After testing the setup, I managed to light the LED, using the Arduino 10-bit PWM signal (using Time1 library), down to 54 microseconds.
If the applied PWM signal implies that the ON time is shorter than 54 microseconds, then the LED does not lights up. I am not sure why is this. the ON time of the LED driver is 200 ns, and it is suposed to support frequencies up to 1 kHz. Any idea why this is happening? 
I was thinking that it might be because the LED driver will be OFF below a certain threshold (0.15 V according to the data sheet). When I measure the apparent voltage of the PWM signal, I get around 34 mV (in accordance with the calculated considering the set duty cycle) So I think that at some point the LED driver just does not detects the applied 1.25 V signal anymore, but it was supposed to support up to 1 kHz....
In any case, 54 us flash duration is not short enough. 
Now, I am thinking in a solution: Using a kind of inverted electronic switch (I am not sure if that is the right term) to control the connection between the LED driver control pin and ground. As I said before, if the LED driver control pin is not grounded, the LED is ON; if I conected to ground, the LED is OFF. So I want a king of inverter that will Disconect the 1.25 V line in response to an Arduino signal. Like here.
In that exaple, an optoisolator was used. However, I need something faster. I want flashes in the order of 2 microseconds. Could use a kind of "inverted mosfet" (or whatever is called) to do this job? In other words, how can I get the Arduino to cut a 1.25 V line with a speed of 2 us?
Thanks in advance!!! 