100 90 80 70 60 90 30 20 “«8— «8“— y*— &) Frequency (GHz) 8.14.1
F ig . 8.14 A M mode-locking w ith Pg=5; averaged spectrum over 50 pulses w ith center frequency a t 130GHz (8.14.1), steady-state photon num ber (8.14.2) and ca rrie r num ber (8.14.3) versus tim e
Photon Number (lunit=10^)
8.14.2
499.66 îsaT îi lé é .b i ië ë .ë ë
Tim e (ns) C a rrie r N um ber (lunit= 10® )
k10"3 2190 2180 2175 2170 2165 8.14.3 2160 2155 2150 2145 2140 Tim e (ns)
8.4.2 N um erical S im ulation E xcluding the L in e w id th Enhancem ent Factor
F or the same d riv in g conditions, b u t fo r the lin e w id th enhancem ent fa cto r set to zero, we have obtained the spectrum shown in Fig.8.15.1 and the pulse shape displayed in F ig. 8.15.2. As expected, th e sp e ctru m is sym m etric. A ccording to our s im u la tio n , the pulse w id th decreases to
8.6ps i f th e lin e w id th enhancem ent fa cto r is reset to zero. The tim e -
bandw idth product is also reduced fo r pg=0 and is equal to 0.43. T h is tim e- b a n d w id th product is in close agreem ent w ith K uizenga and Siegm an's re s u lt^ '^ fo r A M mode-locking o f a homogeneous laser.
In th is section, our aim was to dem onstrate the basic n u m e rica l m odel fo rm u la te d in C hapter 7.2.3. In our m odel fo r A M m ode-locking, the
d iffe re n ce betw een m ode-locking w ith pg=5 and Pq= 0 is m uch m ore
pronounced th a n in the case o f c u rre n t m o du la tio n (S ection 8.2). The
in clu sio n o f the the coupling coefficient is needed in order to provide an
explanation fo r the cause o f th is difference.
8.5 Sum m ary
In th is chapter we presented num erical sim u la tio n s o f g a in -s w itc h in g and m ode-locking o f sem iconductor lasers. The objective o f o u r gain- sw itch in g sim u la tio ns were to illu s tra te the behaviour o f the averaged single-mode rate equations. In p a rtic u la r, we compared the operation o f a s o lita ry laser to its m onolithic external cavity equivalent, and emphasised the reduced responsiveness o f a m o n o lith ic la se r m o dulated a t h ig h frequencies. U sing our frequency-dom ain model, we dem onstrated mode- lo c k in g by c u rre n t m o dulation, A M , FM m ode-locking and F M la se r o p e ra tio n o f m o n o lith ic lasers, and achieved v e ry good consistency between a ll these sim ulations.
Spectrum (arbitrary units)
no too 90 80 70 60 8.15.1 so 40 30 20 V6Ô Vm 146' ‘ Vm Frequency (GHz) Photon N um ber (lu n it= 1 0 ^ )‘4a:a6“ 4at«— — ntae—
8.15.2
Tim e (ns)
F ig . 8.15 A M mode-locking w ith Pç=0; averaged spectrum (8.15.1) and steady-state pulse shape (8.15.2)
W ith regard to active m ode-locking by cu rre n t m odulation we investigated the tim e e vo lu tio n o f m ode-locking, and the effects o f d e tu n in g o f the m odulating frequency and v a ria tio n o f the bias and RF cu rre n t. The pulse shape and spectrum th a t we produced were in good agreem ent w ith experim ental data reported in the lite ra tu re . D etuning o f the m odulating frequency in our model resulted in cyclic pulse sequences, as predicted by a tra n sm issio n -lin e m a trix model. O ur re sults fo r FM m ode-locking and F M -la se r o peration show tw o d is tin c t types o f b e h a vio u r w h ich are dependent upon the in c lu s io n o f the lin e w id th enhancem ent fa cto r. According to our sim ulations, the lin e w id th enhancem ent fa cto r provides a selection m echanism in FM m ode-locking. In F M -la se r operation, the in clu sio n o f the lin e w id th enhancement factor re sults in the generation o f disto rte d FM spectra.