JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 2, JANUARY 15, 2014 309
Characterization of OptomechanicalRF frequency Mixing/Down-Conversion and its
Application in Photonic RF ReceiversFenfei Liu, Student Member, OSA and Mani Hossein-Zadeh, Member, IEEE, Member, OSA
Abstract—We have characterized the process of radio-frequency(RF) frequency mixing and signal down-conversion in radiationpressure driven optomechanical RF oscillators. We have studiedthe dependence of the optomechanical mixing process on RF fre-quency, optical pump power and wavelength detuning and verifiedthe existence of a linear regime where down-converted power isproportional to the RF input power. These outcomes show thatoptomechanical oscillator (OMO) has the potential to be used asfrequency down-converter in RF over fiber links and photonicRF receivers. We have verified the fidelity of the optomechanicaldown-conversion process and demonstrated the first optomechan-ical voice down-conversion from an RF carrier.
Index Terms—Optomechanical oscillation, optical resonators,oscillators, RF Frequency conversion, RF-Photonics.
I. INTRODUCTION
R ECENTLY cavity optomechanics and related devices havebecome the subject of intensive research and develop-
ment [1]–[10]. Since the observation of radiation pressure basedoscillation [11]–[13] and cooling [14]–[17] in optomechanicalmicroresonators, significant progress has been made in the de-sign and fabrication of microresonators with strong optome-chanical coupling strength and large oscillation frequencies [5],[18]–[21] as well as observation and measurement of new clas-sical and quantum phenomena in these devices [22]–[31]. How-ever, less effort has been dedicated to the study of practical ap-plications of optomechanical devices beyond their importance
Manuscript received April 28, 2013; revised August 7, 2013 and October 1,2013; accepted October 4, 2013. Date of publication October 17, 2013; dateof current version December 16, 2013. This work was supported in part by theAir Force Office of Research Grant FA9550-12-1-0049 and in part by NationalScience Foundation under Grant ECCS 1055959.
F. Liu is with the Center for High Technology Materials and the PhysicsDepartment, University of New Mexico, Albuquerque, NM 87106 USA (e-mail: [email protected]).
M. Hossein-Zadeh is with the Center for High Technology Materials and theElectrical and Computer Engineering Department, University of New Mexico,Albuquerque, NM 87106 USA (e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
This paper has supplementary downloadable multimedia material available athttp://ieeexplore.ieee.org provided by the authors. This includes a .avi file. Thevideo shows the correlation between down-converted sound and optomechanicaloscillation. When the microtoroid is coupled to the fiber-taper the optical powerinduces optomechanical amplitude oscillation at the RF career frequency. Theproduct of this oscillation and the original amplitude modulations (up-convertedaudio signal) generates optical amplitude modulation at the audio frequency thatcan be heard from the speaker. When the microtoroid (OMO) is decoupled fromthe fiber-taper, the local oscillator and the mixing function (provided by the mi-crotoroid) are eliminated and the detected signal is still the up-converted audiosignal that cannot be heard from the speaker. This material is 118 MB in size.
Digital Object Identifier 10.1109/JLT.2013.2286329
as platforms for exploring fundamental physical phenomena.Given the recent progress toward fabrication of monolithic op-tomechanical cavities [19]–[21], that has enabled their inte-gration with on-chip optoelectronic systems, it is important toexplore the potential functionalities hidden in the mutual interac-tion between optical and mechanical modes of optomechanicalmicrocavities. Optomechanical wavelength conversion [8], pho-tonic clock [7], [10], optomechanical memory [30], mass sens-ing [31], optomechanical wavelength routing [29], RF down-conversion [7], [9] are applications that have been proposedand/or demonstrated so far. Between the two manifestationsof optomechanical interaction in microcavities (i.e., amplifica-tion/oscillation and cooling), optomechanical oscillation is abetter candidate for practical applications where atmosphericpressure and room temperature operation, simplicity, and costare important factors. Here we focus on characterization of RFfrequency mixing in optomechanical domain and its potentialapplications in RF/IF over fiber communication systems andoptomechanical radio receivers.
The idea of RF frequency down-conversion based on optome-chanical oscillation was proposed and demonstrated in ref. [9].Preliminary experiments have shown that if the optical pumppower is modulated by a suppressed-carrier RF signal with acarrier frequency equal to the optomechanical oscillation fre-quency, the detected output spectrum of the optomechanicaloscillator (OMO) will contain the baseband signal [9]. In otherwords OMO may simultaneously function as local oscillator andRF mixer in optomechanical domain. Here for the first time wecharacterize the performance of the OMO as an RF frequencymixer and down-converter. Our experiments and theoretical cal-culations have demonstrated the existence of a linear dynamicrange where the signals can be down-converted with reasonablefidelity.
We use the silica microtoroid OMO as our experimental plat-form. As the first reported OMO [11]–[13], silica microtoroidis a simple and elegant optomechanical resonator that can op-erate at room temperature and atmospheric pressure with rela-tively low threshold power and phase noise [7], [10]. Throughmany years of characterization and modeling, the main prop-erties of this OMO are carefully studied and characterized [1],[7], [10]–[13], [32]–[35]. Although for our study we use sil-ica microtoroid OMO, with minor modifications the analysisand the outcomes are valid for all kinds of radiation pressuredriven OMOs with different geometries and materials and willbe an important step towards the application of these OMOs inRF-photonics.
310 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 2, JANUARY 15, 2014
II. RF FREQUENCY MIXING AND DOWN-CONVERSION IN OMO
The response of radiation pressure driven OMO to modulatedoptical pump can be evaluated using the differential equationsthat govern the coupled dynamics of the mechanical and opticalmodes [1], [10], [12]:
r′′(t) + γ0r′(t) + Ω2r(t) = Frp(t) =
πε0n2eff s
meff|E(t)|2 (1)
dE(t)dt
+ E(t)[
ωl
2Qtot− iΔω − i
ω0
R0r(t)
]= i
κ
τR
√2Pin
s′cε0neff
(2)
Eout(t) =√
1 − κ2Ein(t) + iκE(t). (3)
The first equation describes the motion of the harmonic os-cillator in the presence of radiation pressure, and the secondequation describes the variation of circulating optical field (E)in the resonant cavity. Here r is the radial displacement of thetoroidal region, Ω = 2πfOMO , R0 is the major radius of themicrotoroid, γ0 is the intrinsic mechanical damping factor, meffis the effective mass, neff is the effective refractive index of theoptical mode, c is the speed of light in vacuum, s and s′ arecross-sectional areas of the optical mode in the microtoroid andwaveguide, respectively, ωl = 2πνl is the pump laser frequency,ω0 = 2πν0 is the resonant frequency of the optical cavity, Δω= ωl – ω0 is the optical frequency detuning, τR is the photonroundtrip time, Pin is the optical power coupled to the micro-cavity, Q0 , Qext and Qtot are the intrinsic, external and totaloptical quality factors, respectively. κ (=(τRω0 /Qext)1/2) is thecoupling coefficient between the waveguide and resonator, andEin is the input optical field (i.e., at the coupling junction themagnitude of the coupled E-field from the waveguide into thecavity is equal to κEin is). When Pin is constant and largerthan the optomechanical oscillation threshold power (Pth), theoptomechanical gain exceeds mechanical loss and the periodicmotion of r at an eignmechanical frequency of the structure(fOMO ∼ fmech) ensues [10]–[13]. This harmonic motion man-ifests itself as amplitude modulation of the optical output power(i.e., Pout ∝ |Eout |2 ∝ Cos(2πfOMO t)). So far mainly time-independent (CW) optical input power (Pin) has been used inall experimental and theoretical studies.
Once modulated by an RF signal (in general an RF carriermodulated by a baseband signal), Pin becomes a time varyingfunction. Assuming a Mach–Zehnder (MZ) modulator is usedfor amplitude modulation, Pin(t) can be written as:
Pin(t) =Po
2{1 + Cos (φ0 + M [1 + mCos(ωbt)]Cos(ωRF t))}
(4)where ωRF (=2πfRF ) is the RF carrier frequency, ωb (=2πfb )is the baseband (data) frequency, M = πVRF /Vπ (VRF is the am-plitude of the RF carrier), m is the RF modulation index and P0is the input optical power to the modulator. m is determined bythe baseband power and the properties of the electronic mixer.In order to simulate the RF spectrum of the OMO optical out-put power in the presence of a modulated input power, one canderive Pout(t) (∝|Eout(t)|2) using Eqs. (1)–(4), and then cal-
culate its Fourier transform. We refer to this method as the timedomain differential equation method or TDE. Although TDEapproach can accurately predict the output of an OMO drivenby a modulated optical pump, it is a time consuming numer-ical calculation and does not clearly show the role of variousparameters in the optomechanial RF mixing process.
Here we also use a semi-empirical approach based on oscilla-tory transfer function (OTF) approximation to estimate the out-put spectrum of the OMO with modulated pump by expandingthe response based on the oscillation in the absence of modula-tion (m = M = 0). This approach reveals the relation betweenoptomechanical oscillation and mixing/down-conversion and isuseful for studying the behavior of the RF OMO mixer in prac-tical applications.
When fOMO is smaller than the optical resonant bandwidth(weak retardation regime), and the pump power is small enoughsuch that P
(1)OMO > P
(n)OMO (where P
(n)OMO is the nth harmonic
in the spectrum of the OMO [10], [35]) the optomechanicaloscillation can be explained as the modulation of the pumplaser by an oscillating Lorentzian transfer function [35]. Theoscillatory transfer function (OTF) of the optomechanical cavityabove threshold (Pin > Pth) can be written as:
TOMO =Eout
Ein=
j(ωl − ω′0) + 1
τ − 2τe x t
j(ωl − ω′0) + 1
τ
(5)
where
ω′0(t) = ω0 [1 + Aω0Cos(2πfOMO t)]. (6)
Here τex and τ are the external and total decay times of the(τex = Qext /ω0 and τ = Qtot /ω0) and ω0(t) is the resonantfrequency of the optical mode that oscillates with a frequencyfOMO . Aω0 is the oscillation amplitude of the resonant fre-quency (ω0) that can be estimated using the optomechanicalgain equation [1]. Here Aω0 is considered a known functionof Pin /Pth , Δω and characteristics of the optomechanical res-onator. To maximize the linearity of the input amplitude modu-lation the modulator should be biased at quadrature (φ0 = π/2)and VRF /Vπ << 1. So (4), is simplified as:
Pin(t) = |Ein(t)|2 =P0
2
{1 + M
[Cos(ωRF)
+m
2Cos[(ωRF + ωb)t] +
m
2Cos[(ωRF − ωb)t]
]}
=P0
2Q(ωRF , ωb). (7)
Consequently the spectrum of the optical output power canbe written as:
Pout(t) = |Eout(t)|2 = |Ein (t)|2 ×∣∣∣∣∣j(ωl − ω′
0(t)) + 1τ − 2
τe x t
j(ωl − ω′0(t)) + 1
τ
∣∣∣∣∣2
=12Q(ωRF , ωs) ×
{P0
∣∣∣∣∣j(ωl − ω′
0(t)) + 1τ − 2
τe x t
j(ωl − ω′0(t)) + 1
τ
∣∣∣∣∣}2
.
(8)
LIU AND HOSSEIN-ZADEH: CHARACTERIZATION OF OPTOMECHANICAL RF FREQUENCY MIXING/DOWN-CONVERSION 311
The second term in (8) is simply the output of OMO in theabsence of pump modulation. So it can be written as [35]:
P(0)OMO + P
(1)OMOCos(ωOMO t) + P
(2)OMOCos(2ωOMO t) + h.o.t
(9)where h.o.t represents the higher order terms, P
(n)OMO (n =
1,2. . .) is the amplitude of the optical power oscillating atn × fOMO when input power Pin is constant and Pin is equal toP0 . P
(0)OMO is the portion of the transmitted optical power that
is not modulated by the optomechanical oscillation (at a givenoptical power). In other words P
(n)OMO /P (0)
OMO is the nth orderoptomechanical modulation index. Since the OTF approach isonly valid when P
(1)OMO > P
(2)OMO >> P
(3)OMO , and we are only
interested in first order mixing effects, we can ignore the higherorder terms (n > 1). When optical input power is constant (M =0 and m = 0), (8) results in the typical spectrum of an OMO withan input power of P0 /2 that consists of fOMO and its harmonics.
Pout(t) =12
{1 + M
[Cos(ωRF)
+m
2Cos[(ωRF + ωb)t] +
m
2Cos[(ωRF − ωb)t]
]}
×[P
(0)OMO + P
(1)OMOCos(ωOMO t)
]
=12
[P
(0)OMO + P
(1)OMOCos(ωOMO t)
]
+M
2Cos(ωRF)
[P
(0)OMO + P
(1)OMOCos(ωOMO t)
]
+[
Mm
4Cos[(ωRF + ωb)t] +
Mm
4Cos[(ωRF − ωb)t]
]
×[P
(0)OMO + P
(1)OMOCos(ωOMO t)
]. (10)
If the optical input power is modulated by a single-tone RFfrequency (m = 0, M �= 0), the last term in Eq. (10) vanishesand
Pout(t) =P
(0)OMO2
+MP
(0)OMO2
Cos(2πfRF t) +P
(1)OMO2
× Cos[2πfOMO t]+MP
(1)OMO4
{Cos[2π(fOMO +fRF)t]
+ Cos[2π(fOMO − fRF)t]
}. (11)
The last term in equation (11) is the modulated optical powerat mixed frequencies (f± = fOMO ± fRF) so the average de-tected RF power at f± can be written as:
PRF ,± =
[GD (0.25 × M × P
(1)OMO)
]2
2RL(12)
where GD (unit: V/W) is the photodetector conversion gain(GD = responsivity (A/W) × transimpedance gain (V/A)) andRL is the load resistor driven by the photodetector. M 2 is propor-tional to RF input power (PRF -in), so Eq. (12) predicts a linearrelation between the up/down-converted RF powers (PRF ,±)
and PRF -in. It is important to note that Eq. (12) is only validwhen the optical input power (Pin) is small enough to avoidharmonic oscillation (P (1)
OMO > P(2)OMO >> P
(3)OMO) and M is
small enough to keep Pin(t) > Pth . These conditions imposea fundamental limit on the linear dynamic range of the OMOmixer.
Next we consider the case of an RF carrier (fRF) equal tofOMO and modulated by a baseband signal with an RF mod-ulation index of m �= 0. For the sake of simplicity we con-sider a single frequency baseband fb . As shown below whenfRF = fOMO , the optomechanical mixing inside the oscillatingcavity generates a baseband modulated optical output power:
Pout(t)=[Mm
4Cos[(ωOMO + ωb)t]+
Mm
4Cos[(ωOMO − ωb)t]
]
×[P
(0)OMO + P
(1)OMOCos(ωOMO t)
]= .....
+MmP
(1)OMO
4Cos(ωbt) +
MmP(1)OMO
8
× {[Cos(2ωOMO − ωb)t] + [Cos(2ωOMO + ωb)t]} .
(13)
Note that the terms proportional to P(0)OMO are ignored because
they do not generate any power at fb . The first term on the right-hand side is the down-converted optical signal so the averageRF power detected at fb is equal to:
PRF−b =
[GD (0.25 × M × m × P
(1)OMO)
]2
2RL. (14)
In conclusion, if the oscillation power at the fundamental fre-quency (P (1)
OMO) is either measured or calculated, Eqs. (12) and(14) can predict the power in the mixed or down-converted com-ponents. Note that here we have ignored the filtering effect ofthe OTF and therefore the responses are frequency independentbut only valid when fRF < (ν0 /Qtot).
III. EXPERIMENTAL RESULTS
In this section we present the results of experimental charac-terization of the optomechanical mixing and down-conversionprocess.
A. Experimental Arrangement
Fig. 1 shows the experimental configuration used for char-acterizing the RF frequency mixing/down-conversion in an op-tomechanical oscillator (OMO). Here a silica microtoroid servesas the radiation-pressure driven OMO. The optical input power(Pin) to OMO is provided by a tunable near-IR laser (λlaser =1550 nm, νlaser = 194 THz). The amplitude of the laser outputis modulated in a Mach–Zehnder electro-optic (EO) modulator(Vπ = 4.3 V and Ins. Loss = 2.1 dB). The modulated opticalinput power is coupled to the OMO using a silica fiber-taper.The optical output power (Pout) is detected by an amplifiedphotodetector that converts it to an electric signal with a conver-sion gain GD (4 × 104 V/W). The detected signal is monitoredby an oscilloscope and analyzed in an RF spectrum analyzer.
312 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 2, JANUARY 15, 2014
Fig. 1. Experimental configuration used for characterizing RF frequencydown-conversion/mixing in optomechanical oscillators.
The measured power on the RF spectrum analyzer is referredto as “detected RF power” while the corresponding modulatedoptical power is referred to as “detected optical power.” Two sce-narios are considered corresponding to the two cases discussedin Section II: 1) The optical input power is directly modulatedby a single frequency (fRF �= fOMO) RF signal (dashed line inFig. 1) to characterize the mixing process. 2) The optical inputpower is modulated by a modulated RF carrier (fRF ± fb , wherefRF = fOMO) to characterize the down-conversion process. Inall experiments, the laser wavelength is blue detuned relative tothe resonant wavelength of the optical microcavity (λr−λlaser <0) and Pin > Pth to maintain stable optomechanical oscillation.
B. Single-Frequency Mixing
In the first set of measurements the amplitude of the opti-cal input power (Pin) was modulated by a single-frequency RFsignal (frequency = fRF ). Fig. 2(a) shows the RF spectrum ofthe detected OMO optical output power (Pout). As predictedby the last term in Eq. (11), the frequency mixing process in-side the oscillating cavity generates two frequency sidebandsaround the optomechanical oscillation frequency (fOMO). Ac-cording to Eq. (11), the amplitude of the two sidebands aroundfOMO (with frequencies defined as f+ = fOMO + fRF andf− = fOMO − fRF ) should be equal to (M /4)P (1)
OMO , where
P(1)OMO /2 is the modulated optical output power at fOMO in the
absence of pump modulation. The detected RF power at eachfrequency component (measured by feeding the photodetectedcurrent to the RF spectrum analyzer) is given by Eq. (12). TheRF power detected at fRF corresponds to the second term inEq. (11). Fig. 2(b) shows the detected RF power at the two sideband frequencies (i.e., f+ and f−) plotted against modulatingRF power (PRF -in), at constant Pin and wavelength detuning(Δλ=λr−λlaser). The existence of a linear regime where PRF ,±
Fig. 2. (a) RF spectrum of the Pout when Pin is amplitude modulated at fRF .(b-e) Detected RF power at f+ (=fOM O + fRF ) and f− (=fOM O − fRF )plotted against: (b) modulating RF power (PRF ), when fRF = 5 MHz, QL =3.1 × 106 , ΔλN = 0.55 and Pin /Pth = 3.6. The solid line is the calculatedbehavior using the OTF method. (c) Normalized optical power (Pin /Pth ), when,fRF = 5 MHz, ΔλN = 0.55, M = 0.15, and QL = 3.1 × 106 . (d) Normalizedwavelength detuning (ΔλN = Δλ/δλL ), when fRF = 5 MHz, QL = 3.1 ×106 , M = 0.15 and Pin /Pth = 3.6. (e) Modulating frequency (fRF ), whenΔλN = 0.55, QL = 3.1 × 106 , M = 0.15, Pin /Pth = 3.6. In part (f) Thesimulated 3 dB bandwidth for the up (down)-converted detected RF powers isplotted against the bandwidth of the loaded optical resonance.
is proportional to PRF -in, is in good agreement with the predic-tion of Eq. (12) (solid line). However as mentioned before thedynamic range of this linear regime is fundamentally limited bythe resonant optomechanical interaction. A detail experimentaland theoretical study of the impact of intrinsic and external pa-rameters on linear dynamic range is beyond the scope of thispaper.
Fig. 2(c) shows f+ and f− plotted against normalized opticalinput power (Pin /Pth), at constant PRF and ΔλN . The solidlines in these plots are the calculated behavior using the OTFmethod Eq. (12). Fig. 2(d) shows the detected RF power at f+and f− plotted against normalized wavelength detuning (ΔλN =Δλ/δλL , where δλL is the linewidth of the loaded optical res-onance), at constant PRF -in and Pin . Since wavelength depen-dence of P
(1)OMO is ignored in Eq. (12), the TDE is used for theo-
retical estimation. The efficiency of the mixing is controlled byΔλN and the optical input power simply defines the power levelof the local oscillator. Fig. 2(e) shows f+ and f− plotted againstmodulating frequency (fRF), at constant PRF -in, Pin and Δλ.Here again the solid lines are calculated using Eq. (1)–(3)since in the OTF method the filtering effect of the optical trans-fer function is not taken into account and therefore it cannotpredict the effect of fRF variations on the amplitude of the
LIU AND HOSSEIN-ZADEH: CHARACTERIZATION OF OPTOMECHANICAL RF FREQUENCY MIXING/DOWN-CONVERSION 313
Fig. 3. RF spectrum of the OMO detected output spectrum when fRF >δνL > fOM O . Here fOM O = 12 MHz and fRF = 500 MHz.
mixed components (i.e., f+ and f−) specially when fRF ≥ΔνL .Fig. 2(f) shows the simulated 3 dB bandwidth for the up (down)-converted detected RF powers as a function of bandwidth of theloaded optical resonance. Qualitatively the reduction of P+ andP− as fRF gets closer to the optical bandwidth of the loadedoptical mode (δνL = νr /QL ) can be explained by the spectraldependence of the circulating optical power inside the cavity.In Eq. (8) it is assumed that P0 enters the cavity and drivesthe OMO (that is true for constant P0). However in the pres-ence of the modulation, the optical input power is distributedbetween the CW component and sidebands (at νL ± fRF ). Aslong as Δν (=νlaser – νr ) < δνL , the CW component entersthe cavity while depending on magnitude of fRF the sidebandscan be partially or fully rejected by the cavity. ConsequentlyP0 depends on fRF and when fRF > δνL effectively only theCW component drives the oscillation and P0 is reduced by twotimes the optical power in the sidebands. Clearly when fRF <δνL the variation of P0 is a relatively complicated function offRF and depends on δνL and ΔλN . When fRF > δνL , stillthe interference between the components that miss the cavity(i.e., νlaser ± fRF ) and the optomechanically modulated wavecoupled out of cavity generates mixed frequency components.Fig. 3 shows the RF spectrum of the detected OMO output whenfRF > δνL > fOMO . The optomechanical sidebands up to sec-ond order harmonic are visible as sidebands around fRF . Sofor fRF > δνL > fOMO the optomechanical oscillation is up-converted as side bands around fRF with an efficiency that isindependent of fRF but it is controlled by ΔλN .
C. Optomehcnical Down-Conversion from RF Career
In the second set of experiments we have used a suppressedcarrier RF signal (m >> 2) to modulate optical input power tothe OMO. The RF carrier (fRF) is modulated by a single-tonebaseband (fb) signal with an modulation index of m ∼ 20 (RFcarrier power is 20 dB smaller than the sidebands). As predictedby Eq. (14), when fRF = fOMO , the mixing of fOMO with thesidebands (fRF ± fb) in optomechanical domain, generates adown-converted signal at the baseband frequency (fb). Upondetection in a photodetector and low-pass filtering, an electriccurrent proportional to the baseband signal will be generated.So as shown previously [9], OMO simultaneously serves asmixer and local oscillator in optical domain and is effectivelya photonic homodyne RF-receiver [36]. Fig. 4(a) and (b) show
Fig. 4. (a) Measured RF spectrum of the Pin when RF carrier (fRF ) ismodulated by a single frequency baseband (fb ). (b) Measured spectrum ofPRF−out when fRF = fOM O . PRF-b is the detected RF power at fb (downconverted baseband signal). PRF-1 and PRF-2 are the detected RF powerat fundamental optomechanical oscillation frequency (fOM O ) and its secondharmonic (2fOM O ). (c) Schematic diagram showing the spectrum of the RFand optical signals flowing through the system. (d) Calculated RF spectrum ofthe optical output power using the time-domain coupled differential equation.
the RF spectrum of the optical power entering (a) and exiting(b) the OMO. After up-conversion to optical frequencies (in theEO-modulator) and passing through the OMO, the optomechan-ical oscillation increases the amplitude of the modulated opticalpower at fRF = fOMO . Originally the modulated componentat fRF is 20 dB smaller than the sidebands and after pass-ing through OMO it becomes 20 dB larger than the sidebands.Once mixed with the sidebands (fRF ± fb), the large compo-nent at fRF = fOMO generates optical amplitude modulation atfb . Fig. 4(c) is a schematic diagram showing the spectrum ofthe RF and optical signals flowing through the system. Fig. 4(d)shows the simulated spectrum of PRF−out using Eqs. (1)–(3)that is in good agreement with the measured results.
Next we characterize the behavior of the down-converted op-tical power (Pb) as a function of input RF an optical powers.According to (13), Pb is proportional to M × m × P
(1)OMO /4 and
PRF-b is calculated by (14). M and m are determined by thecharacteristics of the RF mixer, the LO power and the basebandsignal power fed to the electronic mixer. In the weak harmonicgeneration regime (where OTF approximation is valid), P
(1)OMO
is proportional to Pin /Pth [10]–[13]. To verify the predicted lin-ear relation between PRF-b and Pb with PRF -in and Pin /Pth ,we have measured three different microtoroidal OMOs. Fig. 5(a)shows PRF-b plotted against PRF -in and Fig. 5(b) shows Pb plot-ted against Pin /Pth . Wavelength detuning and optical couplingstrength are kept constant in these measurements. Wavelengthdetuning (ΔλN ) affects the down-conversion process throughits impact on P
(1)OMO .
Fig. 6 shows PRF-b and PRF-1 (detected RF power at fOMO ),plotted against ΔλN . According to (13), Pb is proportional toP
(1)OMO and P
(1)OMO ∝ Pin /Pth (ΔλN ). Pth (ΔλN ) is a function
of QL,Q0 , Qmech and meff of the corresponding optical and
314 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 2, JANUARY 15, 2014
Fig. 5. (a) Measured detected down-converted RF power (PRF-b ) plottedagainst PRF -in for three different OMOs: Red diamonds: Pin = 2.2 Pth ,ΔλN ∼ 0.6; Green triangles: Pin = 2.4Pth , ΔλN ∼ 0.86; Black squares:Pin = 3.2Pth , ΔλN ∼ 1. (b) Measured down converted optical power(Pb ) plotted against normalized input optical power Pin /Pth . Red diamonds:Pth = 116.5 μW and ΔλN ∼ 0.7; Green triangles: Pth = 86 μW, ΔλN ∼0.86; Black squares: Pth = 58 μW, ΔλN ∼ 0.62. For all cases fb = 1.5 MHz.Solid lines are calculated using OTF method Eq. (14) and dashed lines arecalculated using time-domain coupled differential equations (1)–(3).
Fig. 6. Measured RF power at fb (circles) and fOM O (squares) plotted againstΔλN . Here Qtot = 3.8 × 106 , Q0 = 4.5 × 106 , Qm ech ∼ 2700, fOM O =22.9 MHz, Pth = 62 μW, Pin = 1.67Pth , and fb = 1.5 MHz. Solid line: OTFcalculation. Dashed lines: time-domain differential equations (TDE) calculation.
mechanical modes. As expected Pb follows the behavior ofP
(1)OMO when ΔλN is varied.
D. Conversion Gain and Noise
The power conversion gain for OMO based down-convertercan be defined as Gd-OMO = PRF-b /PRF -in. Using Eq. (14) andassuming an input impedance of 50 Ω for the EO-modulator:
Gd-OMO =π2m2G2
D (P (1)OMO)2
16V 2π (1 + m2/2)
=π2m2RLP
(1)RF−OMO
2V 2π (1 + m2/2)
.
(15)
So similar to electrical down-converters, the conversion gaininside OMO is proportional to the optomechanical oscillationpower. We can also define a noise figure (NF) for the optome-chanical frequency down-converter:
NF =SNRin
SNRout= 1 +
Nadd
Gd-OMONin. (16)
Here Nin is the input noise and Nadd is the noise added by theoptical system. Nadd in the optomechanical down-conversionprocess is generated by the laser noise (both amplitude andphase), photodetection noise, and OMO noise. The laser noisecontributes to Nadd through the sidebands and also by affectingthe OMO noise.
The fluctuation of laser power (relative intensity noise, RIN)and its frequency stability directly affect the OMO power fluc-tuations. For example, the tunable laser in our experiment hada RIN better than −90 dB and frequency stability of about4 × 105 Hz. For fOMO = 75 MHz, Pin ∼ 180 μW, ΔλN ∼0.5 and Q0 /Qtot ∼ 0.1, the calculated relative amplitude fluctu-ation, δP
(1)OMO /P (1)
OMO , is less than –26 dB. Using Eq. (15) andfor PRF -in = −20 dBm this translates to an amplitude noisein the down-converted signal (δPRF-b ) less than −60 dBm. Inaddition to amplitude fluctuations, the noise in OMO frequency(δfOMO ) also contributes into distortion of the down-convertedsignal. Basically if (fOMO − fRF = ε �= 0) then instead of onecomponent at fb two components near fb will be generated (i.e.,fb ± ε). Note that for smaller values of m < 5, the optomechan-ical injection locking mechanism [22] naturally suppresses εwhen fOMO − fRF is originally small enough. Optomechanicalfrequency fluctuation is also linked to laser power and wave-length detuning fluctuations through optical spring and thermaleffect [10]. For our system δfOMO was less than 50 Hz.
The impact of the laser phase noise on the phase and am-plitude noise of the OMO is not very well understood and thedominant source in the overall phase noise of OMO may changedepending on its mechanical-Q [33], [34]. It has been shown thatfor typical laser and microtoroid the phase noise in 1/f 2 regimeis limited by thermal noise [27]. More importantly the contri-bution of OMO phase noise to Nadd is not trivial and requiresfurther studies.
To summarize, evaluation of different noise mechanisms andtheir contribution in the optomechanically down-converted sig-nal is complicated and requires experimental and theoreticalinvestigations that are beyond the scope of this paper.
E. Optomechanical Waveform Down-Conversion
To examine the fidelity of the optomechanical down-conversion process we have also modulated the input power(PRF -in) with various waveforms. Fig. 7(a) shows temporalvariation of the baseband signals (fb = 100 kHz) before mixingwith the RF carrier (in this case fRF = 75.5 MHz). After mixing(up-conversion) the resulting RF signal drives the MZ modula-tor (see Fig. 1) and subsequently the modulated optical power(Pin) is fed to the OMO. The detected RF power (PRF−out) ispassed through a low-pass filter (with a pass-band <2 MHz) toeliminate the frequency components near fOMO and 2fOMO .
LIU AND HOSSEIN-ZADEH: CHARACTERIZATION OF OPTOMECHANICAL RF FREQUENCY MIXING/DOWN-CONVERSION 315
Fig. 7. (a) Temporal variation of the input voltage (baseband signal) fed to themixer (before up-conversion). From top to bottom: sin wave, 50% square wave,and 50% triangle wave. They all have a frequency of fb = 100 KHz and aremixed with a carrier frequency of fRF = 75.5 MHz before being fed to the MZmodulator. The frequency of the baseband signal was limited by the availablewaveform generator. (b) Detected down-converted signal from the OMO. HereQtot = 1.6 × 106 , Q0 = 1.55 × 107 , Qm ech ∼ 3200, fOM O = 75.5 MHz,Pin = 2 × Pth and ΔλN ∼ 0.6.
Fig. 8. (a) Experimental configuration used for demonstration of optomechan-ical audio down-conversion from 74.5 MHz RF carrier. Video: (click to viewthe video): the video shows the correlation between down-converted sound andoptomechanical oscillation. When the microtoroid (OMO) is decoupled fromthe fiber-taper, the local oscillator and the mixing function (provided by the mi-crotoroid) are eliminated and the detected signal is still the up-converted audiosignal that cannot be heard from the speaker. (b) Proposed configuration for anall-optical wireless radio receiver based on resonant electro-optic modulator(REOM) and optomechanical oscillation. The sensitive resonant electro-opticmodulator (microdisk or microring [39]–[41]) directly receives the RF signalfrom an antenna and the OMO down-converts the baseband signal.
Fig. 7(b) shows the temporal variation of the down-convertedsignals. Note that the narrow bandwidth of the optical mode,that is effectively a low-pass filter in optical domain, acts asa natural noise suppression mechanism. These results demon-strate the good performance of OMO as a signal down-converterand its potential to serve as an all-optical RF receiver.
IV. OPTOMECHANICAL RADIO RECEIVER
To demonstrate the potential of OMO based receiver in ra-dio communication, we have examined our system using anaudio baseband signal (fb within 20 Hz–20 kHz range). Theexperimental setup is shown in Fig. 8(a). The sound wave is
generated by a computer (MP3 file) and mixed with the RFcarrier (fRF = fOMO = 74.5 MHz) in an RF mixer. After am-plification the resulting signal drives the MZ modulator. Themodulated laser power is fed to the OMO and finally the outputpower is fed to a photodetector that drives an amplified speaker.When the input optical power to OMO is larger than Pth , theaudio signal can be heard from the speaker. As the video linkedto Fig. 8(a) shows, when the microtoroid is decoupled from thefiber taper, the sound vanishes because the speaker do not re-spond to the up-converted audio signal (fOMO ± fb). The soundcan be recovered by coupling back the microtoroid to the fibertaper. Ideally in a photonic RF/microwave receiver all electroniccomponents are replaced with their photonic counterparts to re-duce size, weight, power consumption and provide immunity toEMI (electromagnetic interference).
Although various configurations have proposed for replacingthe electronic front-end with high sensitivity antenna-coupledoptical modulators [36]–[41], all-optical data down-conversionstill remains as a challenging task. So far few techniqueshave been proposed and demonstrated that enable RF down-conversion from a transmitted carrier RF signal in optical do-main. Nonlinear optical modulation [40], optical filtering [41]and nonlinear photodetection [42] are the most important ones.However for a suppressed carrier RF signal (typically used inwireless communication) still a local oscillator should be pro-vided by modulating a laser using and electronic LO or com-bining two lasers in a photodetector to generate the desiredoscillation. To our knowledge currently OMO is the only re-ported all-optical device that can simultaneously serve as localoscillator and mixer.
Fig. 8(b) shows a proposed configuration for an all-opticalwireless radio receiver based on resonant electro-optic modula-tor (REOM) and optomechanical oscillation. Here the sensitiveresonant electro-optic modulator (microdisk or microring mod-ulator [43]–[45]) directly modulates the laser power by the re-ceived RF signal (from an antenna) and the OMO down-convertsthe baseband signal.
V. APPLICATION OF OMO IN RF-OVER-FIBER AND
IF-OVER-FIBER LINKS
Optomechanical RF down-conversion is also a promisingtechnology for radio-over-fiber (RoF) links [46], [47]. In bothRF-over-fiber and IF-over-fiber architectures, at some point thebaseband or the IF signal has to be down-converted from theRF carrier. Typically the down-conversion process is performedin electronic domain using local oscillators and mixer simi-lar to conventional homodyne and or heterodyne RF receivers.Fig. 9(a) and (b) show two typical link configurations. In bothcases an electronic local oscillator (LO) and a frequency mixerare employed for down conversion (either to IF or basebandfrequencies). Here PRF -in is the RF power received from theantenna or other sources. Fig. 9(c) shows the proposed OMObased configuration where the electronic mixer and local oscilla-tor are replaced by an OMO that takes over the down-conversiontask in the optical domain. Since the OMO is naturally drivenby the optical carrier (laser power), the power consumption of
316 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 2, JANUARY 15, 2014
Fig. 9. (a) Conventional RF-over-fiber link. (b) Conventional IF-over-fiberlink. (c) OMO based IF-over-fiber link.
Fig. 10. Measured down-converted RF power PbRF (PIF ) plotted againstPRF -in using OMO mixer (blue diamonds) and electronic mixer (red rectanglesfor the configuration shown in Fig. 9(b) and (c). Here fb = 1.5 MHz, Qtot =1.6 × 106 , Qm ech ∼ 3200, fOM O = 75.5 MHz, and Pin = 2Pth = 230 μW.
the new configuration [see Fig. 9(c)] is reduced by eliminatingthe power consumed by the electronic LO. Moreover the com-plexity of the link is reduced by replacing two electronic circuits(i.e., LO and mixer) by a single photonic component.
We have compared the down-conversion efficiency of thesystems in Fig. 9(b) and (c) using a single frequency basebandsignal (1.5 MHz) and 75.4 MHz carrier. Fig. 10 shows PRF-bplotted against PRF -in for the configuration shown in Fig. 9(b)and (c). The laser power, RF amplifier gain and the detectorwere identical for both links. For the same RF input powerdown-conversion efficiency in the link with the optomechanicaloscillator is more than ten times better. Moreover in the elec-tronic version [see Fig. 9(b)] in addition to the power consumedby the laser, RF amplifier and the photodetector, the local oscil-lator consumes about 200 mW to generate the 7 dBm requiredto feed the mixer.
Clearly the power consumption of OMO based link is also lessthan the conventional RF-over-fiber system shown in Fig. 9(a),where not only a fast photodetector (with a bandwidth matchedto the RF carrier) should be used, but also post detection ampli-fication is needed to drive the mixer.
VI. CONCLUSION
We have characterized the RF frequency mixing processinside a radiation pressure driven OMO. Both coupled time-domain differential equations and our semi-analytical modelare in good agreement with experimental measurements. Ourstudy shows that OMO based RF frequency mixing and down-conversion can emerge as one of the practical applications ofoptomechanical oscillation. Note that although the frequencies
of the OMOs used in this study were below 100 MHz, simplyreducing the resonator size can increase the frequency of themechanical resonator. Recently very small monolithic OMOswith oscillation frequencies above 1 GHz have been demon-strated [5], [18]–[21]. Since the oscillation frequency is ulti-mately limited by the bandwidth of the actuating optical mode(fOMO<ν0 /Q0), for high frequency operation the optical-Q andtherefore the power efficiency of the OMO should be reduced.One solution for this issue is optomechanical oscillation basedon two-level coupled optical modes [48] where the oscillationfrequency is decoupled from the optical bandwidth. The next,and probably a more important, disadvantage of OMO is thelack of an efficient frequency tuning mechanism. As shown pre-viously with a careful design, the oscillation frequency of anOMO can be switched between two (and possibly three) dif-ferent values corresponding to different mechanical modes [9];but continuous tuning has not been demonstrated yet. The ad-vent of electrically tunable optomechanical resonators [49], [50]and other novel tuning methods may eventually solve this issue.Meanwhile given the small size and possibility of integratingmany OMOs with different frequencies on a single chip, eventhe single frequency OMO might become a useful device incertain applications.
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Fenfei Liu (S’13) received the B.S. degree in physics from University of Sci-ence and Technology of China, Anhui, China, in 2005, and the M.S. and Ph.D.degrees in physics from University of New Mexico, Albuquerque, NM, USA,in 2009 and 2013, respectively.
From 2006–2009, he was a Research Assistant in Biophysics Laboratory,University of New Mexico, where he was involved in optical and fluorescencestudies of phospholipid layers and cell membranes. From 2009–2013, he wasa Research Assistant in the M. H. Z. Microwave Photonics Research Groupat Center for High Technology Materials (CHTM), University of New Mex-ico, where he worked on application of high-Q optical micro-resonators andoptomechanical oscillation. He is a Student Member of the Optical Society ofAmerica.
Mani Hossein-Zadeh (S’00–M’05) received the B.S. and M.S. degrees inphysics from the Sharif University of Technology, Tehran, Iran, in 1995 and1997, respectively, and the M.S. and Ph.D. degrees in electrical engineeringfrom the University of Southern California (USC), Los Angeles, CA, USA, in2001 and 2004, respectively.
From 1995 to 1998, he worked on experimental nonlinear optics and lasersystems as a Research Assistant with the Medical Physics Laboratory, SharifUniversity of Technology. From 1999 to 2005, he was a Research Assistant withthe Advanced Electronics and Photonics Laboratory, USC, where he performedresearch on microwave photonic devices and systems, specifically microdiskmodulators and photonic RF receivers. From 2005 to 2008, he was a Post-Doctoral Scholar with the Vahala Research Group and Center for Physics ofInformation (CPI) at California Institute of Technology (Caltech). At Caltechhe worked on fluidic optical resonators, free microtoroid optical resonators andoptomechanical interaction in ultra-high-Q (UH-Q) optical microresonators. Heis currently an Assistant Professor of electrical and computer engineering at theUniversity of New Mexico, Albuquerque, NM, USA. His research activitiesinclude resonant RF/microwave photonic devices, optomechanical oscillation,resonant photonic biosensing and mid-IR microresonators and microlasers. Hereceived the NSF CAREER Award and is a Member of the Optical Society ofAmerica (OSA) and SPIE.
