Mode pulling

We now briefly discuss the frequency shift (called mode pulling) of the passive resonator frequencies by the presence of an active medium [325]. The phase shift for a stationary standing wave with frequency Vp and round-trip time Tp through a resonator with mirror separation d without an active medium is 

The index of refraction n v) is related to the absorption coefficient a (v) of a homogeneous absorption profile by the dispersion relation (3.24a, 3.24b) 

The resonance width Avr of gas laser resonators is of the order of 1 MHz, while the homogeneous width of the amplifying medium is about 100 MHz. Therefore, when Avr Avm, (5.74) reduces to 

This demonstrates that the mode-pulling effect increases proportionally to the difference of cavity resonance frequency Vr and central frequency vq of the amplifying medium. At the slopes of the gain profile, the laser frequency is pulled towards the center. 

The amplifying medium shifts the frequency of the oscillating mode from 2 p to in such a way that 

The time average of the spectral distribution of the output intensity 

0a = TtVaTii = 2Tiv n v2)2dlc = mn. This gives the condition 90 

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The achievable pulse length is determined by the total number of modes that can contribute to the pulse. The broader the frequency comb the shorter the possible pulse length, ideally reaching the so-called Fourier limit. In fact, the spectral width is usually limited by the width over which the GVD and higher order terms can be compensated for by mode pulling [5,6]. Cavity modes that are outside this bandwidth are suppressed without the help of the Kerr-lens effect and do not oscillate. 

Failure Mode Pull Failure Mode Pull ... 

An analysis of the commercialised biotransformations (Fig. 1) shows that in 50% of the processes only hydrolases are being used. This is in line with the analysis of Faber [4], who showed that about 60% of the research publications on biocatalysis deal with hydrolases. The reason for this is partly that making a molecule is more difficult than breaking a molecule. However, hydrolases are also used in the reverse mode, pulling the equilibrium towards synthesis by water removal during the reaction, for example... 

Because of its index of refraction n(v), it shifts the eigenfrequencies of the passive resonator (mode-pulling). 

The frequency of a passive resonator mode (L = 15 cm) lies 0.5Avd away from the center of the Gaussian gain profile of a gas laser at A = 632.8 nm. Estimate the mode pulling if the cavity resonance width is 2 MHz and Avd = IGHz. 

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