On a class of bimodal oscillations powered by a steady, zero-frequency force-Implications to energy conversion and structural stability.

I propose that there exists in natural and artificial environments a class of resonant oscillations that can be excited directly by a steady, zero-frequency force such as that of wind, water, electric field. A member of this class comprises two normally independent oscillating modes of a system, for example, a building or bridge, which, separately, cannot be driven by a zero-frequency force. Agreeing on terms of collaboration, the two modes engage in a joint oscillation powered by the steady zero-frequency force in which they drive each other, one directly and the other parametrically. I observed a bimodal vibration belonging to this class in a home shower where the two modes are the pendulum excursion and the torsional twisting of a freely suspended showerhead which break into a joint oscillation above a threshold value of the water flow rate. I advance a theoretical model which predicts and explains the main features of the observations. The model constitutes an extension to two modes of a proposal and demonstration in 1883 by Lord Rayleigh and Michael Faraday for the excitation of a single resonant mode by modulating a system parameter at twice the resonance frequency. The proposal is credited with the launching of parametric physics. The Experiments section of this report consists of three linked video clips photographed in the home shower which support the basic theoretical assumptions. The ubiquity of zero-frequency forces, such as that of wind, and their direct conversion to alternating on-resonance system vibrations endows the class with an amplified destructive potential with implications for structural stability.

Consequences of quantum noise control for the relaxation resonance frequency and phase noise in heterogeneous Silicon/III-V lasers.

We have recently introduced a new semiconductor laser design which is based on an extreme, 99%, reduction of the laser mode absorption losses. In previous reports, we showed that this was achieved by a laser mode design which confines the great majority of the modal energy (> 99%) in a low-loss Silicon guiding layer rather than in highly-doped, thus lossy, III-V p[Formula: see text] and n[Formula: see text] layers, which is the case with traditional III-V lasers. The resulting reduced electron-field interaction was shown to lead to a commensurate reduction of the spontaneous emission rate by the excited conduction band electrons into the laser mode and thus to a reduction of the frequency noise spectral density of the laser field often characterized by the Schawlow-Townes linewidth. In this paper, we demonstrate theoretically and present experimental evidence of yet another major beneficial consequence of the new laser design: a near total elimination of the contribution of amplitude-phase coupling (the Henry [Formula: see text] parameter) to the frequency noise at "high" frequencies. This is due to an order of magnitude lowering of the relaxation resonance frequency of the laser. Here, we show that the practical elimination of this coupling enables yet another order of magnitude reduction of the frequency noise at high frequencies, resulting in a quantum-limited frequency noise spectral density of 130 Hz[Formula: see text]/Hz (linewidth of 0.4 kHz) for frequencies beyond the relaxation resonance frequency 680 MHz. This development is of key importance in the development of semiconductor lasers with higher coherence, particularly in the context of integrated photonics with a small laser footprint without requiring any sort of external cavity.

Quantum Wave-Particle Duality in Free-Electron-Bound-Electron Interaction.

We present a comprehensive relativistic quantum-mechanical theory for interaction of a free electron with a bound electron in a model, where the free electron is represented as a finite-size quantum electron wave packet (QEW) and the bound electron is modeled by a quantum two-level system (TLS). The analysis reveals the wave-particle duality nature of the QEW, delineating the point-particle-like and wavelike interaction regimes and manifesting the physical reality of the wave function dimensions when interacting with matter. This QEW size dependence may be used for interrogation and coherent control of superposition states in a TLS and for enhancement of cathodoluminescence and electron energy-loss spectroscopy in electron microscopy.

Kicking the habit/semiconductor lasers without isolators.

In this paper, we propose and demonstrate a solution to the problem of coherence degradation and collapse caused by the back reflection of laser power into the laser resonator. The problem is most onerous in semiconductor lasers (SCLs), which are normally coupled to optical fibers, and results in the fact that practically every commercial SCL has appended to it a Faraday-effect isolator that blocks most of the reflected optical power preventing it from entering the laser resonator. The isolator assembly is many times greater in volume and cost than the SCL itself. This problem has resisted a practical and economic solution despite decades of effort and remains the main obstacle to the emergence of a CMOS-compatible photonic integrated circuit technology. A simple solution to the problem is thus of major economic and technological importance. We propose a strategy aimed at weaning semiconductor lasers from their dependence on external isolators. Lasers with large internal Q-factors can tolerate large reflections, limited only by the achievable Q values, without coherence collapse. A laser design is demonstrated on the heterogeneous Si/III-V platform that can withstand 25 dB higher reflected power compared to commercial DFB lasers. Larger values of internal Qs, achievable by employing resonator material of lower losses and improved optical design, should further increase the isolation margin and thus obviate the need for isolators altogether.

Higher-order QAM data transmission using a high-coherence hybrid Si/III-V semiconductor laser.

We experimentally demonstrate the use of a high-coherence hybrid silicon (Si)/III-V semiconductor laser as the light source for a transmitter generating 20 Gbaud 16- and 64- quadrature amplitude modulated (QAM) data signals over an 80 km single-mode fiber (SMF) link. The hybrid Si/III-V laser has a measured Schawlow-Townes linewidth of ${\sim}{10}\;{\rm kHz}$∼10kHz, which is achieved by storing modal optical energy in low-loss Si, rather than the relatively lossy III-V materials. We measure a received bit error rate (BER) of ${4.1} \times {{10}^{ - 3}}$4.1×10-3 when transmitting the 64-QAM data over an 80 km SMF using the hybrid Si/III-V laser. Furthermore, we measure a BER of $ {\lt} {1} \times {{10}^{ - 4}}$<1×10-4 with the Viterbi-Viterbi digital carrier phase recovery method when transmitting the 16-QAM data over an 80 km SMF using the hybrid Si/III-V laser. This performance is achieved at power penalties lower than those obtained with an exemplary distributed feedback laser and slightly higher than those with an exemplary narrow-linewidth external cavity laser.

Free-Electron-Bound-Electron Resonant Interaction.

Here we present a new paradigm of free-electron-bound-electron resonant interaction. This concept is based on a recent demonstration of the optical frequency modulation of the free-electron quantum electron wave function (QEW) by an ultrafast laser beam. We assert that pulses of such QEWs correlated in their modulation phase, interact resonantly with two-level systems, inducing resonant quantum transitions when the transition energy ΔE=ℏω_{21} matches a harmonic of the modulation frequency ω_{21}=nω_{b}. Employing this scheme for resonant cathodoluminescence and resonant EELS combines the atomic level spatial resolution of electron microscopy with the high spectral resolution of lasers.

Vernier spectrometer using counterpropagating soliton microcombs.

Determination of laser frequency with high resolution under continuous and abrupt tuning conditions is important for sensing, spectroscopy, and communications. We show that a single microresonator provides rapid and broadband measurement of optical frequencies with a relative frequency precision comparable to that of conventional dual-frequency comb systems. Dual-locked counterpropagating solitons having slightly different repetition rates were used to implement a vernier spectrometer, which enabled characterization of laser tuning rates as high as 10 terahertz per second, broadly step-tuned lasers, multiline laser spectra, and molecular absorption lines. Besides providing a considerable technical simplification through the dual-locked solitons and enhanced capability for measurement of arbitrarily tuned sources, our results reveal possibilities for chip-scale spectrometers that exceed the performance of tabletop grating and interferometer-based devices.

Quantum control of phase fluctuations in semiconductor lasers.

Few laser systems allow access to the light-emitter interaction as versatile and direct as that afforded by semiconductor lasers. Such a level of access can be exploited for the control of the coherence and dynamic properties of the laser. Here, we demonstrate, theoretically and experimentally, the reduction of the quantum phase noise of a semiconductor laser through the direct control of the spontaneous emission into the laser mode, exercised via the precise and deterministic manipulation of the optical mode's spatial field distribution. Central to the approach is the recognition of the intimate interplay between spontaneous emission and optical loss. A method of leveraging and "walking" this fine balance to its limit is described. As a result, some two orders of magnitude reduction in quantum noise over the state of the art in semiconductor lasers, corresponding to a minimum linewidth of [Formula: see text], is demonstrated. Further implications, including an additional order-of-magnitude enhancement in effective coherence by way of control of the relaxation oscillation resonance frequency and enhancement of the intrinsic immunity to optical feedback, highlight the potential of the proposed concept for next-generation, integrated coherent systems.

1.6 kW Yb fiber amplifier using chirped seed amplification for stimulated Brillouin scattering suppression.

In a high power fiber amplifier, a frequency-chirped seed interrupts the coherent interaction between the laser and Stokes waves, raising the threshold for stimulated Brillouin scattering (SBS). Moving the external mirror of a vertical cavity surface-emitting diode laser 0.2 µm in 10 µs can yield a frequency chirp of 5×1017 Hz/s at a nearly constant output power. Opto-electronic feedback loops can linearize the chirp, and stabilize the output power. The linear variation of phase with time allows multiple amplifiers to be coherently combined using a frequency shifter to compensate for static and dynamic path length differences. The seed bandwidth, as seen by the counter-propagating SBS, also increases linearly with fiber length, resulting in a nearly-length-independent SBS threshold. Experimental results at the 1.6 kW level with a 19 m delivery fiber are presented. A numerical simulation is also presented.

On-chip integrated differential optical microring refractive index sensing platform based on a laminar flow scheme.

We propose an on-chip integrated differential optical microring refractive index sensing platform which leverages laminar flow conditions. Close spacing between a sensing and a reference resonator, and sharing the same microfluidic channel allows the two resonators to experience similar environmental disturbances, such as temperature fluctuations and fluidic-induced transients, achieving reliable and sensitive sensing performance. We obtain a noise floor of 80.0 MHz (0.3 pm) and a bulk refractive index sensitivity of 17.0 THz per refractive index unit (RIU) (64.2 nm/RIU), achieving a limit of detection of 1.4×10(-5) RIU in a 30 min and an 8°C window.

High-coherence semiconductor lasers based on integral high-Q resonators in hybrid Si/III-V platforms.

The semiconductor laser (SCL) is the principal light source powering the worldwide optical fiber network. The ever-increasing demand for data is causing the network to migrate to phase-coherent modulation formats, which place strict requirements on the temporal coherence of the light source that no longer can be met by current SCLs. This failure can be traced directly to the canonical laser design, in which photons are both generated and stored in the same, optically lossy, III-V material. This leads to an excessive and large amount of noisy spontaneous emission commingling with the laser mode, thereby degrading its coherence. High losses also decrease the amount of stored optical energy in the laser cavity, magnifying the effect of each individual spontaneous emission event on the phase of the laser field. Here, we propose a new design paradigm for the SCL. The keys to this paradigm are the deliberate removal of stored optical energy from the lossy III-V material by concentrating it in a passive, low-loss material and the incorporation of a very high-Q resonator as an integral (i.e., not externally coupled) part of the laser cavity. We demonstrate an SCL with a spectral linewidth of 18 kHz in the telecom band around 1.55 µm, achieved using a single-mode silicon resonator with Q of 10(6).

Phase-locking and coherent power combining of broadband linearly chirped optical waves.

We propose, analyze and demonstrate the optoelectronic phase-locking of optical waves whose frequencies are chirped continuously and rapidly with time. The optical waves are derived from a common optoelectronic swept-frequency laser based on a semiconductor laser in a negative feedback loop, with a precisely linear frequency chirp of 400 GHz in 2 ms. In contrast to monochromatic waves, a differential delay between two linearly chirped optical waves results in a mutual frequency difference, and an acoustooptic frequency shifter is therefore used to phase-lock the two waves. We demonstrate and characterize homodyne and heterodyne optical phase-locked loops with rapidly chirped waves, and show the ability to precisely control the phase of the chirped optical waveform using a digital electronic oscillator. A loop bandwidth of ~ 60 kHz, and a residual phase error variance of < 0.01 rad(2) between the chirped waves is obtained. Further, we demonstrate the simultaneous phase-locking of two optical paths to a common master waveform, and the ability to electronically control the resultant two-element optical phased array. The results of this work enable coherent power combining of high-power fiber amplifiers-where a rapidly chirping seed laser reduces stimulated Brillouin scattering-and electronic beam steering of chirped optical waves.

"Ideal" optical delay lines based on tailored-coupling and reflecting, coupled-resonator optical waveguides.

We present a design of "ideal" optical delay lines (i.e., constant amplitude and constant group delay over the desired bandwidth). They are based on reflection from coupled-resonator optical waveguides (CROWs). The inter-resonator coupling coefficients are tailored and decrease monotonically with the distance from the input to realize all-pass Bessel filters. The tailored coupling coefficients result in a frequency-dependent propagating distance which compensates for the group velocity dispersion of CROWs. We present a simple formalism for deriving the time-domain coupling coefficients and convert these coefficients to field coupling coefficients of ring resonators. The reflecting CROWs possess a delay-bandwidth product of 0.5 per resonator, larger than that of any kind of transmitting CROW. In the presence of uniform gain, the gain enhanced by slow light propagation and the constant group delay result in efficient and dispersion-free amplifiers.

Designing coupled-resonator optical waveguides based on high-Q tapered grating-defect resonators.

We present a systematic design of coupled-resonator optical waveguides (CROWs) based on high-Q tapered grating-defect resonators. The formalism is based on coupled-mode theory where forward and backward waveguide modes are coupled by the grating. Although applied to strong gratings (periodic air holes in single-mode silicon-on-insulator waveguides), coupled-mode theory is shown to be valid, since the spatial Fourier transform of the resonant mode is engineered to minimize the coupling to radiation modes and thus the propagation loss. We demonstrate the numerical characterization of strong gratings, the design of high-Q tapered grating-defect resonators (Q>2 × 106, modal volume = 0.38·(λ/n)³), and the control of inter-resonator coupling for CROWs. Furthermore, we design Butterworth and Bessel filters by tailoring the numbers of holes between adjacent defects. We show with numerical simulation that Butterworth CROWs are more tolerant against fabrication disorder than CROWs with uniform coupling coefficient.

Synthesis of high-order bandpass filters based on coupled-resonator optical waveguides (CROWs).

We present a filter design formalism for the synthesis of coupled-resonator optical waveguide (CROW) filters. This formalism leads to expressions and a methodology for deriving the coupling coefficients of CROWs for the desired filter responses and is based on coupled-mode theory as well as the recursive properties of the coupling matrix. The coupling coefficients are universal and can be applied to various types of resonators. We describe a method for the conversion of the coupling coefficients to the parameters based on ring resonators and grating defect resonators. The designs of Butterworth and Bessel CROW filters are demonstrated as examples.

Multiple source frequency-modulated continuous-wave optical reflectometry: theory and experiment.

We propose and demonstrate a novel approach to increase the effective bandwidth of a frequency-modulated continuous-wave (FMCW) ranging system. This is achieved by algorithmically stitching together the swept spectra of separate laser sources. The result is an improvement in the range resolution proportional to the increase in the swept-frequency range. An analysis of this system as well as the outline of the stitching algorithm are presented. Using three distinct swept-frequency optical waveforms, we experimentally demonstrate a threefold improvement in the range resolution of a three-sweep approach over the conventional FMCW method.

Sideband locking of a single-section semiconductor distributed-feedback laser in an optical phase-lock loop.

The bandwidth and performance of optical phase-lock loops (OPLLs) using single-section semiconductor lasers (SCLs) are severely limited by the nonuniform frequency modulation response of the lasers. It is demonstrated that this restriction is eliminated by the sideband locking of a single-section distributed-feedback SCL to a master laser in a heterodyne OPLL, thus enabling a delay-limited loop bandwidth. The lineshape of the phase-locked SCL output is characterized using a delayed self-heterodyne measurement.

An exact transverse Helmholtz equation.

We derive an exact equation for the transverse component of the electric field propagating along a given longitudinal z direction in the presence of an isotropic refractive-index distribution n(x,y).

Precise control of broadband frequency chirps using optoelectronic feedback.

We demonstrate the generation of wideband frequency sweeps using a semiconductor laser in an optoelectronic feedback loop. The rate and shape of the optical frequency sweep is locked to and determined by the frequency of a reference electronic signal, leading to an agile, high coherence swept-frequency source for laser ranging and 3-D imaging applications. Using a reference signal of constant frequency, a transform-limited linear sweep of 100 GHz in 1 ms is achieved, and real-time ranging with a spatial resolution of 1.5 mm is demonstrated. Further, arbitrary frequency sweeps can be achieved by tuning the frequency of the input electronic signal. Broadband quadratic and exponential optical frequency sweeps are demonstrated using this technique.