Active Resonators and Laser Modes

Introducing the amplifying medium into the resonator changes the refractive index between the mirrors and with it the eigenfrequencies of the resonator. We obtain the frequencies of the active resonator by replacing the mirror separation d in (5.52) by 

If the pump power is increased continuously, threshold is reached first at those frequencies which have a maximum net gain. According to (5.5) the net gain factor per round trip 

Assume that a wave with the spectral intensity distribution 10(1/) traverses an interferometer with two mirrors, each having the reflectivity R and transmission factor T (Fig. 5.22). For the passive interferometer we obtain a frequency spectrum of the transmitted intensity according to (4.51). With an amplifying medium inside the resonator the incident wave experiences an amplification factor (5.58) per round trip and we obtain, analogous to (4.62) by summation over all interfering amplitudes, the total transmitted intensity as a function of the phase difference  

The total amplification Ix/Iq maxima for = 2q7r, which corresponds to the condition (5.53) for the eigenfrequencies of the resonator with the modification (5.57). For G(i ) 1, the total amplification Ix/Iq becomes 

According to (5.8) the gain profile 00(1/) = exp[-2a(i/)L] depends on the line profile % v-Vq) of the molecular transition E — Ejj. The threshold condition can be illustrated graphically by subtracting the frequency-de-pendent losses from the gain profile. Laser oscillation is possible at all frequencies i L where this subtraction gives a positive net gain (Fig. 5.23). 

Introducing the amplifying medium into the resonator changes the refractive index between the mirrors and with it the eigenfrequencies of the resonator. 

We obtain the frequencies of the active resonator by replacing the mirror separation d in (5.52) by 

The total amplification /t//o has maxima for cp — lqn, which corresponds to the condition (5.53) for the eigenfrequencies of the resonator with the modification (5.57). For G(v) 1, the total amplification Ij/h becomes infinite for (j) = 2qn. This means that even an infinitesimally small input signal results in a finite output signal. Sueh an input is always provided, for instance, by the spontaneous emission of the excited atoms in the active medium. For G(v) = 1 the laser amplifier converts to a laser oscillator. This condition is equivalent to the threshold condition (5.7). Because of gain saturation (Sect. 5.3), the amplification remains finite and the total output power is determined by the pump power rather than by the gain. 

The preceding example illustrates that the passive resonance halfwidth of typical resonators for gas lasers is very small compared with the linewidth of a laser transition, which is generally determined by the Doppler width. The active medium inside a resonator compensates the losses of the passive resonator resonances resulting in an exceedingly high quality factor Q. The linewidth of an oscillating laser mode should therefore be much smaller than the passive resonance width. 

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Mode-locked laser A laser in which many resonant modes are coupled in phase, to yield a train of very short pulses (e.g. ps pulses). The coupling of the modes is obtained by modulation of the gain in the resonator, and can be active (electro-optic modulation of the losses or of the pump intensity), or passive (with a saturable absorber). 

As has been pointed out above, a laser basically consists of an active material and a resonator. The latter enables the build-up of certain resonant modes and essentially determines the lasing characteristics. In most conventional devices, the optical feedback is provided by an external cavity with two end mirrors forming the resonator. With the advent of polymers as active materials, various new feedback structures were invented. Initially, a microcavity resonator device of the type shown schematically in Fig. 6.13 a was employed [48]. 

Without frequency-selective elements inside the laser resonator, the laser generally oscillates simultaneously on many resonator modes within the spectral gain profile of the active medium (Vol. 1, Sect. 5.3). In this multimode operation no definite phase relations exist between the different oscillating modes, and the laser output equals the sum intensities L of all oscillating modes, which are more... 

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