NUMERICALLY INVESTIGATED OF LASER PASSIVELY Q- SWITCHING REGIME

Transcription

1 NUMERICALLY INVESTIGATED OF LASER PASSIVELY Q- SWITCHING REGIME CAMELIA GAVRILA Technicl University of Civil Enineerin, Buchrest, ION LǍNCRǍNJAN Advnced Study Centre - Ntionl Institute for Aerospce Reserch Elie Crfoli, Buchrest, J_J_F_L@yhoo.com ION GRUIA University of Buchrest, rui_ion@yhoo.com Abstrct: In this pper the technique of solid-stte lsers pssive opticl Q-switchin is numericlly investited considerin the cse of lonitudinlly nd trnsverslly uniform photon, popultion inversion nd bsorption centres densities. The coupled differentil equtions definin photon, popultion inversion nd bsorption centres densities re numericlly solved bein the bsis of lser functionl simultion. For vlidtin the results, the numericl simultions re performed usin the SCILAB prorms. The developed SCILAB prorms cn be used for lre rne of sturble bsorption centre nd ctive medi prmeters, minly the initil (low sinl) opticl trnsmittnce of the pssive opticl Q- switch. The results of the numericl simultion re in ood reement with theory proposed in this pper nd with experimentl dt observed in the cse of LiF:F2- pssively Q- switched Nd:YAG lsers. 1. Introduction One min problem of lser physics consists in nlyzin the lser resontor nd bem proption. Since the lser effect ws demonstrted for the first time, there were observed mny theoreticl nd experimentl ttempts to nlyze lser resontor nd bem proption. These nlyses were performed with modellin nd desin purposes pointin to more nd more improved desin. Amon solid stte lsers, those operted in pssive opticl Q-switchin reime constitutes n importnt cteory, hvin lre number of pplictions. The desin of such lsers relies on fine mixture of interconnected physicl phenomen: - production nd proption of electromnetic rdition, with wvelenth situted in visible nd IR spectrl domins; - therml effects produced into lss nd/or crystl mde lser components by electromnetic rdition. Bsiclly lser emitter, whtever how hih is its sophistiction level of desin, considerin more relistic models of the components is setup composed of two min prts: - The ctive medium, ctin s n mplifier of electromnetic rdition, bsiclly becuse of stimulted emission effect; - The resontor, ctin s feed-bck connection, s rection loop nd ssurin the psse of electromnetic rdition throuh ctive medium nd the extrction of output bem.

2 It is helpful to mke n nloy of lser emitter nd electronic oscilltors, mkin clerer the fct tht lser resontor cts s rection loop. Solid stte lsers, which minly use crystls doped with vrious ions s ctive emittin lser centres, represents lre percente of the lsers in use for civilin, industril nd militry pplictions. For mny such pplictions the lser resontors hve to include mny dditionl components such Q-switchin cells, polrizes. Q-switchin cells men tht the qulity fctor of the resontor is not constnt, hvin trnsient reime. For vlidtin the results, the numericl simultions re performed usin the SCILAB prorms. The simultion nd experimentlly observed results re compred ones, in order to obtin some insihts bout their ccurcy. 2. Theory In Fiure 1 the schemtic of pssively Q-switched solid stte lser setup is presented. In prctice, dependin upon the specific lser ctive medium nd pumpin technique, there re little differences between such lser confiurtions. Relted to this experimentl setup one problem to be solved consists in definin system of coupled differentil equtions describin lser prmeters of interest time evolution. The lser prmeters of interest re: n(t) - photon density; N(t) - lser ctive medium popultion inversion density; N(t) pssive Q-switch sturble bsorber round-stte popultion density. A number of pproximtions re mde rerdin this system of differentil equtions, mon which the most importnt consists in considerin the lser prmeter s sptilly uniform inside lser resontor, hvin no lonitudinl or rdil vritions versus opticl xis. In Fiure 2 second importnt feture of the lser presented lser functionl simultion ttempt is presented, nmely the enery-level dirm pplicble for the lser ctive medium nd for the pssive opticl Q-switch. For both lser components modified 4- enery level dirm with the possibility of excited-stte bsorption ws used for describin their functions. Fiure 1. - Schemtic of pssively Q-switched solid stte lser setup. HR - Hih Reflectivity Mirror (~100%); P Polrizer (two qurtz pltes plced t Brewster nle); QSW - Q-Switch crystl; AM - Nd:YAG Lser Active Medium; FL Pumpin Flsh Lmp; OC - Output Coupler (Mirror).

3 Fiure 2. - The dirm of enery levels used for the ctive medium nd sturble bsorber. - round-stte enery level; 1 - first stte enery level; 2 - second stte enery level; 3 - upper enery level; 4 - hiher enery level; σ - round-stte bsorption cross section; σ es - excited-stte bsorption cross section. The followin rte equtions ws used s the nturl form, in order to model solidstte lser pssively Q-switched by sturble bsorber centre system hvin excited stte bsorption [3]: dn dt dn dt dn dt = K N n K N n β K ( N 0 N ) n γ n (1) c = R γ N γk N n (2) p = N N ) K N n ( 0 γ (3) The coupled differentil equtions definin photon, popultion inversion nd bsorption cnters densities re numericlly solved bein the bsis of pssively opticl Q-switched lser functionl simultion. For vlidtin the results, the numericl simultions re performed usin SCILAB prorms. The developed SCILAB prorms cn be used for lre rne of sturble bsorption centre nd ctive medi prmeters, minly the initil (low sinl) opticl trnsmittnce of the pssive opticl Q-switch. The developed SCILAB prorms cn be pplied for pssively Q-switched solid stte lsers of severl types emittin t severl NIR wvelenths, in domin 1 2 μm. 3. Results nd Discussion Differentil equtions (1), (2) nd (3), re solved numericlly in order to define the behviour of specific Q-switched lser system. However, importnt chrcteristics of pssively opticl Q-switched lser system cn be found from nlyzin these three coupled rte equtions. In some specific cses, e.. use of hih contrst pssive opticl Q-switches, numericl simultion results obtined by solvin pproximtions of the studied differentil equtions cn be observed nd compred with those obtined by solvin the differentil eqution system. The results of this comprison re ood enouh, denotin n cceptble reement between the observed results. Results of the computer nlysis re presented in Fiures 3, 4 nd 5. In Fiure 3 the computer simulted lser photon density. Its hlf mplitude time width is in ood reement the

4 experimentlly observed vlue of ~5 ns. The simulted lser pulse time shpe is too brupt, bein different in comprison with the experimentlly observed one, of ~ 1ns. In Fiure 4 the computer simulted popultion inversion density in the ctive medium is presented. In Fiure. 5 the computer simulted time vrition of bsorbtion centres density in the pssive opticl Q- switch crystl is presented. Fiure 3. - The computer simulted lser photon density. Its hlfmplitude timewidth is in ood reement the experimentlly observed vlue of ~5 ns. The simulted lser pulse timeshpe is too brupt, bein different in comprison with the experimentlly observed one, of ~ 1ns. Results obtined in numericl simultion of tunble Cr:LiSAF lser Cr:YSO pssively Q-switched. A sinulr lser pulse is presented. Lser emission wve lenth ll = 850nm [Rp = s -1 ; N0= cm -3 ] Fiure 4. - The computer simulted popultion inversion density in the ctive medium durin lser pulse emission.

5 Fiure 5. - The computer simulted time vrition of bsorbtion centres density in the pssive opticl Q-switch crystl In Fiure 6 the experimentlly observed vritions of lser output enery (in free runnin nd Q-switched reimes) versus pumpin enery re presented. The experiments ws performed on the experimentl setup presented in Fiure 1 nd usin LiF:F 2 - Q-Switch crystl (denoted s smple C0074). Smple C0074 ws obtined by successive 7MeV hih enery electrons nd Co 60 γ irrditions of ф9 76 mm LiF crystls rown by Czochkrlski method. The lser pulse time shpe ws mesured usin n ITT F4014 vcuum photodiode mounted on Tektronix 519 oscilloscope. The response time of this mesurin system ws estimted s ~ 1 ns Fiure 6. - The experimentlly observed vritions of lser output enery (in free runnin nd Q-switched reimes) versus pumpin enery

6 4. Conclusion The most importnt verifiction of the numericl simultion results consist in comprison with experimentlly dt observed for investited lser emitters. In this spect, the ttention ws focused on lser pulse hlf mesure time width (FWHM) nd enery. The results of the numericl simultion re in ood reement with experimentl dt. In this pper, we hve demonstrted the verstility of Scilb prorm with rerd to the modellin nd simultion of solid stte lsers operted in pssive opticl Q-switchin reime. The developed Scilb prorm solid stte lser model ws pplied to one lser instlltion. A ood reement of Scilb prorm with full scle experimentlly observed dt were compred with in ood results. 5. Bibliorfie [1] 1. A. E. Siemn, Lsers (University Science Books, Mill Vlley, 1986). [2] 2. A. G. Fox nd T. Li, Resonnt modes in mser interferometer, Bell Sys.Tech. J. 40, (1961). [3] 3. M. D. Feit nd J. A. Fleck, Jr., Spectrl pproch to opticl resontor theory,appl. Opt. 20(16), 2843{2851 (1981). [4] 4. A. E. Siemn nd H. Y. Miller, Unstble opticl resontor loss clcultion usin the Prony method," Appl. Opt. 9(10), 2729{2736 (1970). [5] 5. M. Streiff, A. Witzi, nd W. Fichtner, Computin opticl modes for VCSEL device simultion, IEE Proc. Optoelectron. 149, (2002). [6] 6. F. Ihlenbur, Finite Element Anlysis of Acoustic Sctterin (Spriner, New York, Berlin, Heidelber, 1998). [7] 7. H.-G. Roos, M. Stynes, nd L. Tobisk, Numericl Methods for Sinulrly Perturbed Differentil Equtions (Spriner, Berlin, Heidelber, 1996). [8] 8. K. W. Morton, Numericl Solution of Convec-tion-Diffusion Problems. (Chpmn & Hll, London, New York, 1996). [9] 9. Y. Sd nd M. H. Schultz, GMRES: A enerlized miniml residul lorithm for solvin nonsymmetric liner systems, SIAM J. Sci. Stt. Comput. 7, (1986).