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Repetitive modulation and passively Q-switched CW diode pumped Nd-doped lasers
Optical Materials 19 (2002) 149–159 www.elsevier.com/locate/optmat
Repetitive modulation and passively Q-switched CW diode pumped Nd-doped lasers Karol Waichman a
a,*
, Yehoshua Kalisky
b,1
Laser Department, Atomic Energy Commission, Nuclear Research Center – NEGEV, P.O. Box 9001, Beer Sheva 84190, Israel b ‘‘Arava’’ Laser Laboratory, Rotem Industrial Park, Mishor Yamin, D.N. Arava 86800, Israel
Abstract We have used diode arrays in a linear configuration to side-pump passively Q-switched and free-running Nd:YAG and Nd:YVO4 lasers. The gain modes of the high absorption YVO4 and the low absorption YAG were analyzed and compared. The gain distribution found was used to evaluate the pump power density, which in turn, was used to calculate the dependence of the laser pulse width on the pumping power. The theoretical Q-switch pulse width was compared with the experimental. The performance of the Q-switched and free-running Nd:YAG and Nd:YVO4 lasers were compared and analyzed. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Diode pumped solid-state lasers based on Nddoped crystals such as YAG and YVO4 have been extensively developed. They are now available as compact, efficient sources both in the 1.06 lm and the frequency doubled wavelength of 532 nm. CW diode pumped solid-state lasers have been sought for various scientific, medical and military applications, where compact, reliable, stable, and highly efficient sources are desirable. Passive Q-switching using inorganic-doped ions such as Cr4þ -doped
*
Corresponding author. Tel.: +972-7-6568367. E-mail addresses: [email protected] (K. Waichman), [email protected] (Y. Kalisky). URL: http://magnet.consortia.org.il/Magnet/English (Y. Kalisky). 1 Tel.: +972-7-6556301. Supported partially by the ‘‘MAGNET’’ program of the Chief Scientist Office at the Israeli Ministry of Industry and Trade.
garnets has an added value in this respect. There are several applications such as fiber optics sensing, or range finding, which require short bursts of high peak power densities, at multi kilohertz repetition rates, and good beam quality [1]. The Nd:YAG has several advantages that helps in scaling up the pump power and consequently increasing the output power. These are the relatively high absorption coefficient (a 8 cm1 at 808 nm for 1.1 at.% of Nd), high thermal conductivity and the capability to grow large crystals, hence, increasing the pumping area. The Nd:YVO4 (1 at.%) is also suitable for both end and side diode pumping schemes. In comparison to Nd:YAG, it has a wider absorption bandwidth (10–12 nm relative to 2–3 nm, FWHM), higher stimulated emission cross-section, and higher absorption coefficient in the spectral range which corresponds to the pumping wavelength of the available commercial diodes. The Nd:YVO4 crystal is less sensitive to diode wavelength variation due to its wide
0925-3467/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 3 4 6 7 ( 0 1 ) 0 0 2 1 3 - 0
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absorption bandwidth. Therefore, more degrees of freedom in diode temperature control and extended diode lifetime is obtained. The matching between the pump mode, which geometry is determined by the pump source and the nature of the crystal, and the laser TEM00 mode, determined by the resonator plays an important role in the laser performance [2–4]. Longitudinal pumping where the pump radiation can be matched by appropriate focusing to the TEM00 laser mode seems the ‘natural’ method for diode pumped solid-state lasers. In fact, optical efficiencies near and above 50%, depending on the pumping scheme, were measured for longitudinal pumping [5,6]. However, end pumping is limited to mid power levels because of the difficulties in scaling the pump system to include several diode bars and due to power delivery limits of the optical fibers. Side pumping has the advantage of simpler scaling for high power operation by adding up pumping elements in various configurations along the laser rod. This include linear arrays [7], stacked arrays [8] and distribution of diode lasers around the rod perimeter [9,10]. A significant drawback of the side pumping is the mismatch between the gain mode and the TEM00 mode. Various schemes were developed to improve the mode matching including reflective coating of the side walls of the laser rod [11–13] and employing various pumping diodes configurations [9,14]. For the Q-switched laser the pump absorption profile dominates not only the laser beam spatial profile but the temporal pulse evolution as well. The pulse width of the Q-switched spike depends on the initial population inversion density of the excited states [15,16]. For example, the pulse width for negligible parasitic losses in a resonator consisting of a medium with uniformly distributed gain is given by: s¼
S P lR lnðni =nf Þ ; c ni 1 lnðni Þ
ð1Þ
where s is the pulse width, SP is a number that characterizes the pulse shape, lR is the length of the resonator and c is the speed of light. ni and nf are the pre- and post-pulse population inversion densities, respectively, normalized with respect to the threshold inversion density. The pulse width is
very sensitive to the pump power density at low pumping powers. For example, according to Eq. (1), increasing the normalized initial population inversion, ni , from 1.1 to 1.4 results in a decrease of the pulse width by more than a decade. The time dependent models applied for the analysis of Q-switched lasers usually assume uniformly distributed initial inversion density (or small signal gain) in the pump volume [17,18]. This assumption should be applied with caution, since, whereas the total pump power is usually known, the actual gain volume is not. This is especially true for side pumping where the gain profile depends both on the geometrical arrangement of the diodes and on the absorption profile of the laser rod and hence it is hard to estimate beforehand the gain profile shape and the gain volume. Since the pulse width depends on the initial inversion density which in turn depends on the pump energy density, it is of importance to characterize the pump absorption profile in order to estimate the pulse width. In this study we examined passive Q-switched operation for the most basic of the side pumping schemes, i.e., a single diode bar or a linear array of bars pumping a laser rod by a single pass absorption. The rate equations for the excited states for the calculation of the temporal development of a Q-switched laser pulse are presented in Section 2. The experimental setup is described in Section 3. In Section 4 we present the measured gain profiles for Nd-doped YAG and YVO4 systems and the laser beam distribution for YVO4 . Based on the measured gain mode profile we found the pump energy density and use it to calculate the laser pulse widths and to compare it to the experimental.
2. Modeling the Nd:YVO4 Q-switched laser pulse temporal development The theoretical model consists of the rate equations for the population inversion density and for the photon density in the resonator [17]. A cross-section of the laser rod is shown schematically in the upper part of Fig. 1, in the x–y plane depicted. It was assumed that for the side pumping employed the pump power and hence the population inversion density are uniform along the
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151
dN N ¼ ccrN U ; dT sf
ð2Þ
dU lM U ¼ crN U ; dT lR tc
ð3Þ
where T is the time, c is the inversion reduction factor [15,17,19], r is the effective stimulated emission cross-section, sf is the fluorescence decay time of the upper level, lM is the length of the active medium, lR is the length of the laser cavity and tc is the decay time of photons in the resonator due to outcoupling, absorption and scattering [20]: tc ¼
Fig. 1. The experimental setup, components identifiers explained in the text. Above: the cross-section of the laser rod and the gain mode.
optical axis, Z. Furthermore, we assumed that the effective cross-section of the gain volume, is an ellipse which area is pwp hp , where wp is the gain half width at 1=e2 height of the long axis, and hp is the gain half width at 1=e2 height along the short axis. As it will be demonstrated in the experimental results, the pumping power affects the width of the pump beam profile and thus the pump power density is not linearly dependent on the pump power. According to Eq. (1), the laser pulse time duration depends on the population inversion density, which in turn depends on the pumping power density. We will introduce the experimental dependence of the pump power density on the pump power in the rate equations. Since the laser pulse widths measured are much higher than the saturation time constant of the saturable absorber Q-switch, the rate equation for the Q-switch population inversion is omitted. The rate equations for the population inversion density, N, and photon density in the resonator, U, are given by:
2lR 1 ; c 2alM þ e ln R
ð4Þ
where a is the absorption coefficient per unit length of the medium, e are the losses in the resonator and R is the reflectivity of the coupling mirror. The Q-switch pulse duration is very short, therefore the spontaneous emission contribution to the intensity and the optical pumping terms were omitted from Eqs. (2) and (3). In addition, it was assumed that the inversion reduction factor, c, in Eq. (2) is 1. It was found [19] that the value of the inversion reduction factor in the range 0.9–1 results in best fit of a model to experimental results. An ‘effective’ stimulated emission cross-section, r was used in Eqs. (2) and (3) due to the fact that only some of the Stark sublevels in the 4 F3=2 upper multiplet participate in lasing. The effective cross-section is: r ¼ fa rs , where fa is the equilibrium fractional Boltzmann occupation factor of the upper laser level within the upper multiplet and rs is the spectroscopic stimulated emission cross-section. The initial condition at T ¼ 0 for the inversion density depends on the pumping power: Ni ¼
P P s f gP ; ðhc=kp Þ VP
ð5Þ
where gP is the pump coupling efficiency consisting of the optical coupling efficiency, mode overlap and the Stokes factor kp =kl , where kp is the pump wavelength and kl is the laser wavelength. h is the Planck constant, and VP ¼ pwp hp lM is the gain mode volume. A small initial value Ui for the photon density was used to initiate the calculation. The choice of Ui affects merely the timing of the laser pulse relative to an arbitrary T ¼ 0.
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The rate equations will be presented in dimensionless form by normalizing N ; U and T, as follows [17]: n ¼ N =Nthr , / ¼ U=U0 , t ¼ T =tc . The normalizing factor for the population inversion density, Nthr , which is the threshold density, is derived by putting dU=dT ¼ 0 in Eq. (3): Nthr ¼
lR crlM tc
ð6Þ
and the normalizing factor for the photon density is: U0 ¼ Nthr ðlM =lR Þ. The final form for the rate equations becomes: dn tc ¼ n/ n ; dt sf
ð7Þ
d/ ¼ ðn 1Þ/: dt
ð8Þ
3. Experimental For the side pumping used in our experiments the pump laser diode array was an OPC A020-808CN, CW laser diode array, with a nominal 20 W output power centered at 808 nm under normal operating conditions. The temperature of the diode was maintained at a constant temperature of 21 0:5 °C by a chiller. The emission center wavelength and spectral width (FWHM) are 805– 809 nm and 2.5–3 nm, respectively, at operating currents of 20–30 A. This corresponds to approximate power levels, ranging from 8 to 15 W of output power of the diode array. The 808 nm laser diode emission was coupled to the laser rods by means of a cylindrical microlens. The resulting pump sheet was a collimated beam with a rectangular cross-section of approximately 10 0:1 mm at the intersection with the rod. Two laser media were studied, unpolished Nd:YVO4 (/3 7 mm, AR/AR coated at 1.06 lm, 1.0 at.%) and a polished Nd:YAG (/3 50 mm, AR/AR coated at 1:06 lm, 1.1 at.%). For the long Nd:YAG rod, three diodes mounted alongside each other were used for the side pumping, hence, the effective length of the gain medium was 30 mm. The rods were mounted on a heat sink water cooled to 21 °C. The experimental setup is
shown schematically in Fig. 1. The pump beam propagates parallel to the x axis and the laser beam parallel to the z axis, the origin of the x–y plane coincides with the laser rod axis of symmetry. The components layout is similar for the three types of measurements, e.g., pump mode fluorescence, free-running laser and Q-switched laser. For the pump mode fluorescence measurements the components layout was as follows: (1) was a CCD camera, (2) were neutral density filters used for attenuation and the back mirror (3) was blocked. For the free-running laser mode, (1) was a power meter for the average power measurements, (2) was an output coupler with R ¼ 85% and radius of curvature, ROC ¼ 5 m and (3) was the laser resonator flat back mirror. For passive Q-switch operation a Cr4þ :GGG element (3 mm thickness, 0.3 at.% of Cr4þ ) was used both as saturable absorber and as a rear mirror (3). The low intensity transmission of this element was T0 88%, it was AR coated @1.064 lm on the front side and HR @1.064 lm on the back side. For this mode of operation the laser pulses were detected by a fast silicon photodiode (1), with risetime <1 ns.
4. Results 4.1. Nd–YVO4 and Nd–YAG gain mode profiles The shape of the gain profile controls the pump power density and the spatial overlap between the gain mode and the laser mode. For various pumping powers, Pp , we measured the pump fluorescence distribution on the laser rod face, representing what we believe to be the x–y gain mode distribution at every section z of the rod length. Figs. 2–5 show the pumping mode characteristics of the side pumped Nd–YVO4 rod. Fig. 2 is a picture taken with the CCD camera of the fluorescence emitted from the face of the rod due to the side pumping, representing the gain mode for Pp ¼ 12:7 W. The rod circumference and the theoretical TEM00 mode of the resonator are outlined in the figure, the pump beam propagates from right to left. Fig. 3 shows the x distribution, along
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Fig. 2. CCD photo of the gain mode in the Nd–YVO4 rod for 12.7 W pumping power. Outlined are the rod circumference and the theoretical TEM00 mode of the resonator.
Fig. 3. Gain mode distribution in the Nd–YVO4 rod in x direction.
the propagation of the pump radiation, of the gain mode. The x distance is normalized with respect to the rod diameter, D, thus the pump light enters the rod at x=D ¼ 0:5. The pump energy is completely absorbed at x=D 0:1, i.e., within 0.6 diameters of the rod. Fig. 4 shows the distribution of the pump fluorescence in the y direction, which is perpendicular to the x–z plane. The gain mode distribu-
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Fig. 4. Gain mode distribution in the Nd–YVO4 rod in y direction.
Fig. 5. Changes in wp and hp as a function of the pumping power.
tion in this direction resembles a Gaussian distribution. Here also, the y distance is normalized with respect to the rod diameter and y=D ¼ 0 coincides with the rod axis of symmetry. Fig. 5 shows the half width of the gain mode (at 1=e2 of the peak energy) in both directions as a function of the pumping power.
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As seen in Fig. 5, the gain half width at 1=e2 height in the x direction, wp , did not vary by more than 3% for pumping powers above laser threshold (Pp > 8 W). On the other hand the 1=e2 half width in the y direction, hp , increased monotonically with the increase in pumping power. This anisotropy of the gain distribution is accounted for asymmetric characteristics of the crystal, namely, orientation dependent absorption coefficients and refraction indices. A linear fit, used later for the laser pulse width calculations, could be found for the dependence of hp on Pp . Mean values for the pump mode dimensions were thus hp wp ¼ 150 750 lm whereas the calculated laser beam TEM00 waist, x0 , of the YVO4 medium resonator was 500 lm. Figs. 6–8 show the pumping mode characteristics of the side pumped Nd–YAG rod. Fig. 6 shows the CCD picture of the gain mode for 12.7 W pumping power. As in Fig. 2, the rod circumference and the theoretical laser TEM00 mode, with x0 400 lm, are outlined, the pump beam propagates from right to left. Figs. 7 and 8 show the x and y distributions, respectively, of the pump fluorescence. Under the normal operation conditions the Nd–YAG rod was pumped by three diodes mounted side by side. It was impossible to take the real gain profiles in this mode since the fluorescence due to the diode arrays far from the camera was dispersed in the rod thus obscuring
Fig. 7. Gain mode distribution in Nd:YAG rod in x direction.
Fig. 8. Gain mode distribution in Nd:YAG rod in y direction.
Fig. 6. CCD picture of the gain mode in Nd:YAG rod for 12.7 W pumping power, the rod circumference and the theoretical laser TEM00 mode are outlined.
the gain profile. Therefore, for the gain distribution measurements only one diode was used, it was located near the edge of the rod close to the camera. The pumping wavelength varied as a function of the diode current from 805 to 809 nm at 20–30 A of the diode current, respectively, which corresponds to 10–15 W pumping power. This wavelength variation changes the gain profile in YVO4
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by 30% and in YAG by 50%. Since the absorption in YVO4 is approximately four times higher than in YAG the effect of wavelength shift on the gain profile in YVO4 is more significant and therefore observable in the experiment. Also, we should mention that the asymmetric shape of the gain profile in YVO4 and the difference between the dependences of hp and wp on the pump power is a result of different absorption coefficients along different crystallographic directions of the a-cut Nd:YVO4 crystal. The absorption at the pump wavelength of the Nd:YAG is smaller than that of the YVO4 , this fact is demonstrated in Fig. 7 which shows that only a fraction of the pump energy is absorbed along the pump beam propagation. As a result, wP was approximately equal to the rod radius for all pumping powers. Measuring the half widths at 1=e2 of the peaks in Fig. 8 indicates that for the YAG case hp was almost independent on the pump power, it was approximately 180 10 lm. Fig. 8 shows also that the position of the peak of the pump mode in the y direction drifted towards the rod perimeter as the pump power was increased. This drift of the pump mode location accounts for the fact that the laser resonator has to be realigned for each pumping power. Table 1 provides a summary of the pump mode geometry in comparison to x0 for both laser media. We can express the matching between the fundamental resonator mode and the gain mode by the gain mode aspect ratio, wp =hp , where wp =hp ¼ 1 represents a good match. From the table it follows that the mode matching of the Nd:YVO4 is superior to that of the Nd:YAG.
155
doped YVO4 and YAG media will favor the higher-order transverse modes of the laser. The TEM00 mode, which builds up the fastest, soon saturates the gain mode volume it occupies giving rise to the buildup of higher-order modes in the not yet saturated parts. Fig. 9 shows the three dimensional representation of the YVO4 laser near field beam profile for 15 W incident pumping power. The figure represents the beam profile for the resonator aligned for maximum laser power. Fig. 10 demonstrates the mode structure sensitivity to the cavity mirrors tuning, by showing the near field contour plots of two different mode structures. Fig. 10(a) shows the contour plot of the multimode, up to TEM20 , beam depicted in Fig. 9. Fig. 10(b) shows a single mode operation obtained by tuning the resonator and consequently loosing 10% of the output power. Fig. 11 shows the power of the Nd–YAG laser and the Nd:YVO4 laser in the free-running mode of operation. Due to a shift in the gain mode location within the rod, as a function of the pump power, both laser resonators were optimized for maximum output power at each pumping power. A maximum average power of 2.5 and 10 W was measured for the Nd:YVO4 and Nd:YAG lasers, respectively. Notice that the slopes for both
4.2. Free-running lasers Due to the structure of the gain modes, as depicted in Figs. 2 and 6, it is expected that both NdTable 1 Pump mode geometry in comparison to the resonator mode waist for Nd:YAG and Nd:YVO4 laser media
x0 ðlmÞ hP ðlmÞ wP ðlmÞ
Nd:YAG
Nd:YVO4
400 180 1500
500 150 750
Fig. 9. 3D representation of the YVO4 laser near field beam profile for Pp ¼ 15 W.
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(a)
lasers in the figure are comparable since for both cases the laser power axis scale equals 0.2 times the pump power axis scale. For moderate pumping powers the slope efficiency of the Nd:YVO4 was marginally higher than that of the Nd:YAG: 40% and 35%, respectively. As the pumping power was increased beyond 12 W, the Nd:YVO4 laser showed a decline in the output power. The roll-off in the laser power for high level pumping was due to thermally induced distortions in the laser rod and the associated lensing and birefringence [21,22]. Because of the low pump absorption of the YAG no decline in laser power was noticed even at the highest pumping powers. 4.3. Passively Q-switched lasers
(b) Fig. 10. Near field contour plots of the YVO4 laser for two different mode structures at Pp ¼ 15 W. (a) multimode, up to TEM20 , beam depicted in Fig. 9; (b) single mode operation.
Fig. 11. Average laser power of free-running Nd–YAG and Nd:YVO4 lasers as a function of pumping power.
We have tested diode-pumped Nd:YAG and Nd:YVO4 lasers for passive Q-switched operation, when both systems were side-pumped. The passive Q-switch element was Cr4þ :GGG. When the Qswitching back mirror was used, a continuous sequence of pulses was generated. The pulse repetition rates were in the kHz frequency domain. Time and amplitude fluctuation were less than 10%, and exhibited disordered behavior with main average modulation frequency and associated sidebands. The pulse train of the Q-switching showed instabilities both in amplitude and frequency. Qualitatively it can be interpreted as a result of dynamic processes in the saturable absorber (such as excited-state absorption, and fast decay within vibronic levels) or excitation of polarization eigenmodes due to thermal-induced birefringence. The jitter in time and amplitude are a result of temperature gradients generated and consequently, thermal-induced birefringence in the laser rod. To demonstrate the passive Q-switching under high thermal load, we pumped Nd:YAG (/3 50 mm) laser rod by three diode arrays, at total input power of 50 W. The results using this system indicated modulation (which depends on the pumping energy) in the 10–50 kHz frequency domain. In the past we reported [7] that the average modulation frequency of YVO4 which changed from 225 to 410 kHz when the diode pump power
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was increased from 10 to 15 W, respectively. The difference in the average modulation frequency between YAG and YVO4 is accounted for the short lifetime of the 4 F3=2 lasing level of Nd-doped YVO4 relative to YAG. The lower thermal conductivity of YVO4 relative to YAG, 5.2 and 11 W/(m K), respectively, also limits the use of excessive pumping power for the YVO4 . Our results are consistent with the results reported by Agnesi et al. [23]. Fig. 12 shows the average output power for Qswitch operation as a function of the pump power for both media. A maximum average power of 0.8 and 4.2 W was measured for the Nd:YVO4 and Nd:YAG lasers, respectively. In the Q-switch mode both lasers output powers exhibited roll-off at certain pumping powers. The slope efficiency of the Nd:YVO4 laser decreased from 0.18 at low pumping power to 0.12 for pumping power beyond 12 W, which was also the roll-off point for the free-running case. The slope efficiency of the Nd:YAG laser declined from 0.25 to 0.13 at 30 W pumping power. Since we did not observe a parallel reduction in the slope efficiency for the free-running Nd:YAG laser, it can be attributed to thermal effects in the saturable absorber back mirror. We believe that by a proper heat removal from both the saturable absorber and the laser rods, laser performance for both Nd:YAG and Nd:YVO4 can be improved. Before the onset
Fig. 12. Average laser power of Q-switched Nd–YAG and Nd:YVO4 lasers as a function of the pump power.
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of the thermal effects, the conversion efficiencies of the Q-switched average power, relative to freerunning mode of the Nd:YAG and Nd:YVO4 lasers, respectively, were 70% and 45%. In what follows we discuss the effect of the pump power on the Q-switched pulse width. The pulse width of the Q-switched spike is reduced with the increase of the diode pumping power [15,16]. We measured the average pulse width of the Q-switched Nd:YVO4 laser as a function of the pumping power and compared our results to the results of a theoretical calculation. The following data was used for the Nd–YVO4 laser calculation: r ¼ 8:2 1023 m2 , sf ¼ 0:98 104 s, gP ¼ 0:15, lM ¼ 7 mm, lR ¼ 150 mm, kl ¼ 1:064 lm, kp ¼ 0:808 lm, R ¼ 0:85. Eqs. (7) and (8) were solved for various Pp with the appropriate hp (Pp ) derived from Fig. 5 for each pumping power. The full pulse widths at half of the maximum / are presented in Fig. 13 along with the measured pulse widths of the Nd–YVO4 laser. In order to comprehend the measured dependence
Fig. 13. Calculated and measured Q-switch laser pulse HWHM of the Nd–YVO4 laser as a function of pumping power. Inset shows calculated and measured temporal evolution of a laser pulse for 15 W pumping power.
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of the pulse widths on the pumping power of Fig. 13, one has to assume that ni , which is proportional to the pumping density, does not change linearly with pump power. Our earlier finding, namely, that for the Nd–YVO4 laser the pump mode spot size increases with the increase in pumping power is consistent with the results of Fig. 13. 4.4. End pumping End pumping is used in the case where efficient operation with good beam quality is required. For this study we pumped longitudinally Nd:YAG and Nd:YVO4 lasers. The laser in both cases was optimized for various output couplers. Both results were obtained using output coupler of R ¼ 95% with ROC ¼ 150 mm. This configuration is also necessary to obtain overlap between the cavity mode and the pump spot. The total optical efficiency of Nd:YAG laser in this configuration is 54%. For the study of the Q-switching performance of CW diode-pumped Nd:YAG and Nd:YVO4 lasers, we used Cr4þ :YAG saturable absorber as the Q-switching element. The sample had low intensity transmission of T0 47%. Qswitching and repetitive modulation of diodepumped Nd-doped crystals were observed when Cr4þ :YAG disk was inserted inside the cavity. For Nd:YVO4 , the mean modulation frequency obtained by FFT analysis had values ranging from 60–100 kHz, at input pump power of 7.3 W. The mean frequency was reduced to 18 kHz at 5.5 W input power level. However, the pulsewidth (FWHM) exhibited the same average value of 100 10 ns at these power values. In the case of diode-pumped Nd:YAG laser, a different behavior was observed. In the same range of pumping power, the mean modulation frequencies obtained varied from 7 to 12 kHz. In the same pumping power, the pulsewidth (FWHM) was shorter than for Nd:YVO4 , namely, 60 ns.
5. Summary CW diode-side-pumped free-running and passively Q-switched Nd:YAG and Nd:YVO4 at rel-
atively high pumping power levels were investigated. The gain mode profiles for both media were measured as a function of the pump power. It was found that for the Nd:YVO4 , which totally absorbed the pumping radiation, the gain mode volume increased with the increase in pumping power. For moderate pumping powers the slope efficiencies of the Nd:YVO4 and the Nd:YAG lasers in the free-running mode were 40% and 35%, respectively. For the passive Q-switch operation using inorganic saturable absorber, we found a decrease in the slope efficiency due to thermal effects both in the laser rods and the saturable absorber. The Nd:YAG medium absorbed little of the pump power and thus in the free-running mode the Nd:YAG laser was not affected by thermal effects. On the other hand, the Nd:YAG laser emits high power, thus, in the Q-switch mode the saturable absorber was affected by the absorbed laser power and the efficiency decreased. The conversion efficiencies of the Q-switched average power, relative to free-running mode of the Nd:YAG and Nd:YVO4 lasers, were 70% and 45%, respectively. We studied theoretically and experimentally the dependence of Q-switched Nd:YVO4 laser pulse width on the pump power. It was confirmed that the pump power density deposited in the laser rod is less than linearly proportional to the pumping power resulting in longer pulse width. References [1] H. Plaessmann, K.S. Yamada, C.E. Rich, W.M. Grossman, Appl. Opt. 32 (1993) 6616; H. Plaessmann, F. Stahr, W.M. Grossman, IEEE Photonics Tech. Lett. 3 (1991) 885. [2] D.G. Hall, Appl. Opt. 20 (1981) 1579. [3] A.J. Alfrey, IEEE J. Quantum Electron. 25 (1989) 760. [4] P. Laporta, IEEE J. Quantum Electron. 27 (1991) 2319. [5] S.C. Tidwell, J.F. Seamans, C.E. Hamilton, C.H. Muller, D.D. Lowenthal, Opt. Lett. 16 (1991) 584. [6] S. Yamaguchi, H. Imai, IEEE J. Quantum Electron. 28 (1992) 1101. [7] Y. Kalisky, S. Levy, L. Kravchik, in: K.I. SchaffersL.E. Myers (Eds.), Laser Material Crystal Growth and Nonlinear Materials and Devices, Proc. SPIE, vol. 3610, 1999, p. 109.
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[16] J.J. Zayhowski, P.L. Kelly, IEEE J. Quantum Electron. 27 (1991) 2220. [17] J.J. Degnan, D.B. Coyle, R.B. Kay, IEEE J. Quantum Electron. 34 (1998) 887. [18] R.S. Afzal, Appl. Opt. 33 (1994) 3184. [19] D.B. Coyle, D.V. Guerra, R.B. Kay, J. Phys. D 28 (1995) 452. [20] W. Koechner, Solid-State Laser Engineering, vol. 1, Optical Sciences, fourth ed., Springer, Berlin, 1996 (Chapter 3.1). [21] M.E. Innocenzi, H.T. Yura, C.L. Fincher, R.A. Fields, Appl. Phys. Lett. 56 (1990) 1831. [22] W. Koechner, Solid-State Laser Engineering, vol. 1, Optical Sciences, fourth ed., Springer, Berlin, 1996 (Chapter 7.1). [23] A. Agnesi, S. Dell’Acqua, C. Morello, G. Piccinno, G.C. Reali, Z. Sun, IEEE J. Quantum Electron. 33 (1997) 45.
Repetitive modulation and passively Q-switched CW diode pumped Nd-doped lasers Karol Waichman a
a,*
, Yehoshua Kalisky
b,1
Laser Department, Atomic Energy Commission, Nuclear Research Center – NEGEV, P.O. Box 9001, Beer Sheva 84190, Israel b ‘‘Arava’’ Laser Laboratory, Rotem Industrial Park, Mishor Yamin, D.N. Arava 86800, Israel
Abstract We have used diode arrays in a linear configuration to side-pump passively Q-switched and free-running Nd:YAG and Nd:YVO4 lasers. The gain modes of the high absorption YVO4 and the low absorption YAG were analyzed and compared. The gain distribution found was used to evaluate the pump power density, which in turn, was used to calculate the dependence of the laser pulse width on the pumping power. The theoretical Q-switch pulse width was compared with the experimental. The performance of the Q-switched and free-running Nd:YAG and Nd:YVO4 lasers were compared and analyzed. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Diode pumped solid-state lasers based on Nddoped crystals such as YAG and YVO4 have been extensively developed. They are now available as compact, efficient sources both in the 1.06 lm and the frequency doubled wavelength of 532 nm. CW diode pumped solid-state lasers have been sought for various scientific, medical and military applications, where compact, reliable, stable, and highly efficient sources are desirable. Passive Q-switching using inorganic-doped ions such as Cr4þ -doped
*
Corresponding author. Tel.: +972-7-6568367. E-mail addresses: [email protected] (K. Waichman), [email protected] (Y. Kalisky). URL: http://magnet.consortia.org.il/Magnet/English (Y. Kalisky). 1 Tel.: +972-7-6556301. Supported partially by the ‘‘MAGNET’’ program of the Chief Scientist Office at the Israeli Ministry of Industry and Trade.
garnets has an added value in this respect. There are several applications such as fiber optics sensing, or range finding, which require short bursts of high peak power densities, at multi kilohertz repetition rates, and good beam quality [1]. The Nd:YAG has several advantages that helps in scaling up the pump power and consequently increasing the output power. These are the relatively high absorption coefficient (a 8 cm1 at 808 nm for 1.1 at.% of Nd), high thermal conductivity and the capability to grow large crystals, hence, increasing the pumping area. The Nd:YVO4 (1 at.%) is also suitable for both end and side diode pumping schemes. In comparison to Nd:YAG, it has a wider absorption bandwidth (10–12 nm relative to 2–3 nm, FWHM), higher stimulated emission cross-section, and higher absorption coefficient in the spectral range which corresponds to the pumping wavelength of the available commercial diodes. The Nd:YVO4 crystal is less sensitive to diode wavelength variation due to its wide
0925-3467/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 3 4 6 7 ( 0 1 ) 0 0 2 1 3 - 0
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absorption bandwidth. Therefore, more degrees of freedom in diode temperature control and extended diode lifetime is obtained. The matching between the pump mode, which geometry is determined by the pump source and the nature of the crystal, and the laser TEM00 mode, determined by the resonator plays an important role in the laser performance [2–4]. Longitudinal pumping where the pump radiation can be matched by appropriate focusing to the TEM00 laser mode seems the ‘natural’ method for diode pumped solid-state lasers. In fact, optical efficiencies near and above 50%, depending on the pumping scheme, were measured for longitudinal pumping [5,6]. However, end pumping is limited to mid power levels because of the difficulties in scaling the pump system to include several diode bars and due to power delivery limits of the optical fibers. Side pumping has the advantage of simpler scaling for high power operation by adding up pumping elements in various configurations along the laser rod. This include linear arrays [7], stacked arrays [8] and distribution of diode lasers around the rod perimeter [9,10]. A significant drawback of the side pumping is the mismatch between the gain mode and the TEM00 mode. Various schemes were developed to improve the mode matching including reflective coating of the side walls of the laser rod [11–13] and employing various pumping diodes configurations [9,14]. For the Q-switched laser the pump absorption profile dominates not only the laser beam spatial profile but the temporal pulse evolution as well. The pulse width of the Q-switched spike depends on the initial population inversion density of the excited states [15,16]. For example, the pulse width for negligible parasitic losses in a resonator consisting of a medium with uniformly distributed gain is given by: s¼
S P lR lnðni =nf Þ ; c ni 1 lnðni Þ
ð1Þ
where s is the pulse width, SP is a number that characterizes the pulse shape, lR is the length of the resonator and c is the speed of light. ni and nf are the pre- and post-pulse population inversion densities, respectively, normalized with respect to the threshold inversion density. The pulse width is
very sensitive to the pump power density at low pumping powers. For example, according to Eq. (1), increasing the normalized initial population inversion, ni , from 1.1 to 1.4 results in a decrease of the pulse width by more than a decade. The time dependent models applied for the analysis of Q-switched lasers usually assume uniformly distributed initial inversion density (or small signal gain) in the pump volume [17,18]. This assumption should be applied with caution, since, whereas the total pump power is usually known, the actual gain volume is not. This is especially true for side pumping where the gain profile depends both on the geometrical arrangement of the diodes and on the absorption profile of the laser rod and hence it is hard to estimate beforehand the gain profile shape and the gain volume. Since the pulse width depends on the initial inversion density which in turn depends on the pump energy density, it is of importance to characterize the pump absorption profile in order to estimate the pulse width. In this study we examined passive Q-switched operation for the most basic of the side pumping schemes, i.e., a single diode bar or a linear array of bars pumping a laser rod by a single pass absorption. The rate equations for the excited states for the calculation of the temporal development of a Q-switched laser pulse are presented in Section 2. The experimental setup is described in Section 3. In Section 4 we present the measured gain profiles for Nd-doped YAG and YVO4 systems and the laser beam distribution for YVO4 . Based on the measured gain mode profile we found the pump energy density and use it to calculate the laser pulse widths and to compare it to the experimental.
2. Modeling the Nd:YVO4 Q-switched laser pulse temporal development The theoretical model consists of the rate equations for the population inversion density and for the photon density in the resonator [17]. A cross-section of the laser rod is shown schematically in the upper part of Fig. 1, in the x–y plane depicted. It was assumed that for the side pumping employed the pump power and hence the population inversion density are uniform along the
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151
dN N ¼ ccrN U ; dT sf
ð2Þ
dU lM U ¼ crN U ; dT lR tc
ð3Þ
where T is the time, c is the inversion reduction factor [15,17,19], r is the effective stimulated emission cross-section, sf is the fluorescence decay time of the upper level, lM is the length of the active medium, lR is the length of the laser cavity and tc is the decay time of photons in the resonator due to outcoupling, absorption and scattering [20]: tc ¼
Fig. 1. The experimental setup, components identifiers explained in the text. Above: the cross-section of the laser rod and the gain mode.
optical axis, Z. Furthermore, we assumed that the effective cross-section of the gain volume, is an ellipse which area is pwp hp , where wp is the gain half width at 1=e2 height of the long axis, and hp is the gain half width at 1=e2 height along the short axis. As it will be demonstrated in the experimental results, the pumping power affects the width of the pump beam profile and thus the pump power density is not linearly dependent on the pump power. According to Eq. (1), the laser pulse time duration depends on the population inversion density, which in turn depends on the pumping power density. We will introduce the experimental dependence of the pump power density on the pump power in the rate equations. Since the laser pulse widths measured are much higher than the saturation time constant of the saturable absorber Q-switch, the rate equation for the Q-switch population inversion is omitted. The rate equations for the population inversion density, N, and photon density in the resonator, U, are given by:
2lR 1 ; c 2alM þ e ln R
ð4Þ
where a is the absorption coefficient per unit length of the medium, e are the losses in the resonator and R is the reflectivity of the coupling mirror. The Q-switch pulse duration is very short, therefore the spontaneous emission contribution to the intensity and the optical pumping terms were omitted from Eqs. (2) and (3). In addition, it was assumed that the inversion reduction factor, c, in Eq. (2) is 1. It was found [19] that the value of the inversion reduction factor in the range 0.9–1 results in best fit of a model to experimental results. An ‘effective’ stimulated emission cross-section, r was used in Eqs. (2) and (3) due to the fact that only some of the Stark sublevels in the 4 F3=2 upper multiplet participate in lasing. The effective cross-section is: r ¼ fa rs , where fa is the equilibrium fractional Boltzmann occupation factor of the upper laser level within the upper multiplet and rs is the spectroscopic stimulated emission cross-section. The initial condition at T ¼ 0 for the inversion density depends on the pumping power: Ni ¼
P P s f gP ; ðhc=kp Þ VP
ð5Þ
where gP is the pump coupling efficiency consisting of the optical coupling efficiency, mode overlap and the Stokes factor kp =kl , where kp is the pump wavelength and kl is the laser wavelength. h is the Planck constant, and VP ¼ pwp hp lM is the gain mode volume. A small initial value Ui for the photon density was used to initiate the calculation. The choice of Ui affects merely the timing of the laser pulse relative to an arbitrary T ¼ 0.
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The rate equations will be presented in dimensionless form by normalizing N ; U and T, as follows [17]: n ¼ N =Nthr , / ¼ U=U0 , t ¼ T =tc . The normalizing factor for the population inversion density, Nthr , which is the threshold density, is derived by putting dU=dT ¼ 0 in Eq. (3): Nthr ¼
lR crlM tc
ð6Þ
and the normalizing factor for the photon density is: U0 ¼ Nthr ðlM =lR Þ. The final form for the rate equations becomes: dn tc ¼ n/ n ; dt sf
ð7Þ
d/ ¼ ðn 1Þ/: dt
ð8Þ
3. Experimental For the side pumping used in our experiments the pump laser diode array was an OPC A020-808CN, CW laser diode array, with a nominal 20 W output power centered at 808 nm under normal operating conditions. The temperature of the diode was maintained at a constant temperature of 21 0:5 °C by a chiller. The emission center wavelength and spectral width (FWHM) are 805– 809 nm and 2.5–3 nm, respectively, at operating currents of 20–30 A. This corresponds to approximate power levels, ranging from 8 to 15 W of output power of the diode array. The 808 nm laser diode emission was coupled to the laser rods by means of a cylindrical microlens. The resulting pump sheet was a collimated beam with a rectangular cross-section of approximately 10 0:1 mm at the intersection with the rod. Two laser media were studied, unpolished Nd:YVO4 (/3 7 mm, AR/AR coated at 1.06 lm, 1.0 at.%) and a polished Nd:YAG (/3 50 mm, AR/AR coated at 1:06 lm, 1.1 at.%). For the long Nd:YAG rod, three diodes mounted alongside each other were used for the side pumping, hence, the effective length of the gain medium was 30 mm. The rods were mounted on a heat sink water cooled to 21 °C. The experimental setup is
shown schematically in Fig. 1. The pump beam propagates parallel to the x axis and the laser beam parallel to the z axis, the origin of the x–y plane coincides with the laser rod axis of symmetry. The components layout is similar for the three types of measurements, e.g., pump mode fluorescence, free-running laser and Q-switched laser. For the pump mode fluorescence measurements the components layout was as follows: (1) was a CCD camera, (2) were neutral density filters used for attenuation and the back mirror (3) was blocked. For the free-running laser mode, (1) was a power meter for the average power measurements, (2) was an output coupler with R ¼ 85% and radius of curvature, ROC ¼ 5 m and (3) was the laser resonator flat back mirror. For passive Q-switch operation a Cr4þ :GGG element (3 mm thickness, 0.3 at.% of Cr4þ ) was used both as saturable absorber and as a rear mirror (3). The low intensity transmission of this element was T0 88%, it was AR coated @1.064 lm on the front side and HR @1.064 lm on the back side. For this mode of operation the laser pulses were detected by a fast silicon photodiode (1), with risetime <1 ns.
4. Results 4.1. Nd–YVO4 and Nd–YAG gain mode profiles The shape of the gain profile controls the pump power density and the spatial overlap between the gain mode and the laser mode. For various pumping powers, Pp , we measured the pump fluorescence distribution on the laser rod face, representing what we believe to be the x–y gain mode distribution at every section z of the rod length. Figs. 2–5 show the pumping mode characteristics of the side pumped Nd–YVO4 rod. Fig. 2 is a picture taken with the CCD camera of the fluorescence emitted from the face of the rod due to the side pumping, representing the gain mode for Pp ¼ 12:7 W. The rod circumference and the theoretical TEM00 mode of the resonator are outlined in the figure, the pump beam propagates from right to left. Fig. 3 shows the x distribution, along
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Fig. 2. CCD photo of the gain mode in the Nd–YVO4 rod for 12.7 W pumping power. Outlined are the rod circumference and the theoretical TEM00 mode of the resonator.
Fig. 3. Gain mode distribution in the Nd–YVO4 rod in x direction.
the propagation of the pump radiation, of the gain mode. The x distance is normalized with respect to the rod diameter, D, thus the pump light enters the rod at x=D ¼ 0:5. The pump energy is completely absorbed at x=D 0:1, i.e., within 0.6 diameters of the rod. Fig. 4 shows the distribution of the pump fluorescence in the y direction, which is perpendicular to the x–z plane. The gain mode distribu-
153
Fig. 4. Gain mode distribution in the Nd–YVO4 rod in y direction.
Fig. 5. Changes in wp and hp as a function of the pumping power.
tion in this direction resembles a Gaussian distribution. Here also, the y distance is normalized with respect to the rod diameter and y=D ¼ 0 coincides with the rod axis of symmetry. Fig. 5 shows the half width of the gain mode (at 1=e2 of the peak energy) in both directions as a function of the pumping power.
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As seen in Fig. 5, the gain half width at 1=e2 height in the x direction, wp , did not vary by more than 3% for pumping powers above laser threshold (Pp > 8 W). On the other hand the 1=e2 half width in the y direction, hp , increased monotonically with the increase in pumping power. This anisotropy of the gain distribution is accounted for asymmetric characteristics of the crystal, namely, orientation dependent absorption coefficients and refraction indices. A linear fit, used later for the laser pulse width calculations, could be found for the dependence of hp on Pp . Mean values for the pump mode dimensions were thus hp wp ¼ 150 750 lm whereas the calculated laser beam TEM00 waist, x0 , of the YVO4 medium resonator was 500 lm. Figs. 6–8 show the pumping mode characteristics of the side pumped Nd–YAG rod. Fig. 6 shows the CCD picture of the gain mode for 12.7 W pumping power. As in Fig. 2, the rod circumference and the theoretical laser TEM00 mode, with x0 400 lm, are outlined, the pump beam propagates from right to left. Figs. 7 and 8 show the x and y distributions, respectively, of the pump fluorescence. Under the normal operation conditions the Nd–YAG rod was pumped by three diodes mounted side by side. It was impossible to take the real gain profiles in this mode since the fluorescence due to the diode arrays far from the camera was dispersed in the rod thus obscuring
Fig. 7. Gain mode distribution in Nd:YAG rod in x direction.
Fig. 8. Gain mode distribution in Nd:YAG rod in y direction.
Fig. 6. CCD picture of the gain mode in Nd:YAG rod for 12.7 W pumping power, the rod circumference and the theoretical laser TEM00 mode are outlined.
the gain profile. Therefore, for the gain distribution measurements only one diode was used, it was located near the edge of the rod close to the camera. The pumping wavelength varied as a function of the diode current from 805 to 809 nm at 20–30 A of the diode current, respectively, which corresponds to 10–15 W pumping power. This wavelength variation changes the gain profile in YVO4
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by 30% and in YAG by 50%. Since the absorption in YVO4 is approximately four times higher than in YAG the effect of wavelength shift on the gain profile in YVO4 is more significant and therefore observable in the experiment. Also, we should mention that the asymmetric shape of the gain profile in YVO4 and the difference between the dependences of hp and wp on the pump power is a result of different absorption coefficients along different crystallographic directions of the a-cut Nd:YVO4 crystal. The absorption at the pump wavelength of the Nd:YAG is smaller than that of the YVO4 , this fact is demonstrated in Fig. 7 which shows that only a fraction of the pump energy is absorbed along the pump beam propagation. As a result, wP was approximately equal to the rod radius for all pumping powers. Measuring the half widths at 1=e2 of the peaks in Fig. 8 indicates that for the YAG case hp was almost independent on the pump power, it was approximately 180 10 lm. Fig. 8 shows also that the position of the peak of the pump mode in the y direction drifted towards the rod perimeter as the pump power was increased. This drift of the pump mode location accounts for the fact that the laser resonator has to be realigned for each pumping power. Table 1 provides a summary of the pump mode geometry in comparison to x0 for both laser media. We can express the matching between the fundamental resonator mode and the gain mode by the gain mode aspect ratio, wp =hp , where wp =hp ¼ 1 represents a good match. From the table it follows that the mode matching of the Nd:YVO4 is superior to that of the Nd:YAG.
155
doped YVO4 and YAG media will favor the higher-order transverse modes of the laser. The TEM00 mode, which builds up the fastest, soon saturates the gain mode volume it occupies giving rise to the buildup of higher-order modes in the not yet saturated parts. Fig. 9 shows the three dimensional representation of the YVO4 laser near field beam profile for 15 W incident pumping power. The figure represents the beam profile for the resonator aligned for maximum laser power. Fig. 10 demonstrates the mode structure sensitivity to the cavity mirrors tuning, by showing the near field contour plots of two different mode structures. Fig. 10(a) shows the contour plot of the multimode, up to TEM20 , beam depicted in Fig. 9. Fig. 10(b) shows a single mode operation obtained by tuning the resonator and consequently loosing 10% of the output power. Fig. 11 shows the power of the Nd–YAG laser and the Nd:YVO4 laser in the free-running mode of operation. Due to a shift in the gain mode location within the rod, as a function of the pump power, both laser resonators were optimized for maximum output power at each pumping power. A maximum average power of 2.5 and 10 W was measured for the Nd:YVO4 and Nd:YAG lasers, respectively. Notice that the slopes for both
4.2. Free-running lasers Due to the structure of the gain modes, as depicted in Figs. 2 and 6, it is expected that both NdTable 1 Pump mode geometry in comparison to the resonator mode waist for Nd:YAG and Nd:YVO4 laser media
x0 ðlmÞ hP ðlmÞ wP ðlmÞ
Nd:YAG
Nd:YVO4
400 180 1500
500 150 750
Fig. 9. 3D representation of the YVO4 laser near field beam profile for Pp ¼ 15 W.
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(a)
lasers in the figure are comparable since for both cases the laser power axis scale equals 0.2 times the pump power axis scale. For moderate pumping powers the slope efficiency of the Nd:YVO4 was marginally higher than that of the Nd:YAG: 40% and 35%, respectively. As the pumping power was increased beyond 12 W, the Nd:YVO4 laser showed a decline in the output power. The roll-off in the laser power for high level pumping was due to thermally induced distortions in the laser rod and the associated lensing and birefringence [21,22]. Because of the low pump absorption of the YAG no decline in laser power was noticed even at the highest pumping powers. 4.3. Passively Q-switched lasers
(b) Fig. 10. Near field contour plots of the YVO4 laser for two different mode structures at Pp ¼ 15 W. (a) multimode, up to TEM20 , beam depicted in Fig. 9; (b) single mode operation.
Fig. 11. Average laser power of free-running Nd–YAG and Nd:YVO4 lasers as a function of pumping power.
We have tested diode-pumped Nd:YAG and Nd:YVO4 lasers for passive Q-switched operation, when both systems were side-pumped. The passive Q-switch element was Cr4þ :GGG. When the Qswitching back mirror was used, a continuous sequence of pulses was generated. The pulse repetition rates were in the kHz frequency domain. Time and amplitude fluctuation were less than 10%, and exhibited disordered behavior with main average modulation frequency and associated sidebands. The pulse train of the Q-switching showed instabilities both in amplitude and frequency. Qualitatively it can be interpreted as a result of dynamic processes in the saturable absorber (such as excited-state absorption, and fast decay within vibronic levels) or excitation of polarization eigenmodes due to thermal-induced birefringence. The jitter in time and amplitude are a result of temperature gradients generated and consequently, thermal-induced birefringence in the laser rod. To demonstrate the passive Q-switching under high thermal load, we pumped Nd:YAG (/3 50 mm) laser rod by three diode arrays, at total input power of 50 W. The results using this system indicated modulation (which depends on the pumping energy) in the 10–50 kHz frequency domain. In the past we reported [7] that the average modulation frequency of YVO4 which changed from 225 to 410 kHz when the diode pump power
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was increased from 10 to 15 W, respectively. The difference in the average modulation frequency between YAG and YVO4 is accounted for the short lifetime of the 4 F3=2 lasing level of Nd-doped YVO4 relative to YAG. The lower thermal conductivity of YVO4 relative to YAG, 5.2 and 11 W/(m K), respectively, also limits the use of excessive pumping power for the YVO4 . Our results are consistent with the results reported by Agnesi et al. [23]. Fig. 12 shows the average output power for Qswitch operation as a function of the pump power for both media. A maximum average power of 0.8 and 4.2 W was measured for the Nd:YVO4 and Nd:YAG lasers, respectively. In the Q-switch mode both lasers output powers exhibited roll-off at certain pumping powers. The slope efficiency of the Nd:YVO4 laser decreased from 0.18 at low pumping power to 0.12 for pumping power beyond 12 W, which was also the roll-off point for the free-running case. The slope efficiency of the Nd:YAG laser declined from 0.25 to 0.13 at 30 W pumping power. Since we did not observe a parallel reduction in the slope efficiency for the free-running Nd:YAG laser, it can be attributed to thermal effects in the saturable absorber back mirror. We believe that by a proper heat removal from both the saturable absorber and the laser rods, laser performance for both Nd:YAG and Nd:YVO4 can be improved. Before the onset
Fig. 12. Average laser power of Q-switched Nd–YAG and Nd:YVO4 lasers as a function of the pump power.
157
of the thermal effects, the conversion efficiencies of the Q-switched average power, relative to freerunning mode of the Nd:YAG and Nd:YVO4 lasers, respectively, were 70% and 45%. In what follows we discuss the effect of the pump power on the Q-switched pulse width. The pulse width of the Q-switched spike is reduced with the increase of the diode pumping power [15,16]. We measured the average pulse width of the Q-switched Nd:YVO4 laser as a function of the pumping power and compared our results to the results of a theoretical calculation. The following data was used for the Nd–YVO4 laser calculation: r ¼ 8:2 1023 m2 , sf ¼ 0:98 104 s, gP ¼ 0:15, lM ¼ 7 mm, lR ¼ 150 mm, kl ¼ 1:064 lm, kp ¼ 0:808 lm, R ¼ 0:85. Eqs. (7) and (8) were solved for various Pp with the appropriate hp (Pp ) derived from Fig. 5 for each pumping power. The full pulse widths at half of the maximum / are presented in Fig. 13 along with the measured pulse widths of the Nd–YVO4 laser. In order to comprehend the measured dependence
Fig. 13. Calculated and measured Q-switch laser pulse HWHM of the Nd–YVO4 laser as a function of pumping power. Inset shows calculated and measured temporal evolution of a laser pulse for 15 W pumping power.
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of the pulse widths on the pumping power of Fig. 13, one has to assume that ni , which is proportional to the pumping density, does not change linearly with pump power. Our earlier finding, namely, that for the Nd–YVO4 laser the pump mode spot size increases with the increase in pumping power is consistent with the results of Fig. 13. 4.4. End pumping End pumping is used in the case where efficient operation with good beam quality is required. For this study we pumped longitudinally Nd:YAG and Nd:YVO4 lasers. The laser in both cases was optimized for various output couplers. Both results were obtained using output coupler of R ¼ 95% with ROC ¼ 150 mm. This configuration is also necessary to obtain overlap between the cavity mode and the pump spot. The total optical efficiency of Nd:YAG laser in this configuration is 54%. For the study of the Q-switching performance of CW diode-pumped Nd:YAG and Nd:YVO4 lasers, we used Cr4þ :YAG saturable absorber as the Q-switching element. The sample had low intensity transmission of T0 47%. Qswitching and repetitive modulation of diodepumped Nd-doped crystals were observed when Cr4þ :YAG disk was inserted inside the cavity. For Nd:YVO4 , the mean modulation frequency obtained by FFT analysis had values ranging from 60–100 kHz, at input pump power of 7.3 W. The mean frequency was reduced to 18 kHz at 5.5 W input power level. However, the pulsewidth (FWHM) exhibited the same average value of 100 10 ns at these power values. In the case of diode-pumped Nd:YAG laser, a different behavior was observed. In the same range of pumping power, the mean modulation frequencies obtained varied from 7 to 12 kHz. In the same pumping power, the pulsewidth (FWHM) was shorter than for Nd:YVO4 , namely, 60 ns.
5. Summary CW diode-side-pumped free-running and passively Q-switched Nd:YAG and Nd:YVO4 at rel-
atively high pumping power levels were investigated. The gain mode profiles for both media were measured as a function of the pump power. It was found that for the Nd:YVO4 , which totally absorbed the pumping radiation, the gain mode volume increased with the increase in pumping power. For moderate pumping powers the slope efficiencies of the Nd:YVO4 and the Nd:YAG lasers in the free-running mode were 40% and 35%, respectively. For the passive Q-switch operation using inorganic saturable absorber, we found a decrease in the slope efficiency due to thermal effects both in the laser rods and the saturable absorber. The Nd:YAG medium absorbed little of the pump power and thus in the free-running mode the Nd:YAG laser was not affected by thermal effects. On the other hand, the Nd:YAG laser emits high power, thus, in the Q-switch mode the saturable absorber was affected by the absorbed laser power and the efficiency decreased. The conversion efficiencies of the Q-switched average power, relative to free-running mode of the Nd:YAG and Nd:YVO4 lasers, were 70% and 45%, respectively. We studied theoretically and experimentally the dependence of Q-switched Nd:YVO4 laser pulse width on the pump power. It was confirmed that the pump power density deposited in the laser rod is less than linearly proportional to the pumping power resulting in longer pulse width. References [1] H. Plaessmann, K.S. Yamada, C.E. Rich, W.M. Grossman, Appl. Opt. 32 (1993) 6616; H. Plaessmann, F. Stahr, W.M. Grossman, IEEE Photonics Tech. Lett. 3 (1991) 885. [2] D.G. Hall, Appl. Opt. 20 (1981) 1579. [3] A.J. Alfrey, IEEE J. Quantum Electron. 25 (1989) 760. [4] P. Laporta, IEEE J. Quantum Electron. 27 (1991) 2319. [5] S.C. Tidwell, J.F. Seamans, C.E. Hamilton, C.H. Muller, D.D. Lowenthal, Opt. Lett. 16 (1991) 584. [6] S. Yamaguchi, H. Imai, IEEE J. Quantum Electron. 28 (1992) 1101. [7] Y. Kalisky, S. Levy, L. Kravchik, in: K.I. SchaffersL.E. Myers (Eds.), Laser Material Crystal Growth and Nonlinear Materials and Devices, Proc. SPIE, vol. 3610, 1999, p. 109.
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