Solid-state lasers pumped by continuous-wave diode lasers can be Q-switched to obtain high peak power output pulses. The dependence of laser-pulse energy, average output power, peak power, and pulse width on pulse-repetition frequency in Q-switched Nd:YAG and Ho:YLF lasers is determined and compared. At low pulse repetition rates, the much longer upper-stage lifetime in Ho:YLF gives a distinct advantage. At higher pulse rates, the overall laser efficiency and the stimulated emission cross section are more important parameters, leading to an advantage for Nd:YAG. The results are of significance for designing lasers for use in space optical communications and remote sensing systems

Cowles, K.

Hemmati, H.

Marshall, W. K.

English

NASA Technical Reports Server

N89-20345 
TDA Progress Report 42-95 July-September 1988 
Performance of Efficient Q-Switched Diode-Laser-Pumped 
Nd:YAG and Ho:YLF Lasers for Space Applications 
W. K. Marshall, K. Cowles, and H. Hemmati 
Communications Systems Research Section 
Solid-state lasers pumped by continuous-wave diode lasers can be Q-switched to obtain 
high-peak-power output pulses. In this article, the dependence of laser-pulse energy, aver- 
age output power, peak power, and pulse width on pulse-repetition frequency in Q-switched 
Nd:YAG and Ho: YLF lasers is determined and compared. A t  low pulse-repetition rates, 
the much longer upper-state lifetime in Ho:YLF gives a distinct advantage. A t  higher 
pulse rates, the overall laser efficiency and the stimulated emission cross section are more 
important parameters, leading to an advantage for Nd:YAG. The results are of sgnifi- 
cance for  designing lasers for  use in space optical communications and remote sensing 
systems. 
1. Introduction 
Diode-laser-pumped solid-state lasers such as neodymium: 
yttrium aluminum garnet (Nd:YAG) and holmium: yttrium 
lithium flouride (Ho:YLF) are prime candidates for laser- 
light sources for use in deep-space optical communications and 
other applications. Due to the long upper-state lifetimes of the 
Nd3+ and Ho3+ ions doped into the YAG and YLF crystals, 
the energy storage capacity of such laser materials is quite 
high. Using a technique such as Q switching or cavity dumping, 
the stored energy can be extracted in the form of short laser 
pulses with high peak power. (This form is optimal for direct- 
detection optical communications use.) The pulse-repetition 
rate is controllable using an electro-optical or acoustical- 
optical device for Q switching. 
A laser Q switch is effectively an intracavity shutter-when 
the Q switch is closed, optical pumping continues, but stimu- 
lated emission does not occur. During this time, energy is con- 
tinuously stored in the upper laser level. When the Q switch is 
suddenly opened, the stored energy is released in the form of 
a “giant pulse” of laser light, depleting the upper laser level. 
The next laser pulse occurs only after a sufficient population 
of ions is again placed in the upper laser level. 
Efficient diode-pumped continuous-wave (CW) Nd : YAG 
[ l ]  and Ho:YLF [2] lasers were first demonstrated at JPL. In 
this article, the expected output power and pulse character- 
istics of diode-pumped, Q-switched (pulsed) Nd:YAG and 
Ho:YLF lasers are analyzed. In Section I1 below, the basic 
theory needed to  calculate the results of interest is given. In 
Section 111, the factors relevant to a comparison of Q-switched 
lasers are explicitly considered. In Section IV, the results are 
applied to  specific laser examples. 
II. Basic Theory 
The most important factor determining the pulse shape and 
pulse energy in a Q-switched laser is the population inversion 
168 
https://ntrs.nasa.gov/search.jsp?R=19890010974 2020-03-20T03:52:33+00:00Z
density’ of the lasing medium just prior to the opening of 
the Q switch. In this section, we summarize the basic theory 
[3] for determining population inversion, power output, and 
pulse width in a CW-pumped, Q-switched laser. 
In a series of periodic laser pulses, the population inversion 
density of the initial state (i.e., just before a laser pulse), ni ,  
depends on the inversion density of the final state (i.e., just 
after the preceding laser pulse), nf ,  and on the amount of 
pumping that occurs during the period between the laser 
pulses, according to the equation 
where f is the pulse-repetition frequency and rS is the upper- 
laser-level spontaneous decay time. This equation is for con- 
tinuous pumping at a uniform rate. The asymptotic density, 
n, , depends on the pumping rate and is the maximum achiev- 
able inversion density (approached when l/f >> rs). The value 
of n, can be calculated from knowledge of the CW output 
power, P c w ,  obtained when the cavity Q is maintained at its 
maximum value: 
Here, hv is the photon energy, and V is the effective lasing 
volume, n,,, is the threshold inversion density, and q is the 
output coupling factor. The latter two quantities are given 
[41 PI by 
(3) 
In rl 
In g2 t In rl + In r2 - 2p1 v =  (4) 
for stimulated emission cross section u, length of laser rod I ,  
Q-switch maximum single pass transmission E, reflectivities of 
output and rear mirrors, rl and r2,  respectively, and laser-rod- 
loss coefficient 4. 
The population inversion just after the laser pulse, np is 
given2 by the (transcendental) equation 
ni - nf = nrh ln(ni/nf) (5) 
This equation, together with Eq. (1) above, determines the 
values for ni and nf for a given set of conditions. Once the 
change in the population inversion ni -nf is known, the 
energy per pulse is given simply by 
The average power output from the laser is then 
The pulse shape is determined by the laser rate equations. 
From those equations, the peak laser power is found [3] to be 
- (+I] ni-n, ,  [ 1 t In ( - ni)]/ (8) 
1 *th 
‘peak  - 
where tR is the round trip cavity time. Since tR = 2L/c where 
L is the cavity optical path length and c is the speed of light, 
a significant consequence of the equation for Ppeak is that the 
peak output power of a Q-switched laser is inversely propor- 
tional to the cavity length. 
111. Comparison of Lasers 
Consider first the energy per pulse, Epulse. Use of Eqs. ( l ) ,  
( 2 ) ,  and (6 )  gives 
where P- = (n, - n,h)/n,h andSf=(nrh - nf) /n th .  The vari- 
ables 3, and Ff are normalized versions of their “unhatted” 
counterparts, and have ranges0 <R, <-, and 0 <Rf< 1 (i.e., 
the final inversion density is less than the CW laser threshold). 
The exact value of ?$ can be determined only by solving 
Eqs. (1) and (5) numerically. Alternatively, we note from the 
‘The inversion density, n, is the difference between the population 
density of the upper laser level and that of the lower laser level. 
2Subject to the approximation that the effect of pumping during the 
laser pulse is negligible. 
169 
form3 of Eq. ( 5 )  that Zf < q.. Since Pi < I?- by definition, 
0 <Pf<Zw and hence the rightmost factor in Eq. (9) ranges at 
most between 1 and 2. 
Thus, within a factor close to unity, Eq. (9) says that the 
energy per pulse for a Q-switched laser depends only on the 
laser’s CW output power level, the upper-state lifetime for the 
laser, and on the pulse-repetition frequency, and not on other 
factors such as the laser-stimulated emission cross section or 
the passive characteristics of the laser cavity. 
For high pulse rates f >> I / T ~ ,  Eq. (9) reduces to Epulse 
Pcw/f ,  i.e., effectively the laser’s CW power is collected over 
the pump time l/f and emitted as a short pulse. For low pulse 
rates, the pulse energy saturates as the pumping time becomes 
long compared to  the “storage time” 7,. In this latter case, 
Eq. (9) reduces to Epulse Pcw7s. 
Also of significance in comparing two lasers are the respec- 
tive pulse widths. The laser pulse width limits the modulation 
alphabet size, limits the ability to  reduce background light by 
narrowing the signal slot width, and (in the extreme) limits the 
maximum achievable Q-switched pulse frequency. The pulse 
shape can be determined exactly only by numerically inte- 
grating the laser-rate equations. Here we calculate only an 
estimate (actually a lower bound) for the laser pulse width 
given by 
where Epulse and Ppeak are given by Eqs. (6) and (8) above. For 
high pulse rates such that f >> 1/7 and ni - nth << n t h ,  this 
reduces to 
i.e., the pulse width is directly proportional to the pulse rate. 
For low pulse rates,f << 1 / ~ ~ ,  the pulse width approaches a 
constant (minimum), as both the pulse energy and the peak 
power saturate. This constant value is given by 
where F- is defined above. 
’Equation ( 5 )  can be rewritten as (1 + Ci) - In(1 + Zi) = (1 - zf) 
- h(1- pf), where Gi = (?I,.- n,)/n,. 
IV. Specific Laser Examples 
Now consider and compare Nd:YAG and Ho:YLF lasers 
characterized by a single-mode CW output power of 100 mW 
and a cavity length of 3.5 cm. Other laser parameters are given 
in Table 1. The most significant difference between the two 
lasers is that the lifetime of the upper laser level, 7,, is about 
50 times longer in Ho:YLF than in Nd:YAG. The parameters 
for the 100-mW lasers were chosen to represent the (CW) 
lasers reported in [ I ]  and [2]. Scaling to higher powers is 
considered briefly at the end of this section. 
Figure 1 shows a plot of the energy per pulse, Epulse, (given 
by Eq. (9) with the factor (1 tzf/j?-) set equal to  unity) as a 
function of the pulse-repetition frequency. For both lasers, 
the initial state inversion density saturates as the pumping 
time (l/f) begins to be long compared to the respective upper- 
state lifetimes. The saturation value of the pulse energy is 
(7s X 100 mW); hence, for low pulse rates, the Ho:YLF laser 
pulses are about 50 times larger than those for Nd:YAG. For 
high pulse rates, the pulse energies become asymptotically 
equal. (At intermediate pulse rates, the Ho:YLF pulse energy 
is always larger.) 
Figure 2 shows the laser average output power, Pavg, versus 
frequency. The average power goes to zero for low repetition 
rates, and approaches the CW laser power (100 mW) at high 
pulse-repetition rates. Again, values are always higher for the 
Ho:YLF laser. 
Figure 3 shows the estimate on the laser pulse width given 
by Eq. (10). At low pulse-repetition rates, the Ho:YLF pulse 
width is about three times smaller than the Nd:YAG pulse 
width, due mainly to  the effect of a higher 3- for the Ho:YLF. 
For higher pulse rates (above - lo3 per second), the pulse 
widths are controlled by Eq. (1 1); here, since hv and l / o  are 
smaller for Nd:YAG than for Ho:YLF, the Nd:YAG pulse 
width is smaller by a factor of about 4. In the frequency range 
of IO5  to  lo6 per second (upper right corner of Fig. 3), the 
calculated lower bound on the pulse width for both lasers 
exceeds the pulse interval I/f-the laser will not operate in a 
simple Q-switched pulse mode at those frequencies. 
Now consider a simple scaling example-two I-W lasers. 
(Laser parameters are the same as those given in TabIe 1, 
except Pcw = 1 W.) It can be seen from Eq. (9) that Epulse scales 
linearly with PCw (subject to the validity of the approximation 
tif << Z-). Therefore, values of Epulse (andPavg) for 1-W 
lasers are a factor of 10 larger than those for the 100-mW 
lasers shown in Figs. 2 and 3.  Values for rpulse are smaller for 
the 1 -W lasers than those shown in Fig. 3 for 100-mW lasers. For 
high pulse rates, Eq. (1 1) gives a reduction in pulse width by a 
factor of 10. At lower pulse rates, the reduction is not a linear 
h 
170 
factor-calculated values 
1.6 ns and 3.4 ns for Ho:Y 
( m i n )  
of rPulse 
‘LF and Nd:YAG, respectively. 
for the 1-W lasers are 
V. Conclusions 
The Ho:YLF laser shows promise for use in low-data-rate 
optical communications systems, such as would likely be used 
in an Earth-to-spacecraft uplink in an all-optical communica- 
tion system. At pulse repetition rates below 10 kHz, Ho:YLF 
offers higher performance than Nd:YAC in terms of higher 
energy per pulse for similar CW lasers. The upper-state life- 
time, T ~ ,  is the dominant parameter in determining Q-switched 
pulse energy in this regime. Below 1 kHz, the Ho:YLF also 
offers shorter laser pulse widths. The large value of T~ makes 
it easy to pump Ho:YLF far above threshold, resulting in 
short pulse widths. At higher pulse rates, T~ becomes less 
important in determining the pulse energy. In the extreme, the 
pulse energy approaches P J f ,  and hence for two lasers with 
equal input (pump) powers, the pulse energies depend only on 
the relative CW laser efficiencies. In this regime, Nd:YAG 
offers shorter pulses, due mainly to its higher stimulated emis- 
sion cross section, u. 
Higher CW power lasers lead to proportionately higher 
pulsed-mode output powers, and also to  shorter laser pulse 
widths. Hence for communications systems, the benefit of 
higher-power lasers comes not only from basic transmitter 
power considerations, but also from the ability to limit back- 
ground noise by using shorter communications slot widths. 
An understanding of the parameters affecting pulsed laser 
operation is important in designing communications lasers 
for maximum system performance. 
References 
[ l ]  D. Sipes, “Highly Efficient Neodymium: Yttrium Aluminum Garnet Laser End 
Pumped by a Semiconductor Laser Array,” Applied Physics Letters, 47(2), pp. 74- 
77, July 15, 1985. 
[2] H. Hemmati, “Efficient Holmium: Yttrium Lithium Fluoride Laser Longitudinally 
Pumped by a Semiconductor Laser Array,” AppliedPhysics Letters, 5 1(8), pp. 564- 
565, August 24,1987. 
[3] W. Koechner, Solid-Stare Laser Engineering, Chapter 8 ,  New York: Springer-Verlag, 
[4] G .  D. Baldwin, “Output Power Calculations for a Continuously Pumped Q-Switched 
YAG:Nd+3 Laser,” IEEE Journal of  Quantum Electronics, vol. QE-7, no. 6,  pp. 220- 
224. June 1971. 
pp. 397-408,1976. 
171 
Table 1. Parameters for Nd:YAG and Ho:YLF lasers of Section IV 
Parameters Nd:YAG Ho:YLF 
100 
0.23 
1.064 
0.02 
1 .o 
3.5 
0.975 
1.00 
0.987 
0.0023 
8.7 x 10-19 
100 
12 
2.06 
0.02 
1 .o 
3.5 
0.95 
1 .oo 
0.987 
0.0023 
1.0 x 10-l9 
172 
c -3 
I \ Ho:YLF - w 
W 
z W 
w \ 
-- Nd:YAG (x 10) '. >\--  105 106 
100 101 102 103 104 
PULSE-REPETITION FREQUENCY, f, Hz 
Fig. 1. Output energy per pulse, Epu,=, in mJ, versus pulse 
repetition frequency, f, in Hz, for Nd:YAG and Ho:YLF lasers 
described in Table 1. The curve marked Nd:YAG (X10) is the 
Nd:YAG curve multiplied by a factor of 10 for clarity. 
0.101 1 I 
0.06 c / no: Y Lk / 
PULSE-REPETITION FREQUENCY, f, Hz 
Fig. 2. Average output power, Pa,, versus pulse repetition 
frequency, f, for lasers of Table 1. 
1 I I I 1 
v) 
i 
- w 101 
a 
w y 10-1 
2 
10-2 2 
LT 
10-3 1 I I I I I I 
100 101 102 103 104 105 106 
PULSE-REPETITION FREQUENCY, f, Hz 
Fig. 3. Laser pulse width, t ,,,-, versus pulse repetition frequency, 
f, for fasers of Table 1. 
173 


Performance of efficient Q-switched diode-laser-pumped Nd:YAG and Ho:YLF lasers for space applications

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server