Radiation-balanced (athermal) laser

Transcription

1 Rdition-bnced (therm) r Trdition soid-stte mifiers or rs re exothermic. Het generted inside the mifier or r medium, which is cud by the quntum defect, is source of incred temerture nd stress. It cus oor bem quity nd imits the verge outut ower. In 1999, Bowmn rood rdition-bnced (therm) r, in which sing is ccomished by offtting the het generted from stimuted emission by the nti-stokes cooing effect (Bowmn 1999). Let us consider the bsic concets of rdition bnced (therm) r, in which sing nd nti-stokes cooing occur in the sme system of ions doed in the cryst or gss host. Figure 1 iustrtes the energy-eve digrm of r system, where the quntum energy defect is ony of the order of k B T. A soid-stte r of this tye cn be often referred to s qusi-threeeve r. The uer nd ower eectronic eves (mnifods) re sit into mny coy sced subeves. The oution of ech subeve within mnifod is described by Botzmnn occution fctors. We ssume tht trnsitions between the subeves re Figure 1. Energy-eve scheme for rdition-bnced r. urey nonrditive trnsitions, rovided by honon bsortion nd emission. The energy g between subeves is much ess tht k B T thus intr-bnd thermiztion occurs on icocond time sce. Assume tht rditive ifetime of the uer mnifod is on the order of miiconds nd the trnsitions between the uer nd ower mnifods (inter-bnd rextion) re urey rditive, since bndg between the uer nd ower mnifods is rge comred to the energies of the honons. We so ssume the bnce of excited-stte bsortion, energy trnsfer, nd bsortion by nonrditive bckground trnsitions. The r is umed t frequency ν. ν is the frequency of the r fied, nd ν f is the men fuorescence frequency. The tot density of the ions in the host, N T, is equ to the sum of the densities of ions in the first (ground), N 1, nd cond (excited), N 2, mnifods: The rte eqution of the uer eve foows s N T = N 1 + N 2. (1)

2 dn 2 dt W W N 2, (2) where τ is the fuorescence ifetime, W is um rte, nd W s is stimuted emission rte described by the equtions: W I h I W h N N, N N, 2 T 2 T (3) where I, re intensities of the um () nd the r () bems. re the cross ctions of the bsortion () nd stimuted emission () t the um () nd the r () wveengths. In the stedy stte, dn 2 /dt = 0 nd Eq. (1) cn be written s,, W N2 W. (4) Note tht for rdition-bnced mifiction, the bsorbed ower density hs to be equ to the rdited ower density t ny oint in the r medium (Bowmn 1999): h W h W h f N 2. (5) Eq. (5) vid ony for the therm r, is not icbe to trdition exothermic r in which the Stokes energy shift between the um hotons (hν ) nd the r hotons (hν ) ers s het in the mifier medium. The retion for r gin cn be described by the we-known eqution d dz N N. (6) 2 s T Substituting Eqs. (3), (4), nd (5) into Eq. (6) one cn obtin the eqution, which describes the r sign t ny oint, z, ong the ength of the r medium. 0 z ex z 0 ex N z, St T (7) where

3 St A eff h f (8) is the sturtion ower of the r sign nd A eff is the effective re of the mode, which suorts the r sign. To suort growth of the r sign for one-wy rogtion described by Eq. (7) nd to kee the rdition bnce t ech oint in the r medium, the um ower hs to be distributed roery ong the ength of the r medium. This distribution cn be obtined with the he of Eqs. (3) - (5): where z St z z, (9) St St A eff h f. (10) is the sturtion ower of the um sign. It is esiy en from Eq. (9) tht rditionbnced mifiction requires crefu contro of the um ower distribution ong the r medium. Since the vue of the um ower hs to be > 0, in the c of the therm r for ech combintion of the host mteri, ions, um nd sign wveengths, there is minimum vue of r ower inside the r cvity s cn be en from Eq. (9), nd is: min A eff h f, (11) which cn be mified thermy. This minimum intensity cn rve s figure of merit in the ection of mteri nd oerting frequency for rdition-bnced r. As one cn e from Eqs. (4) nd (5) for rdition-bnced oertion of r the men fuorescence frequency, the um nd r frequencies hve to stisfy to the retion: ν f > ν > ν. A comrehensive theory of the rdition-bnced buk soids-stte r hs been rented in the work of Bowmn (Bowmn 1999) nd enhnced for the c of the therm fiber mifier in the er (Nemov & Kshy 2009). Figure 2 iustrtes the evoution of the thermy mified sign nd um ower, which rovides this therm mifiction, with the ength of the fiber mifier for three different inut sign owers. This Yb 3+ -doed mifier bd on ZBLAN fiber with rdius of the

4 core r co = 70 µm. Yb 3+ ion concentrtion ρ ions/µm 3 ermits it to be free from ny co-oertive interctions. As one cn e in Fig.2 the ower of the mified sign chnges most inery with the ength of the mifier for rdition-bnced mifiction. The iner growth of the ower of the mified sign requires n Figure 2. Deendence of the sign nd um owers from the ength of the therm fiber mifier (After Nemov & Kshy 2009). enormous incre in the ength of the fiber for very high outut ower. The reci contro of the um ower nd most iner growth of the mified sign re two rious obstces in the rctic deveoment of rdition-bnced mifiers nd rs. Anysis of the nsitivity nd stbiity of rdition-bnced r to erturbtions in the fied rmeters nd temerture hs been mde (Bowmn et. 2002). It ws shown tht fuctutions in the gin t imits on the vribiity of the um wveength. A um stbiity of 1 nm is suggested for Yb:KGW r. An ctive wveength stbiiztion scheme is rood to minimize the nsitivity of the therm r to mbient temerture fuctutions. Thermodynmics of the rdition-bnced r hs been comrehensivey nyd by Mungn (Mungn 2003). The Crnot efficiency hs been derived for -otic mifiction from considertion of the rditive trnsort of energy nd entroy. The highest Crnot efficiencies resut ony when the system is umed into sturtion. In 2002, Bowmn nd coegues exerimenty demonstrted the first therm r (Bowmn et 2002b). Ner rdition-bnced oertion of the Yb 3+ :YAG r with the net therm oding beow 0.01% hs been demonstrted in the er (Bowmn et. 2010). rogress on the subject cn be found in (Bowmn 2016). Sever schemes of therm rs hve been rood s terntive soutions: 1). Sef-cooing r, in which sing occurs in one system of ions, whie nti-stokes cooing tkes ce in nother system of ions co-doed in the r host (Andrinov & Smrtv 2001). 2). Rmn rs with het mitigtion bd on CARS, in which intrinsic hetmitigtion technique reies on coherent nti-stokes Rmn scttering (CARS)

5 insted of nti-stokes fuorescence (Vermeuen et 2006, 2007, 2007b, 2007c). 3). Atherm rs with n integrted cooer References 3.1). The therm Rmn fiber r, in which cooing with nti-stokes fuorescence in the system of rre-erth (RE) ions comenstes for the het generted inside the ctive medium due to the quntum defect between the um nd the Rmn r wveengths (Nemov & Kshy 2009b, 2009c). 3.2). The therm RE-doed r with n integrted cooer, in which sing tkes ce in the RE doed fiber core nd cooing tkes ce in the RE doed fiber cdding. The RE doed cdding ys the roe of n integrted cooer (Nemov & Kshy 2010, 2010b). Andrinov S. N. & Smrtv V. V. (2001) Soid-stte rs with intern r refrigertion effect. roc. of SIE 4605, Bowmn S. R. (1999) Lrs without intern het genertion. IEEE J. Quntum Eectron. 35, Bowmn S. R., Jenkins N. W., O Connor S.. & Fedmn B. J. (2002) Sensitivity of stbiity of rdition-bnced r system. IEEE J. Quntum Eectron Bowmn S. R., Jenkins N. W., Fedmn B. & O Connor S. (2002b) Demonstrtion of rditivey cooed r. Conf. Lrs Eectro-Ot., Long Bech, CA Bowmn S. R., O Connor S.., Bisw S., Condon N.J., Ronberg A. (2010) Minimizing het genertion in soid-stte rs. IEEE J. Quntum Eectron. 46, Bowmn S. R. (2016) Oticy cooed rs, in in Lr cooing: fundment roerties nd ictions, edited by Gin Nemov, n Stnford ubishing te. Ltd., Singore, Mungn C. E. (2003) Thermodynmics of rdition-bnced sing. J. Ot. Soc. Am. B 20, Nemov G. & Kshy R. (2009) Atherm continuous-wve fiber mifier. Ot. Commun. 282, Nemov G. & Kshy R. (2009b) Fiber mifier with integrted otic cooer. J. Ot. Soc. Am. B 26, Nemov G. & Kshy R. (2009c) Rmn fiber mifier with integrted cooer. IEEE J. Lightwve Techno. 27,

6 Nemov G. & Kshy R. (2010) High-ower fiber rs with integrted rre-erth otic cooer. roc. SIE 7614, Nemov G. & Kshy R. (2010b) Yb 3+ -doed fiber r with integrted otic cooer. roc. SIE 7686, Vermeuen N., Debes C., Fotidi A. A., njotov K. & Thienont H. (2006) Stokes nti-stokes itertive resontor method for modeing Rmn rs. IEEE J. Quntum Eectron. 42, Vermeuen N., Debes C., Muys. & Theinont H. (2007) Mitigting het dissition in Rmn rs using coherent nti-stokes Rmn scttering. hys. Rev. Lett. 99, :1-4. Vermeuen N., Debes C. & Thienont H. (2007b) Mitigting het dissition in nernd mid-infrred siicon-bd Rmn rs using CARS rt I: theoretic nysis. IEEE J. Se. Toics. Quntum Eectron. 13, Vermeuen N., Debes C. & Thienont H. (2007c) Mitigting het dissition in nernd mid-infrred siicon-bd Rmn rs using CARS rt II: numeric demonstrtion. IEEE J. Se. Toics. Quntum Eectron. 13,