The LIGO-II gravitational-wave interferometers (ca. 2006–2008) are designed to have sensitivities near the standard quantum limit (SQL) in the vicinity of 100 Hz. This paper describes and analyzes possible designs for subsequent LIGO-III interferometers that can beat the SQL. These designs are identical to a conventional broad band interferometer (without signal recycling), except for new input and/or output optics. Three designs are analyzed: (i) a squeezed-input interferometer (conceived by Unruh based on earlier work of Caves) in which squeezed vacuum with frequency-dependent (FD) squeeze angle is injected into the interferometer’s dark port; (ii) a variational-output interferometer (conceived in a different form by Vyatchanin, Matsko and Zubova), in which homodyne detection with FD homodyne phase is performed on the output light; and (iii) a squeezed-variational interferometer with squeezed input and FD-homodyne output. It is shown that the FD squeezed-input light can be produced by sending ordinary squeezed light through two successive Fabry-Pérot filter cavities before injection into the interferometer, and FD-homodyne detection can be achieved by sending the output light through two filter cavities before ordinary homodyne detection. With anticipated technology (power squeeze factor $e^{-2R}=0.1\mathrm{}$ for input squeezed vacuum and net fractional loss of signal power in arm cavities and output optical train ${\epsilon }_{*}=0.01)$ and using an input laser power $I_o$ in units of that required to reach the SQL (the planned LIGO-II power, $I_{\mathrm{SQL}}),$ the three types of interferometer could beat the amplitude SQL at 100 Hz by the following amounts $\mu \equiv \sqrt{S_h}/\sqrt{S_h^{\mathrm{SQL}}}$ and with the following corresponding increase $\mathcal{V}=1/{\mu }^3$ in the volume of the universe that can be searched for a given noncosmological source: $\mathrm{Squeezed}\mathrm{input}—\mu \simeq \sqrt{e^{-2R}}\simeq 0.3$ and $\mathcal{V}\simeq {1/0.3}^3\simeq 30$ using $I_o{/I}_{\mathrm{SQL}}=1.\mathrm{}$ $Variational-output—\mu \simeq {\epsilon }_{*}^{1/4}\simeq 0.3$ and $\mathcal{V}\simeq 30$ but only if the optics can handle a ten times larger power: $I_o{/I}_{\mathrm{SQL}}\simeq 1/\sqrt{{\epsilon }_{*}}=10.\mathrm{}$ $\mathrm{Squeezed}\mathrm{varational}—\mu {=1.3(e}^{-2R}{\epsilon }_{*}{)}^{1/4}\simeq 0.24$ and $\mathcal{V}\simeq 80$ using $I_o{/I}_{\mathrm{SQL}}=1;$ and $\mu \simeq {(e}^{-2R}{\epsilon }_{*}{)}^{1/4}\simeq 0.18$ and $\mathcal{V}\simeq 180$ using $I_o{/I}_{\mathrm{SQL}}=\sqrt{e^{-2R}/{\epsilon }_{*}}\simeq \mathrm{3.2.}$

We briefly review basic properties of dielectric whispering gallery mode resonators that are important for applications of the resonators in optics and photonics.

Femtosecond laser-based generation of radio frequency signals has produced astonishing improvements in achievable spectral purity, one of the basic features characterizing the performance of an radio frequency oscillator. Kerr frequency combs hold promise for transforming these lab-scale oscillators to chip-scale level. In this work we demonstrate a miniature 10 GHz radio frequency photonic oscillator characterized with phase noise better than −60 dBc Hz⁻¹ at 10 Hz, −90 dBc Hz⁻¹ at 100 Hz and −170 dBc Hz⁻¹ at 10 MHz. The frequency stability of this device, as represented by Allan deviation measurements, is at the level of 10⁻¹⁰ at 1–100 s integration time—orders of magnitude better than existing radio frequency photonic devices of similar size, weight and power consumption.

We review photonic applications of dielectric whispering-gallery mode (WGM) resonators-tracing the growth of the technology from experiments with levitating droplets of aerosols to ultrahigh-Q solid state crystalline and integrated on-chip microresonators.

The thermal stability of monolithic optical microresonators is essential for many mesoscopic photonic applications such as ultrastable laser oscillators, photonic microwave clocks, and precision navigation and sensing. Their fundamental performance is largely bounded by thermal instability. Sensitive thermal monitoring can be achieved by utilizing cross-polarized dual-mode beat frequency metrology, determined by the polarization-dependent thermorefractivity of a single-crystal microresonator, wherein the heterodyne radio-frequency beat pins down the optical mode volume temperature for precision stabilization. Here, we investigate the correlation between the dual-mode beat frequency and the resonator temperature with time and the associated spectral noise of the dual-mode beat frequency in a single-crystal ultrahigh-Q MgF₂ resonator to illustrate that dual-mode frequency metrology can potentially be utilized for resonator temperature stabilization reaching the fundamental thermal noise limit in a realistic system. We show a resonator long-term temperature stability of 8.53 μK after stabilization and unveil various sources that hinder the stability from reaching sub-μK in the current system, an important step towards compact precision navigation, sensing, and frequency reference architectures.

We demonstrate parametric frequency doubling in a whispering gallery cavity made of periodically poled lithium niobate. This demonstration is an example of utility of such crystalline optical whispering gallery resonators with very high $Q$ factors, which we have fabricated.