Monolithic nonplanar ring oscillators (NPROs) under an applied magnetic field can operate unidirectional single-frequency lasing due to the loss differences among its four eigenpolarizations, where the minimum was empirically estimated to be 0.01%. However, this value has never been verified because the applied magnetic field is not uniformly distributed, making it hard to resolve both theoretically and experimentally. Here, we propose a method to resolve the applied magnetic field through an NPRO by combining finite-element analysis and experimental verification. By introducing the non-uniform magnetic field information to the eigenpolarization theory, the loss differences can be calculated by path integration along the optical path in the NPRO. The critical point, where the bidirectional lasing is emerging, is identified by the relative amplitude noise (RAN) of the laser and by the beating signal between the clockwise (CW) and counterclockwise (CCW) lasing. With this method, we determine that unidirectional operation is possible with loss differences as low as 0.0001% and 0.0003%, corresponding to two different NPRO designs with out-of-plane angles of 90° and 45°, respectively, which increases the precision of the loss differences for unidirectional single-frequency lasing by more than one order of magnitude. Our findings will greatly facilitate NPRO laser design with lowered magnetic field intensity requirements.

Monolithic nonplanar ring oscillators (NPROs) have achieved great success in industry, scientific applications and space missions due to their excellent narrow-linewidth, low-noise, high beam-quality, lightweight and compact performances. Here, we show that stable dual-frequency or multi-frequency fundamental-mode (DFFM or MFFM) can be stimulated directly by tunning pump beam area and divergence angle injected to NPRO. The DFFM has a frequency deviation of one free spectral range of the resonator and thus can be utilized for pure microwave generation by common-mode-rejection. To demonstrate the purity of the microwave signal, a theoretical phase noise model is established, and the phase noise and the frequency tunability of the microwave signal are experimentally studied. Single sideband phase noise for a 5.7 GHz carrier is measured as low as -112 dBc/Hz at 10 kHz offset, and -150 dBc/Hz at 10 MHz offset in the free running condition of the laser, which outperforms its counterparts from dual-frequency Laguerre-Gaussian (LG) modes. The frequency of the microwave signal can be efficiently tunned through two channels, with frequency tunning coefficients of 15 Hz/V by piezo, and -60.5 kHz/K by temperature, respectively. We expect that such compact, tunable, low-cost and low-noise microwave sources can facilitate multiple applications including miniaturized atomic clocks, communication and radar, etc.

Monolithic nonplanar ring oscillators (NPROs) have achieved great success in industry, scientific applications and space missions due to their excellent narrow-linewidth, low-noise, high beam-quality, lightweight and compact performances. Here, we show that stable dual-frequency or multi-frequency fundamental-mode (DFFM or MFFM) can be stimulated directly by tunning pump beam area and divergence angle injected to NPRO. The DFFM has a frequency deviation of one free spectral range of the resonator and thus can be utilized for pure microwave generation by common-mode-rejection. To demonstrate the purity of the microwave signal, a theoretical phase noise model is established, and the phase noise and the frequency tunability of the microwave signal are experimentally studied. Single sideband phase noise for a 5.7 GHz carrier is measured as low as -112 dBc/Hz at 10 kHz offset, and -150 dBc/Hz at 10 MHz offset in the free running condition of the laser, which outperforms its counterparts from dual-frequency Laguerre-Gaussian (LG) modes. The frequency of the microwave signal can be efficiently tunned through two channels, with frequency tunning coefficients of 15 Hz/V by piezo, and -60.5 kHz/K by temperature, respectively. We expect that such compact, tunable, low-cost and low-noise microwave sources can facilitate multiple applications including miniaturized atomic clocks, communication and radar, etc.

Monolithic nonplanar ring oscillators (NPROs) have achieved great success in industry, scientific applications and space missions due to their excellent narrow-linewidth, low-noise, high beam-quality, lightweight and compact performances. Here, we show that stable dual-frequency or multi-frequency fundamental-mode (DFFM or MFFM) laser can be stimulated directly by tunning pump divergence-angle and beam-waist injected to NPRO. The DFFM laser has a frequency deviation of one free spectral range of the resonator and thus can be utilized for pure microwave generation by common-mode-rejection. To demonstrate the purity of the microwave signal, a theoretical phase noise model is established, and the phase noise and the frequency tunability of the microwave signal are experimentally studied. Single sideband phase noise for a 5.7 GHz carrier is measured as low as -112 dBc/Hz at 10 kHz offset, and -150 dBc/Hz at 10 MHz offset in the free running condition of the laser, which outperforms its counterparts from dual-frequency Laguerre-Gaussian (LG) modes. The frequency of the microwave signal can be efficiently tunned through two channels, with frequency tunning coefficients of 15 Hz/V by piezo, and -60.5 kHz/K by temperature, respectively. We expect that such compact, tunable, low-cost and low-noise microwave sources can facilitate multiple applications including miniaturized atomic clocks, communication and radar, etc.