Elección y Desarrollo de un Estilo de Liderazgo

Four of the most important parameters defining the operation of an ultrashort pulse laser are as follows: average power, optical output spectrum, repetition frequency and pulse duration. Average power can be measured simply by a power meter and is the most trivial of the measurements. The optical spectrum can be determined with an optical spectrum analyser while the repletion frequency can be obtained by the use of a fast photodiode and a radio frequency spectrum analyser. All of these are very quick and easy measurements to perform.

The most demanding quantitative measurement is that of the pulse duration because this cannot be done electrically for the ultrashort pulse durations involved. One solution is a technique known as autocorrelation [28] where the pulse duration is calculated for an assumed pulse shape by using the pulse itself as an instrument of metrology. It is very important for accurate measurements when using this method that the shape of the pulses being investigated is known. Despite the fact that sech2 pulses and ones with a Gaussian profile may look similar, significant differences exist (see equation 2.7) in their time-bandwidth products.

2.5.1 The two-photon autocorrelator

Figure 2.8 below shows the basic set up for the two-photon autocorrelator that is at the heart of the method.

In this scheme, which is basically a Michelson type of optical delay line, an incoming pulse is split at the beam splitter. One copy of the pulse strikes a static mirror and is reflected into a detector. The other copy of the pulse strikes a movable mirror. Because mirror M2 is moving backwards and forwards, the optical path difference between the two pulse copies is constantly changing.

Figure 2.8. Two-photon autocorrelator.

At times when the path difference is zero, the two copies will be completely overlapping and interfere constructively, and destructively for a phase difference of. When a path difference exists, the two copies will be out of sync with each other by an amount given by this optical path difference. When the pulses overlap, there will be significantly higher intensity incident on the detector resulting in a nonlinear response. This nonlinear response will only be produced for the period of overlap of the pulses. This is intrinsically connected to the width of the pulse.

Typical ways to achieve this nonlinearity are through the use of a second harmonic crystal placed before the detector or through the use of a diode which will give a quadratic response by means of two-photon absorption. One difficulty in using a nonlinear crystal is that additional alignment must be performed to ensure correct phase-matching in the crystal. In addition, when measuring ultrashort pulses, thin crystals have to be used to ensure that the phase matching bandwidth of the crystal is large compared to the frequency bandwidth of the pulse. When looking for the two- photon signal produced by a laser diode, incident photons with energy greater than the bandgap of the diode will be absorbed in a linear manner for low intensities of light. However, should a suitably intense signal be incident on the detector, then less energetic photons with energies given by ½ Eg<E<Egwill be absorbed by a nonlinear

two-photon process. This will produce the required quadratic response. This approach is polarisation insensitive and is inherently broad bandwidth. It is also cheaper than the SHG crystal approach since an additional photomultiplier tube is not required.

Provided that the two arms of the autocorrelator are aligned perfectly, the detector will measure a signal which is related to the degree of overlap of the two pulse copies. This can be described by the following expression.







In the above expression, G(is the degree of overlap which is a function of the delay time  between pulses. E(t) represents the electric field of the pulse as a function of time. Provided that the autocorrelator is calibrated for a relatively slow frequency response, the device will measure a time averaged intensity autocorrelation. This is defined as follows: 2 ( ) 1 2 ( ) where ( ) ( ) ( ) ( ) i G g I t I t dt g I t dt            





In the above expressions, g(is the background free autocorrelation function. This measurement uses equations which contain information purely regarding intensity. This method contains no information regarding the frequency chirp of the signal. A ratio of 3:1 exists between signal level and background for values of and ±∞ respectively in equation 2.9. This defines the contrast ratio for an intensity autocorrelation. We find that the relationship between the pulse duration pand the

width of the autocorrelationt trace is given by:

p t k

 

  2.25

k is the intensity autocorrelation conversion factor which depends on the shape of the pulse. For a Gaussian pulse, k=1.414 and a sech2pulse has k=1.543. This allows us to calculate the actual pulse duration from the trace assuming a specific shape. Figure 2.9 shows a typical intensity autocorrelation trace.

Figure 2.9. Intensity autocorrelation trace showing 3:1 ratio displaying a FWHM of approximately 30fs

The intensity autocorrelation is the simplest of the autocorrelation techniques and also contains the least information. More complicated techniques such as interferrometric autocorrelations can be employed in order to provide additional information about the pulse, such as its frequency chirp profile.