Generation of High-Purity Higher-Order Laguerre-Gauss Beams at High Laser Power

We have investigated the generation of highly pure higher-order Laguerre-Gauss (LG) beams at high laser power of order 100 W, the same regime that will be used by second-generation gravitational wave interferometers such as Advanced LIGO. We report on the generation of a helical-type ${\mathrm{LG}}_{33}$ mode with a purity of order 97% at a power of 83 W, the highest power ever reported in literature for a higher-order LG mode. This is a fundamental step in proving technical readiness for use of LG beams in gravitational wave interferometers of future generations.

Figure 1

Cartoon of the experimental setup described in the Letter. The main components are labeled. Beam dumps, steering mirrors, wave plates, and polarizers are not shown.

Figure 2

Profile of the ${\mathrm{LG}}_{33}$ beam injected into the MC cavity, with best fit shown for comparison. The insets show an example of fitting of a ${\mathrm{LG}}_{33}$ beam, with the intensity patterns of a measured beam compared to the fit and related residuals.

Figure 3

Light power transmitted by the MC measured as a function of the cavity length (black line). The resonant peaks at 0 and 1 FSR are order-nine modes, nominally ${\mathrm{LG}}_{33}$. The fit to the “${\mathrm{LG}}_{33}$” peak measured data is shown for comparison (blue). The red curve is derived with a numerical model that assumes the following mode power distribution: 75% in ${\mathrm{LG}}_{33}$, 8% in ${\mathrm{LG}}_{63}$, 4% in ${\mathrm{LG}}_{43}$, ${\mathrm{LG}}_{53}$, and ${\mathrm{LG}}_{32}$, and 1% in ${\mathrm{LG}}_{62}$. The insets show CCD images of these non-order-nine modes.

Figure 4

Measurement of the light power at different locations in the setup as a function of the injected laser power. Statistical uncertainties in the measurement data are smaller than the marker’s size and here not reported. Systematic errors in the calibration of each power curve are of order 5%.

Figure 5

Intensity profile of the 83 W ${\mathrm{LG}}_{33}$ beam transmitted by the MC cavity (left) compared with fit residuals (right). Maps have same units and scale.

Figure 6

Top: ${\mathrm{LG}}_{33}$ purity of the beam transmitted by the mode cleaner. Bottom: fraction of the injected light power which is transmitted from the resonant mode cleaner (circles). Dashed lines show average values. Statistical errors are negligible, while calibration uncertainty is here of order 7%.