To create an arbitrary temporal waveform at the output of a high-energy laser amplifier, the temporal waveform of the low-energy input pulse must be shaped to pre-compensate for temporal distortions caused by gain saturation (i.e. the fact that the leading edge of a pulse experiences high amplification than the trailing edge of the pulse due to depletion of available stored energy). The difficulty of pulse shaping is determining the appropriate amount and character of pre-compensation needed. To make the problem of specifying the output shape easier, in MEC we typically boil down the desired targeted output waveform to two parameters: - the temporal length of a pulse segment, specified through the parameter Psns (standing for Pulse segments in ns)
- due to the Highland, these segments must be specified in increments of 0.25ns
- to satisfy users, total pulse lengths are usually specified 0.25ns longer than requested in order to fill out the full requested temporal duration; this is usually added on to the last specified segment duration; for example:
- a 10ns pulse has a specified length parameter of Psns=[10.25]
- a 15ns pulse has a specified length parameter of Psns=[15.25]
- a 20ns pulse with two equal-duration steps (separated by an amplitude discontinuity) has a specified length parameter of Psns=[10, 10.25]
- note: if two adjacent steps are continuous in amplitude at their boundary rather than discontinuous, one point will be deleted automatically to avoid having a repeated point in the middle of the pulse; because of this deletion, the first of the two pulse must be specified one point (0.25ns) longer than desired in order to compensate; for example:
- a 20ns ramp pulse with four equal-duration segments with continuous amplitude boundaries has a specified length parameter of Psns=[5.25, 5.25, 5.25, 5.25]
- if the pulse above contained a discontinuity instead between just the second and third segments, the specified length parameter would instead be Psns=[5.25, 5, 5.25, 5.25]
- the heights at the endpoints of each segment, specified through the parameter SSs (standing for Start/Stop (heights) of segments)
- this is specified as a percentage of the maximum amplitude
- because users typically tolerate positive-gradient slopes better than negative-gradient slopes, percentages of the Start/Stop segment heights are often adjusted by 1-2% for segments meant to have a 0% gradient in order to give some cushion against the much-disliked negative-gradient situation
- each pulse segment needs its own specified Stop/Stop segment heights; for example,
- a 10ns flat-top pulse with 0% gradient has a Start/Stop segment heights parameter of SSs=[[98, 100]] (note the additional 2% to avoid the negative-gradient situation)
- a 15ns quasi-flat-top pulse with 15% gradient has a Start/Stop segment heights parameter of SSs=[[85, 100]]
- a 20ns step pulse, with a 4:1 amplitude ratio between flat-top steps each with 0% gradient, has a Start/Stop segment heights parameter of SSs=[[24,25],[98,100]]
- a 25ns ramp pulse with five equal-duration segments with continuous amplitude boundaries might specify the exact shape of its ramp using a Start/Stop segment heights parameter of SSs=[[10, 15], [15, 25], [25, 40], [40, 90], [90, 100]]
The names from these pulses are also based on these parameters: - for pulses with 1-2 main segments, the duration of each segment (rounded to the nearest ns) is included first
- e.g. '10ns' for a single-segment 10ns pulse or '05ns05ns' for a dual-segmented 10ns pulse with two 5ns steps
- for pulses with 2 main segments (i.e. step pulses), the ratio between the ending amplitudes of each segment is included next
- e.g. '050to100step' (for a step with a 2:1 amplitude ratio) or '020to100step' (for a step with a 5:1 amplitude ratio)
- the percent gradient of each individual segment is included last
- e.g. '00grad' for a 0% (flat-top) gradient or '15grad' for a 15% (quasi-flat-top) gradient
Let's go over a few examples below to help clarify: Pulse shape | Pulse name | Pulse segment durations in ns (Psns) | Start/Stop segment heights in %age (SSs) |
---|
Image Modified | '10ns00grad' | [10.25] | [[98, 100]] | Image Modified | '10ns20grad' | [10.25] | [[80, 100]] | Image Modified | '20ns50grad' | [20.25] | [[50, 100]] | Image Modified | '05ns05ns025to100step' (may or may not also include '00grad00grad' at the end) | [5, 5.25] | [[24, 25], [98, 100]] | Image Modified | '15ns15ns040to100step00grad60grad' | [15.25, 15.25] | [[39, 40], [40, 100]] | Image Modified | 'UserPulse0' (pulses with more than two segments are usually highly individualized and thus often named after the PI) | [5.25, 5, 5.25, 5.25] | [[10, 12], [12, 25], [40, 60], [60, 100]] | Image Modified | 'UserPulse1' (pulses with more than two segments are usually highly individualized and thus often named after the PI) | [5.25, 5.25, 5.25, 5.25, 5.25] | [[10, 15], [15, 25], [25, 40], [40, 90], [90, 100]] |
To make the problem of specifying the input shape easier, in MEC we also boil down the desired input waveform: - the temporal length of a pulse segment is the same for the output waveform as for the input waveform; therefore, no new parameter is needed and reusing the specified segment length parameter Psns is sufficient
- the heights at the endpoints of each segment, specified through the parameter YSSs (standing for YFE Start/Stop (heights) of segments)
- this is completely analogous to the use of SSs above except that the units are not specified as a percentage of the maximum amplitude but rather as the voltage level of the fast photodiode measuring the temporal waveform of the 10Hz YFE laser system as measured by a networked oscilloscope
- as with SSs, each pulse segment needs its own specified YFE Stop/Stop segment heights; for example,
- a 10ns flat-top pulse with 0% gradient may have a YFE Start/Stop segment heights parameter of YSSs=[[0.02, 0.114]]
- a 15ns quasi-flat-top pulse with 15% gradient may have a YFE Start/Stop segment heights parameter of YSSs=[[0.0158, 0.133]]
- a 20ns step pulse, with a 2:1 amplitude ratio between flat-top steps each with 0% gradient, may have a YFE Start/Stop segment heights parameter of YSSs=[[0.0075, 0.0165], [0.0275, 0.115]]
- a 15ns ramp pulse with ten equal-duration segments with continuous amplitude boundaries might specify the exact shape of its ramp using a YFE Start/Stop segment heights parameter of YSSs=[[0.00001, 0.00025], [0.00025, 0.00091], [0.00091, 0.00211], [0.00211, 0.00444], [0.00444, 0.00806], [0.00806, 0.01624], [0.01624, 0.02977], [0.02977, 0.04322], [0.04322, 0.05686], [0.05686, 0.0729]]
Here are the examples from above shown in graphical form to hopefully give a better picture: Goal for input pulse shape... | YSSs | → | Goal of corresponding desired output pulse shape | SSs | Image Modified | [[0.02, 0.114]]
(with Psns = [10.25]) | → → → → → → → → → | Image Modified | [[98, 100]] | Image Modified | [[0.0158, 0.133]]
(with Psns = [15.25]) | → → → → → → → → → | Image Modified | [[85, 100]] | Image Modified | [[0.0075, 0.0165], [0.0275, 0.115]]
(with Psns = [10, 10.25]) | → → → → → → → → → | Image Modified | [[48, 50], [98, 100]] | Image Modified | [[0.00001, 0.00025], [0.00025, 0.00091], [0.00091, 0.00211], [0.00211, 0.00444], [0.00444, 0.00806], [0.00806, 0.01624], [0.01624, 0.02977], [0.02977, 0.04322], [0.04322, 0.05686], [0.05686, 0.0729]] (with Psns = [1.75, 1.75, 1.75, 1.75, 1.75, 1.75, 1.75, 1.75, 1.75, 1.75]) | → → → → → → → → → | Image Modified | [[5.028, 6.355], [6.355, 8.834], [8.834, 13.429], [13.429, 20.141], [20.141, 31.433], [31.433, 50.059], [50.059, 78.878], [78.876, 91.350], [91.350, 96.155], [96.155, 100.0]] (digitized from a crazy request) |
|