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JJAP PROOFS Design of End-Pumped Thin Rod Yb:YAG Laser Amplifiers

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JJAP PROOFS Design of End-Pumped Thin Rod Yb:YAG Laser Amplifiers
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  J  J  A P  P  R  O O F  S  Design of End-Pumped Thin Rod Yb:YAG Laser Amplifiers Sakae K  AWATO à and Takao K  OBAYASHI Graduate School of Fiber Amenity Engineering, Fukui University, 3-9-1 Bunkyo, Fukui 910-8507, Japan (Received September 2, 2002; accepted for publication January 8, 2003) An end-pumped thin rod Yb:YAG laser amplifier architecture is proposed for high-power and efficient pulse amplification of quasi-four-level lasers. A thin and long laser rod with low ion concentration is used and optimum conditions of the lasercrystal properties are discussed for efficient amplification of high-repetition-rate pulses. A high single-pass gain is expectedand the thermal birefringence loss is significantly smaller than the single-pass gain. From these results, high optical conversionefficiency of more than 50% is expected for pulse amplification in the master-oscillator and power-amplifier (MOPA)system. [DOI: 10.1143/JJAP.42.dummy] KEYWORDS: quasi-four-level laser, Yb:YAG, diode-pumped solid-state laser amplifier, end-pumping, thin rod 1. Introduction Yb:YAG material has been investigated in recent yearsfor use as high-power and ultrashort pulse lasers based on ahigh atomic quantum efficiency of 91% and a wide gainspectrum of 9.5nm full width at half maximum (FWHM).However, realization of high intensity pumping larger thanabout 10kW/cm 2 and efficient cooling is required to reducethe re-absorption loss originating from the lower levelpopulation of the quasi-four-level system. Furthermore, highsingle-pass gain of the amplifier is necessary for high energyextraction to overcome the optical loss in the amplifier andthe temperature increase in the laser crystal by high intensitypumping causes unfavorable thermal effects.Several designs of Ytterbium-material pumping architec-ture have been developed for high-power, high-efficiencyoscillation and amplification, including thin disk, 1–5) micro-chip, 6,7) zigzag slab, 8–10) rod 11–14) and fiber 15,16) structures.A thin disk laser was proposed by Giesen et al. , 1) utilizing alongitudinal multi-pass pumping scheme to reduce the quasi-four-level re-absorption laser loss and the longitudinalcooling scheme to reduce thermo optic effects. A continuouswave (CW) multimode output power of 1,070W wasachieved by the multi-disk laser with a high opticalconversion efficiency of 48%. 2) The concept was alsoapplied to a regenerative amplifier of picosecond pulses 5) with average output power of 10.2W and optical conversionefficiency of 16%. The efficiency of the amplifier is lowerthan that of the CW oscillator mainly due to the low single-pass gain of the thin disk Yb:YAG.Ytterbium-glass fiber amplifiers offer a range of propertiessuch as high optical conversion efficiency that makes theman attractive efficient source of ultrashort pulses, because of their high gain characteristics. In the fiber chirped-pulseamplification (CPA) system, an average output power of 5.5W has been achieved with a high efficiency of 37% and ahigh single-pass gain of 32dB. 15) However, pulse energy of the fiber amplifier is limited to about 1mJ, because of itssmall core diameter of 20–100 m m . For many scientific andindustrial applications, the development of high-powerultrashort pulse laser oscillators and amplifiers is requiredwith high-energy, high-efficiency and high-beam-qualityoutput in a compact structure.In the rod geometry, as the pump power increases thethermo-optical stress increases. It is difficult to reduce thestress in the rod laser, as compared to the thin disk or slablaser. For example, the end-pumped rod laser was developedby Bibeau et al. with 2mm diameter, 13,14) and the opticalconversion efficiency and the beam quality characteristicswere lower than those of the end-pumped thin disk andzigzag slab lasers.In this study, we analyze a new architecture of theYb:YAG amplifier for ultrashort pulse amplification withaverage output power of approximately 100W. 17) The basicstructure of the amplifier module is a thin, long rod withtransverse size of less than about 1mm. A similar rodstructure has been found in the four-level laser materi-als. 18,19) However, the basic conditions of the Yb:YAG rodstructure are different from the conventional four-level lasersand new design principles are derived for the suppression of temperature increase and the optimization of the rod size todecrease the loss inherent in the quasi-four-level lasermaterials.Geometry and features of the thin rod Yb:YAG amplifierare described in §2.1. Theoretical treatment of gain andefficiency is presented in §2.2 and thermal effects of theamplifier are discussed in §2.3. 2. Design of End-Pumped Thin Rod Yb:YAG Ampli-fiers 2.1 Geometry and features of the thin rod Yb:YAGamplifier module Schematic of the thin rod Yb:YAG amplifier module isshown in Fig. 1 . Two CW laser diodes (LD) are used forpumping and the output beams are focused on the endsurfaces of the cylindrical thin rod Yb:YAG crystal. Thepump beam is tilted at a center axial angle   p from the rodaxis to separate the laser beam and to increase the absorption Fig. 1. Schematic of the end-pumped thin rod Yb:YAG amplifier module.   p is the center angle of the pump beam. à E-mail: kawato@fuee.fukui-u.ac.jpJpn. J. Appl. Phys. Vol. 42 (2003) pp. 0000–0000Part 1, No. 5A, May 2003 # 2003 The Japan Society of Applied Physics 02R09008 [1]  J  J  A P  P  R  O O F  S  pass length inside the rod. The transverse surface of the rodis coated with high-reflection film to confine the pump beamand to realize uniform pump intensity distribution averagedby multiple reflection inside the rod and the pump intensityis assumed to be transversely uniform. The cooling structureof the thin rod is much simpler than those of the thin disk and conventional rods. The rod is uniformly cooled throughthe transverse surface in contact with metal heat sinks cooledby water.One of the advantages of the thin rod structure is its highgain characteristics due to its long gain length compared tothe thin disk structure. It also exhibits high pulse energyoutput characteristics due to having a large gain areacompared to the fiber structure. The end-pumped thin rodstructure is suitable for efficient cooling because of the largesurface area with small rod volume. 2.2 Unsaturated single-pass gain and storage efficiency The repetitive pulse train with sub-ps to ns pulse width isassumed to be introduced into the amplifier with timeinterval   r . The unsaturated single-pass gain of the amplifieris related to the unsaturated exponential gain   0 ð r  ; Þ as 20) G 0 ð r  ; Þ ¼ exp ½   0 ð r  ; Þ ; ð 1 Þ where r  is the radial position and  is the azimuth angle inthe cylindrical rod. The unsaturated exponential gain isrelated to the emission cross section   f  and the inversionpopulation density Á n ð r  ;;  z Þ as   0 ð r  ; Þ ¼   f  Z  L  0 Á n ð r  ;;  z Þ d  z ; ð 2 Þ where z is the longitudinal position inside the rod and L  isthe rod length. Under the unsaturated condition of the quasi-four-level system, the inversion population density is 21,22) Á n ð r  ;;  z Þ ¼ f f  a ð r  ;;  z Þ þ f  b ð r  ;;  z Þg  p P p   f  r  p ð r  ;;  z Þ h  p À f  0a ð r  ;;  z Þ n t ; ð 3 Þ where n t is the concentration of the Yb laser ions,   f  is thefluorescence lifetime, f  a ð r  ;;  z Þ and f  b ð r  ;;  z Þ are thefractional population of the lower and the upper laser levels,respectively, f  0a ð r  ;;  z Þ is the initial value of the fractionalpopulation of the lower laser level,  p is the pump quantumefficiency and r  p ð r  ;;  z Þ is the pump intensity distribution inthe rod. The absorption efficiency  a is given by integratingthe pump intensity distribution r  p ð r  ;;  z Þ inside the rodvolume V  as  a ¼ Z  V  r  p ð r  ;;  z Þ d V  ; ð 4 Þ where V  ¼ SL  , S  ¼  r  20 is the rod cross section with radius r  0 . For the case of transversely uniform pumping from twoend surfaces of the rod as shown in Fig. 1 , the pumpintensity distribution r  p ð r  ;;  z Þ is simplified to r  p ð  z Þ ¼  ½ exp ðÀ   z Þ þ exp ðÀ  ð  z À L  ÞÞ = ð 2 S  Þ ; ð 5 Þ where  is the effective absorption coefficient for the pumpbeam.The spatial distribution of the fractional populations f  a and f  b is assumed to be uniform in the rod because thetemperature distribution is almost uniform in the rod as willbe shown in §2.3. Thus the unsaturated exponential gain isderived from eqs. ( 2 ) and ( 3 ) as   0 ¼ ð   f  = S  Þð f  a þ f  b Þ  a  p  N  p ½ 1 À  l  N  t = ð  a  p  N  p Þ ; ð 6 Þ where N  t ¼ n t V  is the total number of ions in the rod and N  p is the number of pump photons incident within thefluorescence lifetime   f   N  p ¼ P p   f  = ð h  p Þ ; ð 7 Þ and the ratio of fractional populations is  l ¼ f  0a = ð f  a þ f  b Þ : ð 8 Þ It is shown in eq. ( 6 ) that the gain of the quasi-four-levelsystems is decreased when the total number of ions N  t isextremely large, thus optimization is required.The saturation fluence is given by  J  s ¼ h  L = ½ð f  a þ f  b Þ   f   ; ð 9 Þ where h  L is the laser photon energy. The storage fluence of the amplifier within the time interval   r is  J  st ¼   0  J  s ½ 1 À exp ðÀ   r =  f  Þ : ð 10 Þ The storage efficiency of the amplifier  s is defined by theratio of the storage energy SJ  st and the pump energyintegrated within the time interval   r as  s ¼ SJ  st = ð P p   r Þ ¼  q  p  a ½ 1 À  l  N  t = ð  a  p  N  p Þ ½ 1 À exp ðÀ   r =  f  Þð   f  =  r Þ : ð 11 Þ The storage efficiency depends on the total number of ions  N  t . Therefore the maximum storage efficiency is obtained by d  s = d  N  t ¼ 0 . The optimum total number of ions is alsogiven by d  s = d  N  t ¼ 0 as  N  optt ¼ ln ½  B  p  N  p = l  =  B ; ð 12 Þ and  B ¼   a = ð S  cos   p Þ ; ð 13 Þ where   a is the absorption cross section for the pumpwavelength. The optimum rod length is related to theoptimum number of ions and is given by  L  opt ¼ N  optt = ð n t S  Þ : ð 14 Þ The absorption efficiency is obtained from eqs. ( 4 ) and ( 5 )and is approximated as  a ¼ 1 À exp ½À  N  t  B  : ð 15 Þ The optimum value of the absorption efficiency is obtainedby substituting eq. ( 12 ) into eq. ( 15 ) as  opta ¼ 1 À  l = ð  B  p  N  p Þ : ð 16 Þ As shown in eq. ( 15 ), a small value of  B with a small crosssection of the rod S  and large angle of the pump beam   p leads to the increase of the optimum absorption efficiency  opta . By substituting eq. ( 12 ) into eqs. ( 6 ) and ( 11 ), themaximum unsaturated exponential gain is   max0 ¼ ð   f  = S  Þ  p  N  p 1 À 1 þ ln ð  B  p  N  p = l Þ  B  p  N  p = l   ; ð 17 Þ and the maximum storage efficiency is 02R09008 [2] Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 5A S. K  AWATO and T. K  OBAYASHI  J  J  A P  P  R  O O F  S   maxs ¼  q  p 1 À 1 þ ln ð  B  p  N  p = l Þ  B  p  N  p = l   1 À exp ðÀ   r =  f  Þ   r =  f  : ð 18 Þ From eqs. ( 17 ) and ( 18 ), one can see that large values of theparameter BN  P = l with a small cross section of the rod andlarge incident angle of the pump beam lead to increases inthe single-pass gain and the storage efficiency.In the following numerical analysis, the laser rodtemperature is assumed to be 300K with the pulse interval   r ¼ 50 m s and the center angle of the pump beam   p ¼ 45 deg. For the Yb:YAG parameters, we assume  q ¼ 1 : 0 ,  l ¼ 1 ; 030 nm,  p ¼ 940 nm,   f  ¼ 3 : 0  10 À 20 cm 2 ,   a ¼ 7 : 7  10 À 21 cm 2 and   f  ¼ 0 : 95 ms.The optimum number of ions N  optt and the optimumabsorption efficiency  opta have been calculated as a functionof pump power P p and the results are shown in Figs. 2 and 3 for several rod diameters. It is shown that the optimumnumber of ions N  optt increases with increasing pump powerand increasing rod diameter. The optimum absorptionefficiency  opta also increases with the pump power butdecreases with increasing rod diameter. Therefore thestorage efficiency  s and the unsaturated single-pass gain G 0 are smaller for the large rod diameters as discussedabove.Figure 4 shows the pump power dependence of theunsaturated single-pass gain G 0 for several rod diameters.High gain values are expected at high pump power.However, an extremely high gain value exceeding a factorof about 100 causes a parasitic oscillation and an amplifiedspontaneous emission, and some suppression techniquessuch as use of tapered rod with flanged end-caps structuresbecome necessary as demonstrated in refs. 13 and 14.Therefore rods with diameter smaller than 0.5mm are notsuitable for high-power pumping. The pump power and therod diameter dependence of the storage efficiency  s isshown in Fig. 5 . For the pump power above about 200W, a 0100200300400500    O  p   t   i  m  u  m   n  u  m   b  e  r  o   f   i  o  n  s     N    t  o  p   t Pump power P p [W] Rod diameter: 2 r  0 [mm]0.51.01.52.0   2.53.0 510 x10 18 Fig. 2. Optimum number of Yb ions N  optt as a function of pump power P p for several rod diameters 2 r  0 . 0.60.70.80.910100200300400500    O  p   t   i  m  u  m   a   b  s  o  r  p   t   i  o  n  e   f   f   i  c   i  e  n  c  y      η   a  o  p   t Pump power P p [W] Rod diameter: 2 r  0 [mm]0.51.01.52.02.53.0 Fig. 3. Optimum absorption efficiency  opta as a function of pump power P p for several rod diameters 2 r  0 . Total number of Yb ions is assumed tobe optimized for pump power and rod diameters. 11010 2 0100200300400500    U  n  s  a   t  u  r  a   t  e   d  s   i  n  g   l  e  -  p  a  s  s  g  a   i  n     G    0 Pump power P p   [W]   Rod diameter: 2 r  0 [mm]0.51.01.52.02.53.0 Fig. 4. Pump power dependence of the unsaturated single-pass gain G 0 for several rod diameters 2 r  0 . Optimum number of ions is assumed. 00.20.40.60.810100200300400500    M  a  x   i  m  u  m   s   t  o  r  a  g  e  e   f   f   i  c   i  e  n  c  y      η   s  m  a  x Pump power P p [W] Rod diameter: 2 r  0 [mm]0.51.01.52.02.53.0 Fig. 5. Dependence of the maximum storage efficiency  maxs on pumppower P p and rod diameter 2 r  0 . Input pulse interval of 50 m s and theoptimum number of ions are assumed. 02R09008 Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 5A S. K  AWATO and T. K  OBAYASHI [3]  J  J  A P  P  R  O O F  S  high storage efficiency exceeding 70% is expected for rodswith diameter less than 1.0mm.The thin rod structure can also be used as the gain mediumof the multi-pass or regenerative amplifier. The output pulseenergy is calculated based on the Frantz-Nodvik relation 23) for these amplifiers. Complete spatial overlap of the inputand the amplified beams is assumed. For a pulse with afluence J  0 that is incident in the amplifier, the gain issaturated when the gain equals the loss and the maximumfluence of the amplified pulse is given by 24)  J  max ¼ J  s ln ð 1 À L  a Þ G 0  L  a ð 1 À L  a Þ G 0    L  a " #( )  ½ 1 À exp ðÀ   r =  f  Þ þ J  0 ; ð 19 Þ where L  a is the single-pass transmission loss excluding thequasi-four-level loss of the laser rod. The ratio of themaximum extracted pulse energy to the storage energy givesthe maximum extraction efficiency 20)  maxe ¼  m ð  J  max À J  0 Þ =  J  st ; ð 20 Þ where  m is the mode-matching efficiency between the pumpmode and the amplified laser mode distribution in the rod.The product of the maximum storage efficiency  maxs and themaximum extraction efficiency  maxe is the maximum opticalconversion efficiency  o ¼  maxs  maxe : ð 21 Þ The pump power dependence of the maximum opticalconversion efficiency  o for the regenerative and multi-passamplifier is calculated for several rod diameters assumingthe mode-matching efficiency of 100% and the results areshown in Fig. 6 . A high optical conversion efficiencyexceeding 50% is possible for rods with diameter less than1.0mm at a pump power above 150W. In this calculation,the single-pass loss L  a ¼ 10 % is assumed as a commonvalue in conventional regenerative amplifiers.The optical conversion efficiency is affected by the mode-matching efficiency obtained by eqs. ( 20 ) and ( 21 ). Whenthe gain is saturated in the regenerative amplification, themode-matching efficiency of the amplifier is equal to that of the oscillator. Thus we will adopt the mode-matchingefficiency of the quasi-four-level laser oscillator with aTEM 00 laser beam of e À 2 radius of  r  0 = 1 : 2 as discussed byTaira et al. 22) It is known that at the threshold pump power,the mode-matching efficiency decreases to lower than about50%, but then increases to 85% at high pump power inexcess of threefold greater than the threshold. From Fig. 6 ,we can estimate that the optical conversion efficiency of theamplifier exceeds 50% for rods with diameter less than1.0mm at a pump power above about 250W. Therefore theefficiency of the thin rod amplifier is much higher than thatof the Yb:YAG thin-disk regenerative amplifiers (16%). 5) 2.3 Thermal effects Crystal temperature influences the lower laser levelpopulation and transmission loss in the quasi-four-levellaser material. It is assumed that the outer surface of the rodis effectively cooled and kept at room temperature. Ingeneral, a long rod with low ion concentration is preferablefor efficient cooling of the laser rod. For a long laser rod, theheat flow in the longitudinal direction is extremely smallcompared to that in the radial direction and can be neglectedin the analysis. Based on the diffusion model of the radialheat flow in the circular rod with the thermal conductivity K  c and the heat conversion efficiency defined by  h ¼ 1 À  p  q ,the temperature difference between the position of radius r  and the outer surface r  0 of the rod at longitudinal position z is Á T  c ð r  ;  z Þ ¼  h  a P p 4 K  c r  p ð  z Þ r  20 À r  2 À Á : ð 22 Þ The average value of the temperature increase over the rodvolume V  is needed for the estimation of the quasi-four-levellaser loss and it is given by Á T  a ¼ 1 V  Z  V  Á T  c ð r  ;  z Þ d V  ¼  h  a P p = ð 8  K  c  L  Þ : ð 23 Þ The volume-averaged temperature increase Á T  a as a func-tion of pump power is calculated for several rod diametersand the results are shown in Fig. 7 . In the calculation, weassume K  c ¼ 0 : 14 W/(cmK) and  h ¼ 8 : 7 % for Yb:YAGcrystal. The average temperature increase is less than 3K even at a pump power of 500W for rods with diameter lessthan 1.5mm. The loss of the storage efficiency caused by thetemperature increase is estimated to be less than 1%.The maximum temperature increase can be measured atthe center position of the rod-end section and from eq. ( 22 ) itis estimated to be about 10K at pump power of 500W. Thetemperature increase of the laser rod with ion concentrationof around 1at.% is still low. It is shown that the coolingefficiency of the thin rod structure is high because of thewide cooling area.Thermal focal length for the polarization along the radial r  or circular  direction is written as 25) f  r  ; ¼ 2 K  c S   h  a P p d n 0 = d T  þ  2 n 30 C  r ; þ l ð n 0 À 1 Þ =  L   ÃÈ É ; ð 24 Þ where n 0 is the refractive index,  is the thermal expansion 00.20.40.60.810100200300400500    O  p   t   i  c  a   l  c  o  n  v  e  r  s   i  o  n  e   f   f   i  c   i  e  n  c  y      η   o Pump power P p [W] Single-pass loss:    L i = 10% Rod diameter: 2 r  0 [mm]0.51.01.52.02.53.0 Fig. 6. Dependence of the maximum optical conversion efficiency  o onpump power P p and rod diameter 2 r  0 . Single-pass loss of 10% and theoptimum number of ions is assumed. 02R09008 [4] Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 5A S. K  AWATO and T. K  OBAYASHI  J  J  A P  P  R  O O F  S  coefficient, C  r and C   are the photoelastic coefficients in the[111] direction of the Yb:YAG crystal for radial r  andcircular  polarizations, respectively, and l is the length of the rod-end section over which expansion occurs.The pump power dependence of the thermal focal lengthand the optimum rod length is calculated and the results areplotted in Fig. 8 . Yb:YAG parameters are assumed to be n 0 ¼ 1 : 82 , d n 0 = d T  ¼ 7 : 5  10 À 6 K  À 1 ,  ¼ 7 : 3  10 À 6 K  À 1 , C  r ¼ 0 : 017 , C   ¼ À 0 : 0025 , l ¼ 2 r  0 , and n t ¼ 0 : 5 at.%. Thethermal focusing, the length of which is more than twice theoptimum rod length L  opt , can be compensated by placingconcave or convex mirrors in the laser cavity. At high pumppower, the focal length is short and the short thin-rodstructure is effective in preventing the reduction of themode-matching efficiency. Thus a thin rod with an ionconcentration of approximately 1.0at.% is useful for thecompensation of the thermal focusing effects.If a thermal birefringent crystal is placed between apolarizer and an analyzer with parallel polarization direc-tion, the transmission loss due to the thermal birefringencefor the plane laser beam is calculated by integrating thetransmission loss distribution L  b ð r  ; Þ over the cross-sec-tional area of the rod as 26)  L  a ¼ 1 S  Z  S   L  b ð r  ; Þ d S  ¼ 141 À sinc k  l n 30  ð C   À C  r Þ  h  a P p  K  c   ! ; ð 25 Þ where k  l is the laser wave number.The pump power dependence of the thermal birefringencetransmission loss is calculated and the results are shown inFig. 9 . The loss depends on the absorbed pump power and itis estimated to be small compared to the single-pass gain of the thin rod amplifier with diameter less than 1.5mm. Theloss can be reduced significantly by using simple birefrin-gence compensation techniques. 27,28) 3. Conclusion A thin rod Yb:YAG amplifier has been designed for high-power and efficient ultrashort pulse amplification withaverage output power of approximately 100W. A thin andlong Yb:YAG crystal with low Yb ion concentration is usedand pumped from two end surfaces with a large angle of incidence. The optimum thin rod size is obtained at CWpump power of several hundreds W. The thin rod structurefeatures a high single-pass gain characteristic due to its longlength compared to the thin disk structure, and a high pulseenergy output characteristic due to its large cross sectioncompared to the fiber structure. Although this structure lookssimilar to the conventional thick rod laser with rod diameterlarger than 2mm, 11–14) the thin rod model has the char-acteristics of higher pumping efficiency and high coolingefficiency. The pulse extraction efficiency and the storageefficiency of the thin rod laser are higher than the thick rodlaser. The gain can be chosen to ensure that suppression of parasitic oscillation and amplified spontaneous emission(ASE) without the tapered barrel structure occurs. 13) The volume average temperature increase in the laser rodis estimated to be less than 3K and the increase of the quasi-four-level laser loss is maintained below 1%, thus it can be 012340100200300400500    A  v  e  r  a  g  e   t  e  m  p  e  r  a   t  u  r  e   i  n  c  r  e  a  s  e       ∆     T   a    [   K   ] Pump power P p [W] Rod diameter: 2 r  0 [mm]0.51.01.52.02.53.0 Fig. 7. Average temperature increase Á T  a as a function of pump power P p for several rod diameters. Ion concentration of 0.5at.% and the optimumnumber of ions are assumed. 01002003000100200300400500Pump power P p [W]    T   h  e  r  m  a   l   f  o  c  a   l   l  e  n  g   t   h     f r  ,       φ    [  m  m   ]   O  p   t   i  m  u  m   r  o   d   l  e  n  g   t   h     L   o  p   t    [  m  m   ]    f  φ   f  r   f  φ   f  r   f  φ   f  r   f  r   L opt 0.51.01.52.0Rod diameter: 2 r  0 [mm] Fig. 8. Optimum rod length L  opt and thermal focal length f  r  ; as afunction of pump power P p for several rod diameters. Ion concentrationof 0.5at.% and the optimum number of ions are assumed. 00.10.20100200300400500Pump power P p [W] Rod diameter: 2 r  0 [mm]0.51.01.5    D  e  p  o   l  a  r   i  z  a   t   i  o  n   l  o  s  s     L   a 2.02.53.0 Fig. 9. Depolarization loss L  a as a function of pump power P p for severalrod diameters. The optimum number of ions is assumed. 02R09008 Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 5A S. K  AWATO and T. K  OBAYASHI [5]
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