tailieunhanh - Advances in Optical Amplifiers Part 8

Tham khảo tài liệu 'advances in optical amplifiers part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Slow and Fast Light in Semiconductor Optical Amplifiers for Microwave Photonics Applications 195 Under these conditions a measurement of the small signal modal gain rgo versus I will be equivalent owing to Eq. 44 to a determination of the modal gain rg versus N Ts. Here r is the ratio sacf S of the active to modal gain areas in the SOA. A last relationship between T and Mo is then required to determine the modal gain rg as a function of Mo. It is obtained by substituting rg T in the saturated steady state solution of the carriers rate equation Eq. 11 1 N r T Mo qLsac Ts r 0 38 where the injected current I is now fixed by the operating conditions. Added to the previous relationship between rg and T the Eq. 45 gives another expression of rg as a function of T T2 and I. Consequently rg and T can be known with respect to the local intensity M z and the injected current I. To solve Eqs. 19 we need to express N as a function of Mr z and I. This is equivalent to express N with respect to T since T is known as a function of Mr z and I. Consequently we model our SOA using the well-known equation N AN BIN2 CIV3 Ts 39 where A B and C which are respectively the non-radiative spontaneous and Auger recombination coefficients are the only parameters that will have to be fitted from the experimental results. Using Eq. 39 and the fact that we have proved that N Ts and rg can be considered as function of M z and I only we see that N ra rdg and -ỈM- can also be considered as ỜN r Í a T functions of Mr z and I. This permits to replace Eqs. 19 by the following system -M Tg Mrzi I - r M 40 dE 2 Tg Mrz- I - y E1 L-iEAg MA l Eq 41 z 2 _1_ 2 -E 1 Mo z I p 1 ia rA z M0 z I E 42 IT 2 ự T- I - 7 J E 1 2rA 1 IE 42 with Ag M0 z I M1U I t 43 r 1 ĨM0 Us M I - i Ts M I Eqs. 40 41 and 42 are then numerically solved Eq. 40 gives Mr z with the initial condition M 0 ựỹĩ - where Pin is the optical input power. Mr z can be then introduced into Eqs. 41 42. It is then possible to simulate the optical