Usually the way to high speed pulses, is a Bias T and a pulse generator from HP, HighLand Technology or AvTECH etc.
The Bias T lets you put a DC bias onto the diode, and then AC couple the pulse into the diode. The DC sets right below the lasing threshold.
The Bias T also normalizes things to 50 ohms, allowing use of a commercial pulse generator.
My good friend Dr Lava has it right, a current source that is redirected away from the diode as needed. Usually 3-4 pairs of RF grade diversion devices are used to reduce capacitance at shorter pulses.
Watch out, some place around 1 Ghz to 2 Ghz the diode becomes a very nasty load without proper impedance matching, and becomes a LED for the duration of the pulse.
Also watch your average power, the current density of many diodes is already at the internal limits of the die, you need to back off to 1. avoid the resonance effects above, and b to keep the carrier density down.
As sonnet and OC48 use these kinds of pulses, driver chips are out there, but you really need a special diode package at that point.
Of if your desired bandwidth is under 20 mhz or 100 mhz, you can consider a acousto-optic modulator (usually 7-20 mhz) or a electro-optic modulator (100 mhz or more bandwidth)
As you wish for green, you may need to consider the size and storage time of the Ir to green conversion process, and use either a "microchip" laser, a very short cavity, intracavity passive qswitching, or a external modulation. Microchip lasers have extremely short cavities and "pop" out a self qswitched 3 to 7 nanosecond pulse a few microseconds after the pump diode turns on. The ND:vandate in a cheap laser pointer module has a storage time of 800 uSec or so, and thus you may need to hold the pump diode just below lasing threshold and then drive it to lasing....
What are you probing? if Silicon, 750-820 nm IR is just fine, but otherwise you might need to tune your wavelength to match a bandgap of your semiconductor.
see for example:
Avtech Electrosystems - Nanosecond Waveform Generators
Highland Technology Precision Electronic Instruments
Bias Ts are available from many vendors including Thorlabs...
http://www.ixysrf.com/products/mosfet_driver_ics.html
Steve