POWERPLUSWATERMARKOBJECT3 LECTURE4 LASER TECHNOLOGY ACTIVE RESONATOR IN THIS SECTION

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Active Resonator

POWERPLUSWATERMARKOBJECT3 LECTURE4 LASER TECHNOLOGY ACTIVE RESONATOR IN THIS SECTION Lecture-4 laser technology

Active Resonator

In this section we will analyze the changes that occur if alasing medium is inserted into the resonator. In cw and high-average-power solid state

lasers the dominant effect that distorts the mode structure in a resonator is

thermal lensing. Heat removed from the rod surface generates a thermal gradient.The thermally induced spatial variations of the refractive index causes the laser rod to act as a positive lens with a focal length that depends on the power dissipated as heat from the pump source.

As an introduction to the effect of thermal lensing on the resonator geometry we will first consider a thick lens. This is followed by considering a thick distributed lens that represents a laser rod. Finally at the end of the section the sensitivity of different active resonator configuration to mirror misalignment will be discussed. Perturbation of the thermal lens of the laser rod leads mainly to changes in mode

structure and beam divergence, whereas a misalignment of the resonator mirrors causes a lateral displacement and angular tilt of the output beam, which causes an increase of the diffraction losses and therefore a reduction of output.

POWERPLUSWATERMARKOBJECT3 LECTURE4 LASER TECHNOLOGY ACTIVE RESONATOR IN THIS SECTION

Fig. 1 Geometry and (b) stability diagram of a resonator containing a thin positive lens

Resonator Containing a Thin Lens. The theory necessary to analyze resonators that contain optical elements other than the end mirrors has been developed by Kogelnik .We will apply this theory to the case of a resonator containing an internal thin lens. To a first approximation, this lens can be thought of as representing the thermal lensing introduced by the laser rod. Beam properties of resonators containing internal optical elements are described in terms of an equivalent resonator composed of only two mirrors. The pertinent parameters of a resonator equivalent to one with an internal thin lens are

where

L0 = L1 + L2 − (L1L2/ f ) and f is the focal length of the internal lens; L1

and L2 are the spacings between mirrorsM1,M2 and the lens, as shown in Fig. 1

The stability condition remains unchanged.For the subsequent discussions we find it convenient to express the spot sizes in terms of g1 and g2. By combining R1, R2, and L with the relevant g1 and g2

parameters, can be written

POWERPLUSWATERMARKOBJECT3 LECTURE4 LASER TECHNOLOGY ACTIVE RESONATOR IN THIS SECTION

From (5.36) follows

As an example we will consider a resonator with flat mirrors (R1 = R2 =∞) and a thin lens in the center (L1 = L2 = L/2). From (5.35) and (5.36) we obtain

POWERPLUSWATERMARKOBJECT3 LECTURE4 LASER TECHNOLOGY ACTIVE RESONATOR IN THIS SECTION

For f =∞the resonator configuration is plane–parallel; for f = L/2 we obtain the equivalent of a confocal resonator; and for f = L/4 the resonator corresponds to a concentric configuration.

Resonator Sensitivity to Mirror Misalignment.

For a resonator to be aligned the mode axis must be normal to each of the two mirrors, which means the beam axis passes through the center of curvature of the mirrors. Figure 2 depicts a resonator composed of mirrors M1 and M2 with radii R1 and R2, respectively. The mirrors

POWERPLUSWATERMARKOBJECT3 LECTURE4 LASER TECHNOLOGY ACTIVE RESONATOR IN THIS SECTION

Fig. 2 Misalignment of mirror M1

are seperated a distance L and the center of curvature of mirror M1 is at a point P1, and for mirror M2 the center is at point P2. If mirror M1 is titled by an angle α, the center of curvature of mirror M1 moves by Δ₁ = R1α to point P₁. The resonator axis is rotated by an angle θ and the center of the mode pattern is shifted by Δ₁ and Δ₂ at mirror M1 and M2, respectively. From geometric considerations one obtains

POWERPLUSWATERMARKOBJECT3 LECTURE4 LASER TECHNOLOGY ACTIVE RESONATOR IN THIS SECTION

If we introduce the resonator parameters for g1 and g2 we can examine more closly a few typical resonator configurations. we obtain

POWERPLUSWATERMARKOBJECT3 LECTURE4 LASER TECHNOLOGY ACTIVE RESONATOR IN THIS SECTION

For a resonator with large radius mirrors of equal radii R1 = R2 = R we obtain

POWERPLUSWATERMARKOBJECT3 LECTURE4 LASER TECHNOLOGY ACTIVE RESONATOR IN THIS SECTION

For a confocal resonator (R1 = R2 = L) we have

If the flat mirror of a hemispherical resonator (R1 ≈∞, R2 ≈ L) is tilted, we obtain

Figure 3 shows the alignment tolerance of various types of resonators for a HeNe laser operating single mode . Again, the confocal resonator is far more forgiving for mirror misalignment than the othern types. As is apparent from this figure, the alignment tolerances for a concentric-type resonator (L/R = 2) and a resonator having large-radius mirrors is about the same

POWERPLUSWATERMARKOBJECT3 LECTURE4 LASER TECHNOLOGY ACTIVE RESONATOR IN THIS SECTION

Fig. 3. Alignment tolerance of various types of resonators. Curve shows a reduction of output power by 50% of a He-Ne laser operated in a single transverse mode

Dr. Jassim

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