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Lasers with high spectral purity can enable a diverse application space, including precision spectroscopy, coherent high-speed communications, physical sensing, and manipulation of quantum systems. Already, meticulous design and construction of bench Fabry-Perot cavities has made possible dramatic achievements in active laser-linewidth reduction, predominantly for optical-atomic clocks. Yet there is increasing demand for miniaturized laser systems operating with high performance in ambient environments. Here, we report a compact and robust photonic-atomic laser comprising a 2.5 cm long, 20,000 finesse, monolithic Fabry-Perot cavity integrated with a micromachined rubidium vapor cell. By leveraging the short-time frequency stability of the cavity and the long-time frequency stability of atoms, we realize an ultranarrow-linewidth laser that enables integration for extended measurements. Specifically, our laser supports a fractional-frequency stability of $1times 10^{-13}$ at an averaging time of 20 ms, $7 times 10^{-13}$ at 300 s, an integrated linewidth of 25 Hz that results from thermal noise, a Lorentzian linewidth as low as 0.06 Hz$^2$/Hz, and a passive vibration immunity as low as $10^{-10}$/g. Our work explores hybrid laser systems with monolithic photonic and atomic packages based on physical design.
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Photonic systems and technologies traditionally relegated to table-top experiments are poised to make the leap from the laboratory to real-world applications through integration. Stimulated Brillouin scattering (SBS) lasers, through their unique linewidth narrowing properties, are an ideal candidate to create highly-coherent waveguide integrated sources. In particular, cascaded-order Brillouin lasers show promise for multi-line emission, low-noise microwave generation and other optical comb applications. Photonic integration of these lasers can dramatically improve their stability to environmental and mechanical disturbances, simplify their packaging, and lower cost. While single-order silicon and cascade-order chalcogenide waveguide SBS lasers have been demonstrated, these lasers produce modest emission linewidths of 10-100 kHz. We report the first demonstration of a sub-Hz (~0.7 Hz) fundamental linewidth photonic-integrated Brillouin cascaded-order laser, representing a significant advancement in the state-of-the-art in integrated waveguide SBS lasers. This laser is comprised of a bus-ring resonator fabricated using an ultra-low loss Si3N4 waveguide platform. To achieve a sub-Hz linewidth, we leverage a high-Q, large mode volume, single polarization mode resonator that produces photon generated acoustic waves without phonon guiding. This approach greatly relaxes phase matching conditions between polarization modes, and optical and acoustic modes. Using a theory for cascaded-order Brillouin laser dynamics, we determine the fundamental emission linewidth of the first Stokes order by measuring the beat-note linewidth between and the relative powers of the first and third Stokes orders. Extension to the visible and near-IR wavebands is possible due to the low optical loss from 405 nm to 2350 nm, paving the way to photonic-integrated sub-Hz lasers for visible-light applications.
We present the first demonstration of a narrow linewidth, waveguide-based Brillouin laser which is enabled by large Brillouin gain of a chalcogenide chip. The waveguides are equipped with vertical tapers for low loss coupling. Due to optical feedback for the Stokes wave, the lasing threshold is reduced to 360 mW, which is 5 times lower than the calculated single-pass Brillouin threshold for the same waveguide. The slope efficiency of the laser is found to be 30% and the linewidth of 100 kHz is measured using a self-heterodyne method.
More and more applications require semiconductor lasers distinguished not only by large modulation bandwidths or high output powers, but also by small spectral linewidths. The theoretical understanding of the root causes limiting the linewidth is therefore of great practical relevance. In this paper, we derive a general expression for the calculation of the spectral linewidth step by step in a self-contained manner. We build on the linewidth theory developed in the 1980s and 1990s but look from a modern perspective, in the sense that we choose as our starting points the time-dependent coupled-wave equations for the forward and backward propagating fields and an expansion of the fields in terms of the stationary longitudinal modes of the open cavity. As a result, we obtain rather general expressions for the longitudinal excess factor of spontaneous emission ($K$-factor) and the effective $alpha$-factor including the effects of nonlinear gain (gain compression) and refractive index (Kerr effect), gain dispersion and longitudinal spatial hole burning in multi-section cavity structures. The effect of linewidth narrowing due to feedback from an external cavity often described by the so-called chirp reduction factor is also automatically included. We propose a new analytical formula for the dependence of the spontaneous emission on the carrier density avoiding the use of the population inversion factor. The presented theoretical framework is applied to a numerical study of a two-section distributed Bragg reflector laser.
Ultralow noise, yet tunable lasers are a revolutionary tool in precision spectroscopy, displacement measurements at the standard quantum limit, and the development of advanced optical atomic clocks. Further applications include LIDAR, coherent communications, frequency synthesis, and precision sensors of strain, motion, and temperature. While all applications benefit from lower frequency noise, many also require a laser that is robust and compact. Here, we introduce a dual-microcavity laser that leverages one chip-integrable silica microresonator to generate tunable 1550 nm laser light via stimulated Brillouin scattering (SBS) and a second microresonator for frequency stabilization of the SBS light. This configuration reduces the fractional frequency noise to $7.8times10^{-14} 1/sqrt{Hz}$ at 10 Hz offset, which is a new regime of noise performance for a microresonator-based laser. Our system also features terahertz tunability and the potential for chip-level integration. We demonstrate the utility of our dual-microcavity laser by performing optical spectroscopy with hertz-level resolution.
We demonstrate a hybrid integrated and widely tunable diode laser with an intrinsic linewidth as narrow as 40 Hz, achieved with a single roundtrip through a low-loss feedback circuit that extends the cavity length to 0.5 meter on a chip. Employing solely dielectrics for single-roundtrip, single-mode resolved feedback filtering enables linewidth narrowing with increasing laser power, without limitations through nonlinear loss. We achieve single-frequency oscillation with up to 23 mW fiber coupled output power, 70-nm wide spectral coverage in the 1.55 $mu$m wavelength range with 3 mW output, and obtain more than 60 dB side mode suppression. Such properties and options for further linewidth narrowing render the approach of high interest for direct integration in photonic circuits serving microwave photonics, coherent communications, sensing and metrology with highest resolution.
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