September 1977 / Vol. 1, No. 3 / OPTICS LETTERS 93

Saturation behavior of p-type germanium at CO2 laserwavelengths

C. R. Phipps, Jr., and S. J. Thomas

Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87545Received May 26, 1977

Observed bleaching of single-crystal p-type germanium in the 10-um region obeys an inhomogeneous broadeningmodel for input intensities up to 100 times the saturation intensity l. Bleaching measurements show thatIs variesfrom about 3.2 MW cm- 2 at 10.59 ,um to about 6.8 MW cm-2 at 9.27 jm. No significant variation of f 8 with crystalorientation is seen. Applications to CO2 laser system isolation are discussed.

Introduction

In this Letter we study the dynamics of saturationin p-type (gallium-doped) germanium at many CO2laser wavelengths. P-type germanium saturable ab-sorbers are now being employed at the Los AlamosScientific Laboratory to provide broadband interstageisolation and prepulse contrast enhancement requiredin multi-TW, subnanosecond CO2 laser systems forfusion studies. The main advantages of p-type ger-manium over the reported gaseous absorbers are spec-tral uniformity of small-signal absorption in the 10-gmregion and picosecond excited-state relaxation. Thelatter property indicates that the absorber could pre-vent postpulse as well as prepulse lasing. Furthermore,p-type Ge bleaches sufficiently rapidly with increasingoptical intensity to provide significant temporal pulseshortening. Temporal reshaping in p-type Ge will bereported at a later date.

In the 10-gm wavelength region, the dominant opticalabsorption in p-type Ge is via direct heavy- to light-holeband transitions, for which the 10.6-gm, room-tem-perature cross-section Ch = 6.8 X 10-16 cm2; this variesonly ±6% in the 9-11-gm wavelength interval.1' 2 Ab-sorption not associated with the hole transition is trulynegligible for the optical and physical thicknesses weconsider.3 The room-temperature energy relaxationtime T1 for this two-level system is about 2.6 psec for10.59-,gm excitation. 4

For nsec-duration optical pulses of intensity I, theabsorption coefficient associated with the hole transi-tion is given by the steady-state expression5 :

(I) = Nh( +h (1)(1 + I/I,)n

Here, Nh is the free hole density, I, the saturation in-tensity, and n = (1, ½), respectively, for a homogeneousor an inhomogeneous broadening model of the transi-tion.6 The n = Y2 dependence in Eq. (1) for inhomo-geneous broadening is valid for intensities sufficientlysmall that the power-broadened interaction linewidthAv [full width at half maximum (FWHM)], which de-fines the subset of absorbers interacting with a satu-

rating wave, remains much smaller than the width of thetotal absorber distribution. Then,

(2)Av (I) = 1 (1 + I/II)1/2 (FWHM),7rT 2

where T2, the dipole relaxation time, is 0.09 psec.7'8This gives 115 cm-' for the natural Lorentzian line-width l/rT 2 and a power-broadened halfwidth equalto the optical frequency for 10.6-,um peak intensities of0.9 GW cm-2 . Then Eq. (1) will no longer be valid.

Gibson et al. have shown that the 10.6-,m transitionis readily bleached,4 and reported transmission datawhich, when fit to a homogeneous (n = 1) model, gaveI, = 10 ± 3 MW cm-2 . Note, however, that the twoexpressions given in Eq. (1) converge when I << I,, withI.(n = 1) = 2I8(n = ½). In Gibson's measurements, Inever exceeded I,, and a transmission dynamic rangeTmax/Tmin of only 1.22 was achieved. These two con-ditions generated a limited range of data, which madeit hard to distinguish between the two broadeningmodels.

In a preliminary report9 on the p-type Ge laser iso-lator, we presented optical saturation data for thismaterial at 10.59-gm intensities up to 1 GW cm-2.These were the first transmission measurements at in-tensities sufficient to confirm Keilmann's claim7'10 thatthe responsible germanium valence-band transition isinhomogeneously broadened. Keilmann7 and Bishopet al. 11 have also observed "spectral hole burning" inp-type Ge, indicative of inhomogeneous broadening.Sargent12 has considered the different times requiredfor LO and LA phonon emission in the light- to heavy-hole relaxation cascade and has predicted strong mod-ulation in T1(X) in the 8- to 30-gm interval with corre-sponding modulation of I,(X). In the neighborhood ofthe CO2 laser spectrum, I, maxima at 11.2 and 8.38 gumand an order-of-magnitude smaller minimum at 9.6 gumare predicted. Application of this model shows that I,at 10.6 ,gm should be about twice the minimum value.In considering p-type Ge as a possible CO2 laser isolator,it is necessary that p-type Ge bleach effectively anduniformly in the CO2 laser spectrum to permit propa-

94 OPTICS LETTERS / Vol. 1, No. 3 / September 1977

Input a; ; - ICalorimeter Attenuator Pyroelectric

Detector

Fig. 1.ments.

Experimental setup for optical saturation measure-

gation of broadband pulses required for efnanosecond energy extraction in large lasei

10.5 9 -Mum Saturation

In the first of two experiments, we havedynamics of the saturation of p-type Ge aThe characteristics of Ge:Ga single-crystalwere: resistivity, 0.75 ohm cm (Nh = 4.5 Xoptical path length, L = 0.585 cm; and stransmission, 0.143 at 10.59 gm. Brewsteimination was used with the (111) axis pa]intersection of the sample surface and thplane of the linearly polarized test beam.

The experimental setup is shown in Fig.dard TEA-CO2 oscillator/amplifier systena 0.5-GW, 1.3-nsec signal at 10.59,um, whitially filtered to give a smooth, Gaussian rad:distribution. Six-mm-diameter irises ismeasurements to a central portion of the b(

-

z2 5U)2

I-2Y)

I.-z;Z

'0 8 16 24 32

1 IN - IOUT (MW cm-2 )

Fig. 2. (Peak intensity transmission)-l for G# 1 versus peak absorbed intensity at 10.59 gim.refer to the plane perpendicular to the propagwithin the sample. Dots: experimental data, mlsignal transmission = 0.143. Curve A (broken]lated homogeneous broadening fit to low-intensi9.3 MW cmi 2, small signal tratisinissionll 0.11(solid line): inhomogeneous fit, I, = 3.2 MWsignal transmission = 0.149. Curve B is an excel]dynamic and small signal transmission data.

ficient sub-r systems.

studied thet 10.59 gim.Sample #11015 cm- 3 );!nall signal7-angle illu-rallel to thee incidence

which intensity varied no more than ±5%. These ap-ertures did not disturb the intensity distribution in thetest region. A 10-cm-focal-length lens imaged the inputand transmitted signals (relatively delayed by 8 nsec)onto a pyroelectric detector with the Airy central zoneabout 10 times smaller than the detector aperture. Thecalorimeters provided data from which true peak-inci-dent intensity could be obtained. Calibrated CaF2attenuators13 were used to adjust incident intensity onthe sample and to obtain nearly constant oscilloscopeinput-pulse display amplitude. Peak intensity trans-mission was determined from the displayed input/output pulse amplitudes. In this way, intensity-de-pendent transmission data equivalent to those for auniform space-time incident illumination distributionwere obtained. Self-focusing was negligible.14

The results of this measurement are plotted in Fig.2. For n = 1, Eq. (1) may be recast to describe thetransmission, T = Ioudlin, in the form4 loge(l/T) =-in-Iout)/Is + Nh ahL. Our data are plotted in thisway better to illustrate their deviation from the homo-geneous model. The deviation becomes apparent at Iin

9 MW-2, the upper extreme of the data in Ref. 4.The inhomogeneous model calculation (solid line),

with I, = 3.2 MW cm-2, fits the data exceedingly well.Estimated errors give a ± 15% uncertainty in IJ.

Wavelength-dependence of saturation effect

1. A stan- Further experiments at other wavelengths we're per-i generated formed with a setup somewhat modified from thatch was spa- shown in Fig. 1. For practical reasons, space-time-ial intensity averaged transmission was determined in this experi-solated our ment. The pyroelectric detector was used only toeam, within measure the incident pulsewidth. Measured trans-

mission was compared to computer-generated trans-mission plots' 5 to determine Is at each wavelength.Input peak intensities were as high as 380 MW cm-2.

Ge:Ga Sample #2, used in these experiments, hada large transmission dynamic range Tmax/Tmin 40 foreasy discrimination of I, variation. Resistivity was 1.0ohm cm (Nh = 3.4 X 1015 cm- 3 ) and optical path lengthwas 2.0 cm. Normal incidence and low-loss, bvoadbandantireflection coatings were used, with maximum 2%reflectance per surface for wavelengths studied.

Typical saturation plots from two extremes of themeasured data are presented in Fig. 3; the horizontalaxis is averaged rather than peak intensity. For aver-aged intensities greater than 0.2 GW cm-2, the 10.59-gm

, . data appear to deviate significantly from the modeltransmission calculation. The same tendency has been

40 48 observed repeatedly as, for example, in Fig. 2. Futureexperiments will determine the saturation dynamics ofp-type Ge for intensities up to 1 GW cm-2 , where we

a:Ga Sample expect the transmission model to break down.Intensities The results of I, determinations at five wavelengths

atonvecto smal are summarized in Table I. No significant variation ofasured small I, with crystal orientation was seen.

ity data, Is = Figure 3 shows a transmission dynamic range of 4261. Cudtve B for Sample #2 at 10.59 /Am, Were the transition wecm-2, small have studied homogeneously broadened, this dynamicent fit to the range would have been about 100. The observed dy-

namic range can be increased to an intermediate level

v I I I I I I I

I

A -. \

I I \ I I I

September 1977 / Vol. 1, No. 3 / OPTICS LETTERS 95

1.0

0 S _ *Xw~~~~~~~~alculated

Eo-2 v l Is6.75 MW/cm2

C -

>. 10 10.59 Ime 5 - SST-=0.006 20 -

W3 X=9.55 igm

2 - SST = 0. 00701

. I . , I * 1 o-3 s l 2 5 -a 2 5 I0

1 0 1 0 1.0

Averaged Incident Intensity (GW/cm2)

Fig. 3 Typical space-time-averaged transmission for Ge:GaSample #2 versus (Ii,,) = Wjn/(7rw 0

2Tp) = 0.53 Ii, (peak) attwo wavelengths. Here w0 is the l/e 2 input intensity radius,Tp is the FWHM duration of the input pulse, and Win is theinput energy. Intensities refer to the plane perpendicular tothe propagation vector within the sample. Small signaltransmission was 0.0062 at 10.6 ,m and 0.0070 9.6 ,im. Inboth examples, the fit to the model calculation is good.

with more-damage-resistant coatings now available.Since the germanium isolation device will be used beforea final saturated amplification stage, the system out-put-energy penalty due to its insertion is acceptable.The small- and large-signal broadband performance ofthe device is excellent.

Summary

1. Our data are a direct demonstration of the appli-cability of an inhomogeneously broadened, two-levelmodel to transmission measurements in Ga-doped Geover a large intensity range at several CO2 wave-lengths.

2. I, increases in a monotonic fashion from about 3.2MW cm-2 at 10.6 gm to about 6.8 MW cm- 2 at 9.2 gim.This is an increase of the right magnitude but the op-posite direction with wavelength to that predicted bySargent's model.12 An absence of fine-scale structurein I, (X) is suggested by the 10.57- and 10.59-,gm data.

3. The p-type Ge isolation device has acceptabledynamic range and excellent broadband perfor-mance.

We are especially indebted to Edward Foley, Victor

Table 1. Wavelength Dependence of SaturationIntensity in Monocrystalline Ge:Ga

Wavelength(gim) I, (MW cm- 2

i 15%)

10.59 3.210.57 3.410.26 4.89.55 6.89.27 6.8

Romero, and James Hayden for their valuable assis-tance in various phases of this work, to Sidney Singerand Stephen Czuchlewski for the use of their facilities,and to Joseph Ladish for his many useful computercodes. Joseph F. Figueira gave support and encour-agement since the inception of this study. Specialthanks to Robert A. Fisher for suggestions regarding themanuscript and to Murray Sargent III for helpful dis-cussions. This work was performed under the auspicesof the U.S. Energy Research and Development Ad-ministration.

References1. H. B. Briggs and R. C. Fletcher, Phys. Rev. 91, 1342

(1953).2. A. H. Kahn, Phys. Rev. 97, 1647 (1955).3. See P. J. Bishop and A. F. Gibson, Appl. Opt. 12, 2549

(1973). They show that the room-temperature, free-electron cross-section te 0.15 X 1016 cm2. If Nh= 5X 1015 cm-3 , mass action gives an electron density Ne 1 X 10ll cm-3 , so that Ne oie/Nh ah - 4 X 10-7. Satura-tion cannot increase this ratio by much more than anorder of magnitude. The carrier-independent absorptioncoefficient at room temperature is 0.013 cm-' and is onlysignificant in physically thick, optically thin samples.

4. A. F. Gibson, C. A. Rosito, C. A. Raffo, and M. F. Kimmitt,Appl. Phys. Lett. 21, 356 (1972).

5. W. W. Rigrod, J. Appl. Phys. 34, 2602 (1963).6. Homogeneous broadening refers to the case in which each

absorber in an ensemble would have the same resonantfrequency except for power broadening. In an ensembleof inhomogeneously broadened absorbers, a distributionof resonant frequencies exists so that only a subset of theensemble can respond to a weak optical signal. Thissubset broadens with intensity. In the present case, themechanism for inhomogeneous broadening is providedby periodic crystal fields, which cause a momentum-dependent splitting of the two levels. Reference 7 con-tains a good discussion of this subject.

7. F. Keilmann, IEEE J. Quant. Electron. QE-12, 592(1976).

8. The observed width in a weak off-resonant probe,strong-saturator experiment is larger than the interactionwidth, and is given by (lh7rT2 )[1 + (1 + I/IS)1/2]. Thisdistinction is unimportant at very high intensities.

9. C. R. Phipps, Jr., S. J. Thomas, and J. F. Figueira, in Di-gest of Conference on Laser and Electro-Optical Systems(Optical Society of America, Washington, D.C., 1976),paper WA6.

10. Fritz Keilmann graciously sent us a preprint of Ref. 7(before we presented our paper cited in Ref. 9) showingthat the heavy- to-light-hole transition should be inho-mogeneously broadened. This enabled us to interpretcorrectly our data when the Ref. 9 paper was present-ed.

11. P. J. Bishop, A. F. Gibson, and M. F. Kimmitt, J. Phys.D 9, L101 (1976).

12. M. Sargent III, Opt. Commun. 20, 298 (1977).13. For the first experiment, these were separately checked

for linearity of transmission with incident intensity up to1.5 GW cm 2 .

14. We have observed the onset of whole-beam self-focusingin p-type, Gaussian-illuminated samples with 50 timesgreater intensity-thickness products than in this exper-iment. These data suggested that dn/dI is of the order10-5 per GW cm-2 .

15. Actual input space and time distributions were measured.Deviation from Gaussian behavior was not a dominantsource of error in the computer-generated data fit.