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We first demonstrated a continuously and widely giant-pulse duration tunable laser based on a short monolithic Nd:YAG/Cr:YAG ceramic by cavity-length control in 100 Hz operation. The tuning range of pulse duration τ was from 0.5 to 9 ns as keeping peak powers of over 0.5 MW up to 6 MW. The characteristics of the ceramic laser was discussed in detail such as cavity-length dependent beam pattern and divergence, pulse shape, pulse energy due to the transverse and longitudinal modes, and an elliptical polarization status. Laser induced breakdown in laboratory air was investigated as a function of τ in sub-nanosecond region using the developed laser. Air-breakdown threshold intensity Ith was measured using three different focusing conditions. We confirmed that 1) the measured Ith was almost constant at the longer τ than τCI named as limit-pulse-duration of cascade ionization (CI), 2) Ith had ~τ−2 scaling for τ < τCI, 3) the increase of Ith is not connected to a specific intensity level, and 4) τCI was not constant and depended on focusing conditions. These phenomena were discussed with considering temporal-spatial intensity of laser.
© 2017 Optical Society of America
1. Introduction
Laser induced breakdown (LIB) in gases has been studied extensively since the advent of powerful lasers and the technological progress for the shorter pulse. LIB in air has been explained by different ways along pulse duration τ. Cascade ionization (CI) [1–3] is considered as the mechanism for long pulse durations of over 1 nanosecond (ns). CI process can be explained by three steps briefly; 1) initial seed free-electrons, 2) acceleration of the free electrons by inverse Bremsstrahlung, 3) multiplication by collisional ionization. The initial electrons can exist naturally or can be produced from impurities of air through multi-photon ionization (MPI) at a leading part of pulse. The latter two steps are collisional processes taking time, repeated up to reach the critical electron density for plasma production. On the other hand, CI processes cannot play a role in a short pulse of less than 1 picosecond (ps). Even inverse Bremsstrahlung requires a time scale of an order of ps in one atmospheric air due to the mean free time of electron. Laser filamentation [4] is alternative mechanism of air-breakdown for femtosecond (fs) pulses. Once Kerr self-focusing, started at a critical power (GW level), overcomes natural diffraction, the self-focal size becomes smaller and smaller resulting in plasma production via MPI and tunnel ionization. With the higher power, multiple plasma channels are generated by the dynamic balance between self-focusing, diffraction, and defocusing by plasma [4].
However, for intermediate ps pulse region, the mechanism is unclear due to contribution of MPI to CI process. Wang et al. reported that breakdown threshold of intensity Ith is almost constant for a long pulse duration of over than ~1 ns at 1.06 μm [5]. On the other hand, Van Stryland and Williams et al. [6,7] reported that Ith has ~τ−1 scaling in 30-140 ps region at wavelengths of 0.53 and 1.06 μm. Nevertheless, there are still open questions about the reason of ~τ−1 scaling and the degree of contribution of MPI due to lack of data between the “pulse duration gap [8]”. In fact, since we cannot have access to the pulse gap for a long time, there is a lack of knowledge about air-breakdown based on CI in sub-ns region. In addition, the knowledge about pulse duration dependent breakdown energy in gas is practically useful for laser ignition. Laser ignition has been the focus of attention to various combustion fields because of its advantages: freedom of ignition point, minimal ignition delay, multiple ignition points, burst ignition, wide acceptance of mixture ratio and pressure, etc. Giant pulse ceramic micro-laser have boosted laser ignition field such as ‘world first micro-laser ignited gasoline engine vehicle [9]’, because of its high peak power (>MW), compact structure, stability, and low cost [8–10].
In fact, we once reported a preliminary study on breakdown threshold intensity using a focusing lens in sub-ns region elsewhere [11]. However, because we tuned the pulse duration by exchanging Cr:YAG ceramics and single crystals with different initial transmittances and using output couplers with different reflectances, it was difficult to keep the beam shape and pulse shape. In this paper, we first demonstrate a pulse duration tunable system based on a monolithic Nd:YAG/Cr:YAG ceramic micro-laser by cavity length control for a smooth change of laser quality. Then, breakdown threshold of laboratory air is investigated as a function of pulse duration in sub-ns region at different focusing conditions.
2. Pulse duration tunable laser
2.1 Experimental setup
The pulse duration τ of Q-switched lasers is given by, where τc is the cavity lifetime ( = the cavity round-trip time / the cavity round-trip loss), r is the initial inversion ratio, and η(r) is the energy extraction efficiency. Therefore, the shorter cavity generates the shorter pulse for the same medium and reflection loss. An analytical solution of a well-established Q-switched laser model allows an accurate prediction of τ for real laser system [12–15]. We developed a pulse duration tunable laser using a monolithic Nd:YAG/Cr4+:YAG ceramic with a dimension of 3 x 3 x 7 (L) mm3. The small monolithic ceramic size allows to access sub-ns region. Figure 1 shows a schematic of the pulse duration tunable system with a photo of monolithic ceramic. The Nd-doping rate was 1.1% and the initial transmittance T0 of Cr:YAG was 30%. The input-surface was high-reflection (HR) and anti-reflection (AR) coated at 1064 and 808 nm, respectively. The output-surface was AR coated at 1064 nm. A separated mirror with a reflectance of 50% at 1064 nm was used for output coupling. The cavity length was adjusted by moving the output coupler set on a motorized translation stage. A fiber (ϕ = 0.6 mm) coupled quasi continuous wave diode laser (wavelength, 808 nm; repetition rate, 100 Hz; peak power, 120 W; pump duration, 500 μs) was used for end pump source. The pump conditions are kept for cavity length control. The pump beam from the fiber was collimated in the ceramic as a diameter of 1.2 mm (full width half maximum; FWHM). A high-speed InGaAs photodetector (<25 ps rise time) was used for pulse duration measurements. A compact spectrometer with a resolution of 10 pm and CMOS camera was used to measure wavelength spectrum and beam pattern, respectively.
2.2 Results and discussion
The laser operated stably at 100 Hz repetition rate for continuously adjusting the cavity length widely once the laser starts with output coupler alignment. The critical alignment condition of the planar-planar cavity during cavity length control may be released with the assistance from thermal effects due to the high power of pump, such as acting like a concave-planar cavity. The pulse duration was tuned from 0.5 to 9 ns (FWHM) by increasing the optical cavity length lc from 14 to 270 mm with the pulse energy of over 2.65 mJ, as shown in Fig. 2(a). Figure 2(b) shows the measured delay time between pump and laser, which was determined by comparing the leading part of pump pulse with a duration of 500 μs and laser pulse. The delay time increased linearly to the cavity length (in other words, the round-trip time) of around 150 mm and increased exponentially for the longer cavity. The exponential increase is attributed to additional oscillation of longitudinal modes requiring the higher pump energy, as will be discussed later. The required pump duration was 270 μs (corresponding pump energy of 32.4 mJ) for the shortest cavity and 477 μs (57.2 mJ) for the longest cavity, respectively. Nevertheless, we used the constant pump duration of 500 μs (60 mJ) because of continuous pulse duration tuning without a time interval to restart pump laser after adjusting pump duration. The optical-to-optical conversion efficiency was 5% for the shortest cavity and 8% for the longest cavity, respectively. The maximum pulse duration of 9 ns was limited by the delay time of 477 μs close to the pump duration. The whole pulses had high peak powers ( = pulse energy/pulse duration) of over 0.5 MW as shown in Fig. 2(b). The peak power was 6 MW for the shortest pulse duration and decreased with the expansion of pulse duration due to the similar pulse energy, but the decrease stopped at 0.5 MW from around 150 mm of cavity length because of the increased pulse energy. The energy increase of the long cavities is also attributed to the longitudinal modes added from single mode oscillation. It will be discussed below.
Fig. 2 a) Measured pulse duration and energy as a function of optical cavity length. The measured pulse duration was compared to theoretical calculation. b) Corresponding peak powers versus optical cavity lengths.
Figure 3(a) shows the measured pulse shapes at the short cavity lengths of less than ~110 mm. Near Gaussian pulse shape was changed to be asymmetrical as increasing the cavity length due to may be the contribution of higher transverse modes. The change of pulse shape results in pulse duration broadening and make the deviation from the theoretical calculation as shown in Fig. 2(a). The calculation was based on an analytical solution of a well-established passively Q-switched laser model with physical parameters [12–15]. For the longer cavity lengths, the measured pulses show beating of longitudinal modes, which is shown in the inset of Fig. 3(b). The free spectral range (FSR) of longitudinal modes was estimated by fast Fourier transform of the beating forms, showing well agreement with the calculation result as shown in Fig. 3(b).
Fig. 3 a) Measured pulse shapes for short cavity cases. b) Evaluated free spectral range (FSR) by fast Fourier transform of the pulse shape with beating between longitudinal modes. Inset: typical pulse shape at lc = 174 mm.
We measured wavelength spectra of whole pulses that have a single peak in 10 pm resolution. The single peak can guarantee single longitudinal mode operation of the short cavity with FSR larger than 10 pm resolution at least.
Figure 4(a) presents the captured beam patterns at different cavity lengths. The higher transverse modes were easily oscillated with the fundamental mode at the short cavities due to enough pump beam size to gain higher modes, but the higher modes were suppressed at the long cavities. The beam divergence depended on the presence of higher modes as shown in Fig. 4(b). The laser beam had a half angle divergence of ~2 mrad at lc of ~50 mm, but the divergence was decreased with cavity length increase and had the almost constant value of ~1 mrad for the long cavities of over ~120 mm. Measured M2 values were typically 3 and 1.2 for the short cavities and long cavities, respectively. On the other hand, ceramic lasers have random polarization due to randomly distributed micro-particles in ceramics in general. However, we observed that our ceramic laser can be oscillated with near linear polarization at low repetition rates of less than 30 Hz. It could be a possible reason that slightly different reflectance between orthogonal waves at the output surface of monolithic ceramic due to non-perfect parallelism. For 100 Hz repetition rate, the polarization state was degraded to be elliptical due to thermal effect induced birefringence and depolarization. The ratio of the minor axis component to the total output, Emin/(Emin + Emaj) was 261.5% for whole cavity lengths at 100 Hz. The ratio was reduced ~5% at 30 Hz.
Fig. 4 a) Measured beam patterns at different optical cavity lengths. No higher order modes are observable for lc greater than 120 mm. b) Measured half angle divergence versus optical cavity length. The laser beams have small divergence of about 1 mrad for lc greater than 120 mm.
3. Air-breakdown
3.1 Experimental setup
Figure 5(a) shows schematic of experimental setup for air-breakdown. We carried out air-breakdown using the developed pulse duration tunable laser with a repetition rate of 100 Hz. The pulse energy was varied with a half-wave plate and a polarizer. The linearly polarized laser was focused in laboratory air with three aspheric focusing lenses with focal length f of 6.24, 8, and 11 mm. The beam size on focusing lens was measured by a CMOS camera positioned at the same distance from laser. M2 value was measured using a system (Cinogy) and the pulse shape was measured using a 13 GHz oscilloscope coupled with a high-speed InGaAs photodetector (rise time; < 25 ps). Breakdown was confirmed by observing the visible breakdown spark at near right angle using a collecting lens and another high-speed GaAs photodetector (rise time; < 30 ps). We defined the breakdown threshold as the required energy for 100% breakdown success. Figure 5(b) shows the measured 100% breakdown spark train (top) for 320 laser pulses (bottom). For a slightly lower energy than the threshold, some laser pulses failed in breakdown resulting in missing in the spark train. 100% breakdown threshold was chosen because of its clarity and its value as a parameter for practical applications such as laser ignition [9,10].
Fig. 5 a) Schematic of experimental setup for air-breakdown. Three lenses were used for focusing, respectively (f = 6.24, 8, and 11 mm). b) Measured 100% breakdown spark train (top) for 320 laser pulses (bottom)
3.2 Results and discussion
Figure 6(a) shows the measured air-breakdown threshold fluence Fth as a function of pulse duration in a range from 0.5 to 0.65 ns (FWHM) using a focusing lens (f = 6.24 mm). The threshold has a minimum fluence of ~1.0 kJ/cm2 around 0.6 ns. The threshold has the ~τ scaling in the longer pulse region, but it deviates from the scaling and has ~τ−1 scaling for the shorter pulses. The confirmed ~τ scaling for the long pulse region agrees with the reported experimental result [5]. Breakdown threshold can be well defined for a tight focusing with assistance from MPI of impurities in air [16,17]. The measuring range was limited by current minimum cavity length for short pulse and by keeping almost the same conditions such as pulse shape, M2, and beam shape for long pulse, respectively. No measurement was carried out with the degraded pulse shape such as 0.69 ns as shown in Fig. 6(b). The fluence was calculated with the measured threshold energy and the calculated spot size. The focal spot size was estimated assuming Gaussian beam propagation with the measured beam size on focusing lens (~3 mm) and M2 value of ~3. The measured pulse duration was an averaged value of over one thousand pulses. The error bars in the threshold only represent the energy fluctuation of pulses.
Fig. 6 a) Measured air-breakdown threshold fluence as a function of pulse duration. The measurement for long pulse range was limited before pulse shape degradation such as 0.69 ns as shown in b). b) Measured typical pulse shapes in the range of 0.5-0.7 ns.
We compared breakdown threshold energies Eth for three different focusing lenses (f = 6.24, 8, and 11 mm) as shown in Fig. 7(a). The breakdown energies were 0.5-1 mJ level in the pulse durations of 0.5-0.65 ns. The threshold energies are a function of not only τ but also focusing condition. It is attributed to the diffusive electron loss out of the focal volume [18]. Another loss due to inelastic collision also could depend on the focal volume [18]. In the view point of energy saving, a moderate focal volume such as the circled symbols in Fig. 7(a) is better for laser induced gas breakdown. There is a tradeoff between low (high) breakdown energy and high (low) diffusive loss.
Fig. 7 Measured breakdown threshold energies a) and intensities b) as a function of pulse duration in laboratory air for three focusing lenses with focal lengths of 6.24, 8, and 11 mm.
The minimum breakdown energies are clearly observed for every focusing condition but their pulse durations are different, which will be discussed later. The local pulse duration is named as a limit-pulse-duration τCI of CI. Figure 7(b) shows the calculated threshold intensity Ith from the measured breakdown energy. The almost constant breakdown thresholds at different intensities became increased beyond around τCI for all focusing conditions, which has ~τ−2 scaling. This means that the reason of Ith increase is not connected to a specific intensity level. Therefore, intensity dependent phenomena such as MPI and saturation of CI rate due to a high intensity (or strength of electric field) [19] cannot be the main reason of the increase of Ith.
Even so, it is still a challenge to explain Ith increase with a theoretical model. To the best of our knowledge, even the almost constant Ith for long pulses cannot be explained properly with existing simple rate equations to determine electron density n(t) in the CI process such as or [18,20], where α and I(t) is an avalanche (rate) coefficient and intensity of laser pulse, respectively. According to the rate equations, the electron density increases exponentially with the power of τ. This means that the longer pulse is efficient and can have the lower Ith.
We believe that CI process should be discussed with consideration of temporal-spatial intensity of laser. By assuming an initially focusing Gaussian laser pulse, the temporal-spatial intensity is given by
where r2 = x2 + y2, w0 is the beam waist size, w2(z) = w0{1 + (z/z0)2} with z0 = πw02/(λM2) being the Rayleigh length, I0 is the peak intensity, t0 is the central temporal position of the laser pulse and τ is the pulse duration. Then, an intensity level Is to a peak intensity I0 has an isointensity contour boundary rFigure 8(a) shows the calculated time varying isointensity contour at the intensity level Is with 40% of I0, where we set w0 = 10 μm, λ = 1 μm, M2 = 1, t0 = 0, and the time range from -τ /2 to τ /2 with an interval of 0.1τ. The isointensity boundary has one cycle of increasing, a maximum, and decreasing during τ. Figure 8(b) presents the isointensity contours at different intensity levels (20%-80%) to I0 for a fixed time of t = 0.Fig. 8 a) Calculated isointensity contours at Is = 0.4 × I0 for the time range from - τ /2 to τ /2 with an interval of 0.1τ. b) Calculated isointensity contours at different intensity levels (20%-80%) to I0 for a fixed time of t = 0.
Therefore, the ratio of intensity change in space is inversely proportional to τ, which can affect CI process in time domain resulting in a decrease of CI rate for the longer pulse. This could be a possible reason of the almost constant Ith at τ>τCI. It is notable that the integrated number of molecules inside the isointensity boundary and volume [21,22] during different pulse durations are the same if the pulses have the same I0. In other words, the number of effective molecules participating in CI process are equal for different pulse durations with the same I0.
On the other hand, the increase of Ith at τ<τCI is not clearly explained so far, but we believe that it is attributed to the lack of time to finish CI process for breakdown. The acceleration and multiplication of electrons are collisional processes with a discrete time delay due to the mean collision time between electron and molecule. If the time delay affects more a short pulse resulting in a decrease of CI rate, the higher peak intensity is required to finish the work with an increased number of effective molecules in the larger isointensity volume for the same Is. On the other hand, air-breakdown can be succeeded at the lower Ith for the weaker focusing, because the longer Rayleigh length allows the wider isointensity boundary. The weaker focusing can take enough number of effective molecules to finish breakdown with the lower Ith. The weaker focusing seems sustainable the breakdown up to the shorter τ without intensity increase, because τCI is slightly shifted to the shorter pulse for the weaker focusing as shown in Fig. 7. The larger number of effective molecules for the weaker focusing could be the reason, but further investigation on pressure dependence should be followed to confirm it directly. Finally, we point out that Ith could be saturated from the ~τ−2 scaling for the shorter pulses, because of an additional contribution of MPI due to enough high intensity level for MPI [6,7].
4. Summary
We developed a compact, high peak power, widely, and continuously pulse duration tunable system operating at 100 Hz repetition rate based on a monolithic Nd:YAG/Cr:YAG ceramic micro-laser by cavity-length control. The pulse duration tuning range of 0.5-9 ns was achieved by adjusting the optical cavity length from 14 to 270 mm as keeping peak powers of over 0.5 MW. The characteristics of the laser depending on cavity-length due to the presence of higher transverse modes and additional longitudinal modes were discussed in detail. We applied the developed laser to air-breakdown threshold measurement as a function of τ in sub-ns region using three different focusing conditions. We confirmed that the almost constant breakdown threshold intensity Ith gradually increases and has ~τ−2 scaling as τ passes through a limit-pulse-duration τCI. The limit-pulse-duration may be related to the number of molecules participating in CI process, which can be deduced from focusing dependent τCI. However, further studies with pressure control should be followed to clarify the limit-pulse-duration.
Funding
New Energy and Industrial Technology Development Organization (NEDO)
Acknowledgments
Authors thank Denso Corporation, Konoshima Chemical Company Ltd., and Ricoh Company Ltd. regarding on NEDO project and Dr. Masaki Tsunekane for the contribution of laser developments.
References
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