Simultaneous Q-Switching and Mode-Locking in a
Diode-Pumped Nd : YVO
4
–Cr
4+
: YAG Laser
Yung-Fu Chen and S. W. Tsai
Abstract—Parametric studies of passive Q-switching and
mode-locking in a Nd3+: YVO4–Cr4+: YAG laser were theoret-ically carried out. Simultaneous mode-locking and Q-switching was also experimentally studied. It was found that over 90% of the output power could be mode-locked in a diode-pumped passively
Q-switched Nd3+: YVO4–Cr4+: YAG laser. The average pulse duration of the mode-locked pulse train was estimated to be around110 150 ps. The highest peak power of a single pulse near the maximum of the Q-switched envelope was greater than 100 kW.
Index Terms—Cr4+: YAG, diode-pumped, mode-locked, Nd3+: YVO4, passively Q-switched.
I. INTRODUCTION
I
N THE LAST few years, a number of neodymium-doped vanadium-based crystals have been identified as promising materials for diode pumped lasers, particularly yttrium ortho-vanadate (YVO ) and gadolinium orthoortho-vanadate (GdVO ) [1]. Several advantages over Nd : YAG crystals include a larger emission cross-section, a pump power threshold, a wider absorption bandwidth, and a polarized output. For example, the wider absorption bandwidth means that the laser output power is less sensitive to drifting of the diode pump wavelength due to a change of temperature or aging. The linearly polarized laser output is beneficial not only to nonlinear wavelength conversion, but also to avoiding undesired birefringent effects.Chromium-doped yttrium aluminum garnet (Cr : YAG) provides a large absorption cross section in the m spectral region, which makes it an attractive choice as a passive
Q-switch for Nd-doped lasers [2]–[4]. It is, however, usually
difficult to operate a diode-pumped, passively Q-switched Nd : YVO laser with Cr : YAG as the saturable absorber. The main difficulties arise from the fact that a Nd : YVO crystal has a high stimulated emission cross section. For good passive Q-switching, absorption saturation in the absorber must occur before gain saturation in the laser crystal (the second threshold condition) [5]. Therefore, a cavity is required that has a small beam area in the Cr : YAG crystal. Even though passively Q-switched Nd : YVO and Nd : GdVO lasers have been demonstrated [6], [7], the output pulse energy and
Manuscript received July 27, 2000; revised December 8, 2000. This work was supported in part by the National Science Council of the Republic of China under Contract NSC-89-2112-M-009-059.
Y. F. Chen is with the Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan 30050, R.O.C. (e-mail: [email protected]).
S. W. Tsai is with the Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C.
Publisher Item Identifier S 0018-9197(01)02325-9.
Fig. 1. Configuration of passively Q-switched mode-locked Nd : YVO laser.
peak power are obviously lower than those of Nd : YAG laser because these crystals have larger emission cross-sections.
The relaxation time of the first excited-state in the Cr : YAG is in the microsecond region, which prevents mode locking by saturable absorption. Nevertheless, recent investigations [8] show that excited-state absorption (ESA) in Cr : YAG is rather significant and the relaxation time from higher-lying levels to the first excited state is in the sub-nanosecond region. This property indicates that there could be a potential to use this excited-state absorption for generation of Q-switched and mode-locked pulses. This possi-bility has been observed by experiments in which Q-switched mode-locked pulses were generated by use of Cr : YAG in a flashlamp-pumped Nd : YAG laser with a modulation depth of approximately 30 70% [9].
Although the large gain cross section of the Nd : YVO crystal in comparison with that of Nd : YAG is unfavorable for obtaining passive Q-switched operation, it is, as is the wider gain bandwidth, favorable for mode-locked operation. Therefore, it is of practical interest to achieve simultaneous mode-locking and
Q-switching in the Nd : YVO –Cr : YAG laser for increasing the peak power. In this paper, we present a passively Q-switched and mode-locked diode-pumped Nd : YVO laser by use of a Cr : YAG crystal as the saturable absorber. Parametric studies of pulsed mode-locking were performed. The experimental con-figuration and the results for different Cr : YAG crystals are described and discussed.
II. EXPERIMENTAL
Fig. 1 outlines the basic laser setup. The pump power is a 20-W fiber-coupled diode-laser array (Coherent, FAP-81-20C-800-B), with the output wavelength of the 0018–9197/01$10.00 © 2001 IEEE
lasers at 25 C ranging from 807 to 810 nm. The fibers were drawn into round bundles of 0.8-mm diameter with a numerical aperture of 0.18. A focusing lens with 20-mm focal length and 85% coupling efficiency was used to re-image the pump beam onto the laser crystal. The waist diameter of the pump beam was about 400 m. The -cut 0.3-at.% Nd , 10-mm-long Nd : YVO crystal was 0.5 wedged and coated for high reflectivity at 1064-nm ( 99.9%) and high transmission at 808-nm ( 95%) on one side. The other side was antire-flection coated at 1064 nm. The Nd : YVO crystal of only a low doping concentration was used to avoid thermally induced fracture [10]. The laser crystal was wrapped with indium foil, and mounted in a water-cooled copper block. The water temperature was maintained at 17 C. The cavity was designed to easily allow mode matching with the pump beam, and to provide the proper spot size in the saturable absorber. Several Cr : YAG crystals with different initial transmissions were used in the experiment. Both sides of the Cr : YAG crystal were antireflection coated at 1064 nm. The resonator consisted of two spherical highly-reflective (at 1064 nm) mirrors M1 and M2, with radii of curvature of 50 and 10 cm, separated by 60 cm. The flat output coupler was 1.0 wedged. The total cavity length was approximately 1 m. The ratio between the effective area in the gain medium and in the saturable absorber can be easily changed by changing the position of the Cr : YAG crystal. Moving the Cr : YAG crystal away from the output coupler decreases the ratio in the present cavity. The experimental result shows that a ratio of greater than 3.0 is sufficient for effective Q-switching. This result is consistent with the theoretical analysis of the following section.
III. ANALYSIS
A. Q-Switching
The physical meaning of the second threshold in a passively
Q-switched operation is whether the saturable absorber will
sat-urate first, thereby allowing the photon density to increase and thus producing a giant pulse. Alternatively, the gain will begin to saturate first, so that the photon density never increases suf-ficiently to develop a giant pulse. To model the operation of a passively Q-switched laser, we shall assume uniform pumping of the gain medium, and the intracavity optical intensities in the gain medium and in the absorber as axially uniform. We also omit the spontaneous emission of the laser and the absorber. The coupled rate equations have been used to model a passively
Q-switched laser in many investigations [11]–[14]. Here, we
extend the previous results by including the influence of intra-cavity focusing and the ESA effect. The coupled equations for a three or a four level gain medium are modified as
(1) (2) (3) (4)
where
intracavity photon density with respect to the effec-tive cross-sectional area of the laser beam in the gain medium;
population density of the gain medium; length of the saturable absorber;
ratio between the effective area in the gain medium and in the saturable absorber;
ground-state population density in the saturable ab-sorber;
excited-state population density in the saturable ab-sorber;
total population densitiy in the saturable absorber; GSA cross section in the saturable absorber; ESA cross section in the saturable absorber;
stimulated emission cross section of the gain medium; length of the gain medium;
nonsaturable intracavity round-trip dissipative optical loss;
reflectivity of the output mirror;
inversion reduction factor ( and corre-spond to, respectively, four-level and three-level sys-tems (see [11]);
and is the round-trip transit time of light in the cavity of optical length , where is the speed of light.
Dividing (2) by (3) and integrating gives
(5) where
(6) and is the initial population inversion density in the gain medium. is determined from the condition that the round-trip gain is exactly equal to the round-trip losses just before the
Q-switch opens. Thus
(7) where is the initial transmission of the saturable absorber. Dividing (1) by (2) and substituting (5) into the result gives
(8)
where
(9) Since the first derivative of with respect to at is zero, the criterion for achieving Q-switching is whether the second derivative of with respect to at has a positive or a
negative sign. If positive, the photon density will grow. Using (8), the second derivative of with respect to is given by
(10)
Setting in (10), the criterion for a giant pulse to occur is then given by
(11) Inserting (6) into (11), the criterion for the second threshold becomes
(12)
The main difference between the present derivation and the pre-vious result [5] is that we take account of the influence of ex-cited-state absorption and intracavity focusing. In addition, (12) is of practical importance because the parameters used in the present derivation, such as and , are directly related to the design of a passively Q-switched laser. For the Cr : YAG passively Q-switched Nd : YVO laser, , [8], cm [8], and the emission cross section of Nd : YVO , , is cm [15].
Following the derivation of previous work [11]–[13], the pulse energy is given by
(13) where is the solution of the equation
(14)
To consider the dependence of the output energy on , we used (13) and (14) to calculate the output pulse energy in a Cr : YAG passively Q-switched Nd : YVO laser as a func-tion of for several initial transmissions and . Fig. 2 shows the calculation results. It can be seen that the output pulse energy initially rises as the ratio is increased above the second threshold. As the ratio is sufficiently large, the output energy saturates at a larger value for a smaller . To obtain a nearly optimum output pulse energy, the ratio was designed to be greater than 3.0 in the passively Q-switched Nd : YVO –Cr : YAG laser.
Fig. 2. Calculation results for the output pulse energy in the passively
Q-switched Nd : YVO –Cr : YAG laser as a function ofA=A for several initial transmissionsT and R = 0:55.
B. Mode-Locking
The nonlinear absorption of saturable absorbers was first suc-cessfully employed for simultaneous Q-switching and mode-locking of solid-state lasers in 1965 [16], [17]. One desirable condition for good pulsed mode-locking is that the saturable absorber should have a short enough lifetime to recover its ab-sorption between individual noise bursts, so that the preferred pulse does not bring several closely following noise spikes up along with it. Another important condition is that the build-up time of the Q-switched pulse has to be sufficiently short be-cause of the limited round trip time of the intensity fluctuation. In early technologies, dyes were commonly employed in pulsed mode-locked solid-state lasers. However, a flowing dye solution temperature controlled within 0.1 C must be used to achieve stable and reproducible performance because a change of 1% per degree in absorption was found in the diluted dyes. Further-more, mixing with handling of the dye solution, and maintaining proper dye concentration, proved cumbersome. Due to these in-herent shortcomings, the replacement of the dyes by a solid-state element is desirable.
In comparison with dye solution, Cr : YAG has better thermal and mechanical properties, resulting in a higher damage threshold. However, its relaxation time is in the microsecond region, which generally would not be allowed to obtain mode locking. Semiconductor saturable absorber mirrors or Kerr-lensed mode-locked systems are commonly used technologies in pulsed solid-state lasers [18], [19]. Nev-ertheless, when the intracavity intensity is high enough, all of the Cr ions are quickly excited to the first excited-state, and strong ESA causes a great quantity of Cr ions to accumulate in higher-lying levels. Since the relaxation time of the ESA is relatively short ( 0.1 ns) [20], passive mode-locking with a Cr : YAG saturable absorber would be possible if strong intensity fluctuations are introduced, and the pulse buildup time is sufficiently short [21].
The fluctuation mechanism is believed to be mainly respon-sible for generating ultrashort pulses in a laser Q-switched by nonlinear absorbers [21], [22]. According to this mechanism, the picture of ultrashort pulse formation is the following. In the linear stage of generation, the fluctuations of intensity arise due to the interference of a great number of modes having a random phase distribution so that the radiation consists of a chaotic collection of ultrashort peaks. In the nonlinear stage, where bleaching of the absorber takes place, the most intensive fluctuation peaks are compressed and amplified faster than all the weaker ones. Kryukov and Letokhov [22] used the fluctua-tion mechanism to prove that the ratio of the peak pulse power to the mean background power can be given by
(15) where is the number of axial modes at the end of the linear stage of buildup and is the nonlinear parameter related to the pulse compression in the nonlinear stage of the developing. To obtain the high pulse-to-background ratio, and should be as large as possible.
During the linear stage of the intensity fluctuation buildup, the number of axial modes decreases due to the natural selection toward the center of amplification line given by [22]
(16) where
initial number of axial modes; threshold gain;
pulse build-up time.
In most cases, the nonlinear parameter is given by [22] as (17) where is the speed of the gain increase due to pumping at the time of threshold. From (15)–(17) it can be found that a shorter pulse build-up time generally leads to a larger and a larger , and a higher pulse-to-background ratio.
Since a short pulse build-up time is of benefit to the genera-tion of the Q-switched and mode-locked pulses, it is practically useful to make an estimate of the build-up time for a simple sit-uation. The Q-switch build-up time in a laser can be estimated from a solution of the single mode rate equations. The addi-tion of simultaneous mode locking and the presence of multi-mode oscillations will not significantly change the build-up time [23], [24]. If the pulse build-up time is short compared to the upper-level lifetime of the inversion density, then a good esti-mate for is given by [5]
(18) with
(19) where is the threshold inversion density after the absorber is bleached. The absorber is assumed to be fully bleached in the analysis. Note that full bleaching is not a necessary condition for obtaining Q-switching. Owing to the excited-state absorp-tion, the final transmission of the saturable absorber will be
Fig. 3. Dependence of the coefficient of pulse-build time onT for several values of front mirror reflectivityR for Cr : YAG ( = 0:28).
, where the factor is defined in (9). Therefore, the threshold inversion density after bleaching of the absorber is given by
(20) The difference between (7) and (20) arises from the different losses incurred by the absorber without any bleaching and with complete bleaching.
Substituting (7) and (20) into (19), the pulse build-up time coefficient is rewritten as
(21)
Fig. 3 provides a demonstration of the dependence of on for several values of for Cr : YAG ( ) . For the demonstration, we used a typical value of in the calculation. It can be seen that the lower the initial trans-mission, the shorter is the build-up time for a given output re-flectivity. On the other hand, the build-up time can be clearly reduced by lowering the output reflectivity for a given initial transmission. However, a lower output mirror reflectivity also results in a higher threshold. Therefore, the output reflectivity is typically chosen to range between 50%–60% for pulsed pas-sive mode-locking [25].
IV. RESULTS ANDDISCUSSION
Initially, we used an output coupler with 55% to generate simultaneous Q-switching and mode locking. Fig. 4 shows the average power of the passively Q-switched and mode-locked pulse train with respect to the pump power for saturable
Fig. 4. Experimental results for average power of the passively Q-switched mode-locked pulse train with respect to the pump power for saturable absorbers ofT =80%, 60%, 50%, and 40%, respectively.
absorbers of 80%, 60%, 50%, and 40%, respectively. The highest average output power is obtained with a 80% Cr : YAG crystal and the Nd : YVO laser generates an average output power 4.7 W in the TEM mode at an incident pump power of 17-W. The lasing threshold and optical slope efficiency are 3.2 W and 34.5%, respectively. For a Cr : YAG crystal of initial transmissions of 60%, 50%, and 40%, the maximum average output powers are reduced to 4, 3.5, and 3.0 W, respectively, because of the increasing losses incurred by the saturable absorbers. The lasing threshold and the slope efficiency are 4.3 W and 31.5% for the 60% crystal, 5.1 W and 29.4% for the 50% crystal, and 6.0 W and 27.3% for the 40% crystal, respectively.
The pulse temporal behavior was recorded by a LeCroy 9362 digital oscilloscipe (500-MHz bandwidth) and a fast Si p-i-n photodiode with a rise time of 0.35 ns. Fig. 5 shows the repeti-tion rate of the Q-switched pulse train with respect to the pump power for the four Cr : YAG crystals and 55%. It can be seen that the lower the initial transmission of the Cr : YAG crystal, the lower is the repetition rate of the Q-switched pulse train. From Figs. 4 and 5, the pulse energies of the Q-switched pulse train at an incident pump power of 17 W are 75, 120, 140, and 165 J for saturable absorbers of 80%, 60%, 50%, and 40%, respectively. A typical oscilloscope trace is presented in Fig. 6, showing a train of Q-switched pulses. The pulse-to-pulse amplitude fluctuation of the Q-switched pulse train was found to be less than 10%.
The expanded temporal shape of a single Q-switched pulse for saturable absorbers of 80%, 60%, and 40% is shown in Fig. 7. It can be seen that a lower not only shortens the width of the pulse envelope, but also reduces the CW background in the Q-switched and mode-locked pulse. This result is consistent
Fig. 5. Experimental results for pulse repetition rate of the Q-switched pulse train with respect to the pump power for saturable absorbers ofT =80%, 60%, 50%, and 40%, respectively.
Fig. 6. Oscilloscope traces of a train of Q-switched pulses.
with the previous analysis that a lower shortens the pulse build-up time, as shown in Fig. 3, which is beneficial for the gen-eration of the Q-switched and mode-locked pulses. The pulse build-up times were estimated to be about 590, 320, and 200 ns for saturable absorbers of 80%, 60%, and 40%, respectively. On the other hand, the theoretical results shown in Fig. 3 are 560, 297, and 198 ns for saturable absorbers of 80%, 60%, and 40%, respectively. Apparently, the theoretical calculations are in good agreement with the experimental results. When the value of in our system is smaller than 0.6, nearly complete mode locking with more than 90% of the output power mode-locked is achieved. Although the results shown in Fig. 7 were mea-sured at 10 W of absorbed pump power, the envelope pulse-width changes by less than 5% over the range of the absorbed pump power (8 17 W). The mode-locked pulses inside the
Fig. 7. Expanded temporal shape of a single Q-switched pulse for saturable absorbers ofT = 80%, 60%, and 40% with R =55% at the pump power of 10 W.
Fig. 8. Autocorrelation trace of the Q-switched mode-locked pulse.
Q-switched pulse envelope had a repetition rate of 148 MHz. The mode-locked pulse duration inside the Q-switched pulse was measured using an autocorrelator (KTP type II interaction) in a collinear configuration [26]. The average pulse duration (FWHM) was estimated to be about 110 150 ps for 0.6, as shown in Fig. 8. Fig. 9 shows the dependence of the enve-lope pulse width and the peak power of the Q-switched pulse train on the initial transmission at an incident pump power of 17 W. The peak power of a single pulse near the maximum of the Q-switched envelope was greater than 100 kW for .
Fig. 9. Dependence of the envelope pulse width and the peak power of the
Q-switched pulse train on the initial transmission at an incident pump power of
17-W.
To investigate the stability of the mode-locking process, we changed the spot size in the absorber by moving the absorber away from the output coupler. It was found that increasing the spot size in the absorber leads to a decrease in the pulse en-ergy of the whole bunch. However, the modulation depth of the mode-locking pulse train is almost not influenced by the change
Fig. 10. Expanded temporal shape of a single Q-switched pulse forT =50% andR =70% at a pump power of 10 W.
of the beam size in the absorber. It has also been found that mode-locking operation is insensitive to the alignment of the ab-sorber. Therefore, the key parameter for mode-locking is the ini-tial absorber transmission, whereas tight focusing only affected passively Q-switching operation.
Finally, we replaced the output coupler ( 55%) with a 70% one to study the influence of the output reflectivity on the modulation depth of the mode-locked pulse. In this case, the modulation depth of the mode-locked pulse decreased sig-nificantly, as shown in Fig. 10. The reason is that a higher output reflectivity will lengthen the pulse-build up time, as anticipated by Fig. 2.
V. CONCLUSIONS
We have demonstrated the use of Cr : YAG crystal to ob-tain a high-power diode-pumped Nd : YVO laser operating in a
Q-switched mode-locked mode. Theoretical analysis shows that
a lower initial transmission of Cr : YAG crystal is of benefit to the generation of the Q-switched mode-locked pulses for a given output reflectivity. On the other hand, the value of the output re-flectivity should be low enough for simultaneous mode-locking and Q-switching. Experimental results show that over 90% of the output power in a passively Q-switched Nd : YVO laser was mode-locked by using 60% and 55%. The peak power of a single pulse near the maximum of Q-switched envelope was greater than 100 kW. We believe that its high reliability and sta-bility make this laser of considerable interest for applications.
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Yung-Fu Chen, photograph and biography not available at the time of
publica-tion.
