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Characteristics of small signal gain spectrum and static gain saturation of integrated twin-guide semiconductor optical amplifier (ITG-SOA) are theoretically investigated and compared with those of SOA. A comprehensive ITG-SOA model is proposed to effectively extend the application range of previous models. The model considers the interaction between carrier density and photon density as well as the longitudinal variation of phase-match degree induced by input power. Two kinds of ITG-SOAs are expected to have different small signal amplification characteristics. The unique gain saturation characteristics of ITG-SOA, which have been well explained, show great promise in wavelength conversion: enhanced extinction ratio, reduced input pump power level, and quasi-digital response.
©2006 Optical Society of America
1. Introduction
Integrated twin-guide semiconductor optical amplifier (ITG-SOA, as shown in Fig. 1), in which light amplification and input-output are performed separately by an active waveguide and a passive waveguide, was proposed by Kambayashi et al [1]. The architecture manner of ITG-SOA is one of the important ideas used to construct future photonic integrated circuit. For example, ITG-SOA based optical switch (ITG-SOA-Switch) matrix most probably becomes a key monolithic integrated device in future optical packet switching networks [2]. The active waveguide of ITG-SOA is actually a SOA, whose material refractive index is changed with the carrier density variation due to stimulated emissions [3]. Because of the optical power amplification in active waveguide and the periodical power transfer between active and passive waveguides, different parts of active waveguide have different phase-match degrees to passive waveguide, also changed with input power. So input power determines the efficiency of optical power transfer between active and passive waveguides, thus influences the amplification characteristics of ITG-SOA intensively. Partial characteristics of ITG-SOA have been studied in previous models [1,4]. But these models neglect the interaction between carrier density and photon density in active waveguide; the degree of phase match between active and passive waveguides is supposed to be uniform along the whole propagation direction and invariable with input power. Thus the application range of these models is restricted, for example, gain saturation characteristic of ITG-SOA can not be studied with these models.
In this paper, we investigate two basic characteristics of ITG-SOA, i.e., the gain spectrum under small signal amplification and the static gain saturation by using a comprehensive numerical model. The model takes into account the interaction between carrier density and photon density as well as the non-uniform spatial distribution of phase-match degree induced by input power. The unique characteristics owned by ITG-SOA are explicitly explained, and their promising applications are discussed. Individual quantitative analysis results will vary with the given device parameters, so the simulation results of ITG-SOA are compared with those of the SOA whose device parameters are the same as those of the active waveguide. This may be helpful for general understanding and designing ITG-SOA.
2. Model
For simplicity, the active waveguide is assumed to have negligible reflectivity at the end facets in our simulation, therefore only the forward-traveling waves exist. As shown in Fig. 2, the coupling region of ITG-SOA is divided into a number of small sections, and various material and structural parameters throughout section i are assumed to be constant in the time interval t to t + ∆t, ∆t =∆z×neff /c, ∆z is section length, neff is effective refractive index, c is the speed of light in free space. Ar,i represents the normalized envelope function of the optical field into section i, where the subscript r equals 1 or 2, corresponding to passive guide or active guide respectively. N, n, g, β, and Γ are carrier density, refractive index, material gain coefficient, propagation constant, and confinement factor respectively.
Fig. 2. Schematic of the coupling region of ITG-SOA divided into a number of small sections with equal length.
To account for the interaction between carrier density and photon density in active waveguide, we solve the rate equation in each section as [5]
where J is the injected current density, e is the electron charge, d is the active region thickness, R is the recombination rate term. Ac is the cross-sectional area of active waveguide, h is the Planck constant, v is input light frequency, =(|A 2i,j|2+|A 2,i+1,j|2)/2 is the average power in section i of active waveguide, and the subscript j corresponds to different input light. Amplified spontaneous emission has been excluded in Eq. (1).
The recombination rate term R is given by
where c1 , c2 , and c3 are recombination constants.
The material gain coefficient is assumed to be cubic dependence on wavelength [6]
where gN , a1 , a2 , and a3 are gain constants, λt is the peak wavelength at transparency carrier density Nt , λp is the peak wavelength at carrier density N 2i.
When the carrier density in section i is obtained, the refractive index change of active waveguide is then calculated by assuming that refractive index change depends linearly on the carrier density. Based on the acquired lateral distribution of refractive index, a slab waveguide mode solver [7] is used to calculate the lateral optical field distributions, confinement factor, and propagation constant in section i.
Once the input amplitudes A 1,ij and A2,ij at time t are known, the output amplitudes A l,i+1j and A 2i+lj at time t+∆t can be calculated by Eq. (4) deduced from Ref 4.
where αint , and g2 are the intrinsic loss coefficient and the material gain coefficient of active waveguide respectively. k is the coupling coefficient [7] between active and passive waveguides. Here, the net modal gain coefficient g2net is connected with the normalized amplitude gain coefficient g2A in Ref. 4 by g2net =2Kg2A ; the net modal gain coefficient glnet of passive waveguide is assumed to be zero.
The evolution of the input signal inside SOA is expressed as following
Combining Eq. (1), Eq. (4) and the slab waveguide mode solver, the longitudinal variations and time-dependent of various parameters of ITG-SOA can be calculated self-consistently. Replacing Eq. (4) by Eq. (5), the longitudinal variations and time-dependent of various parameters of SOA can also be obtained.
3. Characteristic analyses
As a practical example, we use the model above to investigate the characteristics of an ITG-SOA constructed by bulk InGaAsP/InP material, whose layer parameters are described in Table1. The materials of active and passive waveguides are all lattice-matched to InP, and their bandgap wavelengths are 1.55 μm and 1.2 μm respectively. The refractive index (RI), RI change, and the differential RI dn/dN (in Table2) of active waveguide are calculated with temperature 300 K is assumed [3,8]. When the injected carrier density is 3×1018cm-3 and no light is incident, the effective refractive index of active guide is equal that of passive waveguide. The thickness of each waveguide has been designed carefully so that only the lowest-order fundamental mode exists; also there is a sufficient confinement factor for the active waveguide. Only the fundamental transverse mode is considered in our paper. Apart from Table 1, other device parameters [6] used in our calculations are listed in Table 2.
Table 1. Layer Parameters of the ITG-SOA Used in the Calculations
Table 2. Other Parameters Used in the Calculations
Fig. 3. Optical power distribution along the propagation direction: (a) Under small signal amplification; (b) The input power approaches 3 dB saturation point of ITG-SOA(800μm).
Using our model and the parameters mentioned above, the second and third power peaks in the passive waveguide appear at Z=400 μm and 800 μm respectively (The first power peak is at Z=0) under small signal amplification, as shown in Fig. 3(a), in which, the input continuous-wave (CW) signal wavelength is 1550 nm. So, in order to obtain maximal amplifier gain, the coupling region lengths of 400 μm and 800 μm are chosen in our simulation; and the shortened forms of corresponding ITG-SOAs are ITG-SOA(400μm) and ITG-SOA(800μm) respectively. Since the positions where the second and third power peaks appear in the passive waveguide will change with the variations of spacer layer thickness or other parameters, ITG-SOA(400μm) and ITG-SOA(800μm) represent actually two kinds of ITG-SOAs. As shown in Fig. 3(a), the small signal gain (SSG) of ITG-SOA(800μm) is equal to that of a SOA with 400 μm length because the optical signal spends half the time in each waveguide of ITG-SOA. So the SOA with 400 μm length is chosen for the comparison with ITG-SOA. Figure 3(b) will be described later.
Figure 4(a) shows the simulated SSG spectra of ITG-SOA(800μm), ITG-SOA(400μm) and SOA; the comparison data of the SSG spectra are listed in Table 3. Three conclusions can be obtained from the comparison. Firstly, the wavelength ranges of 3 dB bandwidth of the three SSG spectra can all cover the C band (1530~1565 nm); Secondly, the 3 dB bandwidth of ITG-SOA is obviously narrower than that of SOA. It is arising from wavelength-induced phase mismatch between active and passive waveguides. Thirdly, The 3 dB bandwidth of ITG-SOA(800μm) is obviously narrower than that of ITG-SOA(400μm). The reason is that further amplified signal in the second half optical path (400~800 μm) of ITG-SOA(800μm) consumes more carriers, thus gives rise to more phase mismatch between active and passive waveguides. Although the 3 dB bandwidth of ITG-SOA(800μm) is reduced, but its SSG value is doubled in dB compared with that of ITG-SOA(400μm).
Table 3. Comparison data of the SSG spectra
The simulated amplifier gains versus input power characteristics are shown in Fig. 4(b), in which the input CW signal wavelength is 1550 nm. Two features in the gain saturation behavior of ITG-SOA are noteworthy, which are differing prominently from SOA.
The first important feature shown in Fig. 4(b) is that when the input power approaches 3 dB saturation point, the gain of ITG-SOA starts to decrease sharply until attaining its first valley. The feature is arising from the combination of the gain-saturation property of active waveguide and the saturation-induced phase mismatch between active and passive waveguides. Saturation-induced phase mismatch not only prevents the power in the active waveguide from returning completely to the passive waveguide but also shortens the peaks period distance. As shown in Fig. 3(b), for ITG-SOA(800μm), when input power (-13 dBm) approaches 3 dB saturation point (-12.4 dBm), the third power peak of the passive waveguide has left the output port towards input port, resulting in rapidly decrease of amplifier gain. Once the third power valley appears at the output port, the gain also falls to its first valley. So the saturation input power of ITG-SOA(800μm) is obviously smaller than that of SOA. However, the saturation input power of ITG-SOA(400μm) is obviously higher than that of SOA, because its gain is much smaller than that of SOA, resulting in much smaller carrier depletion.
The second noticeable feature is that the gain curve of ITG-SOA exhibits damped periodic oscillations around 0 dB midline with the further increase of input power; and its oscillation peaks are obviously lower than the SOA gains till 20 dB input power. For ITG-SOA(800μm), as an example, when the fourth power peak of the passive waveguide appears at the output port, the gain also rises to its first peak after saturation. Higher input power will make the fourth power peak move towards input port, resulting in the gain decrease once again… Such repetition causes the gain curve to oscillate with increasing input power. During the procedure, the gain-saturation level of active waveguide and the saturation-induced phase-mismatch degree between active and passive waveguides aggravate more and more, resulting in reduced oscillation amplitude and obviously small peak gains compared with those of SOA. And the tendency is that the input signal will no longer be amplified in the active waveguide, only existing a very small part of power exchange between the two waveguides.
4. Application prospects of ITG-SOA
The above analyses reveal several important application features of ITG-SOA. Firstly, as a small signal amplifier, ITG-SOA(400μm) has high saturation input power, relatively wide bandwidth, but small gain; reversely, ITG-SOA(800μm) has low saturation input power, relatively narrow bandwidth, but high gain. Secondly, since only a small increase of input power around 3 dB saturation point can cause a big decrease of gain, highly efficient wavelength conversion operation is possible. The output extinction ratio can be improved compared with that of the input pump signal in a moderate pump power range. Moreover, for ITG-SOA(800μm), the input pump power level can be considerable reduced compared with XGM, which make the wavelength conversion more easily be realized. Furthermore, as shown in Fig. 4(b), the maximal oscillation gain peak of each kind of ITG-SOA is considerable smaller than its SSG value; this can be used to achieve quasi-digital wavelength conversion function over a wide input power levels and ranges.
5. Conclusion
The characteristic analyses of SSG spectrum and static gain saturation of ITG-SOA have been accomplished by using a comprehensive numerical model, accompanied by the comparison with the characteristics of SOA. The model has considered the interaction between carrier density and photon density as well as the longitudinal variations of phase-match degrees induced by input power, which greatly improves the application range of previous models. The simulation results reveal that two kinds of ITG-SOAs with different coupling region lengths can be selected to realize different SSG characteristics. Most important, the application prospects of ITG-SOA in wavelength conversion are very attractive: enlarged extinction ratio from steep threshold-like nonlinear response, reduced input pump power level, and quasi-digital wavelength conversion over a wide range of input power conditions.
The model presented here can be directly used to investigate the dynamic characteristics of ITG-SOA. Furthermore, with only a small modification, a feasible simulator can be obtained to study the static and dynamic characteristics of ITG-SOA-Switch. These issues will be addressed elsewhere.
Acknowledgments
The authors thank Dr. Siyuan Yu of the University of Bristol for useful discussions. This work was supported by the Chinese Natural Science Foundation under Grant No. 60577007.
References and links
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