Cavity round-trip time

The output is thus a continuous train of pulses separated by the dye cavity round-trip time. Even though the pump laser pulses may be of the order of 200 ps long, dye laser pulses of less than 10 ps can be achieved by synchronous pumping. This is because the dye molecules have extremely large stimulated emission cross-sections and the dye laser pulse passing through the dye stream immediately de-excites the dye molecule, in a few picoseconds, by stimulated emission [13]. 

Where L is the cavity length and c is the velocity of light the Tp parameter is the cavity round-trip time. The width of the pulse (FWHM) is given approximately by... 

The time delay between successive transmitted pulses equals the cavity round-trip time Tr = 2L/c. The nth pulse therefore is detected at the time t = 2 L/c. If the time constant of the detector is large compared to Pr, the detector averages over subsequent pulses and the detected signals give the exponential function... 

If the modulator is placed inside the laser resonator with the mirror separation d and the mode frequencies = vo m cjld (m = 0,1,2,...), the sidebands coincide with resonator mode frequencies if the modulation frequency / equals the mode separation Av = cjld. The sidebands can then reach the oscillation threshold and participate in the laser oscillation. Since they pass the intracavity modulator they are also modulated and new sidebands y = vq i 2/ are generated. This continues until all modes inside the gain profile participate in the laser oscillation. There is, however, an important difference from normal multimode operation the modes do not oscillate independently, but are phase-coupled by the modulator. At a certain time the amplitudes of all modes have their maximum at the location of the modulator and this situation is repeated after each cavity round-trip time T = 2d c (Fig. 6.8c). We will discuss this in more detail The modulator has the time-dependent transmission... 

An AM modulator in the laser resonator adjusts its loss periodically. The resonator loss is very high for some time, and light waves with certain phases during this period are attenuated no laser output develops. The inverse is true for the subsequent period of low resonator loss. The AM modulator period equals the cavity round trip time, i.e. Tam = 2.Llc = Tp. Because of this specific periodicity the AM modulator locks the modes to each other. AM modulation can be achieved using a Pockel cell or an AO modulator, similar to the devices shown in Figure 3.12. 

This function is periodic, with period T equal to the cavity round-trip time (Fig. 9.16) it corresponds physically to the fact that one light pulse is propagating back and forth inside the cavity at all times. Since part of this pulse is transmitted outside the cavity everytime it strikes the output coupler reflector, the laser output consists of a train of pulses equally spaced in time by T The zeros in E(r) on either side of the primary pulse peaks are separated by the duration 2T/ 2k + 1), which gives an upper bound estimate cf the laser pulse width Tp. For a 1-m optical path length cavity, the round-trip time T is 2Ejc = 6.67 ns. If 9 axial modes are forced to oscillate in phase with equal... 

The maxima occur when the denominator in (9.12) approaches 0). The pulse separation is the time taken for light to go back and forth in the cavity ("cavity round-trip time") and is typically 10 ns (Ins <- 30cm). From... 

Production of picosecond pulses is achieved as follows. A nanosecond pulse from a Q-switched laser may be converted, by various optical techniques known as mode-locking, into a train of even shorter pulses separated from one another by a few nanoseconds (actually the cavity round-trip time). One of these can be isolated from the train and amplified. 

The presence of the AO modulator within the laser cavity causes a loss of energy at times other than the round-trip time for the photons and the nulls In the AO crystal. If the cavity length matches the AO crystal frequency, then the photons accumulate in a single bunch and bounce back and forth together within the laser cavity. This is the mode-locked condition. 

The optimum gain for the dye-laser pulses is achieved if they arrive in the active medium (dye jet) at the time of maximum inversion AN(t) (Fig. 6.15). If the optical cavity length d2 of the dye laser is properly matched to the length d of the pump laser resonator, the round-trip times of the pulses in both lasers become equal and the arrival times of the two pulses in the amplifying dye jet are synchro-... 

Control loop tuning was another important aspect that needed to be addressed to make the system widely applicable without requiring extensive testing or expertise on the part of the user, in particular, the dynamic characteristics of the process as seen by the measurement system depend upon the number of cycles between measurements, which is determined by the round trip time of the TCS. This depends upon the number of measurements made within a round trip, and therefore on the number of cavities and sections, which is both job and machine dependent To address this issue, an analytical method was developed and implemented to compute controller gains explicitly accounting for the actual TCS round trip time. 

FIGURE 21 In the pump phase the timing diagram for the cavity-dumped case is identical to the Q-switched case. After switching the Pockels cell to enable lasing, the cavity loss now is very small since, for a cavity-dumped architecture, the reflectivity of both resonator mirrors is 100%. Once the power in the cavity has reached the maximum value, the Pockels cell is again switched and ejects the intracavity intensity from the laser in a pulse equal to the round-trip time of the resonator cavity. 

Mode-locking does not occur spontaneously in a simple laser cavity. Either it must be actively driven by a cavity element which introduces cavity losses with a period of exactly T/2 (i.e., one-half the optical round-trip time), or it must be... 

Each axial mode has its own characteristic pahem of nodal planes and the frequency separation Av between modes is given by Equation (9.4). If the radiation in the cavity can be modulated at a frequency of cjld then the modes of the cavity are locked both in amplitude and phase since t, the time for the radiation to make one round-trip of the cavity (a distance 2d), is given by... 

The envelope function defines the pulse repetition time T = 27r/u>r by demanding A(t) = A(t — T). Inside the laser cavity the difference between the group velocity and the phase velocity shifts the carrier with respect to the envelope after each round trip. The electric field is therefore in general not periodic with T. To obtain the spectrum of E(t) the Fourier integral has to be calculated ... 

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