Radial and azimuthal polarized doughnut modes

The cylindrical symmetry obtained on precision alignment of the cavity provided conditions for the generation of various circular modes by shifting the lens about

6.3. OBSERVATION AND RESULTS 56 its initial position, d = f_ax along the resonator axis. There were found two regions where AP and RP doughnut modes appeared: one of these regions was closer to HR (at lens positions d < f_ax), the other was shifted further towards OC (at lens positions d > f_ax). These regions will be referred conventionally as the HR region and OC region respectively. In these regions, the doughnuts remained stable over small lens shifts, l = 1 mm. For lens positions between these two regions intensity profiles with a central hole (that is a distinguishing characteristic of a doughnut) were distorted. Figure 6.2a-d shows four groups of CCD camera images of AP and RP doughnut modes in near-field which were obtained using c-cut YVO₄ and α-BBO crystals in the resonator of the length, L = 114 cm with the lens f = 10 cm sans any intra-cavity diaphragm at pump power about 1 W.

Position of the lens relative to the HR surface in each case, d, is indicated alongside the corresponding sequence of images. Each group of images included frames; one registered directly at the output and the others recorded through a linear polarizer (arrows indicating the transmission axis of the polarizer in each case) placed in front of the camera on a rotating mount. The orientation of mode lobes relative to the arrows in the frames clearly classifies them as AP (a, d) and RP (b, c) doughnuts. Intensity profiles of doughnuts in far field were similar to their near field patterns. This proves the single-mode nature of the observed output. In some cases, doughnuts were observed with an admixture of modes of higher-order, figure 6.2c. The intensity of these modes increased with pump power. But these higher order modes could be easily removed using an intra-cavity diaphragm.

With intra-cavity c-cut YVO₄, AP doughnut mode was observed in the ‘HR region’, figure 6.2a. The RP doughnut mode oscillated in the ‘OC region’, fig-ure 6.2b. Contrastingly, resonator with intra-cavity c-cut α-BBO generated RP doughnut mode in the ‘HR region’ and the AP mode in the ‘OC region’, figure 6.2(c,d). Near the threshold of generation, at 1 W pump power, the Yb:YAG laser output power (doughnut mode) was 6 mW. Using an intra-cavity diaphragm it was possible to produce doughnut beams of high quality with output power over

6.3. OBSERVATION AND RESULTS 57

c-cut YVO

(a) (b)

c-cut α -BBO

(c) (d)

d < f

d > f

Figure 6.2: CCD camera images in near-field of AP and RP doughnut modes generated from Yb:YAG laser cavity with birefringent (a,b) c-cut YVO₄ or (c,d) α-BBO crystals and lens f = 10 cm placed at distance d < f_ax or d > f_ax from HR surface. The transmission axis of linear polarizer placed before the camera is indicated by arrows in the corresponding frames wherever used.

60 mW at 4 W pump power.

The width of the HR or OC regions that allowed oscillations in doughnut modes was w ≈ 0.8 mm while the width of the entire zone separating the HR and OC regions was W ≈ 11mm. Similar AP/RP doughnut modes were observed using other lenses. While the width of the HR and OC regions appeared to match in all cases with w = 1 mm, the separation zone between these regions, W, showed dependence on the focal length of the lens used. For example, in cavity L = 114 cm, W≈1 mm was observed with lens f = 5 cm, whereas W≈6 mm was observed with f = 7.5 cm. The width, W was also affected by the cavity length L. For the cavity with lens f = 5 cm, the separation zone widened, W ≈ 3 mm when length of cavity was reduced to L = 71 cm. Very narrow W in the range 0.05-0.15 mm

6.3. OBSERVATION AND RESULTS 58 were observed in cavities of L = 114-117 cm with f = 3.5 cm lens.

For lens placed within the HR region, the laser generated doughnut modes with spot diameters 2-4 mm at the output. Angular divergence of these modes was 0.6-1.0 mrad. However, in the OC region, spot sizes of beams generated measured 1 mm or smaller and had a larger divergence up to 5 mrad. We indicate beams with smaller and larger divergences conventionally as ‘parallel’ and ‘conical’ beams. So,

‘parallel’ beams were confined within the HR region and ‘conical’ beams existed in the OC region. Spot sizes and divergence of ‘conical’ beams could be changed within a small range of lens shifts within the OC region. It was also observed that the divergence of ’conical’ beams could be compensated to ≈ 1 mrad using an extra-cavity lens. Propagation factor for doughnut modes, M² was determined based on measurements of the Rayleigh range [58] of the focused beam yielding M² = 2-2.5 (theoretical M² value for doughnut modes, M² = 2 [86]).

The polarization purity of output doughnuts was measured (both for ‘parallel’

and ‘conical’ beams) according to [82] using a 300 μm-wide slit and the polariza-tion analyzer, mounted on graduated rotapolariza-tion stages. Radial slices of a beam were selected by the slit, transmitted through an analyzer and sent to the power-meter.

The position of the beam spot on the slit was monitored using a CCD camera. For each orientation of the slit, and at angular positions of the analyzer correspond-ing to minimum and maximum of the transmission, laser radiation transmitted through the analyzer was measured and the ratio of the maximum to the minimum of transmitted power was estimated. This polarization extinction ratio (PER) was used as the measure for the level of the RP or AP at the output of the laser. PER values in the range of 50−90 : 1 were registered. The use of a circular 3-4 mm diaphragm in the cavity helped to improve polarization contrast. The highest PER values, up to PER = 100:1 were observed for conical beams.

In the separation zone when the width was as wide as W = 10 mm (for f = 10 and 20 cm) along with lens shifts, the axial minimum intensity of the mode gradually transformed to bell-shaped beam profiles at the output. Such profiles

6.3. OBSERVATION AND RESULTS 59 (unpolarized or with a linear polarization) dominated almost over all the length of the separation zone. For W < 5 mm, it was possible to follow the transfor-mation of oscillations from one polarization state to the orthogonal one. Figure 6.3 shows recordings of one such transformation from AP to RP observed at the output from cavity, L = 114 cm, enclosing lens f = 5 cm, c-cut YVO₄ crystal and intra-cavity diaphragm of 3 mm diameter for lens shifts between the HR and OC regions. Displacements of the lens are indicated by micrometer readings on the lens translation stage, l. Using the extra-cavity polarizer it was possible to observe (shifting the lens in little steps) the transition from the mode with the dominant AP-like, figure 6.3a to the RP-like mode, figure 6.3c. Inside the separation zone, there was a definite position of lens indicative of AP to RP transfer, figure 6.3b, where the mixture of doughnut and Gauss-like modes linearly polarized in orthog-onal directions was observed. Doughnuts or mode compositions with two off-axial minima were observed at polarization transfer in cavities with lens of f = 3.5 cm.

l = 6.65 mm l = 6.70 mm

l = 6.72 mm

(a) (b) (c)

Figure 6.3: Mode profiles and polarization change observed on shifting the lens f = 5cm in the Yb:YAG laser cavity between HR and OC regions.