Bound soliton fiber laser

Transcription

1 Bond soliton fiber laser D. Y. Tang, B. Zhao, D. Y. Shen and C. L School of electrical and Electronic Engineering, Nanyang Technological Uniersity, Singapore W. S. Man and H. Y. Tam Department of Electrical Engineering, Hong Kong Polytechnic Uniersity, Hng Hom, Hong Kong Experimental stdy on the soliton dynamics of a passiely mode locked fiber ring laser firstly reealed a state of bond soliton operation in the laser, where two solitons bind together tightly with fixed plse separation. We frther report on the properties of the bond-soliton emission of the laser. In particlar, we demonstrate both experimentally and nmerically that, like the single plse soliton operation of the laser, the bond soliton emission is another intrinsic featre of the laser. PACS nmbers: 4.55.Wd, 4.81.Dp, 4.60.Fc, 4.65.Sf 1

2 Self-started, passiely mode locked fiber lasers as a potential sorce of ltrashort optical plses hae been intensiely inestigated [1-7]. A generic featre of the lasers fond is that nder sitable operation conditions, they can emit the so-called soliton plses - optical plses that are sech-form shaped and hae nearly transform-limited bandwidthdration prodct. Under a soliton operation not only the otpt plses of the lasers become ltrashort, bt also the plse to-plse energy and peak power become ltrastable, which was fond to be qantm noise limited [8]. Soliton emission of the lasers is a natral conseqence of the nonlinear plse propagation in the fiber caity, where de to the balanced action between the fiber optical Kerr effect and the caity dispersion on a plse, whose shape and dration become nchanged with the propagation. Althogh in a passiely mode-locked fiber laser, apart from the optical fiber other optical components sch as the gain medim and otpt copler coexist in the caity, which affect the detailed dynamics of the formed plses. It is neertheless demonstrated that nder weak inflence of them, the aerage dynamics of the solitons cold be well described by the nonlinear Schrödinger eqation [9]. In this paper we report on states of bond soliton emission and their properties in a passiely mode-locked fiber ring laser. We show both experimentally and nmerically that apart from the single plse soliton emission, the laser can also emit stable, closely spaced soliton pairs. In particlar, when operating in the regime, the bond soliton pair is the only stable strctre of the solitary wae in the laser, it as a nit has exactly the same featres as those of a single plse soliton. For this reason, we refer the fiber laser as a bond-soliton fiber laser.

3 Bond states of solitons hae recently been predicted in the copled nonlinear Schrödinger eqations [10], and the qintic complex Ginzbrg-Landa eqation [11-1]. Formation of bond solitons was explained as a reslt of direct soliton interaction: Solitons formed in these systems hae an oscillating tail, when they interact, their effectie interaction potential has spatial local minima, which gie rise to stable bond solitons. Bond solitons this formed are characterized as that they hae fixed, discrete plse separations, which are independent of soliton propagation. For a passiely modelocked fiber laser when the inflences of laser gain and caity losses, and /or fiber birefringence become strong, its dynamics is actally described by the Ginzbrg-Landan eqation, or its copled forms [13]. The passiely mode-locked fiber ring laser sed in or experiments is schematically shown in Fig. 1. It has a ring caity of abot 5.5 meters long. The caity comprises of a 3.5-meter long 000ppm erbim-doped fiber with a grop elocity dispersion of abot 10 ps/nm km, one piece of 1 meter long single mode dispersion shifted fiber, whose grop elocity dispersion is ps/nm km and one piece of 1 meter long standard single mode fiber (SM-8). The nonlinear polarization rotation techniqe [5] is sed to achiee the self-started mode locking in the laser. To this end a polarization dependent isolator together with two polarization controllers, one consisting of two qarter-wae plates and the other of two qarter-wae plates and one half-wae plate, is sed to adjst the polarization of light in the caity. The polarization dependent isolator and the polarization controllers are monted on a 7cm long fiber bench to achiee accrate 3

4 polarization adjstments. The laser is pmped by a pigtailed InGaAsP semicondctor diode of waelength 1480nm. The otpt of the laser is taken ia a 10% fiber copler and analyzed with an optical spectrm analyzer (Ando AQ-6315B) and a commercial optical atocorrelator (Inrad 5-14-LDA). A 50 GHz wide bandwidth sampling oscilloscope (Agilent 86100A) and a 5 GHz high-speed photo-detector (New Focs 1414FC) were sed to stdy the eoltion of the bond solitons in the caity. In two preios papers [14,15] we hae reported on how to experimentally achiee the bond-soliton operation and some of the basic properties of the obsered bond solitons, respectiely. The key techniqe sed to get stable bond soliton operation of the laser is the intra-caity mode locking of the dynamical laser modes. With this techniqe the inflences cased by the random enironmental noise and the dispersie waes on the soliton interaction cold be sppressed. In or preios experiment we hae also confirmed that the obsered bond solitons hae the characteristics of discrete, fixed soliton separations which are independent of soliton propagation, as predicted theoretically. The states of bond solitons are sally abrptly formed in or laser from a single plse soliton state throgh adjsting the orientations of the waeplates. Howeer, if their orientations are already appropriately set, bond soliton operation can also be directly obtained by simply increasing the pmp power beyond the mode-locking threshold. For the completeness of the paper we hae shown again in Fig. the optical spectra of the bond solitons obsered in or laser. In order to check if the formation of bond states of 4

5 solitons is a generic featre of the passiely mode-locked fiber lasers, in the crrent experiment we hae deliberately changed the caity property of or laser. Or experimental reslts confirmed that with exactly the same techniqe and procedre, the bond states of solitons cold be re-obtained in the laser. With the new fiber laser setp we hae obtained for discrete states of bond solitons as shown. Comparing them with those obtained with or preios fiber laser setp, except the different plse separation and soliton plse width, they hae exactly the same properties. Namely, they are ltra stable and hae discrete, fixed plse separations that are neither dependent on the soliton propagation nor on the exact laser operation conditions, sch as the pmp intensity and the caity detning etc. The change in the soliton plse width is a natral reslt of the total caity dispersion change. In trn it cases the plse separation change of the bond solitons. Neertheless, once a laser setp is fixed, the plse separations of bond solitons obtainable are fixed. Analyzing the plse separations among the for bond soliton states, srprisingly, they hae again the relationship that one is roghly twice of the other as can be easily checked from the spectral modlation of the bond solitons shown in Fig., indicting that this relationship cold be a niersal property of the bond solitons in the fiber laser system and it is independent of the concrete laser setp. Like the single plse soliton operation of the laser, depending on the pmping strength, mltiple bond solitons can also coexist in the laser caity. As an example Fig. 3 shows two oscilloscope traces of sch states. Fig.3a shows that twele bond soliton plses coexist in the laser caity. Note that the plse separation between the bond solitons is abot 90fs and the soliton plse width of the laser is abot 35 fs when a sech-form 5

6 plse shape is assmed. As the detector can t separate the plse separation, in the oscilloscope traces the bond solitons looks like a single plse. When mltiple bond solitons coexist in the laser caity and they are far apart separated, except the spectral or signal strength is increased, there is no difference obserable on the optical spectrm and the measred atocorrelation traces comparing with those of single bond soliton pair in the caity. Based on this experimental eidence together with the reslt shown in Fig. 3, we conclde that all the bond solitons in the caity hae exactly the same property: namely the same soliton separation and same plse energy (there are small peak intensity flctations on the plses shown in the measred oscilloscope traces. We hae checked it and determined that they were de to the sampling problem of the sampling oscilloscope. By redcing the recorded time range of the trace, the flctation disappeared and all the plses had exactly the same height). In all of or experiments in a stable state no bond solitons of different plse separations or different plse energy hae been obsered to coexist, and no nbond solitons with the bond solitons, or bond solitons of higher order (with more than two soliton plses binding together) hae been obsered to coexist, which sggests strongly that in the parameter regime, the only stable plse strctre is the bond soliton pairs of the fixed plse separation. Careflly increasing or decreasing the pmp power, the nmber of bond soliton pairs can be increased or redced one by one. Fig. 3a and b show a case of two consectie states when the pmp power is redced. Initially there were twele bond solitons in the caity, redcing the pmp power to a certain ale one bond soliton pair were sddenly destroyed simltaneosly. After losing one pair of the bond solitons, the rest of the 6

7 bond solitons rearranged their relatie positions in the caity and stabilized finally at a new pattern as shown in the Fig. 3b. In or experiments we fond that the dispersie waes play an essential role in the long rang interaction among the bond solitons. Mediated throgh the dispersie waes, the bond solitons can interact among themseles and form arios states of mltiple bond soliton operation. In fact Fig. 3 shows two cases of the so-called qasi-harmonic mode-locking by some athors in the single plse soliton operation of fiber lasers. States of harmonic mode locking of the bond solitons hae also been freqently obsered. Fig. 4 shows as an example one of these states. In the crrent case eight bond solitons eqally spaced in the caity. We hae also obsered sitations where seeral tens of bond solitons coexist in the caity and form harmonic mode locking. Depending on the interaction between the bond solitons, bnches of bond solitons hae also been reealed in the laser as shown in Fig. 5. Seeral bond solitons can tightly cople together locally to form a bond soliton bnch, and the bnch moe with the fndamental repetition rate in the caity, exactly as also obsered in the single plse soliton case [1-,4]. When the bond soliton pairs interact directly with each other, they behae as a nit: either colliding elastically or simply crossing each other withot damaging their bindings or altering their plse separations. With the high-speed sampling oscilloscope and detector we cold monitor in the real time interact between two bond soliton pairs as shown in Fig. 6. The interaction between the bond soliton pairs clearly exhibits the particle-like natre of the soliton interaction. Bond states of the bond solitons mediated throgh the dispersie waes were occasionally obsered. Howeer, these bond states 7

8 8 are nstable, a small pertrbation can destroy it. All these experimental findings demonstrate that the bond soliton pairs as a nit has exactly all the same properties as those of a single plse soliton in the laser. Based on their properties we conclde that the obsered bond states of solitons cold be another type of solitary wae in the laser and the bond soliton operation cold be an intrinsic featre of the system. To confirm or conclsions, we hae also nmerically simlated the operation of or laser. For this prpose we hae bilt p a theoretical model based on the copled extended nonlinear Schrödinger eqations. Or model takes into accont the birefringence of the optical fiber and the pertrbations cased by the laser gain and caity loss, and has a form: * '' * '' t g g i i t i t i z t g g i i t i t i z g g Ω = Ω = γ γ κ δ β γ γ κ δ β (1) Where and are the two normalized slowly arying plse enelopes along the slow and the fast axes, respectiely. λ π β / n Δ = is the wae-nmber difference, c π βλ δ / = is the inerse grop-elocity difference. κ is the dispersion parameter, γ is the nonlinearity of the fiber. g is the laser gain coefficient and Ω g is the bandwidth of the laser gain. Gain satration of the laser is considered throgh writing ( ) = E s dt g g 0 1 ()

9 where g 0 is the small signal gain and E s is the satration energy. To also accont the effects of other caity components and the caity feedback, we simlate the laser by simply letting the light circlate in the caity, wheneer it meets a caity component we then discretely mltiply the component s transformation matrix to the light. In all of or simlations where it is possible, we hae sed the actal ale of the laser parameters. Using the same theoretical model we hae preiosly simlated the dynamics of single plse soliton lasing of passiely mode-locked fiber lasers, and correctly reprodced the featres sch as the intrinsic soliton waelength tning [16], soliton sideband asymmetry and sbsideband generation [13]. In the crrent simlation we fond that by appropriately choose the linear caity transmission of the laser and the polarization orientation of the polarization dependent isolator, bond states of solitons cold actally be reprodced in or model. In particlar, we fond that with the parameter settings, bond solitons are the only stable state. Fig. 7 shows reslts of or simlations. Three stable bond soliton states with different plse separations hae been reealed in or simlations nder the laser parameter settings. In or simlations in order to find ot the bond soliton states we simply fix the laser parameters and inpt either random initial noise waeform or plses of different shapes to start or simlations, we then wait for ntil a stable state is achieed. We fond that independent of the initial conditions the laser otpt always settled down to one of the bond soliton states. Similar to the experimental reslts, the obtained stable bond solitons exhibit discrete, fixed plse separations. Once a state of bond solitons is obtained, it will remain there for seeral thosand ronds of calclation, een nder slightly changed parameters sch as the small signal gain and satration 9

10 energy, indicating that it is a stable state of the system. Or nmerical simlations hae flly confirmed or experimental obserations. In smmary we hae experimentally stdied properties of bond soliton emission in a passiely mode-locked fiber ring laser, and obsered featres sch as the bond soliton energy qantization, qasi- and harmonic bond soliton mode locking, bond soliton bnching and particle-like interaction between bond solitons. Or experimental reslts hae also reealed that no single plse soliton can coexist with the bond solitons, and when mltiple bond solitons coexist, all bond solitons hae exactly the same properties. Exactly the same featres hae also been obsered for the single plse soliton in the fiber soliton lasers, which sggests strongly that, like the single plse soliton, the obsered bond solitons are another fndamental strctre of stable light plse in the laser, and the bond soliton operation of the laser is in fact an intrinsic featre of the fiber laser. Finally, we note that nmerical simlations on the laser operation hae also confirmed the existence of bond solitons in the laser and its property of discrete, fixed soliton separations, which frther spport or conclsions. Acknowledgement: W. S. Man and H. Y. Tam acknowledge spport by a niersity research grant of The Hong Kong Polytechnic Uniersity. 10

11 References: [1] D. J. Richardson, R. I. Laming, D. N. Payne, V. J. Matsas, M. W. Phillips, Electron. Lett., 7, (1991). [] A. B. Grdinin, D. J. Richardson and D. N. Payne, Electron. Lett., 7, (1993). [3] C. J. Chen, P. K. A. Wai and C. R. Menyk, Opt. Lett., 17, (199). [4] A. B. Grdinin, D. J. Richardson and D. N. Payne, Electron. Lett., 8, (199). [5] V. J. Matsas, D. J. Richardson, T. P. Newson and D. N. Payne, Opt. Lett., 18, (1993). [6] M. J. Gy, D. U. Noske and J. R. Taylor, Opt. Lett., 18, (1993). [7] K. Tamra, E. P. Ippen, H. A. Has and L. E. Nelson, Opt. Lett., 18, (1993). [8] H. A. Has and A. Mecozzi, IEEE J. Qantm Electron. 9, (1993). [9] S. M. J. Kelly, K. Smith, K. J. Blow and N. J. Doran, Opt. Lett., 16, (1991). [10] B. A. Malomed, Phys. Re. A., 45, R831-R833 (199). [11] B. A. Malomed, Phys. Re. A., 44, (1991). [1] N. N. Akhmedie, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Re. Lett., 79, (1997). [13] D. Y. Tang, S. Fleming, W. S. Man, H. Y. Tam and M. S. Demokan, J. Opt. Soc. Am. B, 18, (001). [14] D. Y. Tang, W. S. Man, H. Y. Tam and P. D. Drmmond, Phys. Re. A., 64, ,

12 [15] D. Y. Tang, B. Zhao, D. Y. Shen, W. S. Man and H. Y. Tam, Opt. Commn. 00, sbmitted. [16] W. S. Man, H. Y. Tam, M. S. Demokan, P. K. A. Wai and D. Y. Tang, J. Opt. Soc. Am. B, 17, 8-33(000). a) Han Zhang, Qiaoliang Bao, Dingyan Tang, Lming Zhao, and Kianping Loh,"Large energy soliton erbim-doped fiber laser with a graphene-polymer composite mode locker", Applied Physics Letters, Vol. 95, pp [Fll-text PDF] b) Han Zhang, Dingyan Tang, Lming Zhao and W Xan, Dark plse emission of a fiber laser Physical Reiew A, 80, (009). [Fll-text PDF] c) Qiaoliang Bao, Han Zhang, et.al, Adanced material,nder reiew. (IF=7.896 ) d) Han Zhang, Dingyan Tang, Lming Zhao, Qiaoliang Bao,and Kianping Loh,"Large energy mode locking of an erbim-doped fiber laser with atomic layer graphene", Optics Express, Vol. 17, Isse 0, pp [Fll-text PDF] e) Qiaoliang Bao, Han Zhang, Y Wang, Zhenha Ni, Yongli Yan, Ze Xiang Shen, Kian Ping Loh*,and Ding Yan Tang*, "Atomic layer graphene as satrable absorber for ltrafast plsed lasers", Adanced Fnctional material, In press. (IF=6.779) [Fll-text PDF] f) L. M. Zhao, D. Y. Tang, X. W, Han Zhang, H. Y. Tam, Coexistence of polarization-locked and polarization-rotating ector solitons in a fiber laser with SESAM, Optics Letters, in press (009). g) Han Zhang, Ding Yan Tang, Lming Zhao and Xan W, "Obseration of polarization domain wall solitons in weakly birefringent caity fiber lasers", PHYSICAL REVIEW (Brief report) B 80, 0530 (009).[Fll-text PDF] h) D. Y. Tang, Han Zhang, L. M. Zhao and X. W, Obseration of high-order polarization-locked ector solitons in a fiber laser,physical Reiew Letters, 101, (008).[Fll-text PDF] i) D. Y. Tang, L. M. Zhao, X. W, and Han Zhang, Soliton modlation instability in fiber lasers, Phys. Re. A, in press (009). j) Han Zhang, D. Y. Tang, L. M. Zhao,X. W, "Mlti-waelength dissipatie soliton operation of an erbim-doped fiber laser", Optics Express:17, (009). k) H. Zhang, D. Y. Tang, L. M. Zhao and N. Xiang, Coherent energy exchange between components of a ector soliton in fiber lasers, Optics Express, 16, (008).[Fll-text PDF] l) H. Zhang, D. Y. Tang, L. M. Zhao and H. Y. Tam, Indced solitons formed by cross polarization copling in a birefringent caity fiber laser, Optics Letters, 33, (008).[Fll-text PDF] m) Han Zhang, D. Y. Tang, L. M. Zhao, X. W and H. Y. Tam, Dissipatie ector solitons in a dispersionmanaged caity fiber laser with net positie caity dispersion,optics Express, Vol. 17, Isse, pp (009)[Fll-text PDF] n) X. W, D. Y. Tang, L. M. Zhao, and Han Zhang, "Effectie caity dispersion shift indced by nonlinearity in a fiber laser,"phys. Re. A 80, (009). 1

13 o) L. M. Zhao, D. Y. Tang, Han Zhang, X. W, Bnch of restless ector solitons in a fiber laser with SESAM, Optics Express, 17, (009) p) X. W, D. Y. Tang, Han Zhang, and L. M. Zhao, Dissipatie soliton resonance in an all-normal-dispersion erbim-doped fiber laser, Optics Express 17, (009). q) L. M. Zhao, D. Y. Tang, H. Zhang, X. W, C. L and H. Y. Tam, Period-dobling of ector solitons in a ring fiber laser Optics Commnications,81, (008). [Fll-text PDF] r) L. M. Zhao, D. Y. Tang, H. Zhang, X. W, Polarization rotation locking of ector solitons in a fiber ring laser, Optics Express, 16, (008).[Fll-text PDF] s) L. M. Zhao, D. Y. Tang, Han Zhang, X. W, and N. Xiang, Soliton trapping in fiber lasers, Optics Express, 16, (008).[Fll-text PDF] t) L. M. Zhao, D. Y. Tang, X. W, Han Zhang, Period-dobling of gain-gided solitons in fiber lasers of large net normal dispersion, Optics Commnications, 81, (008).[Fll-text PDF] ) L. M. Zhao, D. Y. Tang, X. W, Han Zhang, C. L and H. Y. Tam, Dynamics of gain-gided solitons in a dispersion-managed fiber laser with large normal caity dispersion, Optics Commnications, 81, (008).[Fll-text PDF] ) L. M. Zhao, D. Y. Tang, Han Zhang, T. H. Cheng, H. Y. Tam, and C. L, Dynamics of gain-gided solitons in an all-normaldispersion fiber laser, Optics Letter, 3, (007). [Fll-text PDF] w) Qiaoliang Bao, Han Zhang, Chnx Pan. Simlation for growth of mlti-walled carbon nanotbes in electric field, Comptational Materials Science, 007, 39(3): [Fll-text PDF] x) iaoliang Bao, Han Zhang, Chnx Pan. Electric-field-indced microstrctral transformation of carbon nanotbes, Applied Physics Letters, 006, 89: y) Qiaoliang Bao, Han Zhang, Chnx Pan. Microstrctral transformation of carbon nanotbes in electric field. Modern Scientific Instrments, 006, Z1: (In English, a jornal in China) z) Han Zhang, Qiaoliang Bao, Chnx Pan. Electrical Force Indced Growth of Well-aligned Carbon Nanotbes and Simlation, Jornal of Chinese Electron Microscopy Society, 006, 5 (spp):5-6.(in Chinese) aa) Qiaoliang Bao, Xiang Ran, Han Zhang, Xiang Qi, Qiang F, Chnx Pan. Synthesis of Well-aligned Unentangled Carbon Nanotbes on Plse Electrodeposited Ni Nanocrystalline, New Carbon Materials, 008, 3(1): (in Chinese) bb) Qiaoliang Bao, Han Zhang, Chnx Pan. Inflence of Electrodeposited Nickel Nanocrystalline on Carbon Nanotbes Growth., Jornal of Chinese Electron Microscopy Society, 006, 5 (spp): (in Chinese) 13

14 Figre captions: Figre 1: A schematic of the passiely mode-locked fiber laser. λ/4: qarter-wae plate; λ/: half-wae plate; PI: polarization-dependent isolator. WDM: waelength-diidendmltiplexer. Figre : Optical spectra of the bond states of solitons obsered. cc) With spectral modlation period of abot 9.1nm. dd) With spectral modlation period of abot 4.7nm. ee) With spectral modlation period of abot.6nm. ff) With spectral modlation period of abot 1.3nm. The soliton plse width is abot 35 fs and the separations between the bond solitons can be calclated from the corresponding spectral modlation periods. Figre 3: Oscilloscope traces of mltiple bond solitons in the caity. The caity rondtrip time is abot 6 ns for the laser. a) With twele bond solitons in the caity. b) With eleen bond solitons in the caity. From a to b the pmp laser power is slightly redced. Figre 4: Harmonic mode locking of the bond solitons. Eight bond solitons are eqally spaced in the caity forming the special mode-locked state. 14

15 Figre 5: Bnching of the bond solitons. Seen bond solitons copled tightly together. No relatie moement among the solitons. Figre 6: Collision between two bond soliton pairs. After collision they still remain as bond solitons of the same property. Figre 7: States of bond solitons calclated from the theoretical model. a, b, c) Bond solitons with different plse separations. e, d, f) The corresponding optical spectra. Parameters sed are γ = 3W -1 km -1, κ = - ps /nm km (for dispersion shifted fiber), κ = 10 ps/nm km (for erbim doped fiber), g 0 = 54, Ω g = π 10 THz, E s = 110, caity length L = 11m, beat length L b = L/. 15

16 Figre 1 D. Y. Tang et al 16

17 Figre (a) D. Y. Tang et. al. 17

18 Figre (b) D. Y. Tang et. al. 18

19 Figre 3. D. Y. Tang et. al. 19

20 Figre 4(a). D. Y. Tang et. al. 0

21 Figre 4(b). D. Y. Tang et. al. 1