Sine-Cosine Techniques for Detecting Fast Optical Frequency Variations With Ultra-High Resolution

Abstract

We introduce the concept of sine-cosine optical frequency detection (OFD) for measuring fast optical frequency variations with the ultra-high spectral resolution for applications requiring rapidly tunable or low frequency-jitter lasers, including coherent detection based distributed sensing and communication systems and tunable diode laser spectroscopy (TDLS) systems, for which conventional spectral measurement techniques cannot meet the speed and spectral resolution requirements. The concept relies on representing the frequency-dependent differential phase of the laser light passing through two different optical paths as sine and cosine functions to calculate the optical frequency, similar to the sine-cosine encoder concept commonly used for obtaining the rotation information of a motor, which can simultaneously achieve both high spectral resolution and wide frequency range without mutual constraints. We present multiple schemes, some are seemingly very different, for implementing the concept and demonstrate that all frequency-related parameters of a tunable light source, including frequency tuning rate, nonlinearity, ripple, range, duty cycle, repeatability, and power swing can be precisely characterized. In addition, the frequency jitter of a fixed narrow line-width laser can also be accurately measured. Ultra-fast optical frequency sweep with a rate in excess of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> nm/s and a resolution down to MHz is demonstrated with a differential delay of only 0.8 mm, suggesting that the concept is feasible to be implemented with photonic integrated circuit (PIC). Our work is attractive for applications such as coherent distributed sensing (OCT, OFDR and FMCW lidar), coherent detection, FBG sensing interrogation and TDLS, especially considering that some schemes can be integrated on PIC chips.