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oscillators directly generating femtosecond pulses with energy exceeding 100 nj are of interest for numerous applications including frequency conversion , metrology , micro - machining , etc . nowadays
oscillators operating at mhz - repetition rates have reached the micro - joule pulse energy frontier without an extra - resonator amplification .
an ingenious idea allowing such an advance is the pulse stretching , that suppresses the instabilities inherent to the high - peak - power oscillators @xcite .
since the pulse is soliton in the negative group - delay - dispersion ( gdd ) regime , its stretching is linearly irreversible .
the issue of pulse compressibility can be solved by a chirped - pulse oscillator ( cpo ) providing : i ) sufficient pulse stretching ( few picoseconds ) , ii ) broad spectrum ( more than 100 nm ) , and iii ) pulse compressibility down to few tens of femtoseconds @xcite .
the remaining issue is that a high - energy oscillator ( including cpo ) is stable only within a confined region of gdd and pulse energy .
the existing theory @xcite predicts that some minimum positive gdd is required for the cpo stabilization against the cw - amplification and this `` threshold '' gdd increases with the energy .
it was found , that the gain saturation is a key factor determining the oscillator stability .
however , the existing models do not take into account the gain dynamics and , thereby , some substantial features of the regime remain unexplored .
for instance , it is unclear why the region of gdd and energy , where a single stable pulse exists , is confined @xcite .    here , for the first time to our knowledge ,
the theory of cpo taking into account the gain dynamics will be presented .
as it will be shown , the gain dynamics provides an explanation for the confinement of the pulse stability region .
the model demonstrates an existence of two main mechanisms of pulse destabilization : the satellite rise in front of the pulse and the cw - amplification .
the cpo conception is based on the pulse energy ( @xmath0 ) scaling with the scaling of resonator period ( @xmath1 ) : @xmath2 ( @xmath3 is the averaged power ) .
since the pulse peak power ( @xmath4 ) scales with the energy : @xmath5 ( @xmath6 is the pulse width ) , one has to stretch the pulse ( i.e. , to increase @xmath6 ) in order to reduce @xmath4 and , thereby , suppress the instabilities causing by the nonlinear effects inside a resonator ( e.g. , the self - focusing inside an active medium ) .
however , in the solitonic regime ( i.e. , when the gdd is negative ) , such a stretching is linearly irreversible .
this means that the femtosecond high - energy pulse can be produced by only nonlinear compression , which worsens its characteristics ( e.g. , enhances the noise ) . in the cpo
, the picosecond pulse has an extremely wide spectrum due to large chirp . as a result ,
the pulse is linearly compressible down to @xmath7 ( @xmath8 is the pulse spectrum width ) .
the experiments demonstrate that such a regime is very stable and reproducible @xcite .
the pulse stability in the cpo can be explained by the combined action of two mechanisms : a pure phase mechanism and a frequency - dissipative one .
the first mechanism is the balance of phase contributions from the pulse envelope @xmath9 : @xmath10 ( @xmath11 is the gdd coefficient , @xmath12 is the local time ranging from @xmath13 to @xmath14 ) and the time - dependent phase @xmath15 : @xmath16 ^ 2 $ ] @xcite . such a balance is possible if the pulse is chirped . however , a pure phase balance is not sufficient for pulse stabilization as the pulse spreads , i.e. some dissipative effects are required to form a quasi - soliton .
the pulse lengthening due to gdd can be compensated by its shortening owing to frequency filtering if the pulse is chirped @xcite .
the chirp results in frequency deviation at the pulse front and tail , and the filter cuts off the high- and low - frequency wings of the pulse , thus the pulse shortens .    the cpo can be described on the basis of the distributed generalized complex cubic - quintic nonlinear ginzburg - landau model @xcite :    @xmath17 + \left [ { \left ( { \kappa   - i\gamma } \right)p(z , t ) - \kappa \zeta p(z , t)^2 } \right]a(z , t).\ ] ]    here @xmath18 is the propagation distance normalized to the cavity length ( i.e. , the cavity round - trip number , in fact ) .
@xmath19 is the instant power , @xmath20 is the square of the inverse spectral filter bandwidth .
the parameters @xmath21 and @xmath22 are the self - phase and self - amplitude modulation coefficients , respectively .
parameter @xmath23 describes saturation of the self - amplitude modulation . in a broadband solid - state oscillator , for example
, parameter @xmath20 is the square of the inverse gain band width multiplied by the saturated gain coefficient .
parameters @xmath22 and @xmath23 are defined by the kerr - lens mode locking mechanism @xcite .    the @xmath24-parameter is the spectrally independent saturable net - loss coefficient , which depends on the instant pulse energy @xmath25 .
below , such a dependence will be referred as the dynamic gain saturation .
it was found @xcite , that a heavily - chirped pulse in cpo can be described as the soliton - like solution of eq .
( [ eq1 ] ) in the limit of time - independent @xmath24 . in this case , the simplest energy - dependence of the @xmath24-parameter is @xmath26    where @xmath27 , @xmath28 and @xmath29 .
the spectrum of the chirped soliton - like pulse has a lorentz profile truncated at some frequency @xmath30 , where the central frequency @xmath310 corresponds to the cpo carrier frequency @xcite .
the chirped soliton - like pulse is stable within the region of its existence , i.e. within the region of @xmath32 @xcite .
positivity of @xmath24 , i.e. stability against the cw - amplification ( vacuum stability ) , can be provided by a certain minimum positive gdd growing with energy .
nevertheless , the existing theory does not take into account the time dependence of @xmath24 provided by the dynamic gain saturation .
let us consider some numerical estimations .
the gain saturation fluency for a ti : sapphire oscillator is @xmath330.8 j/@xmath34 ( @xmath35 is the emission cross - section , @xmath36 is the emission frequency , @xmath37 is the planck s constant ) .
then , the gain variation due to gain saturation per one resonator round - trip is @xmath380.2 ( @xmath391 ps , the mode area @xmath40 equals to 130 @xmath41m@xmath42 , @xmath43200 nj ; and the peak power is close to the stability limit , which is defined by the self - phase modulation coefficient @xmath444.5 mw@xmath45 ) . that is the gain variation per one cavity round - trip
is not negligible unlike that in a low - energy femtosecond oscillator operating in the solitonic regime .
below , the extended theory of cpo taking into account the dynamic gain saturation will be considered .
the cubic nonlinear limit of eq .
( [ eq1 ] ) admits the chirped soliton - like solution @xcite : @xmath46^{1 + i\psi } \exp \left [ { i\omega \left ( { t - \upsilon z } \right ) } + i\phi z   \right],\ ] ] which is frequency ( @xmath47)- and phase ( @xmath48)-shifted and time - delayed ( @xmath49 ) in the presence of the dynamic gain saturation ( @xmath50 is the dimensionless chirp ) :    @xmath51    the pulse parameters are :    @xmath52    in eq . ( [ eq4 ] )
@xmath53 is the net - loss coefficient , @xmath54 is the gain at the pulse peak taking into account its time - delay with propagation , @xmath55 .
one can see a clear manifestation of the dynamic gain saturation : the time - delay and the frequency shift appear .
[ f1 ] shows the gdd - dependence of the chirp parameter @xmath50 for two fixed @xmath22 .
one can see , that the chirp ( @xmath56 ) increases with gdd and its value is sufficiently large to provide an efficient compression ( the pulse width after compression is @xmath57 ) .
growth of the self - amplitude modulation decreases @xmath56 due to reduction of the relative contribution of the self - phase modulation in comparison with the self - amplitude modulation .    [ cols="^ " , ]     on the other hand , both gdd and pump decrease destabilizes the pulse , as well ( @xmath58 in figs .
[ f3],[f4],[f6 ] ) .
the destabilizing mechanism is an appearance of satellite in front of the pulse ( dashed curve in figs .
[ f3 ] ) . as a result of the dynamic gain saturation , the energy transfer from the pulse to satellite destabilizes the cpo .
to determine the operational range of cpo in terms of dispersion and energy variations , an effect of the dynamic gain saturation on the cpo stability has been studied numerically for the first time to our knowledge .
it has been found , that the dynamic gain saturation has a strong impact on a cpo dynamics in contrast to a low - energy (  10 nj ) mode - locked solid - state oscillator .
first , there is some minimum positive net - gdd providing the oscillator stabilization . below this value
the pulse is destroyed by excitation of the satellite before the pulse .
such a satellite is clearly visible in the experiment and can co - exist stably with the pulse within some narrow gdd - range .
second , there is some maximum gdd and its excess fragments the pulse front owing to the cw - amplification .
third , the highest pulse energy at a given repetition rate is limited because the maximum and minimum gdds stabilizing the pulse merge .
the work was supported by the austrian national science fund ( fonds zur frderung der wissentschaftlichen forschung ( fwf ) , projects no .
p20293 and p17973 ) and by the max - planck gesellschaft ( institut fr quantenoptik ) .
a.apolonski ( department fr physik der ludwig - maximilians - universitt mnchen ) is gratefully acknowledged for active discussions and providing the experimental data concerning the high - energy ti : sapphire cpos .
s. h. cho , b. e. bouma , e. p. ippen , j. g. fujimoto , `` low - repetition - rate high - peak - power kerr - lens mode - locked tial@xmath59o@xmath60 laser with a multiple - pass cavity , '' _ opt .
* 24 * , pp . 417419 , 1999 .
a. fernandez , t. fuji , a. poppe , a. frbach , f. krausz , a. apolonski , `` chirped - pulse oscillators : a route to high - power femtosecond pulses without external amplification , '' _ opt .
lett . _ * 29 * , pp . 13661368 , 2004 . v. l.kalashnikov , e. podivilov , a. chernykh , s. naumov , a. fernandez , r. graf , a. apolonski , `` approaching the microjoule frontier with femtosecond laser oscillators : theory and comparison with experiment , '' * new j. phys . * * 7 * , p. 217
v. l. kalashnikov , e. podivilov , a. chernykh , a. apolonski , `` chirped - pulse oscillators : theory and experiment , '' _ appl .
_ b * 83 * , pp . 503510 , 2006 .
a. fernndez , a. apolonski , _
private communication_. v. l. kalashnikov , a. fernndez , a. apolonski , `` high - order dispersion in chirped - pulse oscillators , '' _ optics express _ , pp . 42064216 , 2008 . h. a. haus , j. g. fujimoto , e. p. ippen , `` structures for additive pulse mode locking , '' _ j. opt
. soc . am .
b _ * 8 * , pp . 20682076 , 1991 . b. proctor , e. westwig , f. wise , `` characterization of a kerr - lens mode - locked ti : sapphire laser with positive group - velocity dispersion , '' _ opt .
* 18 * , pp . 16541656 , 1993 . n. n. akhmediev , a. ankiewicz , _ solitons : nonlinear pulses and beams _ , chapman & hall , london , 1997 . v. l. kalashnikov , i. g. poloyko , v. p. mikhailov , d. von der linde , `` dynamical gain saturation in kerr - lens mde - locked cw solid - state lasers , '' _ optical and quantum electronics _ * 31 * , pp . 369365 , 1999 . v. l. kalashnikov , v. p. kalosha , v. p. mikhailov , i. g. poloyko , `` self - mode locking of four - mirror - cavity solid - state lasers by kerr self - focusing , '' _ j. opt .
b _ * 12 * , pp .
462467 , 1995 .
an effect of the dynamic gain saturation on chirped - pulse oscillator was investigated . 
 it was found , that the dynamic gain saturation causes strong perturbations of the pulse front that destabilizes an oscillator . as a result , 
 the chirped - pulse exists only within some limited range of dispersions and there is a limit of energy growth for a given resonator period .