel and Figure 6.wavelength (a) Transmission spectrum the used optical cavity different resonance at 1587.94 nm ofwas asracetrack the probe lightshowing channel.resonance (b) The atzoom-in resonance wavelength at 1587.94 nm wavelength was used asatthe probenm light channel. (b) The zoom-in transmission optical wavelengths. Resonance 1571.86 was used as the pump light channel transmission spectrum at 1571.86 nm with a Lorenz fitting, which shows the optical quality factor, and is spectrum at 1571.86 nm with a Lorenz fitting, which shows the optical quality factor, is Q = 8.4 × 104 . resonance 4 wavelength at 1587.94 nm was used as the probe light channel. (b) The zoom-in

3.2.

Q = 8.4 × 10 . transmission spectrum at 1571.86 nm with a Lorenz fitting, which shows the optical quality factor, is QCharacterization = 8.4 × 104. Optical of of thetheMechanical 3.2. Optical Characterization Mechanical Cantilever Cantilever

the characterization the optical racetrack another important is to After the characterization of optical racetrack cavity,cavity, another important issue isissue to characterize 3.2.After Optical Characterization of the theofMechanical Cantilever characterize the vibration mode of thecantilever. mechanical cantilever. In the experiment, probewith light a with a the vibration mode of the mechanical In the experiment, a probea light power of After the characterization of the optical racetrack cavity, another important issue is to power of 20 µ W at wavelength λ pr = 1587.90 nm was coupled to the cavity and the output light was 20 µW at wavelength λpr = 1587.90 nm was coupled to the cavity and the output light was analyzed by characterize the vibration mode of the spectral mechanical cantilever. In the experiment, a probe light with a analyzed by the oscilloscope. The power density of the mechanical in 7. Figure the oscilloscope. The power spectral density of the mechanical motion ismotion shownisinshown Figure Since the power of 20 µ W at wavelength λ pr = 1587.90 nm was coupled to the cavity and the output light was 7. Since the mechanical cantilever can vibrate in the x and z direction, two mechanical modes are 1.53 mechanical cantilever can vibrate in the x and z direction, two mechanical modes are 1.53 MHz with analyzed the oscilloscope. Theofpower spectral density of with the mechanical is shown in kHz, Figure MHz with by mechanical linewidth 1 kHz, and 2.52 MHz mechanicalmotion linewidth of 1.5 mechanical of 1 kHz, and 2.52vibrate MHz linewidth of 1.5 kHz, respectively. 7. Sincelinewidth the The mechanical cantilever can inwith the xmechanical and z direction, mechanical modes are 1.53 respectively. finite element simulation of the mechanical modes is two shown in the inset figures. It The finite element simulation of the mechanical modes is shown in the inset figures. It should MHz with mechanical linewidth of 1 kHz, and 2.52 MHz with mechanical linewidth of 1.5 kHz, be should be noted that the residual stress due to the fabrication will result in a shift of the practical respectively. The finite element simulation of the mechanical is shown in practical the inset figures. It noted that the residual stress due to the fabrication will resultmodes in a shift of the mechanical mechanical resonance frequency. should be noted that the residual stress due to the fabrication will result in a shift of the practical resonance frequency. mechanical resonance frequency.

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Figure 7. (a) The power(a) spectral density of the measured signals, showing the(b) mechanical vibration motions. The inset is the finite element simulation of the two mechanical vibration modes, which Figure 7. (a) The power spectral density the measured signals, showing the of mechanical vibration correspond x and z direction. Theof zoom-in power density twovibration mechanical Figure 7. (a) Theto power spectral density(b) of the measured signals,spectrum showing the mechanical motions. motions. The inset is the finite element simulation of the two mechanical vibration modes, which oscillators. The inset is the finite element simulation of the two mechanical vibration modes, which correspond to x and correspond to x and z direction. (b) The zoom-in power spectrum density of two mechanical z direction. (b) The zoom-in power spectrum density of two mechanical oscillators. oscillators.


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3.3. Excitation Excitation of of the the Mechanical Mechanical Cantilever Cantilever 3.3. In order order to to demonstrate demonstrate the parametric excitation of mechanical cantilever, aa modulated modulated pump light with withaapower powerofof 200 µW at wavelength λpu1571.50 = 1571.50 nm was coupled the racetrack light 200 µW at wavelength λpu = nm was coupled to theto racetrack opticaloptical cavity cavity to excite the mechanical cantilever. When the modulated frequency is twice the mechanical to excite the mechanical cantilever. When the modulated frequency is twice the mechanical frequency frequency ωp/2π = 3.06 the mechanical excited, whichin is Figure shown8a. in Figure 8a. and The ω MHz, the MHz, mechanical cantilevercantilever is excited,iswhich is shown The black p /2π = 3.06 black andshows red curve showsthermal the original thermal mechanical vibrationsvibrations and amplified vibrations red curve the original mechanical vibrations and amplified separately. It can separately. canpower be seen that the powerisspectral greatly dBm toexcitation −20 dBm. be seen thatItthe spectral density greatly density excited is from −79excited dBm tofrom −20 −79 dBm. This Thisalso excitation can also beindemonstrated in thewhich time domain, is shown Figure in which can be demonstrated the time domain, is shownwhich in Figure 8b, in in which the8b, mechanical the mechanical cantilever excited by the light. The8a peak 8a is −25 dBm, which cantilever is excited by theispump light. Thepump peak in Figure is −in 25Figure dBm, which corresponds to corresponds to 12.5 mV rms (35 mV pp) in Figure 8b. The peak in black curves is thermal motion 12.5 mV rms (35 mV pp) in Figure 8b. The peak in black curves is thermal motion of the cantilever. of the cantilever.

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(b)

Figure 8. (a) The power spectral density of the measured signals, showing the thermal mechanical Figure 8. (a) The power spectral density of the measured signals, showing the thermal mechanical noise (black curve) and amplified mechanical motions (red curve) when the pump light is in the state noise (black curve) and amplified mechanical motions (red curve) when the pump light is in the state of off and on separately; (b) the time domain traces showing the original mechanical vibrations and of off and on separately; (b) the time domain traces showing the original mechanical vibrations and amplified vibrations separately. amplified vibrations separately.

Then, the wavelength of the pump light was changed to demonstrate the extended working Then, wavelength the pump light was to demonstrate the extended working range. range. The the detuning of theof pump light Δ = λpu − λchanged opu was swept from −80 pm to 50 pm at fixed a power The detuning of the pump light ∆ = λpu − λopu was swept from −80 pm to 50 pm at fixed a power of 200 µW to observe the parametric excitation, which is shown in Figure 9a. It can be seen that the of 200 µW to observe the parametric excitation, which is shown in Figure 9a. It can be seen that the working range is extended from the blue-detuning to red-detuning region with a range of 130 pm. working range is extended from the blue-detuning to red-detuning region with a range of 130 pm. At the same time, increasing the modulation strength can enhance the excitation. In the experiment, At sameoftime, increasing strength can enhance the excitation. In the thethe power the pump light the wasmodulation gradually increased from 0 to 200 µW at fixed −60 pmexperiment, to observe the power of the pump light was gradually increased from 0 to 200 µW at fixed −60 pm to observe the the effect of the modulation strength on the excitation. The detailed experimental results are shown effect of the modulation strength on the excitation. The detailed experimental results are shown in in Figure 9a. It should be noted that the results shown in Figure 9a,b were obtained in different Figure 9a. It should be noted that the results shown in Figure 9a,b were obtained in different conditions: conditions: one is for fixed optical power, while the other one is for fixed optical wavelength. By one is for fixed optical whilethe themechanical other one is for fixed wavelength. increasing the increasing the power ofpower, pump light, motion wasoptical gradually amplified.By The relationship power of pump light, the mechanical motion was gradually amplified. The relationship between the between the peak value and the pump power is shown in Figure 9b with a fitting curve. Even though peak value and the pump power is shown in Figure 9b with a fitting curve. Even though amplitudes amplitudes increase with the optical power, larger optical power will result in the instability of the increase with the optical power, larger optical power will result in the instability of the system due to system due to the thermo-optical effects of the silicon structures. The largest amplitude of the the thermo-optical effects of the silicon largest amplitudecoupling of the mechanical is mechanical oscillator is estimated as 5structures. nm. Since The the optomechanical factor is goscillator om /2π = 450 estimated as 5cavity nm. Since the optomechanical factor is gom /2π = to 450 MHz/nm, the cavity MHz/nm, the frequency shift is 2π × 2.25coupling GHz, which is comparable the cavity linewidth 2π frequency shift is 2π × 2.25 GHz, which is comparable to the cavity linewidth 2π × 2.27 GHz. × 2.27 GHz. It Figure 9b 9b thatthat the the power spectral densities are not with the optical power. It can canbe beseen seenfrom from Figure power spectral densities arelinear not linear with the optical Here, givewe a rough for this nonlinearity. When the mechanical oscillators are excited, power.we Here, give aexplanation rough explanation for this nonlinearity. When the mechanical oscillators are the mechanical nonlinearity starts to play a role. In particular, our theoretical simulation is based on excited, the mechanical nonlinearity starts to play a role. In particular, our theoretical simulation is small linear approximation, so when the mechanical oscillation is large, the nonlinearity [31,32] should based on small linear approximation, so when the mechanical oscillation is large, the nonlinearity be takenshould into account. [31,32] be taken into account.


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(a)

(b)

Figure9. 9. The power spectral density of measured the measured signals the wavelength detuning Figure (a)(a) The power spectral density of the signals whenwhen the wavelength detuning is fromis pmpm to (curves 50 pm (curves are vertically for clarification); (b) value the peak value spectral of power −from 80 pm−80 to 50 are vertically offset foroffset clarification); (b) the peak of power spectral density at the mechanical resonance frequency versus the pump power. density at the mechanical resonance frequency versus the pump power.

4. Conclusions 4. Conclusions In this study, the excitation of optomechanical resonators by periodical modulation was In this study, the excitation of optomechanical resonators by periodical modulation was experimentally demonstrated. A mechanical cantilever is excited by the modulated optical field in an experimentally demonstrated. A mechanical cantilever is excited by the modulated optical field in an optical resonator with an optical quality factor of 8.43 × 104. The working wavelength of the pump optical resonator with an optical quality factor of 8.43 × 104 . The working wavelength of the pump light is extended from blue-detuning to red-detuning region with a range of 130 pm. The excitation light is extended from blue-detuning to red-detuning region with a range of 130 pm. The excitation is is enhanced by increasing the optical power. Compared with conventional mechanical excitation enhanced by increasing the optical power. Compared with conventional mechanical excitation induced induced by the passive back action or active feedback control, this method provides a simple and by the passive back action or active feedback control, this method provides a simple and effective effective approach [33–35]. This demonstration will benefit the optical mass sensor based on the approach [33–35]. This demonstration will benefit the optical mass sensor based on the parametric parametric excitation and be useful for improving performance in practical applications, such as excitation and be useful for improving performance in practical applications, such as gyroscopes with gyroscopes with an extended working range. an extended working range. Acknowledgments:This Thiswork workwas wassupported supportedbybySingapore SingaporeNational NationalResearch ResearchFoundation Foundationunder underthe theIncentive Incentive Acknowledgments: for Research & Innovation Scheme (1102-IRIS-05-01) administered by PUB, and under the Competitive Research for Research & Innovation Scheme (1102-IRIS-05-01) administered by PUB, and under the Competitive Research Program Program(NRF-CRP13-2014-01). (NRF-CRP13-2014-01). Author the AuthorContributions: Contributions:J.H. J.H.and andA.L. A.L.jointly jointlyconceived conceivedthe theidea ideaofofthis thisstudy. study.J.H. J.H.fabricated fabricated thedevices. devices.J.H. J.H.and and M.F.K. performed the theoretical simulations. J.H. performed the measurements with the suggestions of J.W. and M.F.K. performed the theoretical simulations. J.H. performed the measurements with the suggestions of J.W. T.C., J.H. and A.L. analyzed the results. J.H. and A.L. prepared the manuscript. All authors discussed the results andcommented T.C., J.H. and A.L.manuscript. analyzed the results. J.H. and A.L. prepared the manuscript. All authors discussed the and on the results and commented on the manuscript. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.

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