Analysis of Noise Effects in Long Semiconductor Optical Amplifiers

In this letter, we address one of the essential processes to consider in long Semiconductor Optical Amplifiers (SOAs) analysis, which is the noise. Particularly, we investigate the impact of noise effects on the SOA behavior by measuring the gain, the optical signal to noise ratio and the noise figure, referring to numerical simulations. Although its gain dynamics provide very attractive features of high speed optical signal processing, we show that the noise is strong in long SOAs and can limit the performance of the structure. In order to remedy this, we show that using high bias current at moderate input signal power is recommended. INTRODUCTION With the tremendous growth of the Internet and the large increase in traffic demands, which have produced a need for new flexible types of services, the necessity of new generation optical networks for managing the high-speed data flows has appeared. One of the most promising technologies for high bit rate optical networks is that related to the exploitation of the huge potential of the SOA amplifier. By integrating the amplifier functionality into the semiconductor material, the same basic component can perform many different applications. The major advantages of SOAs that lead to great innovation in optical communication technique are their capability to operate as multifunctional devices, their compactness, miniaturization and integration, their high nonlinearity and their potentially low production cost. Moreover, they can provide integrated functionality of internal switching and routing functions that are required for optical networks. Wavelength converters [1], optical switches [2], signal regenerators [3] as well as optical logic gates [4], all can be made from SOAs, which will lead to large cost reductions and improved performance in future optical-network equipments. Most of these functionalities are based on the nonlinear effects of SOA as the cross-gain modulation (XGM), the cross-phase modulation (XPM), the four wave mixing (FWM) and the cross-polarization modulation (XPolM), etc. Although lot of remarkable investigations have been performed using short SOAs, the potential of long and ultralong SOAs for high speed all-optical signal processing hasn’t been sufficiently studied yet. Despite long SOAs require special design of the facets in order to prevent unwanted lasing inside the active region, they have proven to be particularly promising devices to perform many key functions, but not in conventional operations. A very attractive feature identified in the work of Slovak et al. [5] is related to acceleration of the inter-band *Address correspondence to this author at the SYS’COM Laboratory, National Engineering School of Tunis (ENIT) B.P. 37 Le Belvedere 1002 Tunis, Tunisia; Tel: +216 71 875 475; Fax: +216 71 872 729; E-mail: [email protected]; [email protected] transitions when SOA length is increased. Moreover, the effect of amplified spontaneous emission (ASE) noise, which is known to limit the SOA performance, may become strong in long devices because each part of the structure contributes spontaneous emission as was mentioned by Bramann et al. in [6]. As noise properties of the optical signal have been the subject of extensive studies [7-10] and are still of interest, we will focus, in this letter, on one of the main processes to consider in SOA analysis, which is the noise effect. Especially, we will concentrate on the impact of noise effects on the behavior and the performance of the long devices. This study is based on analyzing, by numerical simulations, the gain, the Optical Signal to Noise Ratio (OSNR) and the noise figure (NF) of the structure. THEORY The wideband model for a bulk SOA proposed by Connelly in [11, 12] is of interest to consider in studying SOAs characterization, then it is adopted in this paper. It is based on the numerical solution of the coupled differential equations for carrier-density rate and photon-flux propagation for both the forward and backward signals and the spectral components of ASE. The traveling-wave equations for the signal fields are written as follows: dEs,k + (z) dz = j. k + 1 2 .gm (vk ,n) (n) ( ) .Es,k + (z) dEs,k (z) dz = j. k 1 2 .gm (vk ,n) (n) ( ) .Es,k (z) (1) Here, the propagation of the optical field is assumed on the positive or negative z-direction (E + s,k, E s,k) of the SOA structure; k is the propagation coefficient; gm denotes the material gain coefficient; k symbolizes the optical frequency of the Ns signals injected with a power Pin,k before coupling loss (k=1 to Ns); represents the material loss coefficient. The equation (1) is subject to the boundary conditions, which are given by [11]: 62 The Open Optics Journal, 2008, Volume 2 Said et al. Es,k + (0) = 1 R1 ( ). in .Pin,k h.vk + R1 .Es,k (0) Es,k (L) = R2 .Es,k + (L) (2) The signal amplification also depends on the amount of spontaneously emitted noise from the amplifier. The traveling wave equations for the spontaneous emission are given by [11]: dN j + (z) dz = .gm (vj ,n) (n) ( ).N j + (z) + Rsp (vj ,n) dN j (z) dz = .gm (vj ,n) (n) ( ).N j (z) Rsp (vj ,n) (3) where N + j and N j are, respectively, the spontaneous emission photon traveling in the positive and negative z-direction; Rsp denotes the emission noise coupled into N + j and N j. The carrier density at position z in the SOA structure is determined from the steady-state solution to the rate equation [11]: dn dz = I e.d.L.W R(n) d.W gm (vk ,n).Ns,k + (z) k=1 Ns d.W gm (vk ,n).Ns,k (z) k=1 Ns gm (vj ,n). N j + (z) + N j (z) ( ) j=1 Nm 1 (4) I denotes the amplifier bias current, which is assumed to have a uniform distribution across the active region width; R represents the recombination rate term; e is the electronic charge; N + s,k and N s,k are, respectively, the photon rate of the wave in the positive and negative z-direction.. NOISE EFFECTS IN A SOA STRUCTURE One of major processes to consider in SOA analysis is the amplified spontaneous emission noise, because it strongly affects the structure performance. So, the injected signal and the ASE noise interact nonlinearly as they propagate along the SOA structure. Then, the interaction correlates different spectral components of the noise. Consequently, we can distinguish three types of noise which are the shot noise, the signal-spontaneous beat noise and the spontaneous-spontaneous beat noise. The power of the ASE noise generated internally within the SOA is given by: PASE = 2.nsp .h. .(G 1).B0 (5) where G is the gain at the optical frequency , h represents the Planck’s constant, B0 is the optical bandwidth and nsp refers to the population inversion factor. For an ideal amplifier, nsp is equal to 1, corresponding to a complete inversion of the middle. However, in the usual case, the population inversion is partial and nsp > 1. The shot noise results in the detection of the received total optical power due to the signal and the power of the ASE noise. It is given by the following equation: Nshot = 2.e 2 .Be G.Pin h. + nsp .B0 .(G 1) (6) where Be is the electrical bandwidth of the photo-detector. The noise contribution due to the signal exists as well there is no optical amplifier; this later simply modifies the signal power, then the shot noise power related to this introduces a supplementary shot noise that is associated to the detection of the ASE. The two intrinsic components related to beat noise are produced at the same time when optical signals and ASE coexist together. The first type of beat noise which is the signal-spontaneous beat noise occurs between optical signals and ASE having frequency close to that of the optical signals. It is given by the following equation: Ns sp = 4. e h. .Be .Pin .nsp .G.(G 1) (7) The second type which is the spontaneous-spontaneous beat noise occurs between ASEs. It is expressed as follows: Nsp sp = e 2 .(2B0 Be ).Be .nsp 2 .(G 1) (8) The signal-spontaneous beat noise is preponderant for a strong input signal, whereas the spontaneous-spontaneous beat noise is dominating when there is an injection of a small input power. Compared to the shot noise and the signalspontaneous beat noise, the spontaneous-spontaneous beat noise can be significantly minimized by placing an optical filter having a bandwidth B0 after the amplifier. A convenient way to quantify and characterize the noise and describe its influence on the SOA performance is in term of Noise Figure (NF) parameter. It represents the amount of degradation in the signal to noise ratio caused by amplification process, and it is defined as the ratio between the optical signal to noise ratio (OSNR) of the signal at the input and output of SOA: NF = (S / N )in (S / N )out (9) The OSNR of the input signal is given by the following equation [13]: (S / N )in = Pin 2.h. .Be (10) The OSNR of the input signal is proportional to the optical power of the input signal, or more specifically to the input number of photons per unit time (Pin/h ). Whereas, the OSNR of the output signal is defined by: (S / N )out = e.Pin .G h. 2 . 1 Nshot + Ns sp + Nsp sp (11) Accordingly, by substituting equations (6), (7), (8), (10) and (11) into (9), the noise figure can be written as follows: NF = 1 G + 2.nsp . G 1 G + h. .B0 .nsp .Pin .(G 1) Pout 2 + h. .(2B0 Be ).nsp 2 .Pin .(G 1) 2 2.Pout 2 (12) In practical case, the last two terms can be neglected because the ASE power is weak compared to the signal power; else the spontaneous-spontaneous beat noise can be miniAnalysis of Noise Effects in Long Semiconductor Optical Amplifiers The Open Optics Journal, 2008, Volume 2 63 mized by placing an optical filter at the output. So the noise figure can be rewritten as [14]: NF 1 G + 2.nsp . G 1 G (13) Since spontaneous emission factor (nsp) is always greater than 1, the minimum value of NF is obtained for nsp=1. So, for large value of gain (G>>1), the noise figure of an ideal optical amplifier is 3dB. This is considered as the lowest NF that can be achieved. This implies that every time an optical signal is amplified, the signal to noise ratio is reduced to the half. SIMULATION RESULTS AND DISCUSSION For simulating the noise effect in the SOA device and its impact on the behavior of the structure, we used available OptiSystem software. The physical features of the structure are listed in Table 1. The CW input signal power ranges from -40 to 10 dBm at wavelength =1.55 m. By varying the bias current and the power injected at the SOA input and by modifying its active region length, we measured, using a dual port WDM analyzer, the variation of Gain, NF and OSNR at the output of the structure. Consequently, as shown in obtained results, these parameters will be changed not only with the input signal power variation but also as a function of the SOA length, the confinement factor and the bias current. Table 1. Device Parameters used in the Simulation Symbol Description Value I Bias current 0.3 0.5 A in Input coupling loss 3 dB out Output coupling loss 3 dB R1 Input facet reflectivity 5e-005 R2 Output facet reflectivity 5e-005 L Active layer length 1000 1300 m W Active layer width 3 m d Active layer height 0.25 m Optical confinement factor 0.25 0.45 A Nonradiative recombination coefficient 360 000 000 1/s B Bimolecular recombination coefficient 5.6e-016 m^3/s C Auger recombination coefficient 3e-041 m^6/s vg Group velocity 75 000 000 m/s me Effective mass of electron in the CB 4.1e-032 Kg mhh Effective mass of a heavy hole in the VB 4.19e-031 Kg mhl Effective mass of a light hole in the VB 5.06e-032 Kg Arad Linear radiative recombination coefficient 10 000 000 1/s nr Active refractive index 3.7 The SOA output power versus the input power is shown in Figs. (1) and (2) for cases of bias current I= 300 mA and I= 500 mA, respectively. We can notice that when there is augmentation of SOA active region length, the output power will clearly decreases. In this case, in order to obtain higher output powers, the bias current should be increased. Moreover, there will be a saturation of the output power when the SOA input power is increased.