Work has begun to develop a radiation-pressure-dominated tabletop optical facility in our lab. The experimental goal for the first stage of the project is to build a cavity containing a suspended mirror, produce an optical spring, and control it. This is the foundational step necessary for the group.
Current progress has focused on procurement and characterisation of the AlGaAs mirror chip shown in figure6.4, which has been kindly donated to our group by T. Corbitt, J. Cripe et. al. from LSU. The micro-oscillators on this chip have resonant frequencies far lower than we would like for an experiment to demonstrate bandwidth broadening, however we are using this one first
to become familiar with handling the chip and to achieve our primary experimental goals, which do not have the same strict frequency requirements as described in section6.3.
We first need to understand the behaviour of the micro-oscillators on the chip when they are not driven by radiation pressure. In particular, we wish to measure each mirror’s mechanical Q-factor and resonant frequency. This is achieved by using a simple Michelson to measure the in-axis displacement of the mirror after a short excitation was applied. We have developed the setup in-air to perform initial tests.
laser PD 50:50 NPBS 20mm f=20mm 50:50 NPBS Faraday Isolator 4 2 f=±200mm CCD L=30mm L=30mm Micro-oscillator chip PZT1 PZT2 Test Mirror Reference Mirror
Figure 6.12: Schematic diagram of the optical layout used to characterise mirrors on the AlGaAs chip.
The core optical layout is shown schematically in figure6.12and photographed in figure 6.13. A quarter-wave-plate (λ/4) linearises the polarisation of the input beam from the 500 mW 1064 nm laser. A half-wave-plate (λ/2) is used in conjunction with a faraday isolator to prevent back- reflection into the laser. We also use this to attenuate the input beam power, together with several low-reflectivity turning mirrors in the input path (not depicted), producing a final input power of ∼ 10 mW. This is sufficiently low that the radiation pressure force on the test mirror will be negligible. A pair of ±200 mm lenses are used to collimate the beam, resulting in a spot size of approximately 1 mm.
The Michelson interferometer is formed from a 50:50 non-polarising beamsplitter (NPBS), a refer- ence arm with a high-reflectivity reference mirror, and the test arm containing the micro-oscillator chip. The arms of the Michelson interferometer are identical in length and short, so that it is easy to align and the resulting interference pattern has a fundamental Gaussian intensity distribution. The smallest micro-mirror on the chip has a diameter of 50 µm, therefore to be able to characterise
Test Mirror Reference Mirror BS PD CCD f=20mm
Figure 6.13: Core Optics of the in-air Michelson setup. The mirror shown in the test arm was replaced with the mirror chip, mounted on a 3-axis manual translation stage, once the setup had been pre-aligned. The optical path is marked in red.
all mirrors, the spot size on the mirror should be significantly smaller than this; ideally w ∼ 10 µm. We achieve this by including a 20 mm lens in the arm of the test mirror and aligning the chip so that it sits exactly at the focal point. This results in a ‘2f system’ in the test arm that means the beam spot size returning to the beamsplitter is unaffected by the lens. It also results in the Michelson becoming immune to angular misalignment of the test mirror; this feature is used to ensure that the mirror is at the focal point.
A second NPBS is used to split the output of the Michelson so that it can be measured using both a photodiode (PD) and CCD camera. The photodiode is used for our final measurements; the CCD is useful for determining if the chip is correctly aligned in the direction transverse to the beam axis, since if the beam is clipped by hitting the edge of one of the mirrors, its shape will be distorted.
The chip is mounted on a 3-axis manual translation mount, formed from three linear stages, so that different micro-oscillators can be selected and the distance between the chip and focusing lens fine-tuned. Both the reference mirror and chip are also mounted to linear piezoelectric crystals (PZTs). PZT2, mounted to the chip, is used to excite the micro-mirrors by driving the chip near their expected resonant frequencies. PZT1 is used to tune the Michelson so that it sits at the middle of a fringe. The motion of the test mirror in the beam axis is smaller than the laser wavelength, therefore the voltage measured on the photodiode is directly proportional to the displacement of the mirror. Finally a ‘ring-down’ measurement is made by cutting the input excitation at PZT2 and recording the amplitude of the mirror displacement as it returns to its un-excited state.
Figure 6.14: In-air ‘ringdown measurement’ of micro-mirror ‘A’ (see figure6.4). The raw data is fit to a decaying sinusoid with tight constraints, based on well known values for the mirror resonant frequency f0, initial amplitude a and offset c, resulting in a Q-factor of 50 ± 12.5.
Figure 6.14shows the result for one of the largest mirrors on our chip, marked ‘A’ in figure6.4, which has a diameter of 400 µm. The resonant frequency is known to be approximately 320 Hz, and the initial amplitude and offset can be well identified, therefore a decaying sinusoid was fit to the data using tight constraints, resulting in a mechanical Q-factor measurement of Qm= 50.0 ± 12.5.
This is very low compared to the order-104− 105values expected of AlGaAs micro-oscillators, but
not unexpected. It is highly likely that this is caused by significant air damping. As planned, we are currently migrating the setup to our vacuum tank so that these measurements can be repeated, and extended to all micro-oscillators of interest for our experiment.