Apparently it shouldn't be problem, since you can capture it with DSO. Beside BW, also the slew time is important. But what is the setup?

@MarkoBuršič, if you're asking for the exact setup, the detector output is an SMA cable, which is sent into an amplifier (that I would like to figure out what I need), which is sent into the time-tagging "qutau" via sma.

So 50 ohm impedance? You need at least 1000 V/µs slew rate, probably a video amplifier.

@MarkoBuršič, yes, 50 Ohm impedance. Also I have added an extra section describing my attempt to get it working with a ZPUL-30P amplifier from minicircuits. It sort of works, but I think it's not perfect and am looking for advice for a betters solution.

Quick search, looking at spec, some AD8009 : analog.com/media/en/technical-documentation/data-sheets/… seems very good candidate. Since there are better specialist about this topics than me on this forum, you will soon get a better match. In my opinion, you should look for such device, that you can buy an evaluation board for it.

@StevenSagona I'd like to know a lot more about the detector, itself. Single-photon detectors exhibiting something like an exponential decay? That almost always indicates a statistical (large number) process. So is the photon stripping up multiple free particles that exhibit the usual random Poisson behavior (quantum) which when integrated through a low-pass looks like an exponential decay? Or what? I'd love to hear details. (Which may have nothing to do with an answer for your time-stamper.)

Also the true fact is that your scope DS1102 has only 100MHz BW, so the signal is even steeper. Try with the best DSO you have.

@jonk It is probably from a SPAD array or sipm without pulse shaping given the impulse response.

How accurate is "accurate"? How much delay can you tolerate between the start of the input pulse and the start of the amplified pulse?

And does your solution need to be off-the-shelf? (if so, with which connectors?) Or are you looking to solder something?

Just a quick tip when using your scope, if you plug in a FAT32 formatted USB stick, and press the print button, it makes a screenshot of the screen, and puts it on the USB drive. You get nice looking screenshots that way

It's important for you to keep aware of your count rate and the possibility of two pulses coming close together that they pile up, or even two at the same time. If you have random pulses at say 10,000/sec (you will have both noise and real photons) then every ten seconds two will happen within 1 nanosecond of each other for example. If you are using a pulsed laser rather than CW laser, then you will have to be much much more careful about pileup.

The reason that pileup is problematic for you is that depending on the type of pulse shaping you have, the two events will register as a single event but at a time somewhere between the two pulses. For low count rates you can still have precision timing even with more slowly shaped pulses (good shaping electronics and design (bipolar pulses) will allow timing precision to a tiny fraction of the rise time), but you can't tolerate pileup as well in that case.

If you have money to throw around, the electronics which are designed specifically for this sort of application will come in NIM crate format, something like this: ortec-online.com/products/electronics/amplifiers. They'll be massively overpriced compared to a homebuilt solution, but will have all the tuning knobs you want if you buy the right one. There's enough of them around that you can probably find them second hand on ebay for a decent discount

Thanks everyone for the comments. I'll try to answer everything here.

@jonk, my expertise isn't in solid state physics, so I can't explain the details very well but it's a superconducting nanowire detector. From what I understand the occurs because photons hitting the nanowire temporarily break the superconducting nature and change the voltage temporarily. Why exactly that effect is exponential I'm not sure.

@uhoh, the detectors are often used to try to characterize such properties, and sometimes we expect photons to be directly on top of eachother or very close - so this is why I'm interested in improving things to be as good as possible.

@Ferrybig, thanks for the recommendation of the screenshot. in other scopes i know you can save the data in a textfile but then i'd have to plot it in matlab/excel/etc and was lazy - but I'll try the screenshot method nexttime!

@StevenSagona speaking of superconducting nanowire detectors which I learned about after reading this answer. This sounds like quite a fun project. Nuclear and particle physics experiments push single photon fast timing to its limits, and as long as pileup is under control they intentionally shape the pulses to some extent to minimize timing jitter which comes from the finite number of electrons reaching the anode after multiplication and their spread in arrival times.

@StevenSagona The fastest rise time is not necessarily the best for jitter minimization and timing precision for both electron statistics and system noise (thermal electrons, shot noise, dark current, etc.). There's a lot of signal processing math, but there was something about differentiating the pulse and adding it back in to produce a bipolar pulse who's zero crossing is independent of amplitude...

it's a half-century old now or longer, but it is really worth finding some standard text on timing techniques and nuclear/particle physics is one source for such "ancient wisdom."