COMPREHENSIVE INVESTIGATION MODELING FOR SEMICONDUCTOR OPTICAL AMPLIFIER (SOA)

This paper presents the effects of the input signal on the gain and carrier density response of a semiconductor optical amplifier (SOA). The SOA is modeled using a segmentation method. The input bias current input power, wavelength and the length of SOA required for amplification and switching functions are investigated. Moreover, the effect of temperature on SOA operation is investigated, as well as the thermo-optical effect. The operation principle is simulated, and the results show the input boundary conditions and requirements in which the SOA can be used as an amplifier and as a switch.


INTRODUCTION
As the demand for network capacity is rising due to the rapid increase in the Internet traffic volume, there is a growing need for all-optical based systems.The all-optical based system should offer much greater bandwidth and higher reliability than the traditional copper cables and the optoelectronic based communication technologies.
In the beginning, optical fiber network started as a simple connection with no routing capability.The use of wavelength division multiplexing (WDM) and optical time division multiplexing (OTDM) increased the overall capacity of the point-to-point optical fiber transmission systems.
The development of second-generation high speed systems, such as the synchronous optical network and the synchronous digital hierarchy, offered supplementary switching and routing capabilities to the network [1]- [2].Optical add/drop multiplexers and optical cross connectors were further introduced to the network in order to offer wavelength routing capabilities [3]- [4].However, in such systems, the switching process is still performed in the electrical domain requiring optical-electrical-optical (O-E-O) conversion modules [5]- [6].To meet the network speed and capacity demands and to overcome the bottlenecks of O-E-O conversion, ultra-fast photonic networks that rely on photonic signal processing are required.The next generation optical network is aimed to carry out all the processing in the optical domain, operating at speeds (hundreds of gigabits per second) well beyond the existing electronic devices [7]- [12].It is important to note that an all-optical processing technology is not a replacement, but is a complementary alternative, to electrical processing, particularly at the backbone optical layer.Both circuit and packet switching could be adopted in all-optical networks.
However, packet switching is more flexible than circuit switching in throughput and switching speed [13].An all-optical network offers transparency, implying that data can be carried at a range of bit rates and protocols and can also support different higher layers.
The development of high capacity optical networks increased the demand for new optical devices that are able to perform in almost all-optical functions.The key processes in all-optical switching are regeneration and wavelength conversion, where SOA is the key building block.Among all-optical switches [14], ultra-fast all-optical switches based on the SOA, such as Mach-Zehnder interferometers (MZI) [15]- [21] are the most promising candidates for the realization of all-optical switching and processing applications compared to other switches, such as ultra-fast non-linear interferometers (UNIs) [22]- [23] and terahertz optical asymmetric demultiplexers (TOADs) [24]- [26].
The use of SOA-based Mach-Zehnder interferometer (SOA-MZI) schemes will allow the processing of packets 'on-the-fly' in future photonic routers.The SOA-MZI is used in almost all functions inside a photonic router, such as clock extraction circuits, header/payload separation, optical flip-flops, wavelength converters, all-optical gates and switching [27]- [34].The performance of SOA, in terms of the gain temporal behavior, the carrier density and stimulation emission, is affected by several factors, including the dimensions of the waveguide and input parameters, such as the external bias current and the power and wavelength of the propagating input signal.Controlling these factors will lead to improving and optimizing the SOA amplification and/or switching characteristics, as well as the uniformity of the generated output signal that is necessary to reduce the system power penalty.
This paper proposes a segmentation model of the SOA based on numerical and mathematical equations.The model is used to analyze the impact of the input parameters and propagating signals on the SOA carrier density and its gain response to further understand the SOA operation.The segmentation model has been introduced in modeling the semiconductor devices [35].However, the segmentation model used in this paper takes into account the differential gain effect and the temperature effect of the semiconductor optical amplifier.It also investigates switching operation in more details.Moreover, the dynamic behavior of SOA, including opticalthermo-effect and dynamic range will be thoroughly investigated.
Next stage will be dealing with optimization of SOA parameters to maximize the output gain for amplification and optimization of SOA non-linear characteristics when used in optical switching.The boundaries and conditions necessary for the input parameters to achieve the 180º induced phase shift are managed for switching function in SOA-based optical switches.
The paper is organized as follows; in the next section, the principle of SOA is presented.Section three introduces the mathematical model used, including segmentation model and rate equations of SOA with phase shift equations.Section four presents the results and discussion.The conclusion is then drawn.

PRINCIPLE OF SOA
SOAs amplify incident light through stimulated emission.An electrical pump current is used to excite the electrons in the active region of the SOA.When the optical signal travels through the active region, it causes these electrons to lose energy in the form of photons and get back to the ground state.The stimulated photons have the same wavelength as the optical signal, thus amplifying the optical signal as shown in Figure 1.The basic working principle of a SOA is the same as a semiconductor laser, but without feedback.Figure 1.SOA amplifications due to stimulation emission process [36].

METHOD 3.1 Segmentation Model
In order to understand the factors affecting the SOA gain and the emerging output signals, a segmentation model of the SOA is introduced, where the SOA is divided into ten equal segments of length l=L/10 each.The model helps in identifying the small changes that occur within the short length of each segment.Ten segments were chosen for a sufficient accurate investigation on the change in the carrier density and the signal gain along the SOA.

Mathematical Model
The rate equations in small segments in an SOA are iteratively calculated while taking the carrier density change and the SOA length into account [37].

Rate Equations
When light is injected into the SOA, changes occur in the carrier and photon densities within the active region of the SOA.These changes can be described using the rate equations.The gain medium of the amplifier is described by the material gain coefficient,  (per unit length) which is dependent on the carrier density N and is given by [38]: where  0 is the carrier density at transparency point and  1 is the differential gain parameter.The net gain coefficient   is defined by: where   is the internal waveguide scattering loss and Γ is the confinement factor, which is the ratio of the light intensity within the active region to the sum of light intensity [39].The total gain  of an optical wave experienced at the location z of an SOA can be calculated according to: assuming a constant carrier density at any given location z within the active region of the SOA.Therefore, the average output power   over the length of the SOA becomes: where  is the length of the SOA and   is the input signal power.where   is the DC bias current injected to the SOA,  is the electron charge and  is the active volume of the SOA: where  and  denote the width and the thickness of the active region, respectively.() is the recombination rate, h is the Planck constant and h is the light frequency.The definition for R (N) used in this model is given by: where  is the non-radiative coefficient recombination at defects and traps,  is the spontaneous radiative recombination coefficient and  is the Auger recombination coefficient.The cubic equation is the best to fit the real gain coefficient g.The material gain coefficient depends on both the carrier density  and the input signal wavelength λ and can be rewritten as [40]: where  2 and  3 are empirically determined constants that are chosen to fit an experimentally measured SOA gain curve.λN is the peak gain wavelength and ∈ is the gain compression factor.The peak gain wavelength is given by: where  0 is the peak gain wavelength at transparency and  4 denotes the empirical constant that shows the shift of the gain peak.

Phase Shift Equations
Changes in the carrier density take place with the propagation of the input signal pulse through the SOA, hence affecting its propagation coefficient (via the non-linear refractive index variations in the SOA active region).Because of the finite carrier lifetime, the leading edge of the input pulse experiences a different phase shift relative to the lagging edge.This process is (SPM).Let ∆ represent the effective refractive index variation within the active region [39]: where dn/dN is the refractive index shift coefficient and   is the carrier density at steady state (i.e., with no input signal launched to the biased SOA).The total phase shift experienced by the propagating input signal is [40]: A thermo-optical effect is a change in the optical properties of a material in response to temperature.The thermo-optical effect may eventually lead to unstable operation of the SOA, since the effective refractive index changes as a function of temperature.A linear approximation for the effective refractive index as a function of temperature is given as shown below [41]: where  0 is the refractive index at room temperature,  0 . 0 for silicon device is 3.48314 [42].
( ∆ ∆ ) is the index variation with temperature (thermo-optical coefficient).The total phase shift experienced by the propagating input signal is [40]:

RESULTS AND DISCUSSION
The rate equations shown in the previous section are derived via Matlab to investigate the gain response of the SOA model while employing the segmentation method.The standard SOA parameters used are given in Table 1.The segmentation method involves dividing the SOA into ten equal segments of length l=L/10 each.The carrier density is assumed to be constant within a segment.However, the carrier density changes from one segment to another depending on its input power and the carrier density of the previous segment using equation (5).In all of the equations, the segment length l will replace the SOA length L for segment total gain and carrier density calculations.
Figure 2 shows the dynamic range of a semiconductor optical amplifier (SOA); that is the input power range within which an SOA can be operated error free.It is among the most important parameters describing the usability range of an SOA in an access network.Figure 3 shows the normalized gain response of the SOA using the physical parameters in Table 1.As it can be seen, the gain of the SOA increases rapidly up to a steady state value, where it becomes almost constant.This increase is due to the injection of the bias current to the SOA, hence resulting in a large number of electrons to overcome the energy gap to reach the conduction band.

Amplification
In order to use the SOA as an amplifier, it is necessary to ensure that the signal will not be affected by the SOA non-linear response that occurs when the SOA gain reaches its saturation value as shown in Figure 4, where the SOA decreases sharply to the saturation level.The reason for such response is that a depletion of the carrier density happens due to the continuous stimulation emission process.A range of input pulse signals with optical power values from 1 mW to 10 mW were applied to the SOA, and the signal output gains are illustrated in Figure 5.
As it can be seen from Figure 5, the simulated result is in clear agreement with the measured result.As expected, the figure shows that, for both curves, at a fixed wavelength, the gain gradually decreases with increasing the input power level.This effect is because a signal with higher power will interact with a larger number of excited electrons in the conduction band, thus resulting in increased depletion in the carrier density and the SOA gain.This process is applied for 1550 nm wavelength.As it can be noted from 1 mW input power at measured and simulated curves, the gain values obtained are 100 and 98 respectively; where it should be noted that the small discrepancy between the measured and simulated curves is due to simulation accuracy.

Input Signal Wavelength Investigation
The wavelength of the input signal has a direct impact on the SOA gain as can be seen from the third order gain coefficient equation.The depletion of the SOA gain that occurs due to the injection of input signal is directly related to the input power.Therefore, in order to understand these effects, the SOA gain as a function of the input power, for a range of wavelengths in the C-band (1530 to 1565 nm), is illustrated in Figure 6.As expected, the SOA gain reduces with increasing the input signal power at all wavelengths.This gain reduction is because a signal with higher power level will interact with a larger number of excited electrons in the conduction band, thus resulting in higher depletion of the carrier density and the SOA gain.From the figure, it is observed that at lower wavelengths, lower gains are achieved.
Figure 6.SOA gain as a function of input signal power when operated in the C-band.

Applied Bias Current Investigation
The applied current that is used for biasing the SOA has also a direct impact on the SOA carrier density and gain.At higher bias current, the larger number of electrons that overcome the energy gap will lead to an increase the carrier density, thus leading to an increased SOA total gain.In Figure 7, the SOA gain reduces with increasing the input signal power and this response appears at all bias current values at 1550 nm wavelength.On the other hand, higher biasing current values result in higher SOA gain achievement.The highest gain achieved is 48 dB with a 40% drop from the steady state value at a bias current of 200 mA and a power of 1 mW.For lower values of bias current, the gain profile is almost flat.For example, injecting the same 1 mW input at 100 mA current, 46.4 dB gain is achieved with just 0.6% drop from steady state.These results correspond to the number of electrons available for amplification in the conduction band.
Figure 7. SOA gain versus input signal power for a range of bias currents at a wavelength of 1550 nm.

SOA Length Investigation
The length of the SOA is an important physical parameter that affects the total gain.The dependence of the gain on the SOA length is plotted in Figure 8 for a range of input power values at 150 mA bias current.For short lengths (< 100 µm), where the depletion of N is negligible, the gain is the same for all values of   .On the other hand, for longer lengths (< 700 µm), the gain is increasing, peaking at L of ~500 µm beyond which the gain drops.The result confirms that the gain is higher for lower values of   .For longer length (800 µm -1.5 mm) SOAs, maintaining a stable applied bias current, the number of electrons per unit length is smaller because of lower current density.Therefore, in order to achieve high gain at longer length SOAs, the applied bias current needs to be increased in order to maintain the number of electrons per unit length.

Switching
On the contrary to amplification, in order to use cross phase modulation (XPM) and self phase modulation (SPM) characteristics of SOA for the switching function, the signal should experience a phase shift of 180º for the complete deconstructive interference [43].Therefore, phase shift calculation employing Equations ( 10), ( 11), ( 12) and ( 13) is crucial for setting the boundaries for the SOA switching function.The phase shift could be induced by the input signal injected to the active region of the SOA.

Input Signal Wavelength Investigation
The phase shift experienced by the input signal is directly proportional to the depletion of N as defined in (10) and (11).As a result of changes in the refractive index Δn, change is induced in phase shift.Figure 9 shows the phase shift as a function of the input power for a range of wavelengths in the C-band.To achieve an induced phase shift of 180 o at 1550 nm wavelength, the input signal power is 60 mW, where the induced phase shift increases with increasing the input power.

Applied Bias Current Investigation
To explain the effect of bias current on the induced phase shift of the input signal, Figure 10 explains the induced phase shift of the input signal achieved at a range of input power at different biasing current values.From Figure 10, it can be observed that at higher bias current values, the input signal propagating along the SOA induces more phase shift.Higher biasing results in higher SOA gain.From the third term in (5), which shows the depletion of the carrier density, one can observe that higher gain results in more N depletion.Therefore, the phase shift increases accordingly.
Figure 9. Induced phase shift experienced by the input signal power for a range of wavelengths.

SOA Length Investigation
It is important to explain the dependence of the shift of the input signal on the SOA length.It is known that lower gains are achieved at short (< 100 µm) and long (> 700 µm) SOA lengths.It was shown in Figure 10 that higher input power induces more phase shift, which explains the response in Figure 11.The figure shows the induced phase shift corresponding to the input power at different SOA lengths at 150 mA bias current.It can be concluded that the maximum phase shift is achieved at 500 µm.
Figure 11.Induced phase shift of the input signal achieved as a function of the input signal power for a range of SOA lengths at 150 mA bias current.

SOA Temperature Investigation
The temperature of the SOA is an important parameter that affects the total gain and phase shift.
The dependence of the gain on the SOA temperature at a wavelength of 1550 nm is shown in Figure 12.It can be noticed that the input signal propagating along the SOA induces the temperature dependence of SOA.The temperature dependence of the peak signal gain is approximately (-0.2) dB/K.Figure 13 shows that, due to temperature effect on medium gain, the SOA gain decreases with increasing temperature.Such investigation is carried out by using Equations 10, 12 and 13.Temperature can be controlled to obtain a certain phase shift that will become a function of temperature.
Figure 13.Temperature effect on phase shift.

Differential Gain Effect
To calculate the saturation power, the following relationship can be used [44]: where  is the reasonable unsaturated gain,   is the effective carrier lifetime.
Figure 14 shows the effect of differential gain on the linearity of the device.Moreover, increasing the differential gain leads to a decrease in the linear region, in terms of 3 dB bandwidth, meaning a decrease in saturation power.On the other hand, decreasing the differential gain leads to an increase in the linear region, meaning an increase in saturation power.
Figure 14.SOA gain as a function of the input power; the 3-dB saturation input power is marked.

CONCLUSION
The total gain response of an SOA model using the segmentation method has been simulated.CW probe and pump signals have been applied to the proposed segmentation of SOA model in order to investigate the corresponding gain response.The results have been discussed to achieve amplification and all-optical switching.The optimum performance conditions regarding the input signal power, the bias current and the signal wavelengths have been investigated for the SOA, to function as an amplifier and a switch.Furthermore, thermos-optical effect on total gain and phase shift has been introduced.Moreover, the effect of differential gain on the linear region has been investigated.The model can be extended to investigate vertical cavity SOA.

Figure 3 .
Figure 3.The Normalized gain response of the SOA with no input signal.

Figure 4 .
Figure 4. Normalized gain response of the SOA due to continuous wave (CW) probe.

Figure 5 .
Figure 5. Signal output gain corresponding to the input power at a wavelength of 1550 nm.

Figure 8 .
Figure 8. SOA gain responses as a function of SOA length for a range of input power levels with 150 mA bias current.

Figure 10 .
Figure 10.Induced phase shift of the input signal achieved versus the input signal power for a range of biasing current values.
radiative process in long wavelength lasers.The dynamic equation for the change in the carrier density within the active region of the device is given by: The carrier density rate equation expresses the conservation of carriers inside the active layer.It takes into account the current density and the net rate of carrier generation and recombination averaged over the active layer.The recombination rate consists of spontaneous and stimulated recombination.The spontaneous recombination rate includes the radiative and non-radiative components.The nonradiative recombination takes into account the Auger recombination, which is generally the dominant non-

Table 1 .
Physical parameters of the SOA.