The present invention relates generally to a technique for measuring pulse duration and coherence time of ultrashort light pulses using second harmonic generation (SHG) autocorrelators and more particularly to an SHG autocorrelator which does not introduce dispersion and therefore does not alter the pulse profile in time.
Recently, lasers have been developed which are able to generate laser pulses with pulse widths as short as about 6 femtoseconds (fs). For a number of reasons, it is desirable to be able to measure the pulse duration of such pulses.
A 6 fs laser pulse has a wide bandwidth on the order of 40 nanometers (nm) of the wavelength spread because of the uncertainty principle. The wide bandwidth will cause the pulse duration to change upon traveling through various media such as glass or liquids due to the wavelength dependence of the index of refraction. The pulse will be delayed and also be broadened in time because of the wavelength dependence of the index of refraction of the media.
The pulse delay arises from the dispersion of the group index of refraction which is expressed as follows using first order approximation: ##EQU1## where .tau..sub.DELAY is the time delay of the pulse, L is the thickness of the dispersive media, c is the velocity of light in a vacuum, n.sub.g (w) is the group index of refraction at wavelength w, w.sub.c is the wavelength at peak intensity and .DELTA.w is the wavelength spread of the pulse. For example, a 1 millimeter (mm) thick element made of glass will cause a 10 fs pulse to be delayed by a factor of two times in pulse duration. For a crystal of KDP the time delay for pulses at 600 nanometers and 640 nanometers is: ##EQU2##
The pulse broadening in time because of the group dispersion effect can be expressed as follows: ##EQU3## (for gaussian pulses) where
.tau..sub.0 =input pulse full width at half maximum pulse duration.
.tau..sub.1/2 (L)=output pulse duration after traveling a distance L in material:
.tau..sub.D =(4 ln 2.sub.k "L).sup.2 =dispersion broadening of pulse width; ##EQU4##
.eta.=phase index of refraction; and
.lambda.=wavelength.
For example, for a 100 .mu.m crystal of KDP, .tau..sub.DELAY =1.43 femtoseconds (fs) for 600 nm and 640 nm pulses.
The pulse broadening time .tau..sub.D for (BK-7) glass and for KDP is listed below for a 620 nm pulse for thicknesses of 100 .mu.m, 10 .mu.m and 5 .mu.m. Also shown is the time broadening .tau..sub.1/2 (L) for glass and KDP for .tau..sub.0 =10 fs for thicknesses of 100 .mu.m and 10 .mu.m.
______________________________________ .tau..sub.D .tau..sub.1/2 (L) for .tau..sub.o = 10fs Thickness Glass (BK-7) KDP GLASS (BK-7) KDP ______________________________________ 100 .mu.m 1.645 fs 1.648 fs 10.13 fs 10.13 fs 10 .mu.m 0.164 fs 0.1648 fs 10.00 fs 10.00 fs 5 .mu.m 0.0823 fs 0.0824 fs 10.00 fs 10.00 fs ______________________________________
For 1 mm plates .tau..sub.DELAY =14.3 fs for glass and 14.3 fs for KDP and .tau..sub.D =16.45 fs for glass and 16.48 fs for KDP. For a 10 fs pulse input, .tau..sub.1/2 (1 mm)=19.25 fs for BK-7 glass and 19.28 fs for KDP.
Typical dispersion factors are listed below for reference.
______________________________________ .lambda. ##STR1## ##STR2## ______________________________________ BK-7 GLASS 600 -37609.9 1.935 .times. 10.sup.11 610 -35739.6 1.80720 .times. 10.sup.11 " 620 -33992 1.6895 .times. 10.sup.11 " 630 -32357.3 1.58146 .times. 10.sup.11 640 -30.826.3 1.488 .times. 10.sup.11 KDP 600 -37645.4 1.93795 .times. 10.sup.11 610 -35723 1.80962 .times. 10.sup.11 620 -34023.1 1.6918 .times. 10.sup.11 630 -32386.2 1.58348 .times. 10.sup.11 640 -30.853.3 1.48373 .times. 10.sup.11 ______________________________________
In summation, the thickness of an element should be 100 microns or less to substantially reduce all effects from dispersion. Also, as the thickness increases the amount of dispersion will also increase.
One type of apparatus that is commonly used to measure the pulse duration of ultrashort light pulses is the SHG autocorrelator. In an SHG autocorrelator a pulse of light to be examined is split by a beamsplitter into two beams traveling along different paths. One beam is passed through a stationary optical delay and the other through an adjustable optical delay. The two beams are then combined by a lens in a second harmonic generating (SHG) crystal. The second harmonic pulse generated by the SHG crystal is then detected by a detector.
As can be appreciated, the beamsplitter, the lens and the SHG crystal in an SHG autocorrelator all cause the pulse duration to change due to group velocity dispersion. Thus, the apparatus will produce erroneous pulse duration measurements.
References of interest include Lasers For Ultrashort Light Pulses, J. Herrmann and B. Wilhelm, Chapter 3, North Holland Publishing, 1984; Biological Events Probed By Ultrafast Laser Spectroscopy, R. R. Alfano, Academic Press, Chapter 17, 1982; and Ultrashort Light Pulses, S. L. Shapiro, Springer Verlag, Volume 18, 1977.
It is an object of this invention to provide a new and improved SHG autocorrelator.
It is another object of this invention to provide an SHG autocorrelator in which the dispersion produced is minimized.