Noise spectroscopy of the optical microcavity: nonlinear amplification of the spin noise signal and giant noise
NNoise spectroscopy of the optical microcavity:nonlinear amplification of the spin noise signaland giant noise
S.V. Poltavtsev, I.I. Ryzhov, V.S. Zapasskii, and G.G. KozlovOctober 22, 2018
Abstract
The spin-fluctuations-related Kerr rotation noise of the optical beam reflected froma microcavity with a quantum well in the intermirror gap is studied. In the regime ofanti-crossing of the cavity polariton branches, the several hundred times enhancement ofthe noise signal, or giant noise, is observed. The effect of the amplification of the noisesignal is explained by the nonlinear instability of the microcavity. In the frame of thedeveloped model of built-in amplifier, the non-trivial properties of the noise signal in theregime of the negative detuning of microcavity are described.
Introduction
The study of spin fluctuations by means of optical polarimetry – optical spin noise spectroscopy– becomes more and more popular during the last years [1]. As it was first demonstrated in [2],the spin fluctuations in atomic system cause the fluctuations of its gyrotropy, which can bedetected by means of a sensitive optical polarimeter as a noise of rotation of the polarizationplane of the probe beam (Faraday rotation noise). The frequency spectrum of the observed noiseis connected with the frequency dependence of the magnetic susceptibility by the fluctuation-dissipation theorem and in the simplest case has a Lorentzian shape with its width defined bythe spin relaxation time and centered at the Larmor frequency . Since the sample under studyin the experiments is, as a rule, transparent for the probe beam, the optical noise spectroscopycan be considered as non-perturbative method for observation of the magnetic susceptibility.The growth of popularity of the optical noise spectroscopy during the last years is associatedwith the usage of the fast digital spectrum analyzers, which allow one to detect the magneto-spin noise of atomic and semiconductor systems in the radio-frequency (RF) range [3–5].For the optical noise spectroscopy experimental set-up based on RF spectrum analyzer,several improvements increasing the sensitivity were suggested [6, 7]. Besides, the new methodfor the spin noise detection was suggested in [8], which allows one to observe the spin noise inmicrowave frequency range. proportional to the transverse static magnetic field applied to the studied system in Voight geometry a r X i v : . [ c ond - m a t . m e s - h a ll ] J un he noise spectroscopy of semiconductor systems features its own specificity. The up-to-date technologies of epitaxial growth make it possible to produce the semiconductor systemswith precisely controllable spectral properties - quantum wells (QW) and quantum dots.Recently, the observations of the spin noise in these systems were reported [9, 10], so, atpresent one can speak about the noise spectroscopy of the nano-objects. Placing such anobject into the intermirror gap of a planar Bragg microcavity allows one to increase drasticallythe noise signal observed as a noise of Kerr rotation of the optical beam reflected from sucha complex system [10]. This gives the grounds to believe that optical noise spectroscopy ofsemiconductor nano-objects in microcavities becomes a part of the physics of the microcavities[11].In the present paper, we study the properties of the Kerr rotation noise of the optical beamreflected from (Al,Ga)As Bragg λ -microcavity with GaAs QW at the center of the intermirrorgap. We use the sample with spatial gradient of specral position of the cavity photon modedescribed in [12,13]. In the region of the sample where the frequency of the cavity photon modeis well below that of QW resonances (region of negative detuning) the RF noise spectrum ofthe Kerr rotation displays non-trivial bimodal shape described in [10]. The most unusualbehaviour relates to the region, where the cavity photon mode frequency is close to the QWexciton resonance (region of anti-crossing), where the several hundred times increase of thenoise signal, the giant noise , is observed. In our paper we show that the above properties ofthe noise signal can be explained by the nonlinear instability of the microcavity giving riseto the increase of the sensitivity of the reflectivity coefficient to the noise fluctuations of therefraction index within the intermirror gap.The paper is organized as follows. In the first section, the experimental set-up, the sampleunder study and the results obtained are described. In the second section, the hypothesisof a built-in amplifier is formulated for the explanation of the giant noise observed in ourexperiments. On the basis of this hypothesis the formula describing the bimodal noise spectrumin the regime of negative detuning is obtained. In the third section, all observed propertiesof the sample under study are qualitatively explained by the suggested simple model of theinstable nonlinear resonator. All the results obtained in the paper are briefly summarized inConclusion. We study the sample representing the planar Bragg λ -microcavity with GaAs QW (102/200/102˚AAlAs/GaAs/AlAs) placed in the center of the intermirror gap (see [10, 12] for the sampledetails). Note that in our experiments the strong coupling regime described in [12] was partlyviolated by optical nonlinearity (see [13] for details). Experimental set-up used in our study isbuild for the observation of the Kerr rotation noise and described in detail in [10], therefore wewill restrict ourselves by a brief reminding. The linearly polarized monochromatic probe beamfrom tunable Ti:sapphire laser was focused to ∼ µ m spot of the sample in normal direction.The sample was placed in the closed cycle cryostat and cooled down to 3 ÷ δν = 200 MHz) balanced photodetector.2he fluctuations of the magnetization in the intermirror gap (related to the spin fluctuationsof free carriers or excitons in QW) cause fluctuations of polarization of the reflected beam andcan be detected as a noise electric signal on the output of the photodetector. The wavelengthof the probe beam was tuned to maximize the amplitude of the noise signal.A typical experiment on the spin-noise spectroscopy [2–5] implies measurement of the RF-spectrum of this signal as a function of magnetic field strength. This spectrum is detectedusing a spectrum analyzer and, in the simplest case, has a Lorentzian shape with the peakposition shifting linearly with magnetic field strength. From the reflectivity spectra of thestudied sample (presented in [12]) it is seen that the spectral position of the cavity photonmode reveals a strong spatial dependence. Bearing this in mind, it is convenient to specify thefollowing three regions of the sample:(1) The region of negative detuning , where the frequency of the cavity photon mode is belowthose of QW resonances. The region of negative detuning corresponds to the spatial intervalon the sample surface x ∈ [0, 0.3] mm with respect to the sample edge (see [13] for details).(2) The region of anti-crossing of the polariton branches , where the frequency of the cavityphoton mode ”passes” through the frequencies of QW resonances ( x ∈ [0.3, 0.9] mm).(3) The region of positive detuning , where the frequency of the cavity photon mode becomeshigher than those of QW resonances ( x > . The region of negative detuning.
The Kerr-rotation-noise power spectra measured in thisregion of the sample at different Voight magnetic fields are presented in Fig.1 (noisy curves).These spectra exhibit the non-trivial bimodal shape at non-zero magnetic fields: besides theordinary spin noise peak at Larmor frequency, whose shift in magnetic field is defined by g -factor | g | ≈ .
35, there is a well pronounced maximum at zero frequency. The amplitude ofthis maximum decreases with rising magnetic field, while its spectral position does not dependon the field strength. Dependence of the noise spectra on the probe beam intensity displaysnoticeable deviation from quadratic growth, which corresponds to the optical nonlinearity.The amplitude of the zero-frequency maximum in the noise spectrum demonstrates the mostpronounced nonlinear behavior: the ratio between the amplitude of this maximum and that ofthe maximum at Larmor frequency (at fixed magnetic field) diminishes with decrease of theprobe intensity. The typical value of the noise signal in this sample region is of the order ofthe shot noise of the probe whose intesity in our experiments ∼ The region of polariton branches anti-crossing.
By varying the probe spot around the anti-crossing region it was possible to locate the areas of giant noise , where the amplitude of thenoise signal at zero magnetic field was several hundred times larger than that in the region ofnegative detuning. The spectrum of the giant noise has the form of the peak at zero frequencywith width ∼ ÷
20 MHz, whose amplitude reduced with increasing of magnetic field (Fig.2a).The amplitude of the giant noise peak reveals the essentially nonlinear behavior with varyingof probe intensity: steep increase at moderate intensities of the probe and reduction at theintensities > Noisy curves – experiment, smooth dashed curves – fitting by Eq. (1).The above spectra were measured by means of spectrum analyzer in the RF-range with lowerlimit of 5 MHz. The direct observation of the output of the polarimetric detector by meansof the oscilloscope revealed that the giant noise is accompanied by the chaotic low frequencyoscillations of the reflected beam polarization with characteristic frequencies ∼ −
50 kHz.The mentioned instability appeared at strong enough intensities of the probe. The intensity ofthe reflected beam exhibited similar behavior.
The results presented in the previous section unambiguously show the important role of theoptical nonlinearity in the formation of the Kerr rotation noise signals observed in our experi-ments. The nonlinear behavior of the optical cavities is well known and studied in detail [14–16].In our case, the nonlinearity is caused not only by the resonant increasing of the electromagneticfield in the microcavity, but also by using of the sharp focusing of the probe beam.The reflectivity spectra measured at different positions of the probe (in mm with respect tothe sample edge) at the sample surface for two probe intensities, 0.3 mW and 3 mW, are shownin Fig.3 and allow one to judge about the degree of optical nonlinearity. The observation ofreflectivity spectra Fig.3 and the detection of the noise spectra were performed under similarconditions.It is seen from the Fig.3 that the influence of the increase of the probe beam intensityon the reflectivity spectra is well-pronounced even in the region of the negative detuning and4igure 2: (a) spectrum of giant noise at different magnetic fields. (b) the amplitude of thespectrum of giant noise at zero magnetic field at various intensities of the probe beam. Inset:noise spectra in the region of giant noise for various intensities of the probe.5igure 3: The reflectivity spectra of the studied microcavity with QW at different relativespectral position of the cavity photon mode and QW resonances. The spectra 0 – 0.3 mmcorrespond to the region of the negative detuning; spectra 0.3 – 0.9 mm to the region ofanti-crossing of the polariton branches. Measurements were carried out for the probe beamintensities 3 mW ( red curves ) and 0.3 mW ( blue curves ).6ecomes dramatic in the region of anti-crossing of the polariton branches, where the giantnoise is observed. This behavior of the reflectivity spectra allows us to suggest the followingqualitative explanation of the oscillatory instability of the microcavity described in the previoussection.After switching on the resonant probe beam, the amplitude of oscillations of the opticalfield in the microcavity starts to grow. Due to the nonlinearity of the medium in the inter-mirror gap , the microcavity can tune out of the resonance. This leads to the decreasing ofthe amplitude of the optical field in the microcavity and, consequently, it tunes back to theresonance and the amplitude of the optical field starts to grow again, so, this process occursrepeatedly. The similar scenario of self-excitation is described in [14].This (or similar) mechanism of self-excitation (i.e. appearance of the oscillations of theamplitude of the field) of the microcavity must exhibit a threshold behavior as a function ofthe probe beam intensity. It is well known that the similar systems are very sensitive to thevariation of their parameters at the threshold of self-excitation. For this reason, it is naturallyto expect the dramatic growth of the sensitivity of the reflection coefficient of the nonlinearmicrocavity to the fluctuations of the optical properties of the medium in the intermirror gapwhen the probe intensity is close to the self-excitation threshold. This is confirmed by theanalysis of the simple model presented in the next section. In our opinion, the appearance of the giant noise from the regions of the sample with strongoptical nonlinearity is related to the pre-threshold growth of the sensitivity of reflection coeffi-cient of the nonlinear microcavity to spin fluctuations .Based on this hypothesis, we can write the following expression for the noise signal S corresponding to the fluctuations of the Kerr rotation: S = ( ξ + 1) M , where M is the noisesignal from a hypothetical linear microcavity and ξ – is a factor accounting the amplificationof the polarimetric response of the microcavity to the fluctuations of optical properties ofthe medium in the intermirror gap related to the medium nonlinearity. In agreement with theaforesaid, the factor ξ should depend on the intensity I of the probe ξ = ξ ( I ), with ξ ( I = 0) = 0and, when I is close to the threshold of self-excitation I c , it must be ξ ( I → I c ) (cid:29)
1. Therefore,one can say that nonlinearity of the microcavity leads to the appearance of some built-inamplifier of its polarimetric response with amplification factor ξ ( I ). Since in our experimentsthe dependence of the noise power on frequency ω is observed, one should take into accountthe possible frequency dependence of the amplification factor: ξ = ξ ( I, ω ).As it was mentioned in the previous section, the noise signal from our sample exhibitnoticeable nonlinear character even in the region of the negative detuning where no giant noiseis observed. In what follows, we show that the hypothesis of the built-in amplifier naturallyexplains the presence of the zero-frequency maximum in the noise spectrum described in thefirst section. To do this, we assume that the frequency dependence of the amplification factor ξ has the shape of the zero-centered Lorentz curve with a width ∆: ξ ( I, ω ) = ξ ( I )∆ π L (∆ , ω ),where L (∆ , ω ) ≡ π − ∆ / [∆ + ω ], and ξ = ξ ( I, related, for instance, to the saturation of the QW exciton resonance and the polarization of the reflected radiation either exactly, to the fluctuations of the gyrotropy the simple model described in the next section justifies the dependence of this type
7n our experiments: S ( ω ) = (cid:18) ξ ( I ) π ∆ L (∆ , ω ) + 1 (cid:19)(cid:20) L (∆ e + æ h, ω − gβh/ ¯ h ) + L (∆ e + æ h, ω + gβh/ ¯ h ) (cid:21) (1)Here, the factor in the square brackets corresponds to the classical spin noise spectrum in themagnetic field h : the Lorentzian peak with half-width at half-maximum ∆ centered at Larmorfrequency gβh/ ¯ h . The parameter æ describes the noticeable broadening of the noise spectrumin the large magnetic field observed in our experiments (this effect can be explained by smalldispersion of g -factors of the spins responsible for the noise signal). The results of fitting ofthe experimental noise spectra by Eq. (1) are presented in Fig.1 (smooth curves). The valuesof the fitting parameters are: ξ = 2 . , ∆ = 2 π × e = 2 π ×
20 MHz, æ = 2 π × . , g = 0 . ξ ≈
2, which leads tothe bimodal shape of the observed noise spectrum: the amplitude of the zero-frequency peak inthe noise spectrum (corresponding to the low-frequency spectral components of spin noise am-plified by the built-in amplifier) and the amplitude of the maximum at Larmor frequency havethe same order of magnitude. Upon decreasing the probe intensity, the amplification factor ξ (governed by the optical nonlinearity) is decreasing. This leads to the observed suppression ofthe zero-frequency maximum in the noise spectrum. In the regions of the sample possessinglarger optical nonlinearity (the regions of anti-crossing of the polariton branches), where thegiant noise is observed, the amplification factor grows and in the spots of giant noise has anorder of several hundreds. The Eq. (1) shows that in this case the observed signal representsonly the spin noise amplified by the built-in amplifier - the unity in round brackets in Eq.(1) canbe neglected. Due to the fact that the effective amplification takes place only for the spectralcomponents with frequencies < ∆, only the spin noise components with frequencies < ∆ areobserved and spectrum of the giant noise has monomodal shape (Fig.2). When magnetic fieldbecomes non-zero, the amplitude of these components becomes lower because the maximum ofthe spin noise spectrum (at the Larmor frequency) is shifting towards high frequencies. Thisexplains the observed reduction of the giant noise in magnetic field. The development of the detailed model of nonlinear oscillator (which take into account the con-crete mechanism of optical nonlinearity, spatial inhomogeneity of the microcavity and focusingof the probe beam) at the present stage of the research seems to be premature. In this section,we develop the simplest model of instable nonlinear resonator exhibiting strong enhancement ofsensitivity of its reflectivity to the fluctuations of the refractive index of the intracavity mediumat the threshold of the self-excitation. Despite the fact that in our experiments we observe the polarization properties of the reflected beam, the below simple model reveals, in our opinion, In some regions of our sample the spin noise spectrum has the shape close to the ”triangular” whose spectrum has maximum at the Larmor frequency qualitative properties of our microcavity and to the considerable extentjustifies the suppositions of the above hypothesis of built-in amplifier.Let’s consider an effective oscillator with the eigen frequency ω and the width of resonance∆ ω and put it into the correspondence to our microcavity. Then, the amplitude A of the fieldoscillations in the microcavity is given by the relationship: A = ıE ∆ ω √ Qω − ω + ı ∆ ω Q ≡ ω ∆ ω , (2)where E and ω – are amplitude and frequency of the optical oscillations in the incident beam,and quantity Q (at ω ∼ ω ) is the resonator Q-factor (we assume Q (cid:29) R of the wave reflected from the cavity, can be presented as the sum of the amplitude r t E of thewave corresponding to the probe reflected by the top mirror ( r t – is the reflectivity coefficientof the top mirror) and the amplitude tA of the wave escaped from the cavity through the topmirror ( t – is the transmission coefficient of the top mirror, | t | (cid:28) R = r t E + tA . UsingEq. (2) one can express t via the cavity resonant reflection coefficient r res = R/E | ω = ω , whichcan be easily estimated in the experiment and for the high Q-factor symmetrical cavities is asmall real number | r res | (cid:28)
1. After that, the following relationship for the reflected field canbe obtained: R = r t E + ( r res − r t ) A/ √ Q .The fact that the refractive index of the intracavity medium is dependent on the intensity | A | of the intracavity optical field, can be the reason for the optical nonlinearity of the micro-cavity under study. In the simplest case, this fact can be taken into account by assuming thatthe eigen frequency of the cavity ω depends on the intensity of the optical field | A | . In ourmodel, we consider this dependence to be non-local (retarding) and consisting of two contri-butions: the fast one Ω f (with characteristic time T f ) and the slow one Ω s (with characteristictime T s (cid:29) T f ): (cid:26) ω = ¯ ω + Ω s + Ω f ˙Ω s ( f ) + Ω s ( f ) /T s ( f ) = ν s ( f ) | A | (3)Here, ¯ ω is the eigen frequency of the cavity in linear regime, ν s and ν f – are constants describingabove contributions and related to the cavity nonlinearity. If we measure time in units of ∆ ω − ,frequencies – in units of ∆ ω , and if the amplitude of the intracavity field is defined by thedimensionless quantity a ≡ A/ √ QE , then, using Eqs. (2) and (3) one can obtain the followingset of equations describing the dynamics of our nonlinear resonator: [1 + ız ] a = 1 z = b − θ s − θ f ˙ θ s ( f ) + θ s ( f ) /τ s ( f ) = g s ( f ) | a | g s ( f ) = ν s ( f ) QE ∆ ω θ s ( f ) ≡ Ω s ( f ) / ∆ ω b ≡ ω − ¯ ω ∆ ω , (4)where τ s ( f ) ≡ ∆ ωT s ( f ) , and the quantity z = [ ω − ω ] / ∆ ω corresponds to the | a | -dependingdimensionless detuning of the cavity. If the parameters of the cavity acquire some variations,the amplitude of the field in the cavity reaches its steadystate value with the characteristic The similar mechanism of optical nonlinearity leading to the oscillating regime of GaAs-based opticalresonator, was described in [15, 16] ∼ ∆ ω − , which we assume to be unit. Therefore, the set of Eqs. (4) makes sense underthe condition ∆ ω − (cid:28) T s ( f ) , which we will assume to be satisfied.Let’s now show that the above model of nonlinear cavity describes the spontaneous oscil-lations of the field amplitude a in the cavity. For this reason, we consider the behavior of ourcavity at the time scales much greater than T f . Under this assumption, one can consider thefast contribution Ω f to be instantaneous and write θ f = c | a | (where c ≡ g f τ f ). After that theset of Eqs. (4) can be reduced to the form [1 + z ] | a | = 1 z = b − θ s − c | a | ˙ θ s + θ s /τ s = g s | a | (5)From the first two equations, one can express | a | via θ s . Since the dependence | a | ( θ s ) isobtained by solution of a cubic equation, it can be multivalued function. This can be shownby graphical analysis of equation for the detuning z (which can be obtained making use of therelationship | a | = [1 + z ] − ), whose solutions correspond to the crossing-points of the Lorentzcurve y = c/ [1 + z ] and a line y = b − θ s − z . If the amplitude | c | of the lorentzian is smallenough, the equation for the detuning has the single real root z ≈ b − θ s . Otherwise, it can beshown that if | c | > c cr = 8 √ / θ s , for which the equation for thedetuning has three real roots z , z , z . Therefore, at | c | > c cr (below we will consider c > | a | ( θ s ) becomes multivalued and in the above interval of θ s has the form ofS-shaped curve (see Fig. 4 where the interval of ambiguity is θ s ∈ [ θ l , θ r ]). At decreasing | c | ,the region of ambiguity decreases and vanishes at | c | = c cr : θ l = θ r | c = c cr . Using the dependence | a | ( θ s ) presented at Fig.4, one can completely describe the dynamics of considered model ofnonlinear cavity. Each point of the plain ( | a | , θ s ) maps the state of the cavity at an arbitrary10ime moment. For actuall dynamics of the nonlinear microcavity this point must belong to theS-shaped curve (Fig.4) – in this case the first two equations of the set (5) are satisfied. Thecharacter of motion of the mapping point along this curve is defined by the third equation ofthe set (5) and represents the moving of the mentioned point towards the crossing-point of the S -shaped curve and a line | a | = θ s /g s τ s . This point corresponds to the stationary state of thesystem.Two essentially different types of motion are possible. The first type takes place if theposition of line | a | = θ s /g s τ s is similar to that of line OQ . In this case the mapping pointmoving from the starting point A along the S -shaped curve to the right will reach the point G , where it will stay infinitely long. The second type of motion takes place if the parametersof the system are such that the line | a | = θ s /g s τ s crosses the S -shaped curve at some point G (cid:48) within the returning fragment BD of the multivalued interval [ θ l , θ r ] (for example as the line OO (cid:48) at Fig.4). In this case, the mapping point moving from the point A along the S -shapedcurve towards the point of stationary state G (cid:48) will come to the point B , from which the systemwill jump to the point C . After that, the mapping point will proceed its movement towards thepoint G (cid:48) (corresponding to the stationary state of the system) along the fragment CD . At thepoint D the system, again, will jump to the point E , and so on. Therefore, in the case of thesecond type of motion, the mapping point moves periodically along the loop EDCB consistingof two verticals ED and CB and of two fragments EB and DC of the S -shaped curve. It isseen from Fig.4 that in order to gain the oscillatory regime at c >
0, the condition g s < θ s = g s | a | ( θ s ) − θ s /τ s . Takingthis into account, one can write the following relationships for the dimensionless time intervals τ EB ( τ DC ), during which the mapping point passes the fragment EB ( DC ), and for the totalperiod τ A of oscillations: τ EB ( DC ) = (cid:12)(cid:12)(cid:12)(cid:12) (cid:90) EB ( DC ) dθ s g s | a | ( θ s ) − θ s /τ s (cid:12)(cid:12)(cid:12)(cid:12) τ A = τ EB + τ DC (6)The multivalued function | a | ( θ s ) (Fig.4) entering these relationships can be obtain eithernumerically or by means of Cardano formula. The direct calculations by Eq. (6) have shownthat the period of oscillations significantly depends on the intensity-related parameters of theproblem, c and g s , and can be by order of magnitude smaller than τ s . Therefore, the abovetreatment is justified if τ s exceeds τ f more than by an order of magnitude.Concluding the consideration of the oscillatory regime of the above model of nonlinearcavity, we itemize the main conditions of the self-excitation: (i) | c | > c cr = 8 √ /
9. It meansthat the intensity | A | of the field in the cavity must be high enough, so that nonlinear shiftof the eigen frequency must be of the order of the resonance linewidth ∼ ∆ ω . (ii) The line | a | = θ s /g s τ s (at g s c <
0) should cross the S -shaped curve within the multivalued region.Note that mutual position of mentioned line and S -shaped curve depends on the dimensionlessdetuning b . By varying parameter b one can violate the self-excitation regime of the cavity.Let’s consider now the response of the above cavity to a small modulation of detuning δb Note that, as it is seen from for the reflectivity spectra in the anti-crossing region (Fig.3), the similarcondition (at least qualitatively) actually holds. c < c cr . In this case, the set of Eqs. (4) has astable stationary solution (we denote it by a , z , θ s , θ f ), which can be obtained from Eq. (4)by omitting the terms ˙ θ s and ˙ θ f . The problem we are interested in can be formulated now ina following way: let’s replace b → b + δb ( t ) , δb/b (cid:28) δr of the reflection coefficient of the cavity in the vicinity of stationary regime to the smallmodulation of detuning δb ( t ). In accordance with a standard procedure, one should present thesought solution of (4) in the form a ( t ) = a + δa ( t ) , z ( t ) = z + δz ( t ) , θ s ( t ) = θ s + δθ s ( t ) , θ f ( t ) = θ f + δθ f ( t ), and find the quantities δa, δz, δθ s , δθ f in the first order of the perturbation theoryin δb . It is convenient to perform the calculation of the quantities q ≡ δaa ∗ ] and v ≡ δaa ∗ ], which are connected with the variation of the cavity reflectivity by means of relation δr = ( r res − r t )[ q + ıv ] / a ∗ . If the temporal behavior of δb represents harmonic oscillations withfrequency ν , then for the amplitudes of quantities q and v (we denote them as q and v ) onecan obtain the following expressions: | v | = | χ ( ν ) δb | | q | = | z χ ( ν ) δb | , (7)where susceptibility χ ( ν ) is defined as χ ( ν ) = 2[1 + z ] − z [ g f τ f / (1 − ıντ f ) + g s τ s / (1 − ıντ s )] . (8)The stationary detuning z entering these formulas can be obtained from the equation b − z = g f τ f + g s τ s z , (9)which has the unique real solution in the stable regime of the cavity considered here. Using theEq. (8) for the susceptibility, one can calculate its behavior at the threshold of instability, c → c cr . The results of such calculation are presented in Fig.5, which shows that the amplitude of thesusceptibility χ ( ν ) (and consequently the amplitude δr of the reflection coefficient modulation)considerably grows, when c → c cr with its shape being in qualitative agreement with that forthe amplification factor (excluding the narrow dip at ν = 0). The widths of the main maximumand of the central narrow dip of the function | χ ( ν ) | are defined by τ f and τ s Therefore, our model successively reproduces the main qualitative properties of the realmicrocavity, itemized at the beginning of this section. For this reason, the more detailed (andquite possible) analysis of the model is not required at present stage of the research and werestrict ourselves by two remarks only: (i) the central narrow dip of the function | χ ( ν ) | isconditioned by the requirement g f g s <
0, which is necessary for the cavity self-excitation.For this reason, this dip, probably, has a physical sense. (ii) the assumption concerning thepossibility of the slow and fast components of the response of refractive index to the probeintensity changes seems not to be fantastic: the fast part of this response can be associatedwith bleaching of excitonic susceptibility of the QW, and the slow part - with the slow processesof redistribution of the photogenerated electrical charge. Measurement of the noise spectrum in the frequency region < | χ ( ν, c ) (1 + b ) | calculated for c = g f τ f = 0 . , . , . , . , and 0 .
9. Other parameters are: b = 1 , τ s = 2 × , τ f = 0 . τ s , g s = − . c/τ s onclusion The properties of the Kerr rotation noise of the optical beam reflected from the Bragg micro-cavity with the QW in the intermirror gap are studied at various detuning between the cavityphoton mode and the QW resonances. In the region of anti-crossing of polariton branches,several hundred times enhancement of the noise signal, we call it giant noise , is discovered.This effect is explained on the basis of the hypothesis of built-in amplifier - the pre-thresholdenhancement of the polarimetric sensitivity of the nonlinear microcavity to the fluctuationsof the gyrotropy in the intermirror gap. The properties of the noise signal in the region ofnegative detuning between the cavity photon mode and the QW resonances are also explainedin the frame of the built-in amplifier hypothesis.Note that the described effect of nonlinear amplification, possibly, can be used for theenhancement of the sensitivity of the noise spectroscopy measurements. For this purpose, oneshould manage to control the parameters of the built-in amplifier, in particular, to make itsfrequency response homogeneous in the frequency range up to ∼
200 MHz.
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