TỔNG HỢP TẤT CẢ BÀI NGHIÊN CỨU MỚI NHẤT VỀ VẬT LÝ BẰNG TIẾNG ANH

39-44TRANSVERSE DISTRIBUTION OF PUMP POWER IN THEDIODE-LASER SIDE-PUMPED SOLID-STATE LASER ROD MAI VAN LUU, DINH XUAN KHOA, AND VU NGOC SAU Vinh University HO QUANG QUYAcademy of Militar

Communications in Physics, Vol 19, No 1 (2009), pp 39-44

TRANSVERSE DISTRIBUTION OF PUMP POWER IN THEDIODE-LASER SIDE-PUMPED SOLID-STATE LASER ROD

MAI VAN LUU, DINH XUAN KHOA, AND VU NGOC SAU

Vinh University

HO QUANG QUYAcademy of Military Science and Technology

Abstract Based on the assumption that Gaussian pump power of diode laser bar is the same

at any cross-section along the laser rod and its curvated surface plays as thin lens, the expression describing the pump intensity distribution inside laser rod was obtained by transfer matrix To have the cross-section of active volume or excited volume coincides with one of laser mode volume, the dependence of pump intensity distribution on location of outside pump beams is investigated

by simulation.

I INTRODUCTIONRecently, the diode laser-pumped solid-state lasers from the very small [1] to thekilowatt level of output power [2,3] are interested and developed by because of their efficientuse in high technology Mode size optimization in laser-diode end-pumped lasers has beeninvestigated [4,5] Side-pumping geometry can be used to achieve higher output powers[6] For analysis in above-mentioned work, there were the following assumptions made:Distribution of diode bar around the rod is assumed to produce an azimuthal uniformillumination; reflection and refraction effects are not considered; to separate the calculation

of the absorption profile from how the pump light travels from the diode bar to the surface

of the rod, one describes the pump beam from the diodes only after the beams have enteredthe rod; the pump beam is assumed to travel through the rod only once, i.e reintroduction

of a pump beam through reflectors is not discussed; a single-absorption coefficient can beused to describe the absorption process Consequently, these assumptions lead to that:first, it is not suitable for optimality of pump stored energy in laser rod; second, one cannot choose the optimal parameters for matching between the size of the pump volume andlaser mode one; thirdly, it is still not assumed the laser rod as a focusing lens, which is

a important fact influences on the pump energy distribution.To advoid above problems,

we present a four-side-pumped structure for solid-state laser and a new cross-sectionalgeometry of the laser rod pumped by diode bar Pumped by four laser-diode bars, whichhas a Gaussian distribution in far field, so transverse intensity distribution in active rod

of solid-state laser can be changed and influences on dimension of effective “pencil” andthen on laser beam structure

40 TRANSVERSE DISTRIBUTION OF PUMP POWER IN THE DIODE-LASER SIDE-PUMPED

II PUMP INTENSITY DISTRIBUTION

As shown in Keming’s work [7] and Carts’s work [8], the cross-sectional geometry

of the laser rod pumped by four laser diode bars can be illustrated in Fig 1 The diodesources are assumed to have a Gaussian emittance profile (transverse distribution) andare conditioned such that they are effectively arrayed uniformly around the rod, i.e theyuniformly distribute along axis-z

y

y 0 r 0

Fig 1 a- Cavity geometry for four sides-pumping module, b- Cross-sectional

geometry of Gaussian beam outside and inside rod

We assume that the laser rod has a radiusr0and a refractive index n, the Gaussianbeam of laser diode bar in cross-section of laser rod, which is placed at point y0 fromoutside surface of rod, has a complex amplitude [9]:



−j ky − j k

x22R(y)+ jξ(y)



(1)where, y is the proprating direction and x is expanding direction,

W (y) = W0



1 +yb

ξ(y) = tan−1(y/b) is the excess phase (i.e.,initial phase), (5)and b is the Rayleigh range (see Fig 1b)

Propagating through the rod from one side, the phase of this beam will be changed

as well as after propagating through thin lens (see Fig 1a) with focal length [9]

MAI VAN LUU et al 41

Win0 = M W0; bin= M2b; Win = Win0



1 +byin

21/2

;

M = Mt

√ 1+t; t = y b

0 −r 0 /(n−1); Mt= r 0

y 0 (n−1)−r 0

42 TRANSVERSE DISTRIBUTION OF PUMP POWER IN THE DIODE-LASER SIDE-PUMPED

time is proportional to sum of intensities of all pump lasers at that time With consideringthat the delay time between all lasers is less than lifetime of upper laser level (it meansthat phase mitmach between all laser beams can be negleted), so that the pump intensitydistribution for two opposite sides-pumping is given by

Itwoside(x, y) = Iin(x, y) + Iin(x, −y) (15)and similarly, for four sides-pumping is given by

If ourside(x, y) = Itwoside(x, y) + Itwoside(y, x) (16)III SIMULATION AND DISCUSSION

We assume that the parameters of pump beam chosen to be W0 = 1mm, λ = 860nmand the parameters of laser rod chosen to be r0 = 6mm, and a refractive index, n =1.78 The location of waist of pump beam is calculated from (12) Now pump intensitydistributions inside the laser rod for side-pumped solid-state laser with two sides and foursides can be obtained as shown in Fig.2a and Fig.2b, respectively

Fig 2 Pump intensity distribution for a two-side-pumped (a) and

four-side-pumped (b) solid-state lasers

In Fig 3 can see overlap pump profile in x-axial plane for one-side-pumped (a) and forfour side-pumped (b) laser In Fig 4 can see overlap pump profile in y-axial plane for oneside-pumped (a) and four-side-pumped (b) laser After comparison between all profiles intwo figures (Fig 3 and Fig 4), we can conclude that the overlap of the pump intensitydistribution at the center of the laser rod closely resembles a Gaussian distribution for thefour-side-pumped laser

The waist (Wp) of the Gaussian overlap can be changed by changing the location ofoutside beam For example, in Fig 5, one can see that the cross section (πW2p) at level withthe same energy in case of y0=10 mm is larger than the one in the case of y0=15mm Thismeans that the effective cross-section defined as cross-section of total intensity distribution

at level of IM AX/e can be chosen so that it coincides with cross-section of the laser mode

MAI VAN LUU et al 43

Fig 3 Overlap pump-intensity profile in the x-axial plane for one-side-pumped

(a) and four-side-pumped (b) lasers

Fig 4 Overlap pump-intensity profile in the y-axial plane for one-side-pumped

(a) and four-side-pumped (b) lasers

volume (πW20L) by changing the location of outside beam (y0) as shown above, when otherparameters as beam waist of pump beam (W0p) and pump wavelength (λ) are given

IV CONCLUSIONThe expression of the pump intensity deposition inside the solid-state laser rodpumped by diode laser bars is introduced The pump intensity distribution, the pumpvolume are dependent not only on parameters of pump beam, but also on parameters oflaser rod and the location of pump beam from the laser rod Since that obtained resultsare useful not only for optimization conversion efficiency, but also for reducing the thermal

44 TRANSVERSE DISTRIBUTION OF PUMP POWER IN THE DIODE-LASER SIDE-PUMPED

Fig 5 Four-side-pump- intensity distribution inside the laser rod with two values

of pump beam location: y 0 = 15 mm (a) and y 0 = 10 mm (b)

effect in laser rod Moreover, the longitudinal distribution of pump intensity in laser modevolume of the side-pumped laser is important question, which will be investigated in thenext article

REFERENCES[1] B J Comaskey, et al., IEEE J Quantum Electron., 28 (1992) 992-996.

[2] N Hodgson, S Dong, and Q Lu, Opt Lett 18 (1993) 1727-1729.

[3] R J St Pierre et al., J Sel.Top Quantum Electron 3 (1997) 53-58.

[4] T Y Fan, and R L Byer, IEEE J Quantum Electron 24 (1988) 895-912.

[5] Y F Chen et al., IEEE J Quantum Electron 33 (1997) 1424-1429.

[6] W Xie et al., Applied Optics 39 (2000) 5482-5487.

[7] Du Keming et al., Appl Optics 37 (1998) 2361-2364.

[8] Y A Carts, Diode Lasers, Nonlinear Optics, and Solid-State Lasers, 1992.

[9] B E A Saleh, and M.C Teich, Fundamentals of Photonics, A Wiley-Interscience Publication (1991) [10] O Svelto, Principles of Lasers, Plenum Press, New York and London, 1979.

Received 11 December 2008

Communications in Physics, Vol 19, No 1 (2009), pp 45-52

INVESTIGATING THE EFFECT OF MATRICES AND DENSITIES

ON THE EFFICIENCY OF HPGE GAMMA SPECTROSCOPY

USING MCNP

TRUONG THI HONG LOAN, DANG NGUYEN PHUONG,

DO PHAM HUU PHONG, AND TRAN AI KHANHFaculty of Physics, University of Natural Sciences,Vietnam National University, Ho Chi Minh City

Abstract When determining radioactivities in environmental samples using low-level gamma spectroscopy, in order to raise detection limit, voluminous samples are used It takes in account for the self-absorption (self-attenuation) of gamma rays in samples The self-absorption effect is small or large depend on the sample shapes, matrices and densities In this paper, we investigated the effect of some regular matrices such as water, soil, epoxy resin on the detector efficiency Some analytical formulas for the correction of matrix and densities for soil sample was established and applied to calculate some activities from standard sample of IAEA-375.

I INTRODUCTIONOne of the most important problems of radioactivity measurement is investigatingthe detection efficiency There are lots of factors can affect the efficiency such as: incidentgamma ray energy, measuring geometry, electronic system, detector itself, other effectslike coincidence summing or self-absorption Among them, self-absorption is the mostinteresting effect when investigating activities of environmental samples because of theirlarge volumes

One of the most regular geometries used in investigating activities of environmentalsamples is Marinelli beaker geometry, which has 3π measuring geometry, so the efficiency

is very high Usually, Marinelli beaker samples have large volumes so the self-absorptioneffect of these samples is significant

With the MCNP4C2 code [1], by simulating the measuring processes of tal samples using the HPGe spectroscopy in Nuclear Physics Laboratory, we investigatedthe effect of matrices and densities on the efficiency Based on that, a correction methodwas presented to calculate detection efficiencies for environmental samples

environmen-II CONFIGURATION OF SPECTROSCOPY - SAMPLE USED IN

SIMULATION AND EXPERIMENTII.1 HPGe spectroscopy

The HPGe detector in Department of Nuclear Physics, model GC2018, is a coaxialdetector with configuration showed in Fig.1, including a germanium cylinder crystal with

52 mm outer diameter, 49.5 mm height Inside the crystal, there is a hole with 7 mm

diameter, 35 mm depth There are outer n-type contact layer (lithium layer), inner p-typecontact layer (boron layer) of the crystal The detector is hold in an aluminium box with1.5 mm thickness [3].

There is a lead shield outside detector to absorb gamma rays from environment andsuppress spectrum background The interactions between gamma rays and lead shieldlayer produce X-rays with energies in the range 7388 keV These X-rays can be detected

by detector and effect on the gamma spectrum To limit this problem, the copper andtin liners were lined covering the lead shield with the thickness of 1.6 mm and 1 mmrespectively The X-rays emitted by lead will be absorbed by the tin, and X-rays from thetin (about 2530 keV) will be absorbed by cooper Finally, the cooper emits low energyX-rays (about 8 keV) which does not present on the spectrum

Fig 1 The configuration of HPGe detector (in milimeter)

III SIMULATION OF PEAK EFFICIENCY CURVES OF HPGE

DETECTOR WITH MATRICES AND DENSITIESIII.1 Matrices used in simulation

To investigate the effect of matrices on detection efficiency, we need to simulate theefficiencies with and without matrices There were three types of matrices to simulate:soil, water and epoxy resin The simulated volumes were the same with all types, thesimulated densities were 0.5 g/cm3, 1.0 g/cm3 and 2.0 g/cm3

Three types of matrices [3]: Soil (% mass of atom in molecular): hydrogen 2.2%,oxygen 57.5%, aluminium 8.5%, silicon 26.2%, iron 5.6%; Epoxy resin (% mass of atom

in molecular): hydrogen 6.0%, oxygen 21.9%, carbon 72.1%; Water (% mass of atom inmolecular): hydrogen 11.11%, oxygen 88.89%

To obtain the efficiency without matrix, simulated sample was chosen is air samplewith density 0.00129 g/cm3

, includes 79% nitrogen and 21% oxygen The size and volume

of this sample is the same as soil, water and resin samples

The simulated results of air matrix (efficiencies without self-absorption) were sented in Table 1

pre-Table 1 Detection efficiencies with air matrix (ε 0 )

Radionuclide Energy (keV) Detection efficiency (ε0)

There are some comments based on the above results:

- The difference between soil, water and epoxy resin in compare with air samplesincreases when densities of matrices increase This can be explained when we know that if

Fig 3 Efficiencies at density 0.5 g/cm 3

Fig 4 Efficiencies at density 1.0 g/cm 3

Fig 5 Efficiencies at density 2.0 g/cm 3

the density increases, the number of gamma rays can reach detector will decrease (because

of losing more energy by interacting with matrix), so the efficiency will decrease

- In the energy range below 100 keV, the effect of matrix is more significant than inthe energy range above 100 keV

- With the same density and measuring condition (geometry, volume, energy, ),the efficiencies with different matrices are nearly the same.

With above comments, we can deduce some conclusions: with environmental ples matrices like soil, water and resin, the role of matrix is not important if we just needsuitable accuracy (no need high accuracy) Therefore, when measuring with high energyabove 100 keV, the matrix correction between measured and standard samples can beneglected So, the standard sample preparation will be easier, saving time and cost toobtain the acceptable results

sam-III.2 Self-absorption correction

The self-absorption correction factor is determined by the ratio of efficiencies withand without self-absorption effect:

f = ε

ε0

(2)where f is self-absorption correction factor, ε is efficiency with self-absorption effect, ε0

is efficiency without self-absorption effect

Different environmental samples usually have different matrices This will be theobstacle for measuring with large number of samples In this part, the investigation of f

by simulation of soil matrix with different densities in the range from 0.5 to 2.0 g/cm3

wascarried out to figure out the dependence of detection efficiency on density and energy withthe same measuring geometry Based on that, when measuring the activity of sample withany density in the investigated range, we use this correction factor to calculate detectionefficiency

Table 2 presented the calculated results obtained from simulation of self-absorptioncorrection factor f of soil sample with energy E and density ρ

Based on the dependence of f on E as in Fig 6, we can approximate f for energy

E as follow:

With different densities, fitting values of f for E, we got the parameters a, b and c.With a, b, c obtained from different densities in the investigated range, we realizedthat a, b and c depend linearly on ρ, so the fitting of a, b, c to ρ was carried out [2] Theobtained results were:

sup-Table 2 Self-absorption correction factor of soil sample

E (keV) Self-absorption correction factors f at densities ρ

Fig 6 The dependence of factor f on energy and density of soil matrix

Marinelli beaker with the same geometry as the simulation (Fig 2) The sample density

ρ= 1.503 g/cm3, sample was measured for 3 days with HPGe detector

Activities of long-lived radionuclides were calculated by absolute method:

ε(E).θ.m.tm

(7)

A is the source activity at the time of acquisition (Bq/kg), S is the net peak area

of the concerned peak,

ε(E) is the efficiency at energy E, m is sample weight (kg), θ is the branching ratio

of the observed nuclide at this energy E(%), t : the live time of the measurement (s)

Using formulas (4), (5), and (6) to calculate three parameters a, b, and c:

a= −0.0071 × 1.503 − 0.0054 = −0.01607

b= 0.1144 × 1.503 + 0.0710 = 0.24294

c= −0.5067 × 1.503 + 0.7622 = 0.00063After that, using formula (3) to obtain self-absorption correction factor f

Applying formula (1) to calculate the detection efficiencies without self-absorption

ε0 The actual efficiencies were calculated by formula (2)

Calculated results were presented in Table 3

Table 3 Detection efficiencies at some investigated energies of standard sample