We present a novel technique to frequency lock a laser to an optical cavity. This technique, tilt locking, utilizes a misalignment of the laser with respect to the cavity to produce a non-resonant spatial mode. By observing the interference between the carrier and the spatial mode, a quantum noise limited frequency discriminator can be obtained. Tilt locking offers a number of potential benefits over existing locking schemes including low cost, high sensitivity and simple implementation. The frequency locking of lasers to optical cavities is used for a wide range of scientific applications including frequency stabilization, CW frequency conversion, optical frequency standards and interferometric gravitational wave detection. This process typically requires the generation of an error signal proportional to the difference between the laser frequency and the cavity resonance. Several methods for obtaining an error signal have been used including fringe side locking, HanschCouillaud locking, transmission locking and mode interference locking. Currently the most widely used method is the Pound-Drever-Hall (PDH) technique. The PDH technique utilizes the beat between the carrier field and non-resonant phase modulation sidebands. The sidebands provide a reference for the phase of the carrier field reflected from the cavity. By making a measurement of the phase of the reflected field, a high sensitivity, quantum noise limited measurement of the cavity is possible. The technique presented here, tilt locking, also utilizes interference between the carrier field, and a directly reflected phase reference. In this case the phase reference is a non-resonant higher order spatial mode. This system has the same frequency response and similar sensitivity as the PDH system. Instead of electro-optic encoding and electronic decoding of frequency sidebands, tilt locking uses optical encoding and decoding of spatial modes. A cavity decomposes a misaligned input field into a set of spatial transverse electromagnetic (TEM) modes, which can be approximated by the Hermite-Gauss functions. Higher order Hermite-Gauss modes experience different Gouy phase shifts and thus have different resonant frequencies. Tilt locking uses the first higher order mode, the TEM01 mode, as the phase reference for the TEM00 carrier. The transverse electric field distribution for the TEM00 mode and a TEM01 mode is shown in Fig. 1(a). The error signal is proportional to the magnitude of the interference between these two spatial modes, and is given by the overlap integral. For Hermite-Gauss modes where the entire beam is detected no interference can be measured, with the overlap integral given by, I0,1 = ∣∣∣∣∫ ∞ −∞ ∫ ∞ −∞ ũ00(x, y)ũ01(x, y)dxdy ∣∣∣∣ = 0 (1) where ũ00(x, y) and ũ01(x, y) are the electric field distributions for the normalized TEM00 and TEM01 modes respectively. The integral is zero due to the orthogonality of the Hermite-Gauss modes and no error signal is obtained.
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