Noise figure of vertical-cavity semiconductor optical amplifiers ...

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62 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 38, NO. 1, JANUARY 2002rate equations [10], as well as photon statistics master equations[10]–[13]. Traveling wave equations have been used in orderto take the spatial distribution of carriers, gain, and photonsin in-plane SOAs into account [14]. In a VCSOA, the gain isconcentrated to an extremely small gain region. The signaltraverses the gain region multiple times and experiences thesame gain each time. The traveling wave approach is thereforenot necessary for this case. However, VCSOAs typicallyhave highly reflective mirrors, which greatly affects the noiseproperties. The noise in VCSOAs can be analyzed using thesame methods as for in-plane FPAs. The total output noise froman optical amplifier consists of several different noise terms ofdifferent origin. The terms contributing to the total noise are:beating between amplified spontaneous emission (ASE) componentsand the coherent signal light, beating between differentASE components, and shot noise due to both signal and ASE.The input signal might also have some excess noise and thereceiver adds thermal noise. Signal-spontaneous beat noise isindependent of the input signal power and is the dominatingterm at low signal power. This term depends on the opticalbandwidth of the ASE spectrum. For this reason, a bandpassfilter is normally used after the optical amplifier in order tominimize the amount of ASE reaching the detector. This is notneeded for a VCSOA as the spontaneous emission bandwidthis limited by the Fabry–Perot cavity. Signal-spontaneous beatnoise and shot noise increase with input signal power. Athigh signal powers, signal-spontaneous beat noise is the maincontributor to the output noise. The output ASE, and hencethe signal-spontaneous beat noise, is greatly affected by themirror reflectivity. Considering signal-spontaneous beat noiseto be dominant, the noise factor , defined as input SNR overoutput SNR (the noise figure is defined asand expressed in decibels), is given by[15]. For high signal gain ( ), this reduces toHere, is the population inversion parameter and is the excessnoise coefficient, which describes signal-spontaneous beatnoise enhancement due to finite mirror reflectivity. takes ona value of one for zero reflectivity (the case of traveling waveamplifiers) and values higher than one for finite mirror reflectivities.Using photon statistics master equations as described byShimoda et al. [11], it can be shown that is given by [12](1)(2)wherebottom mirror reflectivity;top mirror reflectivity;single-pass gain;amplifier gain.Here, the signal is exiting the amplifier through the top mirror.VCSOAs can be operated in either transmission or reflectionmode with different expressions for the signal gain . Sinceappears in the denominator of (2), the two configurations are associatedwith significantly different expressions for . In transmission-modeoperation, the signal enters the VCSOA from oneside (bottom) and is collected on the other side (top). In reflectionmode, the signal enters and exits the amplifier from thesame side (top). The amplifier gain of a VCSOA operated intransmission mode ( ) or reflection mode ( ) is given by [5]Here, is the phase detuning off the cavity resonance frequency.For operation at the cavity resonance frequency, the sine termsequal zero. Inserting (3) and (4) back into (2), the excess noisecoefficient for the two cases can be shown to beFor transmission mode and high gain ( ), simplifies toThe excess noise coefficient versus amplifier gain for both casesis plotted in Fig. 1(a) and (b), for different mirror reflectivities.The reflectivity of VCSOA mirrors is typically much higherthan for those of in-plane FP amplifiers due to the shorter activeregion of VCSOAs and, thereby, lower single-pass gain. VC-SOAs demonstrated to date have all used mirrors with reflectivitieshigher than 0.9. is shown here for mirror reflectivitiesof 0.85 and higher. For transmission-mode operation [Fig. 1(a)],equals one when the single-pass gain is.Itisobviouslydesirable to operate the VCSOA close to this ideal valueof , but at the same time be able to vary the signal gain .Itis also desirable to maximize in order to achieve high signalgain. This can be achieved by using low input mirror reflectivity( ) and high output mirror reflectivity ( ). This is evidentfrom Fig. 1(a); a value of close to one over a wide range ofsignal gain is achieved using and .Forsymmetrical devices, is independent of mirror reflectivity.For the case of reflection-mode operation [Fig. 1(b)], is afunction of bottom mirror reflectivity only. -values close toone can be achieved for bottom mirror reflectivities higher than0.99, which is easily obtained using DBR mirrors.A. Inversion LevelIt is desirable to operate an optical amplifier with a populationinversion as high as possible in order to minimize reabsorptionof the signal light, which is detrimental to the noise figure. Thepopulation inversion parameter is defined as [13]where is the carrier density and is the carrier density attransparency. takes on values greater than one for low carrierdensities and reaches unity at complete inversion. A delicateproblem inherent to FPAs is that strong pumping is desiredto reach high carrier density, and thereby minimize , whilethe amplifier still has to be operated in the regime below lasing(3)(4)(5)(6)(7)(8)
BJÖRLIN AND BOWERS: NOISE FIGURE OF VCSOAs 63(a)Fig. 2.threshold.Population inversion parameter versus reflectivity (R 2R ) at lasingbenefit from low mirror reflectivity [2], [7]. It is clear from thediscussion above that low mirror reflectivity is also crucial forachieving a low noise figure.B. Coupling EfficiencyFor any practical application, the often critical parameter isnot the intrinsic noise figure of a device, but rather its fiber-tofibernoise figure. The noise figure is degraded by loss associatedwith a coupling of signal into and out of the device. Thefiber-to-fiber noise factor can be calculated using the equationfor the noise factor of cascaded devices [16] as follows:(b)Fig. 1. Excess noise coefficient versus amplifier gain for: (a) transmissionmodeoperation and (b) reflection-mode operation.threshold. The mirror reflectivity governs how hard the amplifiercan be pumped before it reaches lasing threshold. Lasingthreshold is reached when the round trip net gain equals one,i.e.,. The single-pass gain can be deduced fromthe active region design and the material gain, which is a functionof carrier density. The population inversion can thus belinked to the single-pass gain and, if the reflectivities are known,the population inversion at threshold can be calculated. Fig. 2shows a plot of the calculated population inversion parameterat threshold versus mirror reflectivity ( ) for the devicedescribed later in this paper. This marks the lowest possiblevalue of for a given reflectivity; in practice, a VCSOAhas to be operated at a slightly lower carrier density in orderto avoid lasing. This particular device has an undoped InP–In-GaAsP active region. The gain model for the device is describedin [7]. The plot is valid for transmission or reflection-mode operation.For a reflection-mode device with bottom mirror reflectivityclose to unity, the -axis in the plot represents top mirrorreflectivity. To achieve an below 1.5, the reflectivity has tobe on the order of 0.9 or less. At low reflectivities and high carrierdensities, changes in carrier density have a very small effecton the population inversion and values close to those given bythe figure can be achieved. It has previously been shown thatsaturation output power and high gain-bandwidth product bothThe coupling losses can be modeled by attenuators withand noise figures . For an amplifier with gainand intrinsic noise factor , the total noise factor is thengiven by(9)(10)This equation demonstrates that the input coupling loss directlydegrades the noise factor (in logarithmic units, the inputcoupling loss is simply added to the noise figure), whereasthe output coupling loss is only significant when the gain issmall. VCSOAs have superior coupling efficiency compared toin-plane devices due to the circularly symmetric cross sectionof the optical mode. Coupling loss as low as 1 dB has beenachieved for vertical-cavity lasers to single-mode fiber [17].Similar output coupling efficiency could be achieved for aVCSOA; the input coupling efficiency should be even lower.To summarize the theory, excess noise coefficients close tounity can be achieved, if the mirror reflectivities are chosen carefully(Fig. 1). High population inversion can also be obtained,using low mirror reflectivities and strong pumping (Fig. 2). Thisindicates that intrinsic noise figures close to 3 dB are possibleto achieve. Assuming high gain and input coupling loss of lessthan 1 dB, fiber-to-fiber noise figures of about 4 dB should bepossible for VCSOAs.
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