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Abstract
In this work, a variable-pulse-oscillator is developed and coupled with a burst-mode amplifier for generation of high-energy laser pulses with width of 100 ps to 1 ms and near-Gaussian temporal pulse shape. Pulse energy as high as 600 mJ is demonstrated at 1064 nm, with a super-Gaussian spatial profile and beam quality as good as 1.6 times the diffraction limit. A time-dependent pulse amplification model is developed and is in general agreement with experimentally measured values of output pulse energy and temporal pulse shape of the amplified pulses. Key performance parameters (pulse energy, temporal pulse shape, and spatial beam profile and quality) are analyzed as a function of pulse width across seven orders of magnitude. Additionally, the model is used to elucidate deviations between the simulated and experimental data, showing that the relationship between pulse width and output pulse energy is dominated by the variable-pulse-width oscillator performance, not the burst-mode amplifier.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the past four decades, laser-based optical measurement techniques have become a standard tool for diagnosing and understanding thermo-fluid and combustion processes. Enabled by the introduction of high-energy, Q-switched lasers, a variety of pulsed, nanosecond (ns) spectroscopic techniques are now commonly applied to thermo-fluid and combustion systems including laser-induced fluorescence (LIF), laser-induced incandescence (LII), coherent anti-Stokes Raman scattering (CARS), Raman scattering, Rayleigh scattering, and particle-image velocimetry (PIV) [1]. While pulse widths on the order of 10 ns are typically utilized for these measurements, many such techniques can benefit from either shorter (e.g. picosecond, ps, or femtosecond, fs) or longer (e.g. microsecond, µs) pulse durations. For instance, nonlinear processes such as two-photon LIF and CARS benefit significantly from the use of high-peak-power fs and ps pulses which greatly enhance signal levels while minimizing interference from competing linear processes [2]. In contrast, linear processes such as spontaneous Raman scattering require extremely high pulse energy with low peak power to minimize damage to optical components and avoid breakdown on particles in the flow. This requires optically stretching the pulse to widths exceeding 100 ns [3]. As such, there is a significant need for laser sources with sufficient pulse energy for linear processes, yet with pulse width variability to generate the peak powers required to drive nonlinear processes.
Numerous variable-pulse-width (VPW) laser architectures have been developed for applications including flow and combustion diagnostics [4], laser ignition [5], laser machining [6,7], medical procedures [8], and even conservation of historic artifacts [9]. In general, the pulse width range (e.g. fs, ps, ns, µs, ms) will dictate the technologies that can be used to generate the tunable pulse. For fs pulse widths, coherent coupling of longitudinal modes from two fiber ring lasers was used to narrow the output pulse spectral bandwidth resulting in a variation of the pulse width from 150 fs to 1.5 ps [10]. Similarly, Liu and Cui used an intracavity fiber Bragg grating as a flexible filter to vary the spectral bandwidth of a fiber laser enabling control of the pulse width from 7 to 150 ps [11]. For pulses longer than 100 ps, fast electronics can be used to directly shape laser pulses using a variety of methods. Ong et al. used a high-speed Field Programmable Gate Array based driver to directly pulse a fiber-amplified diode laser resulting in pulse width control from 200 ps to 200 ns at repetition rates up to 1 MHz [6]. RF pulse clipping has also been used to vary pulse widths from 40–300 ns in Q-switched Nd:YAG lasers at rates up to 50 kHz [7]. Optically, Salimbeni et al. used interchangeable fibers in a Q-switched, Nd:YAG-laser resonator to vary pulse width from 100 ns to 2 µs [9]. For longer pulse widths, the flashlamp discharge can be directly varied to produce pulse widths from 300 µs to 10 ms [8]. Because of the electronic and optical limitations of each pulse width regime, the applicability of each individual variable-pulse-width method rarely extends beyond two orders of magnitude, particularly if pulse shape is a significant consideration.
In addition to pulse width, pulse repetition rate and energy is also of particular interest for flow and combustion diagnostics applications. To overcome limitations of low-repetition-rate, high-energy lasers traditionally used in flow and combustion diagnostics, burst-mode lasers were developed, which use a low duty cycle (∼0.1 Hz) to generate high pulse energies (> 1 J) at repetition rates exceeding 10 kHz [4,12]. Although most burst-mode lasers use either flashlamp-pumped [13] or diode-pumped [14] Nd:YAG amplifiers, a variety of oscillator architectures have been employed. Initially, high-speed Pockels-cell slicers were used to generate 10 ns pulses from a continuous-wave (CW) laser, which were subsequently amplified in a flashlamp-pumped burst-mode amplifier [15]. Thurow et al. introduced an acousto-optic modulator (AOM) based pulse forming method that allowed for variation of the pulse width beyond 10 ns, however, the pulse profile changed from Gaussian to top-hat for pulse widths greater than 20 ns [16]. AOM-based shaping has also been used in combination with flashlamp gating to generate pulses as long as 1 ms [17]. Pulsed lasers, both Q-switched and fiber based, were used as oscillators to increase per-pulse energy at 10 ns pulse duration, but are typically restricted to a single repetition rate or specific range of pulse repetition rates [13,18]. Most recently, a mode-locked ps oscillator with pulse picking [19] and an electro-optic modulator (EOM) with ps rise time [20] have been used to produce 100-ps pulses for burst-mode amplification but with limited pulse width tunability.
Nanosecond oscillators have been used with burst-mode amplifiers to enable high-speed PLIF [21], PIV [22], LII [23], planar Doppler velocimetry (PDV) [15], laser-induced breakdown spectroscopy (LIBS) [24], Raman [25] and Rayleigh [26], while picosecond oscillators have enabled high-speed picosecond laser electronic excitation tagging (PLEET) [27], ps CARS [28], and 2D fs/ps CARS [20]. Even so, the pulse width requirements of these diagnostic techniques currently place strict limitations on the choice of oscillator for each system, which can be extremely costly. Therefore, the objective of this work is to develop a single, fiber-based variable-pulse-width oscillator architecture for use with burst-mode laser amplifiers to enable the generation of high-energy, 100-ps to 1-ms-duration laser pulses applicable to linear and nonlinear flow and combustion diagnostics.
2. Laser architecture
2.1 Overview
The VPW laser architecture consist of a highly flexible, low-pulse-energy oscillator and high-gain burst-mode amplifier. These are used, in sequential combination, to shape and amplify an output of narrow-bandwidth, continuous-wave (CW) diode laser, with central wavelength of 1064 nm, into a discrete burst of high-energy pulses with variable pulse duration, repetition rate, and burst length. The system is designed to produce pulses with durations of ∼100 ps to 1 ms, full-width at half-maximum (FWHM), using a series of electro-optic and acousto-optic modulators in combination with fiber-based and free-space amplifiers. The VPW oscillator employs continuously pulsed fiber-based amplification, while the free-space, burst-mode amplifier (described in details in Ref. [14]) is run in a single-shot mode with a shot-to-shot period of 8 seconds.
As shown in Fig. 1, four primary configurations are used within the VPW oscillator to enable pulse generation with widths covering the range of 100 ps to 1 ms. Configuration changes (a-d) are made through automated optical-fiber (Leoni, eol 1 × 2 PM HP) and radio-frequency electromechanical and solid state switches (Mini-Circuits). A narrow-bandwidth CW diode laser serves as the source, with center wavelength of 1064 nm and bandwidth of <350 MHz. No direct linewidth measurements were made using the amplified pulse due to the complication of burst mode operation. Therefore, an assumption of the linewidth being limited by the pulses time-bandwidth product was made. This limit is assumed for each pulse width regime unless limited by the seed lasers linewidth, i.e. longer pulse widths which would allow for a narrower line width than the seed laser could provide. The CW laser is initially amplified through a low-gain booster fiber amplifier (continuous wave operation, Ytterbium-doped fiber) to about 100 mW power. The configurations shown in Fig. 1(a) and Fig. 1(b) employ a fiber-coupled electro-optic modulator (EO Space, 20 GHz bandwidth) as a pulse shaping device, which can produce pulses as short as 100 ps. The configuration shown in Fig. 1(c) employs a fiber-coupled acousto-optic modulator (Gooch & Housego, 200 MHz RF, 10 ns rise/fall time) as a primary pulse shaping device, while a free-space EOM (Conoptics, 400 ns rise/fall time) is used in the configuration shown in Fig. 1(d). Each configuration is classified further by the range of pulse widths produced: 0.1–1 ns (Configuration A, Fig. 1(a)), 1–10 ns (Configuration B, Fig. 1(b)), 10–1000 ns (Configuration C, Fig. 1(c)), and 1–1000 µs (Configuration D, Fig. 1(d)). Each configuration will be described in detail in the following sections. Results from configurations A and B are plotted in red, while results from configurations C and D are plotted in blue throughout the manuscript. The choice of the Configuration is governed by the bandwidth of the electronic components and also by the required contrast between the maximum peak power in the shaped pulse and the amplified background.
Fig. 1. Schematic of variable-pulse-width oscillator and burst-mode amplifier. (a) 0.1 −1 ns configuration. (b) 1-10 ns configuration. (c) 10-1000 ns configuration. (d) 1-1000µs configuration. cw: continuous wave; RF: rado frequency; EOM: electro-optic modulator; AOM: acousto-optic modulator; AWG: arbitrary waveform generator. All fiber coupled components as well as ps Pulse Generator, AWG, and RF Filters were fit into 30” x 16.7” x 5.25” rack mountable enclosure. Two 1 × 2 fiber switches located after Booster Fiber Amp1 and before Fiber AOM allowed to switch optical path from a/b to c/d while RF switches were used to alter signaling pathways between a/b/c/d configurations.
The burst-mode amplifier utilizes custom, dual-wavelength diode amplifiers with maximum pulse duration of 100 ms. The system exhibits excellent burst-to-burst uniformity and beam profile, as described in our previous publications [14,22]. Both uniform and non-uniform bursts of pulses have been successfully amplified in this configuration. Pulse widths of 100 ps and 10–100 ns have been successfully amplified previously using this architecture [14,19].
2.2 Variable-pulse-width oscillator
2.2.1 100-ps to 1-ns pulse width (Configuration A)
In this configuration, the CW laser is first amplified in a low-gain high-power fiber amplifier (Booster Fiber Amp1 in Fig. 1). The amplified output is passed through a high-speed fiber-coupled electro-optic modulator which is used to create individual laser pulses, driven by a picosecond pulse generator with ∼50 ps rise and fall time. The minimum pulse width that can be achieved with the system is ∼100 ps. RF low-pass filters are used to lengthen the rise and fall time of the RF pulse used to drive the EOM, resulting in optical pulses with durations up to ∼1 ns. Within this range the pulse widths must be chosen in discrete steps, coupled to the RF filters. The repetition rate of the pulse train is set by the frequency of the pulse generator while the pulse width is set by the effective rise and fall time of the RF pulse. The ps pulse generator can be triggered internally or externally with jitter less than 8 ps [20].
The series of shaped pulses is then amplified in a high-gain low-power fiber amplifier (“Fiber Amp1” in Fig. 1). A fiber tap after the pulsed fiber amplifier is used to measure the pulse frequency and width and verify pulse stability before amplification to higher pulse energies. The amplified pulse contrast is improved via the fiber-coupled AOM. Although the fiber AOM response (∼10 ns rise and fall time) is slow relative to the EOM, the AOM can be used as a gate with 105–106 extinction ratio to suppress a background between each pulse or as a pulse picker to reduce the pulse repetition rate if synchronized with an external oscillator [20]. The output of the oscillator is split with a fiber tap, used to ensure pulsed operation, before amplification in a high-gain, fiber amplifier (pulsed operation, Ytterbium-doped fiber, “Fiber Amp2” in Fig. 1). Background is further reduced by using a free-space EOM with 103 polarization suppression to gate each pulse.
2.2.2 1-ns to 10-ns pulse width (Configuration B)
Configuration B is optically identical to Configuration A. However, in Configuration B the fiber EOM used to generate the pulse shape is driven by an arbitrary waveform generator (12-bit, 4 GS/s). The AWG is capable of producing user-specified pulse shapes with resolution of 250 ps. In this case, non-Gaussian shapes can be generated and used to pre-compensate the input pulse before amplification through the laser, enabling output pulse generation with Gaussian temporal profiles. In this configuration, the maximum pulse duration is limited to ∼10 ns because of increased noise in the pulsed fiber amplifiers (“Fiber Amp1” and “Fiber Amp2” in Fig. 1).
2.2.3 10-ns to 1-µs pulse width (Configuration C)
In this configuration, the CW laser is amplified through two booster fiber amplifiers in series (see Fig. 1(c)). This is possible because the fiber AOM damage threshold is an order of magnitude higher than that of the fiber EOM. The pulses are then shaped in a fiber AOM, driven by the AWG. The AWG allows for Gaussian-shaped, variable-duration pulses to be created from ∼10 ns to 1 µs in duration. The use of two CW fiber amplifiers before the AOM increases the pulse energy sufficiently to reduce background noise in the high-gain fiber amplifier (Fiber Amp2 in Fig. 1) and in the free-space diode amplifiers. Pulse gating is then performed in the free-space EOM to reduce the background from the fiber amplifiers in the VPW oscillator.
2.2.4 1-µs to 1-ms pulse width (Configuration D)
The long pulse configuration is identical to Configuration C except that the pulse forming is accomplished using the free-space EOM. The fiber AOM is opened for ∼2 ms, resulting in quasi-CW pulses from the oscillator. The AOM gate duration can be adjusted based on the required pulse width and repetition rate. The free-space EOM is driven by the AWG to produce Gaussian pulse shapes with duration of 1 µs to 1 ms. Because the EOM is located at the exit of the fiber amplifier chain, a free-space EOM with aperture of ∼3 mm is used to balance rise/fall time and damage threshold. The output from the EOM is then directly amplified by the burst-mode diode amplifiers. Because of the relatively low 103 extinction ratio of the free-space EOM, Configuration D produces increased background emission relative to Configurations A, B, and C. However, because the pulse widths are substantially longer for Configuration D, the background emission is less than 10% of the pulse energy as measured by setting the pulse amplitude to zero in the AWG.
2.3 Diode amplifiers
The pulses from the VPW oscillator are amplified through a series of single- and double-pass diode-pumped amplifiers. The system has been described previously [14] and will be only briefly discussed here. The free-space amplifiers contain two sets of diodes, operating at different wavelengths, which allow for uniform gain in the Nd:YAG lasing medium over a burst duration of 100 ms. The burst-mode amplifier contains six separate diode amplifier modules with Nd:YAG rod diameters of 2.8 mm, 2.8 mm, 5 mm, 5 mm, 10 mm, and 10 mm, respectively. Each set of amplifiers is optically isolated, spatially filtered, and relay-imaged to the following set of amplifiers in order to reduce the propagation of amplified spontaneous emission (ASE). The 2.8-mm amplifiers are operated in a single-pass configuration, while the 5-mm and 10-mm amplifiers are operated in a double-pass configuration.
The free-space amplifiers can be run in single-shot or burst modes. In burst mode, a series of pulses with envelope of 1–100-ms is amplified with intra-burst repetition rate of 10–1000 kHz. In single-shot mode, used to demonstrate the variable pulse width performance in this work, the intra-burst repetition rate is reduced to 1 kHz and the burst-mode amplifiers are run for only 2.5 ms. The maximum pulse energies of 600 mJ can be generated at 1064 nm in single-shot mode.
3. Time-dependent pulse amplification model
The variable-pulse-width amplifier performance was modeled using a time-dependent treatment of the energy storage and energy extraction processes within the laser medium (Nd:YAG) in order to compute amplification of laser pulses with temporal widths of 100 ps to 1 ms. Although the model closely follows those developed elsewhere [29,30,31], in this work specific consideration is given to transient variations in pump power and temporal pulse overlap within each amplifier. These considerations are critical for modeling pulses longer than 4 ns where the forward and backward propagating pulses overlap temporally and spatially and, therefore, the energy storage and extraction process are coupled.
3.1 Energy storage model
Although the oscillator in this work differs from that used in our prior efforts, the burst-mode power amplifier is identical to the dual-wavelength-diode-pumped amplifier described in detail by Slipchenko et al. [14]. Small signal gain measurements of the 2.8-mm, 5-mm, and 10-mm diameter Nd:YAG rods were used to calculate the stored energy, and corresponding pump power, as a function of time. Because two sets of diodes were used to pump each amplifier, with center wavelengths above and below the peak Nd:YAG absorption line, the small signal gain is nearly uniform between 5 ms and 85 ms. Prior to the steady-state condition achieved at 5 ms, the small signal gain increases rapidly, with two discernable slopes. Because the 0–5 ms time period is important for single shot operation of the burst-mode amplifier in this effort, the experimental absorbed pump power was calculated from the small signal gain. The gain, G, of an amplifier can be expressed as a function of time, t, by the ratio of the input, JIN, and output, JOUT, pulse fluence
For an input fluence which is much less than the saturation fluence, JSAT = 0.667 J/cm2 for Nd:YAG [15], the small signal gain, G0, can be expressed as where JST is the stored energy per area in J/cm2. The stored energy can then be expressed explicitly as a function of measured parameters as The small signal gain was measured for each amplifier as a function of time and pump current. For a pump current of 50 A, a steady state, single-pass gain of 1.5, 6.5, and 9 was measured at 2.5 ms for the 2.8-mm, 5-mm, and 10-mm rods, respectively. The measured gain is much less than that of single-wavelength-diode-pumped amplifiers with measured gains of 28.1 at 50 A for the 5-mm rod [14]. The total energy delivered to the amplifier by the pump diodes can be calculated from the total voltage drop across all diodes and the current. Assuming a constant current and voltage over the 2.5-ms pump duration, the corresponding “stored energy fraction” is 42%.The total energy storage in the amplifier can be described as the sum of the energy in the system, the energy added to the system by the laser diodes, and the energy lost from the system. Here we use a time-dependent form of the Frantz–Nodvik equation [29], assuming constant pump power over the simulation time step, Δt [30]. The time-dependence is applied using a first-order forward finite difference method:
In the case of single-pass small-signal gain where the JIN << JSAT and also PDΔt >> JIN, the third term in the energy storage equation can be neglected since it is much smaller than the second term. The pump power can then be calculated as a function of time from the measured small-signal gain and corresponding stored energy per unit area. Analysis of the measured performance of the burst-mode amplifier is used to quantify the pump power as a function of time for the nominal pump condition of 50 A. Over the first 3 ms of operation, of relevance in the current work, the pump power can be described using a linear function
with constant power, P0, and rate of change, PS. For all amplifiers, P0 dominates the pump power with PS attributed to changes in the absorbed energy as the diodes heat and frequency shift. The values were calculated using the SSG-simplified expressions for Eqs. (1)–5 applied to experimental data and are given in Table 1 at a pump current of 50 A.
Table 1. Amplifier pump power parameters at 50 A
Using the measured diode pump performance and time-dependent energy storage model (Eqs. (3)–5), the gain of each amplifier, or pair of amplifiers for the double pass configuration, can be expressed as a function of time:
The total output pulse energy, Epulse, is calculated as the integrated irradiance. Numerically this is represented as
where the irradiance is in W/cm2, the time step is in s, and the cross sectional area, A, is in cm2. The summation is performed over the entire time simulation from 0–2.5 ms and a sufficiently small time step is used to minimize numerical error.3.2 Impact of pulse width on amplification and output pulse shape
Using the time-dependent laser amplification model, the single-shot pulse energy was simulated as a function of pulse width from 100 ps to 1 ms. The physical spacing between amplifier stages was included, resulting in a time delay between the forward- and backwards-propagating pulses in the double-pass 5-mm and 10-mm amplifiers. Additionally, the beam expansion between the 2.8-mm and 5-mm amplifier stages and 5-mm and 10-mm amplifier stages was used to modify the irradiance between each set of amplifiers.
The input pulse width to the free-space burst-mode amplifier was assumed to be Gaussian with a FWHM corresponding to the nominal pulse width. This assumption is valid for all of the experimental data presented in this work, verified with high-resolution measurements before amplification. Two pulse widths were simulated per decade, and the integrated output pulse energy and temporal pulse shape were computed as shown in Fig. 2(a) and (b), respectively. Constant simulation input pulse energy of 150 nJ was used for all pulse widths in Fig. 2(a). This matches the experimental input pulse energy at 1 µs corresponding to the experimental data in Fig. 2(a), blue square, and (b), blue solid line. Simulation inputs for the diode pump process were taken from the measured amplifier performance data listed in Table 1. All simulations in Fig. 2 were performed with a diode current of 50 A for the 2.8-mm, 5-mm, and 10-mm amplifiers, representing the burst-mode amplifier’s standard operating condition.
Fig. 2. (a) Simulated output pulse energy as a function of pulse width. The blue square is experimental data. (b) Pulse profile before (solid) and after (dashed) amplification with width of 1 µs. Simulated profiles are shown in black and experimental data is shown in blue.
Three distinct regions are observed in the simulated pulse energy data presented in Fig. 2(a), similar to prior work on multi-pass amplifier architectures [31]. From 100 ps to ∼4 ns (Region I), the output pulse energy is relatively constant with a value of ∼660 mJ. For these pulse widths, there is little or no overlap of the forwards- and backwards-propagating pulse in each amplifier. As such, each pulse can be treated independently in each amplifier, although the backwards-propagating pulse experiences lower gain due to energy extraction from the forward propagating pulse.
From ∼10 ns to ∼100 µs (Region II), the output pulse energy is relatively constant with a value of ∼490 mJ. For these pulse widths, there is substantial overlap between the forwards- and backwards-propagating pulse in each amplifier, which are typically separated by one meter or less. Thus, the gain in each amplifier is reduced by energy extraction from the forwards-propagating pulse, thus reducing the total gain experienced by each independent pulse.
Finally, for pulse widths greater than 100 µs (Region III) the pulse energy increases with pulse width, reaching ∼900 mJ at 1 ms. In this case, the pulse width is comparable to the fluorescence lifetime of Nd:YAG and the energy extraction is dependent on pulse overlap, spontaneous emission, and pump energy variation during the pulse [31]. Because the pump rate of the amplifiers, and therefore energy storage rate, is greater than the energy lost to fluorescence, the output energy increases as a result of having more stored energy available during the temporally extended pulse width. This is in contrast to Regions I and II which are much shorter than the fluorescence lifetime. Pulse widths were not simulated above 1 ms since the VPW oscillator was limited to ∼1 ms pulse shaping by the AWG.
For reference, experimental measurements of pulse energy and pulse width are given for a nominal pulse width of 1 µs in Fig. 2(a) and (b), respectively, indicated by the blue square and solid blue lines. The input pulse energy and pulse shape were computed from measured data with integrated energy of 150 nJ and Gaussian pulse width of 889 ± 25 ns (FWHM). The input pulse shape was near-Gaussian as shown by the solid black fit in Fig. 2(b). The output pulse energy was measured as 384 ± 53 mJ, which is 21% lower than the simulated result. However, the simulation does not take into account losses from surface reflections and leakage though mirrors and one would expect the simulated energy to be higher than the measured energy.
The simulated (dashed black line) and measured (solid blue line) output pulse shapes are normalized and shown in Fig. 2(b). The output pulse shape was measured with a photodiode with 1-ns rise time (Thorlabs, Model DET10A) and 20-GHz oscilloscope (80 GSa/s). Two differences are noted between the input and output pulse shapes. First, the timing of the pulse has shifted forward by ∼350 ns relative to the input pulse. While there is a small difference between the simulated and measured pulses, both show a similar shift. This results from preferential amplification of the rising edge of the pulse, which sees significantly higher gain than the falling edge. The experimental data was collected using the same photodiode and reference point in space and time. To acquire the input pulse shape, the 1 kHz pulse train from the oscillator was allowed to pass through the burst-mode amplifier optical path without the diodes enabled. The data shown is the average of ∼1000 pulses because of the very low pulse energy. To acquire the output pulse shape, an aperture was used in front of the photodiode to reduce the total light collected. This ensures the observed shift in time is not due to differences in the optical collection path length.
The second feature is the predicted output pulse shape itself (dashed line in Fig. 2(b)), which exhibits a Gaussian rising edge and asymmetric tail. The same general shape is observed in the experimental data, although additional shoulders are present. These shoulders increase the width of the experimental pulse to 975 ns, which is ∼8% longer than the simulated output pulse width of 900 ns. These shoulders result from non-idealities in the AOM and EOM gating used for pulse generation and ASE suppression and can be modified by changing the timing of the gating. Even so, the experimental pulse shape exhibits the same characteristics features of the simulated amplified pulse, including forward-shifted timing and lengthened width with asymmetric tail, providing an anchor point for use of the model for variable-pulse-width amplification in the current work.
4. Key performance parameters
The performance of the variable-pulse-width, burst-mode laser is measured and modeled across seven decades of pulse width, from 100 ps to 1 ms. Three key performance parameters are considered: integrated pulse energy, temporal pulse shape and width, and spatial beam profile and quality. These parameters are discussed in the following sections.
4.1 Pulse energy
Although the simulations in Fig. 2(a) provide a good reference for understanding the key phenomena driving amplification in Region I, II, and III, in the physical system the input pulse energy is not constant as a function of input pulse width. In Configuration A and B, the pulsed fiber amplifiers cannot safely amplify pulses with peak power exceeding 1 kW. As such, the VPW oscillator output pulse energy is limited by the kW-peak-power restriction and pulse width. At 100 ps, 10–100 nJ are available while 1–10 µJ can be achieved at 10 ns. The linear relationship between oscillator pulse width and pulse energy results in a highly non-linear relationship between output pulse energy from the burst-mode amplifier and pulse width, as shown in Fig. 3. The simulated output energy is shown as a solid line with experimental data from Configuration A and B plotted as red circles. For all data and simulations in Fig. 3, the burst-mode amplifier was operated at the standard condition with diode current of 50 A for the 2.8-mm, 5-mm, and 10-mm amplifier stages. Because the fiber EOM was used to shape the pulse and the fiber AOM was used to gate the pulse in Configuration A and B, non-negligible ASE from the pulsed fiber amplifiers was transmitted into the burst-mode amplifier along with the pulse. In the data presented in this work, the AOM gate was ∼40 ns in width, yielding a low power ASE pedestal on which the higher peak power pulse was carried (peak power ratio of >100:1). After amplification through the burst-mode amplifier, the pulse-to-ASE ratio decreased, such that ∼75% of the output pulse energy at 100 ps was contained in the ASE pedestal. For longer pulse widths the relative contribution of the ASE pedestal is decreased, comprising less than 10% of the output pulse energy at 10 ns. The ASE contribution from the VPW oscillator is included in all simulations of integrated pulse energy and pulse shape for Configuration A and B (100 ps to 10 ns) in this work. The ASE is modeled as a constant power quasi-CW contribution, added to the pulse profile, and with width of 40 ns as set by the gating AOM width. For comparison, the per-pulse energy modeled without ASE contributions is shown as a dashed line in Fig. 3.
Fig. 3. Integrated output pulse energy as a function of pulse width for Configuration A and B (red circles) and Configuration C and D (blue squares). Each data set is acquired at a constant burst-mode amplifier pumping rate for a single pulse and includes contributions from ASE. The solid lines are simulations based on known laser parameters. The dashed line is the modeled pulse energy neglecting contributions from ASE. The normalized deviation between the experimental data and the model are shown in the lower subplot. For comparison, the experimental data point near 1 µs is the same as that shown in Fig. 2(a) and (b).
For Configuration C and D (10 ns to 1 ms), the low-gain booster fiber amplifiers (see Fig. 1) were operated at a constant power, producing a ∼200 mW cw source from which the pulse was “sliced” by the fiber-coupled AOM. As such, the pulse energy varied nearly linearly as a function of pulse width. This resulted in ∼150 nJ at a Gaussian pulse width of 1 µs. As in Configuration A and B, the variability in input pulse energy as a function of pulse width yields a highly non-linear relationship after amplification through the burst-mode amplifier. Experimental data from Configuration C and D is shown in Fig. 3 (blue squares) along with the simulation results. Unlike Configuration A and B where the fiber EOM was used to shape the pulse, the fiber AOM used to shape the pulse in Configuration C and D exhibited a 1000 times higher contrast ratio. Therefore, no discernable ASE pedestal was observed from the VPW oscillator.
In general, the simulated and experimental data presented in Fig. 3 follow similar functional forms. In both cases, output pulse energy increases with increased pulse width for a constant amplifier pump condition. This is not consistent with the simulated results in Fig. 2(a), indicating that the output pulse energy from the system is a strong function of the output pulse energy of the variable-pulse-width oscillator. Of particular interest is the intersection of Configuration B and C around 10 ns. Using Configuration B nearly 600 mJ is produced by the system, while Configuration C produces only 34 mJ at similar pulse widths and the same diode-pumped amplifier pump condition. This highlights the impact of oscillator pulse energy on the output pulse energy, as Configuration B produces ∼103 higher pulse energy than Configuration C from the VPW oscillator. Beyond 10 ns, Configuration B is limited by damage in the fiber amplifiers and the low-gain booster amplifiers in Configuration C and D must be used. Adding a second AWG to drive the fiber AOM in tandem with the fiber EOM would allow optical configuration B to be used instead of the configuration C, enabling increased pulse energies.
4.2 Temporal pulse profile
The generation of specific pulse shapes is important for a variety of applications. Generation of Gaussian, flat-top, and ramp pulse shapes have been demonstrated with the variable-pulse-width system and were previously used to investigate micro-optical ignition of nano-energetic materials [17]. In this work we have focused on generating near-Gaussian pulses over a wide range of pulse widths (100 ps to 1 ms). Among the advantages of Gaussian pulses is the straightforward application of analytical solutions and models which can be difficult to implement for complex pulse profiles. Although the generation of Gaussian pulse profiles is commonly accomplished in high-pulse-energy lasers, the ability to generate Gaussian profiles over seven orders of magnitude in pulse width sets this work apart from previous efforts. To quantify the impact of amplification on pulse shape and width, experimental measurements were taken at nominal pulse widths of 100 ps, 1 ns, 10 ns, 100 ns, 1 µs, 10 µs, 100 µs, and 1 ms with output pulse energy of 90 ± 5 mJ at 100 ps and 209 ± 10 mJ for 1 ns to 1 ms, as given in Fig. 4. Unlike the data in Fig. 3, the gain of Fiber Amp2 (Fig. 1) and the pump power of each free-space diode-pumped amplifier were varied as a function of pulse width. The 100-ps pulse was limited to 100 mJ at 1064 nm to avoid self-focusing in the amplifiers.
Fig. 4. Temporal pulse profiles are shown for single-pulse operation of the burst-mode amplifier with nominal pulse widths of 100 ps to 1 ms. The solid lines are the average of 17 individual waveforms, while the dashed lines are simulations at each condition. All waveforms exhibited uniform pulse energy of 209 ± 10 mJ at 1064. The measured full-width at half-maximum (FWHM) is given for each experimental waveform. Waveforms generated using Configuration A and B are shown in red, while waveforms using Configuration C and D are shown in blue.
For pulse widths of 100 ps to 50 ns, the output pulse shape was measured with a 25 GHz, high-speed photodiode (New Focus, Model 1481) and 20-GHz oscilloscope (Agilent, Infiniium). For pulse widths from 50 ns to 1 ms, a photodiode with 1-ns rise time was used (Thorlabs, Model DET10A). In both cases, the experimental data was collected using the spatial reference point set by an aperture used to control the total light collected by the detector. The waveforms in Fig. 4 are the average of 17 laser shots, normalized by their peak intensity, and centered around zero. Simulations of the output pulses are shown as dashed black lines.
For short pulses using Configuration A and B (100 ps to 1 ns), the pulse profile is limited by either the rise and fall of the ps pulse generator and ps EOM, or the filtering functionality of the RF filter set used to stretch the ps pulse generator signal. As such, strict Gaussian profile generation is not explicitly possible, although the overall pulse profiles at 100 ps and 1 ns follow a nearly Gaussian profile after amplification as can be observed in Fig. 4 (red waveforms). The experimental waveforms have R2 values of better than 0.95 with Gaussian functions, and the simulated pulse profiles show no significant deviations from the experimental waveforms.
For pulse widths from 10 ns to 1 µs (Configuration C), the pulse shape is formed using a high-resolution arbitrary waveform generator (AWG). The AWG is used to impart a Gaussian profile on the AOM input resulting in a nearly Gaussian pulse profile after amplification. A characteristic asymmetric tail is observed in these pulse shapes, becoming more dominant at longer pulse widths, consistent with the simulated waveforms from 10 ns to 1 µs. Although not utilized in the current work, the AWG could be used to pre-compensate the oscillator pulse shape and yield truly Gaussian output pulses.
For pulse widths greater than 1 µs (Configuration D), the AWG produces a Gaussian pulse profile using the free-space EOM for shaping and the fiber-coupled AOM for gating. Because the ∼102 extinction ratio of the single-pass, free-space EOM is less than that of the fiber-coupled AOM, the capability of the free-space EOM to produce specific pulse shapes is reduced at the longer pulse widths. An additional complication also arises from the gain of the free-space burst-mode amplifiers. The high gain and relatively short fluorescence lifetime (230 µs) of Nd:YAG amplifiers makes it difficult to maintain high pulse energy while simultaneously producing symmetric Gaussian pulse shapes. Two primary features are observed in the long pulse width waveforms. As described in Section 3.2, the front end of the pulse is preferentially amplified relative to the back end producing a sharpened rising edge. Additionally, the tail end of the pulse is elongated relative to the front end. These features are especially evident in the 10 and 100 µs waveforms in Fig. 4. In each of those cases the experimental waveforms exhibit more front edge compression than predicted by the model. This disparity may be explained by differences in the measured and modeled pulse energy and challenges in optically shaping the front end of the pulse. With the former, the modeled pulse energy and pulse shape are tightly coupled, specifically the preferential amplification of the rising edge. While this may partially explain the observed deviation, the measured and modeled pulse energies are within ±5% for the data presented in Fig. 4. With the latter, the front end of the pulse is purposefully retarded to artificially smooth the transition and avoid large “spikes” resulting from optically switching the fiber-coupled AOM. This results in delayed growth of the pulse, as clearly observed for 9 µs in Fig. 4, and may explain the observed deviations. Increased contrast ratio and bandwidth of the AWG would alleviate this technical challenge. In contrast, the experimental and simulated waveforms agree well at 1 ms. The sharp drop in energy at the end of the 1-ms waveform corresponds to the time at which the diode pump is turned off in each amplifier.
Although not represented in the averaged waveforms presented in Fig. 4, occasionally micro-pulses (i.e. “spiking”) were observed to occur on the backside of the pulse for widths greater than ∼100 µs (primarily at 1 ms). These occurred randomly and may originate from relaxation oscillations initiated by fluctuations in pump power or feedback in amplification. In order to avoid “spiking” and maintain nearly Gaussian pulse generation, the amplifiers are operated at relatively low power in the long pulse regime. For instance, the 10-mm amplifiers were not used in the 1-ms pulse width case.
4.3 Spatial beam profile and beam quality
Although the temporal pulse profile is of greatest importance in the current effort, the spatial beam profile and quality is also an important performance characteristic. The spatial profile was measured from a ∼4% reflection of the main beam off an uncoated, wedged window, passed through a series of neutral density (ND) filters, and recorded with a single-shot beam profiler (Spiricon, SP620U). The beam profile was recorded for pulse widths of 100 ps to 1 ms in increments of one decade. The pulse energy at each width is consistent with Fig. 4. In general, the profiles are Gaussian or super-Gaussian in nature and have been characterized by their 1/e2 width at the output of the laser system. The calculated beam diameter is given in Fig. 5 for each pulse width. As the pulse width is increased from 100 ps to 100 ns the beam diameter increases from 8.75 mm to a maximum value of ∼11 mm. Above 100 ns the beam diameter is nearly uniform at 11 mm. At 1 ms the diameter reduces to ∼10 mm. This is consistent with the fact that the 10-mm diode amplifiers, which are slightly underfilled, are not required for the 1 ms case. As a point of reference, the final amplifier stages are 10 mm in diameter, although the beams goes through a Galilean telescope before exiting the burst-mode laser system. The telescope is typically used to expand the beam before second harmonic generation, although no frequency doubling was employed in the current work. The insets to Fig. 5 show the two-dimensional beam profile at pulse widths of 100 ps, 1 µs, and 1 ms. The change in beam diameter is better understood by the change in beam shape. At 100 ps the beam shape is nearly Gaussian, while the beam shape at 1 µs is better described as a super-Gaussian with order n = 4. This transformation of the beam towards a top-hat profile occurs as a result of increased energy extraction on the outer ring of the beam at longer pulse widths. As the pulse width is increased to 1 ms, the beam profile transforms from a TEM00 mode to a TEM01* mode, the so-called doughnut mode. This can occur because of several different processes. In this case, the outer ring may be amplified more efficiently because of increased pump absorption in the outer ring of the Nd:YAG rod at long pump pulse widths. Thermal lensing may also play at role long pulse durations. Each pulse is centered 1.5 ms after the diode pumping is initiated. For pulse widths that are short relative to the diode pumping rate (i.e. the heat generated in the rods during the pulse is negligible compared to the total heat in the rods before the pulse), the thermal state of the system is nearly constant as a function of pulse width and limited primarily by the diode pump conditions. However, for relatively long pulse widths (> 10 µs) significant heating of the rods can occur during the laser pulse such that the thermal lensing condition, occurring because of temperature- and stress-induced variations in refractive index, may significantly evolve during the pulse amplification process. Although a detailed analysis of thermal lensing is beyond the scope of the current effort, any contributions are expected to influence the spatial beam profile primarily for long pulse widths. It should be noted that the interference rings observed in the insets originate from the ND filters and beam profiler camera, not from the beam itself.
Fig. 5. Measured beam diameter (1/e2) as a function of pulse width. The inset pictures show the two-dimensional profile at 100 ps, 1 µs, and 1 ms. The intensity is normalized in each inset.
The beam quality was measured by expanding the beam and focusing through a 50.8-mm diameter fused silica lens with focal length of 62.9 mm at 1064 nm [32]. The 1/e beam waist was measured as a function of distance from the lens by scanning a 10-µm diameter pinhole through the beam. Although insufficient data was acquired to perform a standardized M2 measurement, the beam waist at the focus was compared to that of a diffraction-limited beam waist. From 100 ps to 1 µs, the beam was able to be focused to 2.5 ± 0.9 times the diffraction limit. No distinct patter was observed as a function of pulse width with the minimum beam waist measured at 1 ns and maximum beam waist measured at 100 ns.
5. Conclusions
A variable-pulse width oscillator and burst-mode amplifier has been developed which enables generation of near-Gaussian laser pulses with widths from 100 ps to 1 ms and pulse energies as high as 600 mJ at 1064 nm. A time-dependent laser amplification model is developed and used to understand the impact of pulse width on pulse energy and pulse shape over seven orders of magnitude. Good comparisons are observed with experimental measurements of pulse energy and pulse waveforms, and the output pulse energy from the system is shown to be highly dependent on the pulse-width-dependence of the variable-pulse-width oscillator energy. Laser performance is assessed using integrated pulse energy, temporal pulse shape, and spatial beam quality. Over 200 mJ can be generated from 1 ns to 1 ms with near-Gaussian pulse profiles and beam quality as good as 1.6 times the diffraction limit. Although demonstrated with single-shot laser pulses, the system is readily extensible to burst-mode operation. Additionally, arbitrary pulse shaping could be incorporated for pulse widths greater than 1 ns using the time-dependent amplification model, for predicted pulse pre-compensation, and arbitrary waveform generator. As such, the performance and versatility of this system make it suitable for a wide variety of applications including high-speed combustion and fluid-flow diagnostics.
Funding
Air Force Research Laboratory (FA8650-15-D-2518).
Acknowledgments
The authors are grateful for technical discussions with Dr. Jason Mance and Dr. Todd Van Woerkom. This manuscript has been cleared for public release (88ABW-2020-2759).
Disclosures
The authors declare no conflicts of interest.
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