Patent Publication Number: US-2023155342-A1

Title: Pulse equalization in q-switched gas lasers

Description:
PRIORITY 
     This application claims priority to U.S. Provisional Application Serial No. 63/281,044, filed Nov. 18, 2021, the disclosure of which is incorporated by reference in its entirety. 
    
    
     TECHNICAL FIELD OF THE INVENTION 
     The present invention relates to Q-switched gas lasers, such as Q-switched carbon dioxide (CO 2 ) and carbon monoxide (CO) lasers. The present invention relates in particular to changes in laser pulse energy and laser pulse duration of the output of a Q-switched gas laser upon modification of the pulse repetition rate. 
     DISCUSSION OF BACKGROUND ART 
     The laser gain medium of a gas laser is a gas mixture. The optically-active entities providing the laser action are atoms, ions, or molecules. These optically-active entities are usually energized by a high-voltage electric field, either radio-frequency (RF) or direct-current (DC), that generates a gas discharge and thereby produces a population inversion in the optically-active entities. Many gas lasers have been replaced in commercial applications by solid-state lasers, owing to their generally higher efficiency, smaller size, lower cost, and simpler operation. However, certain types of gas lasers remain popular and are the preferred solution for some laser applications. For example, CO 2  lasers and CO lasers see substantial use in industrial processes, such as laser machining, where their infrared (IR) wavelength and high average power are advantageous. 
     CO 2  lasers can deliver IR laser radiation within the wavelength range from about 9 micrometers (µm) to about 11 µm, whereas CO lasers can deliver IR laser radiation within the wavelength range from about 4.5 µm to about 6.0 µm. Average powers as high as about 8 kilowatts can be obtained with CO 2  lasers and CO lasers. 
     Many laser machining applications require that the laser radiation is pulsed. In the case of CO 2  and CO lasers, a pulsed laser beam may be generated by turning on and off the gas discharge in the gain medium. However, the rise and fall times of the laser pulses generated by this technique are dictated by the kinetics of the energy transfer processes in the gas mixture and are typically of order 10 to 200 microseconds (µs). These rise and fall times result in an overall laser pulse duration in the range of tens to hundreds of microseconds, which is too long for certain applications. In particular, these laser pulse durations are too long in many laser machining applications where it is required that the heat-affected zone in the irradiated material is small. When the laser pulse duration is tens of microseconds or more, thermal diffusion in the irradiated material during a single laser pulse causes the heat-affected zone to grow significantly in directions away from the irradiated location. Even for applications that do not require shorter laser pulses, modulation of the gas discharge has the additional drawback that the associated thermal variation leads to optical instabilities. 
     Q-switching is a technique for generating a laser pulses by modulating the intracavity loss of the laser resonator. Q-switching switches the laser resonator between a high-loss state (low Q-factor) and a low-loss state (high Q-factor), while maintaining steady pumping of the laser gain medium. A laser pulse is generated by first operating the laser resonator in the high-loss state to prevent lasing action. In the absence of lasing action, the pumping of the gain medium results in the accumulation of a large amount of energy in the laser gain medium. Next, the resonator loss is abruptly dropped to a low value that enables laser action. After a build-up time, the circulating laser power increases rapidly in this low-loss state and the stored energy is depleted quickly. The outcome is the generation of a laser pulse, typically with a duration in the nanosecond range. Most commonly, Q-switching is performed periodically to generate a train of laser pulses characterized by a pulse repetition rate. 
     Q-switching may be active or passive. In active Q-switching, the laser resonator includes an active loss element, for example an acousto-optic modulator (AOM) or an electro-optic modulator (EOM), that is controlled to either divert or not divert radiation from the resonator to switch the laser resonator between high-loss and low-loss states. Active Q-switching is typically used to generate laser pulses with a pulse repetition rate in the range from a few hundred kilohertz (kHz) down to one kHz or lower. Active Q-switching may be used to generate a single laser pulse on demand. 
     A laser process performed with a pulsed laser beam typically has an optimal pulse repetition rate. The optimal pulse repetition rate depends on the process. Therefore, the most versatile pulsed laser systems are capable of running at a range of pulse repetition rates, sometimes spanning from single-shot to a few hundred kilohertz. It is not uncommon for laser machining processes to entail varying the pulse repetition rate during processing of each single part, thus requiring on-the-fly adjustment of the pulse repetition rate. In the case of a Q-switched laser, adjustment of the pulse repetition rate amounts to changing the duration of the high-loss state of the laser resonator. At least for relatively high pulse repetition rates, such change can affect the amount of energy accumulated in the gain medium before switching to the low-loss state. Consequently, adjustment of the pulse repetition rate may be accompanied by a changed laser pulse energy. 
     SUMMARY OF THE INVENTION 
     Disclosed herein are a Q-switched gas laser apparatus and associated method with bivariate pulse equalization of both laser pulse energy and laser pulse duration. The present apparatus and method utilize active Q-switching and are configured to equalize laser pulse energy and duration over a wide range of pulse repetition rates. One equalization mechanism directly affects the laser pulse energy, while another equalization mechanism directly affects the laser pulse duration. The pulse-energy-equalization mechanism adjusts the loss of the low-loss state of the laser resonator, while the pulse-duration-equalization mechanism adjusts the duration of the low-loss state. For example, when the Q-switch is an AOM, the pulse-duration-equalization mechanism is based on maintaining some amount of diffraction even in the low-loss state, and adjusting this amount of diffraction to achieve a desired pulse energy. For comparison, a conventional Q-switch is turned off entirely during the low-loss state to minimize the loss of the laser resonator. 
     We have realized that equalization of both pulse energy and duration extends the pulse repetition rate range over which uniform pulse energy may be achieved. While it may be possible to achieve uniform pulse energy over a limited range of relatively high pulse repetition rates by using only the pulse-energy-equalization mechanism, the pulse-duration-equalization mechanism facilitates extension of this range to lower pulse repetition rates. Thus, the present bivariate pulsed equalization is useful even when the objective is simply to maintain a uniform laser pulse energy over a wide range of pulse repetition rates, regardless of the laser pulse duration. The pulse-duration-equalization mechanism further enables achieving a desired laser pulse duration over a wide range of pulse repetition rates, thereby providing ultimate laser pulse control. 
     In one aspect, a Q-switched gas laser apparatus with pulse equalization includes a gas laser, a sensor, and an electronic circuit. The gas laser includes a laser resonator having a Q-switch operable to switch the laser resonator between a high-loss state and a low-loss state to generate a pulsed laser beam. The sensor is configured to obtain a measurement of the pulsed laser beam indicative of a laser pulse energy. The electronic circuit is communicatively coupled between the Q-switch and the sensor, and is configured to operate the Q-switch to (a) repeatedly switch the laser resonator between the high-loss and low-loss states to set a repetition rate of laser pulses of the pulsed laser beam, (b) adjust a loss level of the low-loss state, based on the measurement obtained by the sensor, to achieve a target laser pulse energy, and (c) adjust a duration of the low-loss state to achieve a target laser pulse duration. 
     In another aspect, a method for equalizing laser pulses generated by a Q-switched gas laser includes operating a Q-switch of the Q-switched gas laser to repeatedly switch a laser resonator of the Q-switched gas laser between high-loss and low-loss states to generate a pulsed laser beam. The method further includes equalizing laser pulse energy and laser pulse duration of laser pulses of the pulsed laser beam through repeated steps of (a) sampling the pulsed laser beam to obtain a measurement indicative of the laser pulse energy, (b) adjusting a loss level of the low-loss state, based on the measurement indicative of the laser pulse energy, to approach a target laser pulse energy, and (c) adjusting a duration of the low-loss state to approach a target laser pulse duration. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and constitute a part of the specification, schematically illustrate preferred embodiments of the present invention, and together with the general description given above and the detailed description of the preferred embodiments given below, serve to explain principles of the present invention. 
         FIG.  1    illustrates a Q-switched gas laser apparatus with equalization of both laser pulse energy and laser pulse duration, according to an embodiment. 
         FIG.  2    is a timing diagram of a prior-art scheme for Q-switching a laser resonator equipped with an AOM Q-switch. 
         FIG.  3    shows a set of exemplary laser pulses generated by an embodiment of the  FIG.  1    apparatus that implements an AOM Q-switch and is operated according to the prior-art scheme of  FIG.  2   . 
         FIG.  4    shows another set of exemplary laser pulses generated by the same embodiment of the  FIG.  1    apparatus as those of  FIG.  3    but implementing pulse trimming in a deviation from the prior-art scheme of  FIG.  2   . 
         FIG.  5    displays data that further explore the effect of a command pulse duration, controlling the Q-switch, on laser pulse energy and duration at a fixed pulse repetition rate. 
         FIG.  6    is a flowchart for a method for bivariate equalization of laser pulses generated by a Q-switched gas laser, according to an embodiment. 
         FIG.  7    is a timing diagram of a scheme utilized by the  FIG.  6    method to Q-switch a gas laser with bivariate pulse equalization, according to an embodiment. 
         FIG.  8    shows examples of laser pulses generated when operating the  FIG.  1    apparatus with bivariate pulse equalization according to the  FIG.  7    scheme, and implementing dynamic adjustment of both laser pulse energy and laser pulse duration based on measurements from respective sensors, according to an embodiment. For comparison,  FIG.  8    also shows examples of laser pulses generated without pulse equalization. 
         FIGS.  9 A and  9 B  show examples of laser pulse energies and laser pulse durations, respectively, for three different pulse repetition rates, with and without bivariate pulse equalization. 
         FIG.  10 A  illustrates an RF driver that may be implemented in embodiments of the  FIG.  1    apparatus where the Q-switch is an AOM, according to an embodiment.  FIG.  10 B  illustrates an exemplary command signal for controlling this RF driver. 
         FIG.  11 A  illustrates another RF driver that may be implemented in embodiments of the  FIG.  1    apparatus where the Q-switch is an AOM, according to an embodiment. This RF driver is configured to receive separate timing and voltage inputs.  FIG.  11 B  illustrates an exemplary timing command signal for controlling the timing aspect of the RF driver of  FIG.  11 A . 
         FIG.  12    illustrates a controller for bivariate pulse equalization with servo control of both laser pulse energy and laser pulse duration, according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring now to the drawings, wherein like components are designated by like numerals,  FIG.  1    illustrates one Q-switched gas laser apparatus  100  with bivariate pulse equalization. Apparatus  100  includes a gas laser  110 , a sensor  150 , and an electronic circuit  160 . Gas laser  110  includes a laser resonator  116  having a Q-switch  118 . Q-switch  118  is, for example, an AOM or an EOM. 
     Inherently, gas laser  110  also includes a gaseous gain medium  120 . In one embodiment, gas laser  110  is a CO 2  or CO laser and gain medium  120  correspondingly includes CO 2  or CO. At least when gas laser  110  is a CO 2  or CO laser, gas laser  110  further includes one or more electrodes that apply a high voltage electric field through gain medium  120  to pump (energize) the CO 2  or CO molecules therein. In other embodiments, gas laser  110  may be a different type of gas laser with a long upper-state lifetime. Gas laser  110  may include electrodes  122  and  124  positioned on opposite sides of gain medium  120  to generate a discharge in gaseous gain medium  120 . Electrode  122  is coupled to a high-voltage RF source, and electrode  124  is grounded. 
     In the example depicted in  FIG.  1   , resonator  116  is a linear resonator having two end-mirrors  112  and  114  with laser radiation  190  propagating back and forth therebetween. End-mirror  114  is an output coupler with partial reflectivity, for example in the range between 10% and 90%. End-mirror  112  may be a high-reflector with at least 99% reflectivity. In other examples of apparatus  100 , resonator  116  is a linear resonator defined by more than two mirrors, with the propagation path of laser radiation  190  being folded. In yet other examples, resonator  116  is a ring resonator. 
     Q-switch  118  is placed in the propagation path of circulating laser radiation  190 . Electronic circuit  160  controls the operation of Q-switch  118  to pulse laser radiation  190 , such that gas laser  110  outputs a pulsed laser beam  192 . More specifically, electronic circuit  160  operates Q-switch  118  to repeatedly switch resonator  116  between high-loss and low-loss states to set a repetition rate of laser pulses 192P of laser beam  192 . Electronic circuit  160  is capable of varying the pulse repetition rate of laser beam  192  by varying the rate at which Q-switch  118  switches resonator  116  between the high-loss and low-loss states. In other words, electronic circuit  160  is capable of controlling Q-switch  118  to achieve a range of values of the period T between laser pulses 192P. Electronic circuit  160  may receive a repetition rate input  188  that indicates a desired repetition rate of laser pulses 192P. Electronic circuit  160  may receive repetition rate input  188  from an external control system or a user. 
     Electronic circuit  160  is also configured to control and vary the loss imposed by Q-switch  118  in the low-loss state of resonator  116 , to achieve a target energy of laser pulses 192P. Q-switch  118 , sensor  150 , and electronic circuit  160  are arranged in an active feedback loop to exert servo control of the energy of laser pulses 192P. Apparatus  100  splits off a fraction  196  of laser beam  192  and directs laser beam fraction  196  to sensor  150 . Sensor  150  measures the pulse energy E (or a related parameter) of laser pulses of laser beam fraction  196  to obtain a measure of the energy of laser pulses 192P (or another parameter indicative thereof). Sensor  150  communicates this pulse energy measurement to electronic circuit  160 , and electronic circuit  160  adjusts the operation of Q-switch  118  accordingly to achieve a target pulse energy, at least to within some tolerance. 
     The property measured by sensor  150  may be an average energy of laser beam fraction  196  and may be obtained as an average over several or many laser pulses 192P. In one implementation, sensor  150  is a thermopile sensor, a photoconductive or photovoltaic semiconductor sensor, or a bolometric sensor. Alternatively, sensor  150  may be sufficiently fast to measure the energy of individual pulses in laser beam fraction  196 . Apparatus  100  may include one or more beamsplitters to obtain laser beam fraction  196  from laser beam  192 . 
     Electronic circuit  160  is further configured to control the duration of the low-loss state of resonator  116 , defined by Q-switch  118 , as needed to adjust the duration of laser pulses 192P. Electronic circuit  160  may perform this adjustment based on (a) a measurement of a duration of laser pulses 192P or (b) a pre-calibrated relationship between one or more of the pulse repetition rate, the target pulse energy, the pulse energy measurement obtained from sensor  150 , and a target pulse duration. 
     Although not shown in  FIG.  1   , electronic circuit  160  may receive a target pulse energy and a target pulse duration from an external system or a user. Electronic circuit  160  may include one or more of discrete electronic components, integrated circuits, a microprocessor, and a software-equipped computer. 
     Certain embodiments of apparatus  100  include a sensor  152  and direct a fraction  198  of laser beam  192  to sensor  152 . Sensor  152  obtains a measurement of the duration w of laser pulses 192P from laser beam fraction  198  and communicates this pulse-duration measurement to electronic circuit  160 . Electronic circuit  160  may then adjust the operation of Q-switch  118  based on the pulse-duration measurement. Sensor  152  may complete an active feedback loop that allows servo control of the duration of laser pulses 192P to achieve a target pulse duration, at least to within some tolerance. Sensor  152  is, for example, a high-speed optical detector that records the waveform of individual laser pulses 192P. 
     Apparatus  100  may include one or more beamsplitters to split off a fraction of laser beam  192  to sensor  150  and optionally also to sensor  152 . In the example depicted in  FIG.  1   , apparatus  100  includes (a) a beamsplitter  130  that splits off a fraction  194  of laser beam  192  toward sensors  150  and  152 , and (b) a beamsplitter  132  that divides fraction  194  into laser beam fractions  196  and  198 . Beamsplitter  132  may be omitted in embodiments that do not include sensor  152 . Without departing from the scope hereof, apparatus  100  may implement other schemes to obtain laser beam fraction  196 , and optionally laser beam fraction  198 , from laser beam  192 . 
     Electronic circuit  160  may include a controller  162  and a driver  164 . Driver  164  generates an electrical drive signal  182  and supplies drive signal  182  to Q-switch  118  to modulate the resonator loss. For example, when Q-switch  118  is an AOM, driver  164  is an RF driver and drive signal  182  is a high-voltage RF signal. The generation of drive signal  182  by driver  164  is dictated by a command signal  180  received from controller  162 . Command signal  180  defines the repetition rate of laser pulses 192P, the loss of resonator  116  in the low-loss state, and the duration of the low-loss state. For any given pulse repetition rate, controller  162  generates command signal  180  based at least in part on the pulse-energy measurement obtained from sensor  150  and optionally also based on the pulse-duration measurement obtained from sensor  152 . The generation of command signal  180  by controller  162  is further based on the desired pulse repetition rate, for example as defined by repetition rate input  188 . 
     In one embodiment, apparatus  100  is configured as a master oscillator power amplifier (MOPA). In this MOPA embodiment, gas laser  110  is the master oscillator and apparatus  100  further includes a laser amplifier  170  that amplifies laser beam  192 . In the MOPA embodiment, sensor  150  and sensor  152  (if included) may be arranged to sample laser beam  192  before or after amplification by amplifier  170 . It is generally advantageous to sample laser beam  192  after amplification, as depicted in  FIG.  1   . The fraction of laser beam  192  split off toward the sensor(s) may be insignificant when the splitting is after amplification. When the splitting is done prior to amplification, a greater fraction of laser beam  192  must be split of, and the impact on the final power of laser beam  192  delivered to an application (e.g., laser machining) may be significant. Additionally, since the amplified laser beam  192  is the output of MOPA, sampling of the amplified laser beam  192  provides a more direct evaluation of actual output, and the control exerted by electronic circuit  160  may compensate for effects induced in amplifier  170 . 
       FIG.  2    is a timing diagram of a prior-art scheme  200  for Q-switching a laser resonator equipped with an AOM Q-switch.  FIG.  2    shows three graphs  210 ,  220 ,  230  pertaining to the generation of a laser pulse  232 . Graph  210  depicts the temporal evolution of a command signal  212  supplied to an RF driver for driving the AOM. Graph  220  depicts the temporal evolution of an RF drive signal  222  supplied to the AOM by the RF driver. RF drive signal  222  is defined by command signal  212 . The value V c  of command signal  212  switches between two values, V high  and zero. When V c  = V high , the RF voltage V RF  of drive signal  222  has an amplitude ΔV high , and the associated diffraction by AOM imparts resonator loss such that the laser resonator is in a high-loss state. When V c  is zero, V RF  is zero such that the AOM is off, thereby placing the laser resonator in its low-loss state. 
     Graph  230  depicts the temporal evolution of the laser power P L  circulating in the laser resonator. In scheme  200 , a laser pulse  232  is generated by a command pulse  214  of command signal  212  dropping to V c  = 0. Command pulse  214  has a duration Δt between a leading edge at a time t 1  and a trailing edge at a time t 2 . The duration Δt of command pulse  214  defines the duration of the low-loss state of the laser resonator. Acoustic and optical delays impose a delay T delay  from time t 1  to laser pulse  232 . The acoustic delay corresponds to the acoustic wave in the AOM optic, which is generated up until time t 1 , propagating from the transducer completely through the path of laser radiation  190 . The optical delay corresponds to laser radiation initiated by spontaneous emission “building up” by stimulated emission during many round-trips through the energized resonator. In the scenario depicted in  FIG.  2   , the acoustic delay is longer than the optical delay, and therefore laser pulse  232  is generated after time t 2 . 
     Electronic circuit  160  is capable of operating Q-switch  118  according to prior-art scheme  200 . However, prior-art scheme  200  does not provide pulse equalization, and the energy and duration of laser pulses 192P would vary with the pulse repetition rate. 
       FIG.  3    shows a set of exemplary laser pulses generated by an embodiment of apparatus  100  that implements Q-switch  118  as an AOM and is limited to operate according to prior-art scheme  200 . The laser pulse waveforms are recorded by sensor  152  implemented as a high-speed optical detector that detects and records instantaneous laser power as a function of time. In the  FIG.  3    example, the duration Δt of command pulse  214  is 1.0 µs.  FIG.  3    shows the resulting laser pulse waveform recorded at each of the pulse repetition rates 1 kHz, 5 kHz, 10 kHz, 25 kHz, 50 kHz, 75 kHz, and 100 kHz. While the laser pulse waveform is mostly unchanged for pulse repetition rates in the range from 1 kHz to 25 kHz, substantial changes occur as the pulse repetition rate is increased beyond 25 kHz. In particular, the pulse energy exhibits a strong decrease with pulse repetition rate for pulse repetition rates above 25 kHz. In addition, the shape and duration of the laser pulses change when the pulse repetition rate is increased above 25 kHz. The laser pulses generated at pulse repetition rates in the range 1-25 kHz are composed of a main pulse followed by a significant tail  310 . As the pulse repetition rate is increased above 25 kHz, tail  310  gradually disappears and the laser pulse duration decreases correspondingly. 
       FIG.  4    shows another set of exemplary laser pulses generated by the same embodiment of apparatus  100  as those of  FIG.  3    but using a shorter command pulse  214 , a deviation from prior-art scheme  200 . This technique is hereinafter referred to as “pulse trimming”. In the  FIG.  4    example, the duration Δt of command pulse  214  is 0.8 µs.  FIG.  4    shows the resulting laser pulse waveform recorded at each of the pulse repetition rates 1 kHz, 5 kHz, 10 kHz, 25 kHz, 50 kHz, 75 kHz, and 100 kHz. The reduction of command pulse  214  from 1.0 µs to 0.8 µs essentially eliminates tail  310  at all measured pulse repetition rates. However, the laser pulse energy still decreases dramatically when the pulse repetition rate is increased above 25 kHz. Thus, while pulse trimming may help achieve more uniform laser pulse duration and shape across a range of pulse repetition rates, pulse trimming does not equalize the laser pulse energy. 
       FIG.  5    further explores the effect of command pulse duration on laser pulse energy and duration at a fixed pulse repetition rate.  FIG.  5    shows laser pulse waveforms obtained with different command pulse durations at a fixed pulse repetition rate. Each laser pulse waveform in  FIG.  5    is labeled by the corresponding duration Δt of command pulse  214 . Starting with the longest command pulse duration of 1.1 µs, the laser pulse waveform exhibits a substantial pedestal-like tail. The main pulse has a width of about 0.2 µs, and the pedestal-like tail extends the total laser pulse duration by up to about 0.5 µs. As the command pulse duration is decreased from 1.1 µs, this tail is truncated and is essentially eliminated when the command pulse duration reaches 0.7 µs. When the command pulse duration is reduced below 0.7 µs, the laser pulse duration decreases further, now as a result of the width of the main pulse decreasing. In addition, the peak power of the laser pulse decreases. 
     The  FIG.  5    data demonstrate that, at least in certain pulse-repetition-rate regimes, the laser pulse energy is sensitive to the duration of the low-loss state. The  FIG.  5    data also show that, at least in certain pulse-repetition-rate regimes, only a fairly narrow range of command pulse durations provide a clean tail-free pulse while maintaining the full energy of the main pulse. In other words, there is an “optimal” command pulse duration, and even relatively small deviations from this optimal command pulse duration have significant effects. We have found that the optimal command pulse duration increases with pulse repetition rate, at least for pulse repetition rates above a certain threshold rate. 
     Together, the data of  FIGS.  3 ,  4 , and  5    demonstrate strongly coupled relationships between the repetition rate, energy, and duration of laser pulses generated by a Q-switched gas laser, such as gas laser  110 . The nature of these relationships depends on the location in the three-dimensional parameter space spanned by pulse repetition rate, energy, and duration. Additionally, the relationships are sensitive to other parameters, including properties of resonator  116 , gain medium  120 , and the pumping of gain medium  120 . 
       FIG.  6    is a flowchart for one method  600  for bivariate equalization of laser pulses generated by a Q-switched gas laser. Method  600  may be applied to apparatus  100  and overcomes the issues illustrated by the data of  FIGS.  3 - 5    to provide uniform laser pulse energy and duration over a wide range of pulse repetition rates. Method  600  entails operating the Q-switch according to a scheme that is more advanced than prior-art scheme  200 . In the following, method  600  is discussed within the context of apparatus  100 . Method  600  includes steps  610  and  620 , performed in parallel. 
     In step  610 , electronic circuit  160  operates Q-switch  118  to repeatedly switch resonator  116  between high-loss and low-loss states to generate pulsed laser beam  192 , as discussed above in reference to  FIG.  1   . In step  620 , electronic circuit  160  cooperates with sensor  150 , and optionally also sensor  152 , to equalize the energy and duration of laser pulses 192P across a range of pulse repetition rates. 
     Step  620  includes steps  630  and  632 . In step  630 , sensor  150  samples laser beam  192  to obtain a measurement indicative of the energy of laser pulse 192P, as discussed above in reference to  FIG.  1   . Step  630  may implement a step  634  of obtaining this pulse-energy measurement as an average over a plurality of laser pulses 192P. In step  632 , electronic circuitry  160  adjusts the loss level of the low-loss state of resonator  116 , based on the pulse-energy measurement obtained in step  630 , to achieve or at least approach a target pulse energy. Steps  630  and  632  may be performed iteratively, in an active feedback loop, to achieve the target pulse energy. In an example scenario, step  620  achieves a laser pulse energy that is within 10% of the target pulse energy, with the laser pulse energy being evaluated as the energy of a single laser pulse or the average energy of a plurality of laser pulses. 
       FIG.  7    is a timing diagram of one scheme  700  utilized by method  600  to Q-switch gas laser  110 . Scheme  700  is a modification of scheme  200  that enables both pulse energy equalization and pulse duration equalization.  FIG.  7    shows scheme  700  for an embodiment where Q-switching is performed with an AOM. Scheme  700  is readily adapted to other types of Q-switches, for example an EOM. Graphs  720  and  730  of  FIG.  7    provide a more detailed example of step  632 . Graph  720  depicts the temporal evolution of an RF drive signal  722  supplied to the AOM by electronic circuit  160 . As compared to RF drive signal  222  of scheme  200 , RF drive signal  722  is not necessarily zero during the low-loss state of resonator  116 . Instead, RF drive signal  722  generally has a non-zero amplitude ΔV low  during the low-loss state, and electronic circuit  160  adjusts the value of ΔV low  based on the pulse-energy measurement obtained by sensor  150  in step  630 . 
     Graph  730  depicts the temporal evolution of the laser power P L  circulating in resonator  116 . When the AOM is driven by RF drive signal  722 , the drop of RF drive signal  722  from amplitude ΔV high  to a non-zero amplitude ΔV low  results in the generation of a laser pulse  732 . As compared to laser pulse  232  (see  FIG.  2   ) generated when dropping RF drive signal all the way to zero, laser pulse  732  has a lower peak power P peak  and a lower pulse energy E. The reduction in pulse energy E (and peak power P peak ) is a consequence of the AOM imparting a non-zero diffractive loss during the low-loss state of resonator  116 . In step  632 , electronic circuit  160  adjusts ΔV low  as needed to achieve the target pulse energy. For example, when the pulse-energy measurement obtained from sensor  150  indicates that the energy of laser pulses 192P exceeds the target pulse energy, electronic circuit  160  may increase ΔV low  to increase the loss of the low-loss state of resonator  116 . Conversely, when the pulse-energy measurement obtained from sensor  150  indicates that the energy of laser pulses 192P is less than the target pulse energy, electronic circuit  160  may decrease ΔV low . 
     Step  620  of method  600  also includes a step  642 , wherein electronic circuit  160  adjusts the duration of the low-loss state of resonator  116  to achieve or at least approach a target pulse duration. Graphs  720  and  730  of  FIG.  7    provide a more detailed example of step  642 . In this example, electronic circuit  160  adjusts the duration Δt of RF drive signal  722  having amplitude ΔV low . In another example, electronic circuit  160  reduces duration Δt to prevent laser pulse  732  from having a tail, or increases duration Δt to maximize the energy in a main pulse of laser pulse  732 . In yet another example, electronic circuit  160  adjusts duration Δt to achieve a target pulse duration, such as a certain full-width at half-maximum (FWHM) pulse duration. 
     In one embodiment of step  620 , step  642  is preceded by a step 640A, wherein sensor  152  samples laser beam  192  to obtain a measurement indicative of the duration of laser pulses 192P, as discussed above in reference to  FIG.  1   . Step 640A may implement a step  644  of obtaining this pulse-duration measurement from a single laser pulse 192P, or as an average of several single-pulse durations. When step  620  includes step 640A, step  642  is based on the pulse-duration measurement obtained in step 640A. This embodiment may perform steps 640A and  642  iteratively in an active feedback loop. The pulse-duration feedback loop conducted by steps 640A and  642  may be faster than the pulse-energy feedback loop conducted by steps  630  and  632 , especially when the laser pulse duration is obtained from the measurement of a single, or just a few, laser pulses 192P. In an example scenario, step  620  achieves a laser pulse duration that is within 10% of a target pulse duration. 
     In another embodiment of step  620 , step  642  is preceded by a step 640B, wherein electronic circuit  160  either calculates the desired duration Δt of the low-loss state of resonator  116 , or retrieves the desired duration Δt from a lookup table. Electronic circuit  160  may calculate the desired duration Δt from a pre-calibrated functional relationship between (a) target pulse duration and (b) duration Δt and pulse repetition rate and, optionally, also one or more other parameters of gas laser  110  and/or the target pulse energy. For example, it may be possible to achieve a constant laser pulse duration over a range of pulse repetition rates by adjusting duration Δt in manner that depends linearly on the period T between laser pulses 192P (equivalent to the inverse of the pulse repetition rate). Alternatively, pre-calibrated durations Δt as a function of target pulse duration, pulse repetition rate and, optionally, also one or more other parameters of gas laser  110  and/or the target pulse energy may be listed in a lookup table included in electronic circuit  160 . 
     In one scenario, step  610  includes a step  612  of changing the repetition rate of laser pulses 192P. In this scenario, method  600  performs step  632 , and optionally step  642 , in response to the repetition rate change effected in step  612  so as to minimize changes to the laser pulse energy and laser pulse duration caused by the repetition rate change. 
     In embodiments where electronic circuit  160  includes controller  162  and driver  164 , the execution of scheme  700  entails driver  164  generating RF drive signal  722  (an example of drive signal  182 ). Driver  164  generates RF drive signal  722  according to command signal  180  generated by controller  162 . Graph  710  of  FIG.  7    shows the temporal evolution of a command signal  712 . Command signal  712  is one example of a command signal that can cause driver  164  to generate RF drive signal  722 . Command signal  712  is a voltage V c  that alternates between a high value V high  and a low value V low . When V c  = V high , V RF  has the amplitude ΔV high . When V c  = V low , V RF  has the amplitude ΔV low . The value of V low  is a signal value that dictates the value of ΔV low . Each laser pulse 192P is generated after a command pulse  714  characterized by the signal value V low . The value of V low  controls the value of ΔV low  and thus the energy of laser pulse 192P. 
     Controller  162  may set the repetition rate of laser pulses 192P by setting a period between leading edges 714L of successive command pulses  714  to the inverse of the desired pulse repetition rate. In this case, controller  162  adjusts duration Δt of the low-loss state of resonator  116  by adjusting the temporal position of the trailing edges 714T of command pulses  714 . 
     Command signal  712  contains both timing information (times t 1  and t 2 ) and the variable voltage V low . Alternatively, controller  162  may generate a command signal as two separate components, a timing signal and a variable DC voltage. The timing signal may be a transistor-transistor logic (TTL) signal containing TTL pulses similar to command pulses  714  but with a constant signal value V low . The variable DC voltage may be an analog signal, for example a DC voltage of the value V low , that dictates the amplitude ΔV low  or RF drive signal  722 . Often, commercial RF drivers are configured for digital control, rather than analogue control. The command signal may be a digital signal, comprising a digitally encoded time t 1 , delay Δt, voltage values ΔV high , and voltage value ΔV low . 
       FIG.  8    shows examples of laser pulses 192P generated when operating apparatus  100  with bivariate pulse equalization according to scheme  700  and implementing dynamic adjustment of both laser pulse energy and laser pulse duration based on measurement from sensors  150  and  152 . For comparison,  FIG.  8    also shows examples of laser pulses generated when operating apparatus  100  according to prior-art scheme  200  without pulse equalization.  FIG.  8    depicts oscilloscope traces of six laser pulse waveforms measured by sensor  152 . Traces  810 ,  820 , and  830  are obtained at respective pulse repetition rates 10 kHz, 50 kHz, and 100 kHz, using prior-art scheme  200 . Thus, for traces  810 ,  820 , and  830 , V low  is kept at zero and duration Δt is kept constant. Traces  812 ,  822 , and  832  are also obtained at respective pulse repetition rates 10 kHz, 50 kHz, and 100 kHz, but using pulse equalization according to scheme  700  with dynamic adjustment of both the signal value V low  and duration Δt. 
     The measured pulse energies for traces  810 ,  820 , and  830  are 704 microjoules (µJ), 542 µJ, and 355 µJ, respectively, and the corresponding FWHM pulse durations are 105 nanoseconds (ns), 118 ns, and 117 ns. It is clear that, without pulse equalization, the pulse energy changes dramatically when the pulse repetition rate is increased from 10 kHz to 100 kHz. In contrast, when implementing pulse equalization according to scheme  700 , essentially identical laser pulse waveforms are obtained for all three pulse repetition rates, as evident from traces  812 ,  822 , and  832 . With pulse equalization, the measured pulse energies at 10 kHz, 50 kHz, and 100 kHz are 250 µJ, 254 µJ, and 262 µJ, respectively. Furthermore, each of the three pulses has a FWHM pulse duration of 99 ns. 
       FIGS.  9 A and  9 B  show examples of laser pulse energies and laser pulse durations, respectively, for three different pulse repetition rates, 10 kHz, 50 kHz, and 100 kHz, with and without bivariate pulse equalization. Dataset  910  is obtained without pulse equalization, that is, with ΔV low  = 0 and Δt constant. Datasets  920  and  930  are obtained using bivariate pulse equalization according to scheme  700 , with both ΔV low  and Δt being dynamically adjusted based on measurements obtained from sensors  150  and  152 . In the case of dataset  920 , the target pulse energy E target  was 340 µJ and the target pulse duration w target  was 99 ns. In the case of dataset  930 , the target pulse energy E target  was 250 µJ and the target pulse duration w target  was 117 ns. 
     Dataset  910  shows that, without pulse equalization, the laser pulse energy decreases rapidly with pulse repetition rate, with a 2x reduction from 10 kHz to 100 kHz. Additionally, the laser pulse duration is highly sensitive to the pulse repetition rate in a non-obvious manner. In contrast, as seen in datasets  920  and  930 , bivariate pulse equalization is very effective. The target pulse duration is achieved at all three pulse repetition rates, and the pulse energy variation is small. For each of the two different target pulse energies,  340  and 250 µJ, each measured laser pulse energy is within 5% of the target pulse energy. 
       FIG.  10 A  illustrates one RF driver  1000  that may be implemented as driver  164  in embodiments of apparatus  100  where Q-switch  118  is an AOM.  FIG.  10 B  illustrates an exemplary command signal  1080  that controls RF driver  1000 . RF driver  1000  includes a RF oscillator  1010 , a mixer  1020 , and an amplifier  1040 . RF oscillator  1010  generates an RF signal. Mixer  1020  receives this RF signal and further receives command signal  1080  at an “IF” port of mixer  1020 . Command signal  1080  is a variable analog voltage V VA  composed of successive instances of command signal  712  to define the repetition rate of laser pulses 192P, V low , and duration Δt (see  FIG.  7   ). Command signal  1080  is generated by an example of controller  162 . Mixer  1020  modulates the RF signal from RF oscillator  1010  according to command signal  1080 . Amplifier  1040  amplifies this modulated RF signal to generate an RF drive signal  1082  for driving the AOM Q-switch. RF drive signal  1082  is equivalent to successive instances of RF drive signal  722 . RF driver  1000  may further include a low-pass filter  1030  that filters out undesirable harmonics generated by mixer  1020 . 
       FIG.  11 A  illustrates another RF driver  1100  configured to receive separate timing and voltage inputs.  FIG.  11 B  illustrates an exemplary timing command signal  1180  that controls the timing aspect of RF driver  1100 . RF driver  1100  is similar to RF driver  1000  except for further including a digitally controlled analog switch  1150  coupled to the IF port of mixer  1020 . Analog switch  1150  has two analog voltage input ports. One port is kept at the voltage V high , and the other receives V low  from an example of controller  162 . Analog switch  1150  also receives a separate timing command signal  1180  from controller  162 . Timing command signal  1180  is similar to command signal  1080  except for being a digital signal attaining only two values, low and high, without carrying information about V low . Analog switch  1150  switches between V high  and V low  according to timing command signal  1180 , thereby generating command signal  1080 . 
       FIG.  12    illustrates one controller  1200  for bivariate pulse equalization with servo control of both laser pulse energy and laser pulse duration. Controller  1200  is an embodiment of controller  162  and may be implemented in electronic circuit  160  together with RF driver  1100 . Controller  1200  receives an average-power measurement P AVE  of laser beam  192  from sensor  150  and a laser pulse waveform of a laser pulse 192P from sensor  152 . The laser pulse waveform is an instantaneous laser power as a function of time, P INST (t). Controller  1200  processes P AVE  and P INST (t) to generate V low  and timing command signal  1180 , respectively, and then communicates V low  and timing command signal  1180  to RF driver  1100 . The processing of P AVE  serves to achieve a target pulse energy E target , and the processing of P INST (t) serves to achieve a target pulse duration w target . (There may some degree of coupling between laser pulse energy and laser pulse duration, as discussed above in reference to  FIGS.  3 - 5   .) 
     For the purpose of pulse energy equalization, controller  1200  includes a pulse energy calculator  1210 , a summing node  1220 , and a proportional-integral-derivative (PID) controller  1230 . Pulse energy calculator  1210  calculates the pulse energy E from the average-power measurement P AVE  and the pulse repetition rate f rep . Pulse repetition rate f rep  may be received from an external source/signal or defined internally in controller  1200 . Summing node  1220  evaluates the difference ΔE between the calculated pulse energy E and the target pulse energy E target , and generates an error signal indicative of ΔE. PID controller  1230  then determines and outputs a new V low  to reduce ΔE. 
     PID control is just one example of feedback algorithms that may be employed by apparatus  100  and method  600 . Alternatively, apparatus  100  and method  600  may employ a different feedback algorithm known in the art. Accordingly, PID controller  1230  may be replaced by another type of servo controller employing a different principle for minimizing an error signal. 
     For the purpose of pulse duration equalization, controller  1200  includes a waveform analyzer  1250  and a timing signal generator  1260 . Waveform analyzer  1250  analyzes a laser pulse waveform P INST (t) to derive a laser pulse duration w. Timing signal generator  1260  then compares this measured laser pulse duration w to the target pulse duration w target , and adjusts timing command signal  1180  to minimize the difference therebetween. Specifically, timing signal generator  1260  adjusts the duration Δt, as discussed above in reference to  FIGS.  6  and  7   . Timing signal generator  1260  then communicates timing command signal  1180  to RF driver  1100 . 
     Whereas each iteration of adjustment of V low  is based on a sampling of a series of laser pulses 192P, each iteration of adjustment of timing command signal  1180  may be based on a single laser pulse 192P and may therefore be performed on a much shorter timescale. 
     The above discussion based on  FIGS.  7 ,  10 A,  10 B,  11 A,  11 B, and  12    pertains to AOM-based Q-switching. These embodiments may be modified for other types of Q-switching by changing the drive signal for the Q-switch accordingly. For example, when Q-switch  118  is an EOM, the RF drive signals discussed above are replaced by DC drive signals. 
     The present invention is described above in terms of a preferred embodiment and other embodiments. The invention is not limited, however, to the embodiments described and depicted herein. Rather, the invention is limited only by the claims appended hereto.