Nonlinear optical processes on a whole new order

Researchers at AEI Hannover set a new benchmark for the conversion efficiency of higher-order spatial laser modes in second harmonic generation.

12. November 2020

Gravitational-wave detectors measure differential changes in the positions of their two end mirrors caused by a gravitational wave. These changes are so tiny that they can be masked by the likewise tiny, thermally induced vibrations of the mirror surfaces. A laser beam which probes a larger area of these surfaces could mitigate this issue because it would result in a partial cancellation of vibrations at different positions on the mirror surfaces. Such a broad laser beam should preferably operate in a higher-order spatial mode to keep diffraction losses low. Nonlinear processes, namely second harmonic generation and parametric down conversion, are used in gravitational-wave detectors to reduce quantum noise. Such processes are a challenge of its own for higher-order modes because they are generally less efficient. For instance, while conversion efficiencies of the fundamental Gaussian mode in second harmonic generation close to 100% have been reported, the highest result for a higher-order mode has so far only been 10%. The latter was achieved in 2014 for a 2nd order Laguerre-Gaussian mode.  Now, AEI researchers could improve this efficiency by a factor of 4.5 for a beam with an even higher mode order: they achieved a conversion efficiency of 45% for a 9th order Laguerre-Gaussian mode in second harmonic generation. While the interest in higher-order modes has faded in the past due to additional challenges regarding their generation, handling and interaction with astigmatic optical components, this promising result may revive their consideration for future gravitational-wave detectors.

Paper abstract for “Frequency-doubling of continuous laser light in the Laguerre–Gaussian modes LG0,0 and LG3,3

Measured external, corrected, and effective SHG conversion efficiencies of the LG00 and LG33 modes, including the NLCS simulations for the corrected curves. The x axis refers to the full input power for the external and effective efficiencies and to the estimated matched input power for the corrected and simulated efficiencies. Bottom right: CCD picture of the harmonic output field at Pextin = 664 mW for the LG33 mode. A distorted LG66 intensity pattern can be identified.

For future generations of gravitational wave detectors, it is proposed to use the helical Laguerre–Gaussian LG3,3 mode to reduce thermal noise, which limits the detector sensitivity. At the same time, this requires the efficient generation of squeezed vacuum states in the LG3,3 mode for quantum noise reduction. Since this technique includes the process of second harmonic generation (SHG), we experimentally compare the conversion efficiency and harmonic output field of the LG0,0 and LG3,3 modes in a cavity-enhanced SHG using the same 7% doped MgO:LiNbO3 crystal. Conversion efficiencies of 96% and 45% are achieved, respectively. The influence of mode mismatches and astigmatism is analyzed to estimate the ratio of the pump mode-dependent effective nonlinearities to be 𝑑0,0/𝑑3,3∼5. Furthermore, we show that absorption loss in the crystal is more relevant for the LG3,3 mode.

Paper abstract for “Numerical analysis of LG3,3 second harmonic generation in comparison to the LG0,0 case”

For coating Brownian thermal noise reduction in future gravitational wave detectors, it is proposed to use light in the helical Laguerre-Gaussian LG3,3 mode instead of the currently used LG0,0 mode. However, the simultaneous reduction of quantum noise would then require the efficient generation of squeezed vacuum states in the LG3,3 mode. Current squeezed light generation techniques employ continuous-wave second harmonic generation (SHG). Here, we simulate the SHG for both modes numerically to derive first insights into the transferability of standard squeezed light generation techniques to the LG3,3 mode. In the first part of this paper, we therefore theoretically discuss SHG in the case of a single undepleted pump mode, which, in general, excites a superposition of harmonic modes. Based on the differential equation for the harmonic field, we derive individual phase matching conditions and hence conversion efficiencies for the excited harmonic modes. In the second part, we analyse the numerical simulations of the LG0,0 and LG3,3 SHG in a single-pass, double-pass and cavity-enhanced configuration under the influence of the focusing, the different pump intensity distributions and the individual phase matching conditions. Our results predict that the LG3,3 mode requires about 14 times the pump power of the LG0,0 mode to achieve the same SHG conversion efficiency in an ideal, realistic cavity design and mainly generates the harmonic LG6,6 mode.

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