Application of optical single-sideband laser in Raman atom interferometry
Lingxiao Zhu, Yu-Hung Lien, Andrew Hinton, Alexander Niggebaum, Clemens Rammeloo, Kai Bongs, Michael Holynski
AApplication of optical single-sideband laser inRaman atom interferometry L INGXIAO Z HU , Y U -H UNG L IEN , A NDREW H INTON , A LEXANDER N IGGEBAUM , C LEMENS R AMMELOO , K AI B ONGS , AND M ICHAEL H OLYNSKI School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Quantum Metrology Laboratory, RIKEN, Wako, Saitama 351-0198, Japan [email protected] * [email protected] Abstract:
A frequency doubled I/Q modulator based optical single-sideband (OSSB) lasersystem is demonstrated for atomic physics research, specifically for atom interferometry wherethe presence of additional sidebands causes parasitic transitions. The performance of the OSSBtechnique and the spectrum after second harmonic generation are measured and analyzed. Theadditional sidebands are removed with better than 20 dB suppression, and the influence ofparasitic transitions upon stimulated Raman transitions at varying spatial positions is shown to beremoved beneath experimental noise. This technique will facilitate the development of compactatom interferometry based sensors with improved accuracy and reduced complexity. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
OCIS codes: (020.1335) Atom optics; (020.1670) Coherent optical effects; (120.5060) Phase modulation.
References and links
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1. Introduction
Raman atom interferometry (RAI), first demonstrated over 25 years ago [1], has enabled thecreation of the most precise laboratory measurement devices for absolute gravity [2], gravitygradients [3] and rotation [4]. This makes atom interferometry a promising quantum technologyfor applications ranging from fundamental physics in space [5, 6] to practical concerns such ascivil engineering [7]. These applications require the translation of laboratory systems into small,robust and low-power devices, which poses particular challenges for the light source. Raman atominterferometers as illustrated in Fig. 1 use a two-photon transition to couple two hyperfine levelsof the atomic ground state. This allows manipulation of the atom to split, redirect and recombineits quantum mechanical wave function, encoding the gravitational phase shift between the twotrajectories in the relative atomic populations of the two hyperfine levels. This demands two laserbeams with a frequency difference matching the ground state hyperfine splitting, typically severalGHz, and the relative optical phase coherence at the mrad level over several hundred ms.Laboratory versions of the Raman atom interferometer light source have been implementedthrough optical phase locking [8], acousto-optic modulators (AOM) [9] and electro-opticmodulators (EOM) [10]. Some state-of-the-art Raman laser systems have been developed forvery stringent payload limitation and harsh environment [11, 12]. Recent quantum technologydevelopments focus on robust telecoms technology with electro-optic modulation and frequencydoubling [13–16], which in principle allow the realisation of an entire atom interferometer froma single laser source. However, the EOM scheme usually produces a double sideband (DSB)spectrum which contains redundant sidebands. These redundant sidebands not only waste opticalpower but also introduce extra undesirable interactions which affect the system systematicsand impair performance [17]. Here we demonstrate a laser system for RAI, which maintainsthe compactness and simplicity of EOM systems without the adverse effects of the redundantidebands. I DC Bias ! " ∆ $ % & '/% $ % ) "/% * = %,- * = .* = ",- * = . Phase ShifterSplitterSignal Generator
Raman Laser
SeedLaser Q FP Cavity FS EDFA
PPLN-RW FS FP CavityModulator //0
Retro-reflect Mirror ! % ! " ! % ! " ! % * = ",- * = .6 Raman Telescope 𝛚 𝛚 𝛚 𝛚 $% 𝝎 𝒔𝟏 𝐤 𝐬𝟏 ∆ 𝐏 𝐒 𝐹 = 2,𝑚 = 0𝐹 = 1,𝑚 = 0𝐹 = 1,𝑚 = 0 𝐤 𝐬𝟎𝛚 𝐇𝐅𝐒 𝐤 𝐬𝟎 𝐤 𝐬𝟎 𝐤 𝐬𝟏 𝐤 𝐬𝟏 PM Fiber PM Fiber
FS 2 FS 1FP 1FPI 2
DC Biases
Fig. 1: Simplified diagram of the apparatus. A simplified Rb level diagram is included as aninset. The pair of the counter-propagating beams k s ↓ and k s ↑ are resonant with a two-photonRaman transition between the magnetically insensitive hyperfine sublevels m F =
0. FS 1: 1560 nm1:99 fibre splitter. FS 2: 780 nm 1:20 fibre splitter. FPI 1, 2: 1560 nm and 780 nm Fabry-PérotInterferometer, respectively. All fibers are polarization-maintaining.The system relies on I/Q modulator based optical single-sideband generation (OSSB) [18–22],with the novel feature of maintaining the single sideband modulation through an optical frequencydoubling element. Our OSSB system is shown schematically in Fig. 1. The first stage comprisesa 1560 nm fibre laser and an I/Q modulator for single sideband generation. The output is thenconverted into 780 nm by second harmonic generation (SHG) to resonate with the Rb D2 line.The I/Q modulator allows implementing OSSB with a high degree of versatility allowing theoptimization of undesired sideband suppression after the optical frequency doubler. The SHGunavoidably pairs up different spectral components in 1560 nm OSSB and converts them into780 nm, which requires optimization in order to avoid suppressed sidebands in the fundamentalband reemerging in the frequency doubled spectrum. We measure the spectra of our OSSB,including both fundamental and SHG. We finally implement the full-carrier optical single sidebandscheme (FC-OSSB) as an interrogation laser for RAI. We demonstrate that the FC-OSSB Ramanlaser suppresses the influence of undesired sidebands, by measuring the spatial dependence of theRabi frequency and interferometric phase shift and comparing this to that of an EOM modulationscheme. At the end, we include the theory for the I/Q modulator based OSSB, the SHG spectrumof OSSB, and relevant notations in the appendix.
2. Apparatus
Our Raman atom interferometer including an FC-OSSB based Raman laser is illustrated inFig. 1. The Raman laser comprises a highly stable 1560 nm fibre laser (Rock™, NP Photonics), afibre-coupled I/Q modulator (MXIQ-LN-40, iXBlue), an erbium-doped fibre amplifier (EDFA)(YEDFA-PM, Orion Laser), and a nonlinear wavelength conversion module (WH-0780-000-F-B-C, NTT Electronics). The I/Q modulator is essentially a dual parallel Mach-Zehnder modulator(MZM) [20,23]. The in-phase and quadrature ports of the I/Q modulator are driven by the same RFsignal ω m except an RF phase shifter is installed on the quadrature port to generate the necessary / Φ , , are separately controlled by separate precisionvoltage sources. The output of the fibre laser is modulated by the I/Q modulator to generateFC-OSSB, which is amplified by the EDFA to 1 W. The nonlinear wavelength conversion modulebased on a periodically poled lithium niobate ridge waveguide (PPLN-RW) is used to convertthe FC-OSSB signal to 780 nm. The optical power of 780 nm light is approximately 440 mW.The spectra of both 1560 nm and 780 nm are simultaneously monitored by two Fabry-Pérotinterferometers (FPI) (SA210-12B, SA200-5B, Thorlabs) with free spectral range (FSR) 10 GHzand 1.5 GHz respectively. The two major frequencies in the 780 nm FC-OSSB spectrum drive atwo-photon Raman transition between the Rb ground state hyperfine levels with a detuning∆ = Rb atoms are loaded into a 3D magneto-optical trapand then launched into the interrogation region by the moving molasses technique [24, 25].The Raman laser beam is directed into the interrogation region and retro-reflected by a mirror.The light field inside the interrogation region consists of two counter-propagating beams whichcontain two frequencies. In principle, there are four different combinations that can drive thetwo-photon Raman transition used in RAI. Nevertheless, only one pair, as illustrated in Fig. 1,is selected by Doppler selection and the polarization. When the atoms are in the interrogationregion a π / − π − π / ∆Φ RAI of RAI is determined by measuring the population ratio of the ground state hyperfine levels. Inthe case of a local gravity acceleration g , ∆Φ RAI is given by: ∆Φ RAI = cos − ( P P + P ) = ( k eff · g − α ) T (1)where P , are the populations of the ground state hyperfine levels F = 1 and 2, the interferometrictime T is the interval between adjacent Raman pulses, α is the chirp rate of ω m for compensatingthe Doppler shift, and k eff = k s ↑ − k s ↓ is the effective wave vector [1].
3. Results
The system was then used to demonstrate that FC-OSSB can be realized both before and afterthe SHG. According to Eq. (6) and (8), the OSSB spectrum at 780 nm is degraded due to theSHG. The sideband ω s − is not eliminated in 780 nm, and is generated by the sum frequencygeneration (SFG) between the sidebands ω − and ω in 1560 nm. This is expressed as:8 ( + e i π / ) J ( β ) J ( β ) e i ( ω − + ω ) t The sideband ω s is proportional to the term:8 e i π / [ J ( β ) J ( β ) e i ( ω + ω ) t − J ( β ) J ( β ) e i ( ω + ω ) t ] As shown in Fig. 2, the amplitude of these unwanted sidebands depends on the setting of themodulator and the issue is further addressed in the appendix. To optimize the 780 nm FC-OSSB,We start from its counterpart at 1560 nm by adjusting Φ and observing the suppression patternof the different frequency components such as ω − and ω . Further optimization is achieved byadjusting Φ , . Subsequently, the power and the spectrum of 780 nm OSSB are adjusted primarilythrough the modulation depth β but also Φ , . Eventually the temperature of the wavelengthconversion module is adjusted to shift the gain profile and finish the optimization.Figure 3(a) and 2(b) show the spectra of FC-OSSB in 1560 and 780 nm respectively. TheFC-OSSB spectra shown are acquired with a power ratio ω s / ω s , at -3 dB at 780 nm, as desiredfor compensating light shifts. The ω s − is not visible and the ω s is approximately 21 dB below Modulation Depth -100-80-60-40-20020 P o w e r R a t i o ( d B ) s1 / s0s-1 / s0s2 / s0s-2 / s0s3 / s0s-3 / s0s4 / s0s-4 / s0 -3dB Fig. 2: Simulation of the optical power ratio of the sidebands with respect to the carrier after theSHG. The power ratio where is -3 dB is denoted in dashed line. ω s . Meanwhile, concerning the 1560 nm components, the ω − is suppressed better than 20 dBcompared with ω . In the measurement, the RF power applied to the I/Q ports of the modulatoris 13 dBm which corresponds to β ≈ .
74 based on the V π = ω s / ω s should be below -50 dB. The degeneration canbe explained by the unbalanced RF power applied on the I and Q ports and the non-identicalwaveguides on the two arms of the modulator. Cavity Length Scanning (a.u.) 𝛚 "𝟏 𝛚 𝛚 -20.2dB (a) Cavity Length Scanning (a.u.) 𝛚 𝐬𝟐 -21.4dB (b) -16.8dB Cavity Length Scanning (a.u.) 𝛚 "𝟏 𝛚 𝛚 (c) Cavity Length Scanning (a.u.) 𝛚 𝐬𝟎 -16.0dB (d) Fig. 3: The FC- and SC-OSSB spectra. (a) and (c) are the 1560 nm spectra of FC- and SC-OSSB,respectively. (b) and (d) are the 780 nm spectra of FC- and SC-OSSB, respectively. The FSRs ofFPIs are marked by the blue dash lines.The I/Q modulator is also used to realize suppressed carrier OSSB (SC-OSSB). Figure 3(c)hows the spectrum of SC-OSSB in 1560 nm. The ω is suppressed to the noise level. Neverthelessthe extinction ratio of ω − is only better than -15 dB with respect to ω and the suppression of ω s at 780 nm is considerably impaired. This is because the SFG occurs between ω and ω − revives ω s . The revival of the carrier at 780 nm is clearly seen in Fig. 3(d). The ω s is only-16 dB compared with the frequency at ω s . Meanwhile, the ω s amplitude is beneath the noiselevel. Modulation Frequency (GHz) -25-20-15-10-505 R a t i o ( d B ) s1 / s0s2 / s0s-1 / s0 (a) Modulation Frequency (GHz) -25-20-15-10-505 R a t i o ( d B ) s1 / s0s2 / s0s-1 / s0 (b) Fig. 4: The 780 nm sideband ratio verse the modulation frequency. The ratio ω s / ω s is to -3 dBat 6.834 GHz. The subfigure (b) is the red dash boxed region in (a).In many applications the modulation frequency ω m needs to be tuned, for example, Dopplercompensation during free fall in RAI. The tuning of ω m may produce unwelcome side effectssuch as degradation of suppression and power ratio variation of ω s / ω s . These would primarilybe caused by the frequency dependent characteristics of the microwave electronics driving theI/Q modulator. The dependence of the FC-OSSB performance with ω m was investigated, and theresults for ω m within 4–8 GHz are shown in Fig. 4(a). Figure 4(b) shows the enlarged regioncovering the experimental frequency chirping for Doppler shift compensation. During scanning,the OPR of ω s / ω s is set to be -3 dB. The sideband ω s can be suppressed below -20 dBbetween 5 GHz and 8 GHz while the suppression of the sideband ω s − starts to increase below6.8 GHz. This is because the RF devices have a frequency-dependent phase shift, which degradesthe OSSB. However, for the range between 6.8 GHz and 6.86 GHz where the atom interferometeroperates, the sideband ω s − is suppressed below -18 dB. The FC-OSSB laser system was then used to perform a gravity measurement in a Mach-Zehnderatom interferometer, which combines three velocity sensitive Raman pulses [26]. In order tocompensate the Doppler shift between the counter-propagating beams, induced by atoms infree fall, ω m is swept at a chirp rate α . From Eq. (1), at a specific chirp rate, the phase shiftinduced by the gravitational acceleration is canceled and there exists a stationary phase pointindependent of interferometric time T . The value of g is therefore derived from the frequencychirp rate and is given by g = π α / k eff . Figure 5 shows fringes with T equal to 10 ms, 15 msand 30 ms respectively. A central fringe is addressed where the interferometer phase is canceledfor a Doppler compensation. The local gravity g is determined as 9 . ( ) m / s is obtained. Chirp Rate (MHz/s) N o r m a li z e d P opu l a t i on i n F = T=10 msFittingT=15 msFittingT=30 msFitting
Fig. 5: The interferometric fringes for determining local gravity. The chirp rate at the station-ary phase point is 25 , , ±
12 Hz, from which the local gravity can be derived to be9.817239(4) m/s . As demonstrated above, the Raman laser based on OSSB allows the suppression of the unwantedsidebands. Consequently, the interference caused by these unwanted laser lines can be eliminated.To verify this conclusion, the OSSB system is compared to an EOM scheme when applied inatom interferometry. The Raman laser setup is shown in Fig. 6, with only the modulator changingbetween comparisons. ! " Laser modulation I DC Bias Q ! " ! ! $ ! % ! ! &" ! & ! &$ ! &" ! & OSSB
Microwave Chain
EOM ' ( ∆∅ QI (RF) RF ' ( DP-MZMEOM
780 nmOr
I/Q modulator
DC Biases
Fig. 6: The Raman laser system for measuring the spatial dependence of the Raman transitionprobability.
In EOM modulation, there are multiple pairs of frequencies that can drive resonant two-photonRaman transitions. The effective Rabi frequency contains a spatial dependence with a periodicityof λ rf /
2, where λ rf is the wavelength of the RF signal applied on the EOM. This causes the π transition condition to be modified for Raman transitions performed along the interferometryregion. The effect is greater when the detuning ∆ is larger as the relative contribution from theunwanted frequency pairs increases [27].
10 320 330 340 350 360 370 380 390 400
Distance from MOT Center (mm) N o r m a li z e d EOMFC-OSSB
22 mmP1 P2 𝛑𝛑𝟐
Fig. 7: The spatial dependence of the Raman transition probability. The Raman transitionprobabilities are measured along the beam axis with FC-OSSB and EOM Raman lasers. P1(yellow) and P2 (green) represent two atom interferometers operate at different locations.Raman pulses were applied at different positions along the longitudinal direction in theinterferometry region. The pulse duration is set at 50 µ s, which corresponds to the π pulseduration at the start point. The RF frequency applied to the EOM and I/Q modulator is equalto the separation between the ground state hyperfine levels F = 1 and F = 2 ( ≈ .
834 GHz).Figure 7 shows the spatial dependence of the Raman transition. The wavelength of oscillations ismeasured to be 22 mm which matches with the half wavelength of the RF signal. The amplitudeof the Raman transition was reduced a factor of two at the valley compared with the crest. Thesame measurement was repeated in the FC-OSSB scheme, showing that the spatial dependence isremoved to below the experimental noise level. The fluctuation of the Raman transition is less than10%, which is induced by other perturbation, and shows no oscillatory spatial structure. Althoughthe interference effect in EOM scheme can be reduced with small detuning ( ∆ < The unwanted sidebands in the EOM scheme can also induce a position dependent phase shift inatom interferometry [17]. To evaluate the performance of the OSSB system, both schemes wereused to operate a Mach-Zehnder atom interferometer at two different sets of positions, P1 and P2,which are labelled in Fig. 7. The time separation between pulses was set to 10 ms. The sidebandpower ratio ω s / ω s is chosen to be 1/2 to cancel the first order AC Stark shift.Figure 8 shows the atom interferometric fringes acquired by sweeping the chirp rate α underdifferent modulation configurations. In order to further investigate the effect arising from spatiallyvarying Raman transition in EOM scheme, the measurements are performed under two differentassumptions: (1) single global Rabi frequency; (2) spatially dependent Rabi frequency. In thefirst case, the Raman π and π / Chirp Rate (MHz/s) N o r m a li z e d EOM (Uncorrected Raman Pulse)
P1FittingP2Fitting (a)
Chirp Rate (MHz/s) N o r m a li z e d EOM (Corrected Raman Pulse)
P1FittingP2Fitting (b)
Chirp Rate (MHz/s) N o r m a li z e d FC-OSSB
P1FittingP2Fitting (c)
Fig. 8: The interferometric fringes from different Raman laser schemes. From top to bottom, theEOM(U) scheme assuming single global Rabi frequency, the EOM(C) scheme compensatinglocal Rabi frequency variation, and FC-OSSB.Table 1: The phase shifts and the contrasts of the interferometric fringes from different Ramanlaser schemes. The results for P1 and P2 are marked by black and red respectively.Phase Shift (mrad) ContrastP1 P2 P1 P2EOM(U) 1509 2077 22% 12%EOM(C) 1759 1294 20% 19%OSSB 597 596 21% 20%and P2 has a relative phase difference 568 mrad. In addition, the contrast is reduced from 22%to 12%, nearly a factor of two decrease between P1 and P2. After correcting the Raman pulseduration, the fringe contrast at P2 can be recovered to 19% but there is still a spatially dependentphase difference at both P1 and P2. However, with the FC-OSSB scheme, the fringe at P2 isshifted by 1 mrad with a small contrast decrease around 1% compared with the one at P1. Asproposed in the paper [17], the EOM scheme is still adoptable for atom interferometry applicationin high-precise gravity measurement by numerically calculate the phase shift induced by theunwanted laser lines in the EOM scheme, which demands the atom interferometer parameters areprecisely estimated. However, the OSSB approach has been shown to effectively remove theseconcerns, and others, without adding additional complexity to the laser system. . Conclusion
The application of FC-OSSB in atomic physics, especially RAI, is demonstrated in this paper.The suppression of the spatially dependent Rabi frequency and the interferometric phase biasinduced by undesired sidebands, which arise through existing single laser schemes, are shownto be suppressed to a level below the experimental noise of the atom interferometer. Whileenabling these improvements, the compact, robust and single laser nature of the EOM schemeis retained - allowing for the improvement of compact RAI based sensing. In addition, carriersuppression (SC-OSSB) to create an agile single frequency is also demonstrated, enabling futureimplementation as an efficient and broadband optical frequency shifter with the potential tosignificantly improve over techniques such as serrodyne modulation [28]. By aid of versatilemicrowave electronics, in principle, OSSB schemes can be combined to realize a broadly tunablesingle-laser light source for RAI.
Appendix: I/Q modulator based OSSB (I)(II)(1)(2)(3)(4) Optical Phase ShifterPhase Modulator
Fig. 9: Illustration of the simplified structure of a dual parallel Mach-Zehnder modulator. Sinephase modulator: ∆ φ s = β sin ω m t . Cosine phase modulator: ∆ φ c = β cos ω m t . Φ , , : opticalphase shifter.Our I/Q modulator is based on a dual parallel Mach-Zehnder modulator (MZM) [20, 23]. Thesimplified structure is shown in Fig. 9. Sub-modulators, MZM and MZM , act as either single ordouble balance modulators controlled by the phase shifters Φ , . A third sub-modulator MZM is essentially a combiner for MZM , with an extra phase shifter Φ . Each arm of MZM , issimply a conventional phase modulator. Assuming the seed laser frequency ω c and a modulationsignal ω m with modulation depth β , the signals at locations (1)–(4) can be expressed by Besselfunctions: E o = E ( ) + E ( ) + ( E ( ) + E ( ) ) e i Φ = E i e i ω c t [ e i ( β sin ω m t ) + e i (− β sin ( ω m t ) + Φ ) + e i ( β cos ( ω m t ) + Φ ) + e i (− β cos ( ω m t ) + Φ + Φ ) ] = E i e i ω c t ∞ (cid:213) −∞ [ J n ( β ) e i n ω m t + J n (− β ) e i ( n ω m t + Φ ) + J n ( β ) e i ( n ( ω m t + π / ) + Φ ) + J n (− β ) e i ( n ( ω m t + π / ) + Φ + Φ ) ] = E i e i ω c t { C J ( β ) + ∞ (cid:213) n = [ A n J n ( β ) e i n ω m t + B n J n ( β ) e − i n ω m t ]} (2)where J n ( β ) denotes the n th-order Bessel function and the coefficients C , A n and B n arexpressed as below: C = + e i Φ + e i Φ ( + e i Φ ) (3) A n = + (− ) n e i Φ + e i Φ [ e i n π + (− ) n e i ( n π + Φ ) ] (4) B n = (− ) n + e i Φ + e i Φ [(− ) n e − i n π + e i (− n π + Φ ) ] (5)The FC-OSSB can be achieved by setting Φ , , = π / , π / , π / E o = E i [ J ( β ) e i ω c t + ( − e i π / ) J ( β ) e i ( ω c + ω m ) t + e i π / J ( β ) e i ( ω c + ω m ) t + e i π / J ( β ) e i ( ω c − ω m ) t − ( − e i π / ) J ( β ) e i ( ω c − ω m ) t + J ( β ) e i ( ω c + ω m ) t + J ( β ) e i ( ω c − ω m ) t + . . . ] (6)We also can realize the suppressed-carrier optical single sideband (SC-OSSB) by setting Φ , , to π, π, π / E o = E i [ J ( β ) e i ( ω c + ω m ) t − J ( β ) e i ( ω c − ω m ) t + J ( β ) e i ( ω c + ω m ) t + . . . ] (7) OSSB with second harmonic generation
The spectral coverage of OSSB can be further extended to where there are no convenient lightsources or modulators available by nonlinear optical processes such as SHG. Unlike othernonlinear processes, the SHG of OSSB will unavoidably degrade the OSSB because of theself-mixing characteristics. The self-mixing process pairs the different frequency componentsof OSSB and creates undesired frequencies. For simplicity, we assume n =
4. In the case ofFC-OSSB, the SHG signal can be expressed as: FC E S ∝ (cid:15) χ E o ≈ (cid:15) χ E i {[( J ( β ) − J ( β ))] e i ω s t + ( − e i π / ) J ( β ) J ( β ) e i ω s t + ( + e i π / ) J ( β ) J ( β ) e i ω s − t + e i π / [ J ( β ) J ( β ) − J ( β ) J ( β )] e i ω s t + e i π / [ J ( β ) J ( β ) − J ( β ) J ( β )] e i ω s − t + ( + e i π / ) J ( β ) J ( β ) e i ω s t + ( − e i π / ) J ( β ) J ( β ) e i ω s − t + [ J ( β ) J ( β ) − J ( β )] e i ω s t + [ J ( β ) J ( β ) − J ( β )] e i ω s − t } (8)where (cid:15) is the permittivity of vacuum and χ is the susceptibilities of the medium. The shorthandfor the different frequency components is as: ω n = ω c + n ω m ω = ω c , ω = ω c + ω m , ω − = ω c − ω m . . . and "s" is added to the subscript to refer the components after SHG: ω sn = ω c + n ω m ω s = ω c , ω s = ω c + ω m , ω s − = ω c − ω m . . . igure 2 shows the simulation of the optical power ratio (OPR) of the sidebands with respect tothe carriers in 780 nm versus the modulation depth β . Assuming β = .