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We present a giant-pulse generation laser realized by the emission cross-section control of a gain medium in a passively Q-switched Nd:YVO4 microchip laser with a Cr4+:YAG saturable absorber. Up to 1.17 MW peak power and 1.03 mJ pulse energy were obtained with a 100 Hz repetition rate. By combining the Nd:YVO4 crystal with a Sapphire plate, lower temperature difference between a pump region in the gain crystal and a crystal holder was obtained which helped to keep the cavity in stability zone at elevated temperatures and allowed the achievement of the high peak power for this laser system.
© 2016 Optical Society of America
Corrections
9 February 2016: A correction was made to Fig. 7.
1. Introduction
With the recent development of compact, high brightness, single frequency, and passively Q-switched Nd:YAG/Cr4+:YAG lasers, new applications of these sources has become possible. These lasers cover the conventional pulse-gap region of the giant-pulse lasers [1], and are suitable for laser ignition and secondary neutral mass spectroscopy (SNMS) that require high peak power pulses for fuel ignition and particle ionization, respectively [2,3 ]. Combined with output energy levels over several mJ, pulses with a peak power of over a MW are possible. The benefits of using these lasers are the reduced cost and compact design, which means the laser requires less space for installation. Unfortunately, such sources operate at repetition rates of 100 Hz or below [4], so either new materials or another approach is necessary to increase the operational speed and reduce the heat generated in the crystal.
Another material of choice for these applications are Nd3+ doped orthovanadate crystals. Compared with the conventionally used Nd:YAG crystal, the Nd3+ doped orthovanadate crystal has a higher absorption coefficient at 808 nm and 880 nm wavelengths for pump light that is parallel to the π-polarization, which makes it possible to use a crystal with shorter thickness and reduced cavity size [5,6 ]. Additionally, a shorter fluorescent lifetime τf allows an increased repetition rate while maintaining Q-switching efficiency. A previous study on the thermal conductivity of YVO4 showed values that are comparable to those of a YAG garnet [7]. That means a similar heat removal effect can be expected. Furthermore, because of the natural birefringence in YVO4, thermal stress induced depolarization losses are suppressed compared to those of a YAG crystal. However, this crystal’s emission cross-section σem is almost 5 times higher, which makes Q-switch operation more difficult to obtain and, once obtained, has lower energies than the Nd:YAG [8,9 ]. To address this issue, optimization of σem is required.
The most common way to control the σem value is by a temperature change of the gain crystal. Previous works on Nd3+ doped materials showed a σem change over a wide temperature range [10–16 ]. This effect was strongest in a Nd:YVO4 crystal and was equal to −0.5%/°C for a π-polarized emission, compared to an only 0.2%/°C change in the Nd:YAG crystal. Additionally, due to the change of the emission cross-section, the linewidth of the 4F3/2 transition to the 4I11/2 increases, and the spectral line shifts towards longer wavelengths if the temperature of the gain medium increases. This change can be explained by phonon-ion interactions, where the Debye model for phonons is applied to the crystal [15]. In [17], for a passively Q-switched Nd:YVO4 crystal operating at 100 Hz, the energy and peak power reached 24.5 µJ and 7.4 kW, respectively, corresponding to the temperature range from 26°C to 113°C. Similarly, the emission cross-section can be controlled in a cavity utilizing volume Bragg grating (VBG) mirrors. In this case, by changing the temperature of the VBG, the peak emission wavelength shifts along the gain spectrum of the laser crystal allowing control of σem. However, the experiments were done only for a Nd:YAG passively Q-switched microchip laser [18]. In this case, the energy improved by 29% in a temperature range near 140°C. Another approach to reducing σem in a Nd:YVO4 crystal could be switching to a c-cut crystal, where σem is 0.65 × 10−18 cm2, which is comparable to a Nd:YAG crystal. In this case the energy output reached is 18 µJ with a peak power of 21.2 kW [19].
2. Passive Q-switch model
In this work we used the passively Q-switched model rate equations, which were modified by Pavel [20] from Degnan’s work [21] by the additional inclusion of an excited state absorption (ESA) factor and a mode size ratio between the gain medium and saturable absorber (SA). Sakai [22] optimized that model to several equations and showed its validity for his developed Nd:YAG/Cr4+:YAG microchip laser. After solving the rate equations, the following pulse energy Ep and peak power Pp were found (please see the appendix for the full description)
Here ngi, ngt and ngf are the initial, maximum, and final population inversion densities, respectively. α, δ and p describe gain media and SA material properties, and are described in the appendix. σem and γg are the emission cross-section and the thermal population reduction factor for the gain crystal, respectively. Ag is the effective mode area of the gain media. R is the output-coupler-mirror reflectivity, tr is the cavity round trip time, and lg is the gain media thickness.From Eqs. (1) and (2) , the pulse duration can be calculated
To include the temperature dependence of the emission cross-section, one just needs to change σem to σem(T) in all mentioned equations above. New emission cross-sections can be calculated using the following approximation
Here σem(T0) is the emission cross-section at 20°C which has a value of 2.5 × 10−18 cm2, e0 = 1.101, e1 = 5.592 × 10−3 K−1, and e2 = 10.81 × 10−6 K−2. This approximation can simulate the emission cross-section change in the temperature range between 15°C and 200°C for a Nd:YVO4 crystal [15].With the help of the Q-switch model, the output dependence on temperature can be calculated. The trend curves for pulse energy, duration, and peak power were calculated (Fig. 1 ) and each normalized to its maximum value. From these trends, one can clearly see the energy increase due to the heating of the gain material. Also the pulse duration is decreasing while the peak power is increasing. Additionally, one needs to remain aware as the emission cross-section reduces at elevated temperatures, the pump power threshold will increase and lead to generation of higher order modes. The rest of the Q-switch model as well as parameters used in Fig. 1 can be found in part of the appendix.
Fig. 1 Passively Q-switched output parameter dependence on temperature. Output energy, pulse duration, and peak power are normalized to its maximum value.
3. Experimental results
3.1 Laser setup
The experimental setup is shown in Fig. 2 . A quasi continuous wave (qCW) 400 W fiber coupled laser diode at 808 nm wavelength with a fiber core diameter of 600 µm was used. The pump laser beam was put through the polarized beam splitter where the s-polarization was chosen. A pair of collimating-focusing lenses was used to produce a beam size of 1 mm diameter inside the gain crystal. An a-cut Nd:YVO4 crystal with dimensions 7 × 6.5 × 0.92 mm3, where the longest side was aligned parallel to the polarized pump light, was used for maximum absorption. A Sapphire plate with the c-axis transverse to its face surface and having the same dimensions as the gain crystal was attached and pressed together with the Nd:YVO4 crystal in a holder. This configuration helps to remove the heat generated during the laser operation and homogeneously distributes it over the entire surface of the vanadate material. Both surfaces of the Sapphire crystal had an AR coating for 808/880 nm wavelengths as well as the input surface of the Nd:YVO4 crystal had an additional HR coating for the 1 µm wavelength. The output surface of the gain material had an HR coating for the pump light to increase the absorption length and also an AR coating for the laser wavelength. For Q-switched operation, the Cr4+:YAG saturable absorber with a small signal transmission T0 = 20% and (110) orientation was used. Both surfaces of the SA material were AR coated for the laser wavelength. The output coupler (OC) mirror used in this experiment had 50% reflectivity. The cavity length was 11 mm. The composite Saphire/Nd:YVO4 crystal was inserted into the holder and isolated from the ambient environment by an insulator cap. A temperature controller was used to change the temperature of the holder from 30°C up to 200°C using two cartridge heaters symmetrically situated around the composite chip. By using the laser diode driver, pulse operation at 100 Hz and 1 kHz was possible.
3.2 Operation at 100 Hz
Initially, the laser operation was tested at 100 Hz repetition rate, and the output Q-switch parameters such as pulse energy, duration, and peak power at different holder temperatures were measured. Due to the polarized pump used in this work, only 212 W of peak pump power was available for the experiments. Figure 3 shows the results for the output pulse energy dependence on the holder temperature in the range between 30°C and 190°C for 100 Hz. This dependence shows a clear energy increase with increasing holder temperature. The temperature was measured in 10°C step increments, and at every point the cavity alignment was adjusted to ensure the lowest pump threshold. The smallest available holder temperature was 30°C, which is due to the resistive heaters used in our experiments.
Fig. 3 Q-switch output for 100 Hz repetition rate operation for both the single Nd:YVO4 (black square) and composite Sapphire/Nd:YVO4 (red circle) crystals. Pulse energy (a), peak power, (b) and pulse duration (c) are shown.
In this work both single Nd:YVO4 and composite Sapphire/Nd:YVO4 crystals were tested. For the single Vanadate crystal, the output energy and pulse duration at 30°C holder temperature were 89 μJ and 2.2 ns, respectively. The peak power was 40.5 kW. The pump energy for this operation was 4.2 mJ. The maximum possible energy obtained in this configuration was given when the holder temperature reached 150°C. In this case, the output energy and pulse duration reached 644 μJ and 0.96 ns, respectively. The peak power was 670 kW. The pump energy for this operation was 11.7 mJ. Increasing the temperature of the holder, or increasing the pump energy of the laser diode did not result in Q-switch generation. Only some short oscillations were obtained for duration of 1-2 s. Afterwards the generation completely stopped. This can be attributed to an increase in thermal lensing, where as a consequence, the cavity moves away from the stability zone.
For the composite Sapphire/Nd:YVO4 crystal the operational temperature range could be increased up to 190°C. At a 30°C holder temperature, the Q-switched pulse energy and duration were 109 μJ and 2.1 ns, respectively. The output peak power was equal to 55 kW. At this temperature, the pump pulse duration was 20 μs with incident pump energy equal to 4.2 mJ. This was the minimum available pump power for our experiments which was kept and remained sufficient to obtain Q-switched pulses up to 70°C. By gradually increasing the holder temperature even further, the output energy and peak power dramatically increased up to 1.03 mJ with a peak power of 1.17 MW. The pulse duration decreased to 0.88 ns in this case. At this level we increased the pump pulse duration up to 75 μs with a pump energy equal to 15.9 mJ. After increasing the holder temperature farther, the same thermal lensing effect appeared and no Q-switched pulses were obtained.
3.2 Operation at 1 kHz
For the 1 kHz operation, the available peak pump power decreased to 189 W, which can be the result of heating in the fiber that causes the balance between the s and p polarization modes to change. The data obtained are shown in Fig. 4 . Operation with a single Nd:YVO4 crystal at 30°C provided 240 μJ of pulse energy for 4.7 mJ of pump energy. If the holder temperature increased to 40°C, no Q-switching was possible. For this reason, we used 30°C and only changed the pump pulse duration to increase the pump energy. By increasing the pump pulse duration from 25 μs to 40 μs, it was possible to increase the pulse energy up to 500 μJ directly with a pump energy of 7.6 mJ. After increasing the pump energy farther, the oscillations start to blink and then totally disappear. After cooling down the laser and restarting the oscillations with the previous pump energy, the oscillation can only be maintained for a few seconds until they totally disappear. This is the same thermal lensing effect as was described for the 100 Hz operation.
Fig. 4 Q-switch output for the 1 kHz repetition rate operation. (a) Output energy for the single Nd:YVO4 crystal. (b) Output energy for the composite Sapphire/Nd:YVO4 crystal. The caption on both graphs shows the beam profile of the last measured point. The multiple beam peak pattern of the profile is visible.
Another point to notice, during all ranges of operation for a single crystal, the beam profile at 1 kHz has a complex beam pattern with multiple peaks. This is the sign of strong thermal effects in the crystal due to an average power increase by a factor of 10 compared to that at 100 Hz. The temporal profile of the pulse had multiple peaks and beats between them, so it was not possible to measure the pulse duration during laser operation.
After adding the Sapphire plate to the Nd:YVO4 crystal, similar operation to the 100 Hz mode became possible. At 30°C the available Q-switch energy was 94 μJ with a pulse duration and a peak power of 1.31 ns and 72 kW, respectively. The pump pulse duration was 20 μs with a pump energy of 3.8 mJ. The maximum temperature achieved in this case was only 70°C with energy and pulse durations at this point being only 255 μJ and 1 ns, respectively, and the peak power reached was 255 kW. The pump pulse duration was 30 μs with a pump energy of 5.7 mJ. Also, the output beam displayed a complex beam pattern with multiple peaks similar to that obtained for the 1 kHz single crystal operation. After increasing the holder temperature to 80°C, no Q-switch generation was obtained.
4. Discussion of obtained results
4.1 M2 measurements
To explain the large increase in output energy, a Q-switch model as mentioned above was applied to model our experimental results. As shown in Fig. 5 (red dashed line), introducing temperature dependence for the emission cross-section into the Q-switch model cannot explain the energy increase by a factor of 10. Additional parameters should be included.
Fig. 5 Experimental data compared with the Q-switched model discussed in this work at 100 Hz repetition rate for the composite Sapphire/Nd:YVO4 crystal. The black circle represents the measured data, the red dashed line shows model results for the case when the mode size on the gain material is constant and the output energy depends only on the emission cross-section, which changes with temperature. The green dotted and dashed line shows results for an additional mode size change on the crystal due to higher order mode generation.
Due to increasing the threshold for a Q-switch pulse, higher pump power is required. This leads to the case when higher order transverse modes can appear which increase the mode size in the cavity. To investigate this effect, additional measurements of the beam profile were done. For this reason, an M2 measurement was constructed to help estimate the beam size in the gain crystal. A convex lens was placed after the laser and the beam diameter was scanned and measured according to the ISO 11146 standard along the propagation axis. After measuring the beam diameter, the best M2 value was fitted. In this work measurements were done with a Spiricon CCD camera and the BeamStar software package, which has an option to measure the M2 values.
Measurements were done for 100 Hz operation with the composite Sapphire/Nd:YVO4 crystal and are shown in Fig. 6 . From the data obtained it is seen that the M2 is increasing within our temperature range from 1.3 to 4.36 for the x component, and from 1.52 to 4.52 for the y component. The difference in the beam quality for the x and y components is due to an anisotropy in the vanadate crystal, which results in different thermal conductivity values for the vertical and horizontal directions.
Fig. 6 Experimental results for the M2 values at 100 Hz repetition rate for the composite Sapphire/Nd:YVO4 crystal. Vertical and horizontal values are measured.
4.2 Thermal lens calculation
The next step is to calculate the thermal lensing in our laser. In this work we used the equation from [23], where the temperature induced change in the refractive index dn/dT is included. Because of the small cavity size, the pump power induced stress at the front of the Nd:YVO4 crystal surface can result in additional changes in the thermal lensing of the crystal. These two effects should be combined, and the full equation for thermal lensing fth takes the following form
where K(T) is the temperature dependent thermal conductivity of the vanadate crystal, wp is the pump radius, Pin is the incident pump power, ηabs is the absorption efficiency, ηh is the fractional thermal load, α is the coefficient of thermal expansion, and n is the index of refraction. For this calculation the values for thermal expansion and temperature-induced change in the refractive index were taken from [24]. Absorption efficiency was taken to be 0.9 for a double pass transition, and the fractional thermal load was considered to be 0.241 or simply the quantum defect between the pump 808 nm and laser 1064 nm wavelengths. The values for the thermal lensing calculation can be found in Table 1 .
Table 1. Q-switched parameters used for calculation
For a thermal conductivity dependence on temperature, we used the data from Fig. 8 of [7] for the undoped YVO4 crystal, because there is no source to provide values for the 1-at.% doped Nd:YVO4 crystal. Afterwards, we applied the values from Table 2 of the same reference to obtain the thermal conductivity for 1-at.% doped Nd:YVO4 crystal at 25°C. The ratio between the doped and undoped crystal at 25°C was found to be 0.934, which was then applied to find the thermal conductivity values for the rest of the temperature range by the following form: Kdoped(T) = 0.934 × Kundoped(T).
Table 2. Thermal lens and beam size parameters
4.3 Cavity mode size calculation
To calculate the laser mode size in the gain crystal, a two-mirror resonator model with a variable internal lens was employed [25]. The difference in this case was that one arm of the cavity was equal to 0. By including the value for thermal lensing, the fundamental mode size w0l was calculated using the following equation
where λ is the laser wavelength, L* is the equivalent resonator length, and d2 is the distance between the Nd:YVO4 crystal output surface and output coupler mirror. For a description of the model used in this work, please refer to the appendix.Since the previous equation is developed for the fundamental transverse mode, it should be multiplied by an additional factor, which is given by the square root of M2, to get the mode size in the crystal
After obtaining the mode size values for our temperature range, we applied them to our Q-switch model. The fitted result of the mode values we obtained are shown in Fig. 5 (green dash and dot line). From this result, we see a closer agreement with our experimental data compared to the case where only the temperature dependence of the emission cross-section was included.
4.4 Temperature distribution in the Nd:YVO4 crystal
The temperature in the Sapphire/Nd:YVO4 composite crystal was measured for different holder temperatures. For this experiment shown in Fig. 7(a) , the output mirror and saturable absorber crystal were removed and an IR thermal camera (Chino CPA 8000) with a close-up lens and a spatial resolution of 100 μm was placed nearby to measure the temperature of the output surface of the vanadate crystal. The temperature was measured for the same operating conditions as during the Q-switched mode and the temperature difference ΔT between the center peak Tp and holder Th temperatures was obtained. Although the temperature of the crystal was measured in the non-lasing regime, we can assume that the amount of heat generated during Q-switching should be similar. This is likely because the output laser pulse that is equal to, or below 1 ns is much shorter compared to the pump pulse which is at least 20 μs or higher. For this reason our laser can be considered as non-lasing all the time, and we can assume increased heat generation.
Fig. 7 Experimental results for the temperature measurement of the output surface of the composite Sapphire/Nd:YVO4 crystal. (a) The measurement setup: the center peak temperature Tp was measured with an infrared thermal camera and close up lens with 100-μm spatial resolution. (b) Experimental data: the difference ΔT between the center peak Tp and holder Th temperatures was measured. For 100 Hz operation, this difference is almost flat over a wide operational range. For 1 kHz, the temperature difference keeps increasing for the same pump conditions.
In Fig. 7(b), the temperature difference ΔT = Tp-Th results are presented. We can clearly see that the temperature difference at 100 Hz repetition rate has a flat behavior, meaning there is a constant difference between the center peak and side temperatures, which is consistent over a wide range. That can explain the continuous increase in holder temperature during the experiment. On the other hand for a 1 kHz operation, this difference increases with increasing holder temperature and shows high heat generation in the Nd:YVO4 crystal. This increased heating could lead to higher thermal lensing and lead to an unstable resonator condition which would terminate the Q-switch pulse generation. This can explain why the Q-switch operation stopped above 70°C.
5. Conclusions
In this work, experiments were performed to obtain a high peak power, high repetition rate, and passively Q-switched laser based on a Nd:YVO4/Cr4+:YAG crystal combination. For obtaining high energy, an increased pump beam diameter was used. Additionally, to increase the heat removal and homogenize the temperature across the gain material, a Sapphire plate was attached to the Nd:YVO4 crystal. This, as it has been shown in the experiment, helped to homogenize the temperature at the 100 Hz repetition rate operation, but was still not enough at 1 kHz. A Q-switch model was used to fit the experimental data. By including the laser mode size along with the temperature dependent emission cross-section, a close fit to experimental results was obtained. The energy of 1 mJ and peak power of 1.17 MW that were obtained for a 100 Hz operation are the highest when compared with other passively Q-switched Nd:YVO4 laser systems with the Cr4+:YAG crystal as a saturable absorber. For the 1 kHz operation, the maximum peak power obtained was only 255 kW, which is 4 times smaller than the maximum value for the 100 Hz operation. This could be due to increased heat generation inside the gain material and an increased thermal lensing effect.
To further investigate high-energy high-repetition-rate lasers, additional modifications of the cavity design will be considered. Attaching a second heat removal plate will help to remove the heat from the output surface. Moreover, materials such as Diamond or SiC, which have a higher thermal conductivity than the Sapphire crystal, can help to stabilize the thermal lensing effect at higher repetition rates. The mode size of the cavity can be increased by using an unstable resonator design, which not only allows an increase of the output energy of the laser, but also can retain good beam quality by having higher diffraction losses for the higher order modes, compared to a flat-flat cavity.
Appendix 1 Model of the passively Q-switched laser
In this part we present the passively Q-switched model to calculate the output from the microchip laser. After the modification as presented in [20], the rate equations for the photon density ϕ, population inversion density in the gain medium ng, and the population inversion density of the SA absorbing state nSA can be written as
where σg, σSA, and σESA are the emission cross-section of the gain crystal, absorption cross-section, and excited state cross-section of the SA, respectively. γg and γSA are the thermal population reduction factor for the gain crystal and the SA, respectively. τg and τSA are the relaxation times for the gain medium and SA crystal, respectively. Ag and ASA are the effective mode area of the gain and SA crystals, respectively. nSAi is the initial population inversion density of the saturable absorbing state. Wp is the volume pumping rate. The resonator residual loss is described by L, the output coupler mirror reflectivity is described by R, and the cavity round trip time by tr.
To obtain the output parameters for the Q-switch, one can neglect the influence of the optical pumping Wp and that of the gain relaxation term -ng/τg in Eq. (9), and the influence of the SA relaxation term –(nSAi-nSA)/τSA in Eq. (10). The dynamics are characterized by the rapid growth and decay of the pulse and by a decrease of the gain inversion and of the SA ground state population density. Also for the start of Q-switch (t=0), nSAi=nSA. Then the pulse energy Ep and the peak power Pp can be obtained.
Previously we showed the rate equation model and the output parameters for the Q-switch operation, where additional parameters appeared. The δ accounts for the ESA effect of the Cr4+:YAG crystal
α is a parameter determined by the properties of the gain media, SA crystal, and the ratio of the mode areas
and the p parameter is combining all of the losses in the cavity
In a passively Q-switched system, the laser action begins at the moment the population inversion density reaches a value ngi=ng (t=0) that corresponds to a stimulated emission gain that overcomes the losses in the resonator in the presence of the SA with transmission T0. Setting Eq. (8) to zero gives the condition for ngi
The increased flux in the resonator induces a rapid decrease of SA transmission that determines the reduction of ng by stimulated emission, and the further increase of the light flux. The maximum energy emission occurs when dϕ/dng=0, and the population inversion at this point can be calculated by following equation
The moment of time when dϕ/dng=0 corresponds to the maximal slope of the decreasing of ng. Owing to the further decrease of ng, the photon flux diminishes to 0, corresponding to a final population inversion ngf given by
Generally the pulse energy Ep is
with hν as the photon energy at 1.06 µm. The peak power Pp is given by
By numerically calculating Eqs. (15) and (16) , one can obtain several solutions with real and imaginary roots. Out of these solutions, those which are real and in the range of 0<(ngt/ngi and ngf/ngi)<1 are suitable to obtain values for the pulse energy Ep and the peak power Pp in Eqs. (17-18) . With the help of this Q-switched model, the output parameters’ dependence on temperature was calculated and presented in Fig. 1. Additionally, all of the parameters used in this trend calculation can be found in Table 1.
Appendix 2 Two-mirror cavity with an internal lens
In this work as described earlier, the results for the two-mirror cavity with an internal lens was used [25]. The principle for this model is to exchange this type of resonator with an equivalent two-mirror resonator and change the equations to the following
where i,j=1,2 and i≠j. In last three equations, the asterisk denotes an equivalent cavity length L and a stability parameter g. The index i represents the left side of the cavity, and j represents the right side. ρ is the curvature of the cavity mirror; d1 and d2 are the distance from the cavity mirror to the principal plane of the thermal lens fth for the left and right side, respectively. The beam radius at the mirror can be found using the following equation
The beam radius on the principal plane of the thermal lens can be written in the following form
Because the left mirror is coated directly on the crystal, we can consider the left side length d1 equal to 0. The curvature of the cavity mirror ρ is flat and equal to infinity, and L* is equal to d2. By inserting these values into Eqs. (19-23) we can obtain the Eq. (6) in the main section. Also, because we made d1 equal to 0, the beam radius on the left mirror w1 became equal to the beam radius wL on the principal plane of the thermal lens or gain crystal. Table 2 shows the parameters used to calculate the thermal lens and mode size in the cavity.
Acknowledgments
This work was funded by the ImPACT Program of the Council for Science, Technology and Innovation (Cabinet Office, Government of Japan), JST-SENTAN (Japan Science and Technical Agency) and C-PhoST (Consortium for Photon Science and Technology). Also, the authors would like to thank Dr. Y. Sato for the discussion of Nd:YVO4 crystal parameters which were used in this work, especially for the thermal conductivity data provided.
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