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Sensors operating at an exceptional point (EP) are sufficiently sensitive to small perturbations. In this article, we demonstrate that an EP enhances sensing in the frame of a fiber ring cavity. An air gap inserted into a fiber ring cavity couples the clockwise and counterclockwise propagating modes, leading to eigenfrequency splitting. The EP was achieved in a nonreciprocity cavity constructed using an isolator. A fiber displacement sensor was realized by monitoring the splitting strength in the spectrum, which depends on the width of the air gap. The experimental results showed that the sensitivity of the sensor at the EP was sufficiently enhanced as compared to that in the reciprocal cavity.

We determine the equations of the blowup of $\mathbb{P}^n$ along a $d$-fold rational normal scroll $S$, and we prove that the Rees ring and special fiber ring of $S \subseteq \mathbb{P}^n$ are Koszul algebras., To appear on Transactions of the American Mathematical Society

We investigate output power characteristics of a tunable thulium-doped fiber ring laser (TDFRL) by theoretical simulation. The effects of emission wavelength, active fiber length, output coupling ratio and total intracavity loss on laser output power are investigated.

In this paper, we compute the degree of the Kodiyalam polynomials of an ideal in the case where its Rees ring is Cohen—Macaulay and its fiber ring is a domain. We apply this result to some classes of polymatroidal ideals.

A tunable dual-wavelength fiber ring-cavity laser based on semiconductor optical amplifier (SOA) using two external-injected distributed feedback (DFB) lasers is proposed and experimentally demonstrated. When one of the injected DFB lasers operates at 25 °C and the other at 0 °C, a stable dual-wavelength simultaneous oscillation at 1553.68 nm and 1553.90 nm with a wavelength spacing of 0.22 nm is achieved. The wavelength spacing can be tuned by adjusting the operating temperatures of the two injected DFB lasers, and a tuning range from 0.22 nm to 2.95 nm is obtained. Our experimental results demonstrate the new concept of dual-wavelength fiber ring-cavity laser using two DFB lasers injection and the technical feasibility.

We prove results concerning the multiplicity as well as the Cohen–Macaulay and Gorenstein properties of the special fiber ring $\mathscr{F}(E)$ of a finitely generated $R$-module $E\subsetneq R^{e}$ over a Noetherian local ring $R$ with infinite residue field. Assuming that $R$ is Cohen–Macaulay of dimension 1 and that $E$ has finite colength in $R^{e}$, our main result establishes an asymptotic length formula for the multiplicity of $\mathscr{F}(E)$, which, in addition to being of independent interest, allows us to derive a Cohen–Macaulayness criterion and to detect a curious relation to the Buchsbaum–Rim multiplicity of $E$ in this setting. Further, we provide a Gorensteinness characterization for $\mathscr{F}(E)$ in the more general situation where $R$ is Cohen–Macaulay of arbitrary dimension and $E$ is not necessarily of finite colength, and we notice a constraint in terms of the second analytic deviation of the module $E$ if its reduction number is at least three.

The frequency stability of lasers is limited by thermal noise in state-of-the-art frequency references. Further improvement requires operation at cryogenic temperature. In this context, we investigate a fiber-based ring resonator. Our system exhibits a first-order temperature-insensitive point around 3.55 K , much lower than that of crystalline silicon. The observed low sensitivity with respect to vibrations ( < 5 ⋅ 10 − 11 m − 1 s 2 ), temperature ( − 22 ( 1 ) ⋅ 10 − 9 K − 2 ), and pressure changes ( 4.2 ( 2 ) ⋅ 10 − 11 m b a r − 2 ) makes our approach promising for future precision experiments.

We experimentally study the time-dynamics of passive self-mode locking phenomena in a Thulium-doped fiber ring laser operating at ∼ 1976 nm wavelength pumped with 1550 nm.

We report numerical and experimental observations of spontaneous symmetry breaking of Kerr cavity solitons. We show that cavity solitons with mirror polarization states can co-exist and be individually addressed in a symmetric fiber ring resonator.

We experimentally study the phase matching condition of dispersive waves in a pulse-pumped normal dispersion ring resonator. The frequency shift of the dispersive waves strongly depends on the pump synchronization yielding tunable broadband combs.

A novel slow-light reflector composed of a double-ring resonator with a uniform fiber Bragg grating (FBG) incorporated is proposed in this paper, which can be used as a mirror of narrow-linewidth fiber laser, based on its enlarged group delay, and as a high-sensitivity sensor. Its characteristics are investigated theoretically and experimentally in this paper. Compared with the single fiber ring the amplitude of resonance is modulated, the effective mode spacing is expanded greatly, due to the Vernier effect, giving much better mode selectivity. Mode hopping is believed to be suppressed effectively in applications of narrow-linewidth lasers, and resolution will be enhanced in sensor applications.

We explore connections between the generalized multiplicities of square-free monomial ideals and the combinatorial structure of the underlying hypergraphs using methods of commutative algebra and polyhedral geometry. For instance, we show the $j$-multiplicity is multiplicative over the connected components of a hypergraph, and we explicitly relate the $j$-multiplicity of the edge ideal of a properly connected uniform hypergraph to the Hilbert-Samuel multiplicity of its special fiber ring. In addition, we provide general bounds for the generalized multiplicities of the edge ideals and compute these invariants for classes of uniform hypergraphs., 24 pages, 6 figures. The results of Theorem 4.6 and Theorem 9.2 are now more general. To appear in Journal of Algebraic Combinatorics

We study the relationship between the reduction number of a primary ideal of a local ring relative to one of its minimal reductions and the multiplicity of the corresponding Sally module. This paper is focused on three goals: (i) to develop a change of rings technique for the Sally module of an ideal to allow extension of results from Cohen–Macaulay rings to more general rings; (ii) to use the fiber of the Sally modules of almost complete intersection ideals to connect its structure to the Cohen–Macaulayness of the special fiber ring; (iii) to extend some of the results of (i) to two-dimensional Buchsbaum rings. Along the way, we provide an explicit realization of the $S_{2}$-fication of arbitrary Buchsbaum rings.

Let $R$ be a polynomial ring over a field and $I \subset R$ be a Gorenstein ideal of height three that is minimally generated by homogeneous polynomials of the same degree. We compute the multiplicity of the saturated special fiber ring of $I$. The obtained formula depends only on the number of variables of $R$, the minimal number of generators of $I$, and the degree of the syzygies of $I$. Applying results from arXiv:1805.05180, we get a formula for the $j$-multiplicity of $I$ and an effective method to study a rational map determined by a minimal set of generators of $I$., to appear in Acta Mathematica Vietnamica

We present a single-frequency thulium-doped fiber laser (TDFL) with a narrow linewidth of 20 kHz. Stable single-longitudinal-mode (SLM) lasing operation at 1957 nm is achieved using a segment of un-pumped polarization-maintaining thulium-doped fiber (PM-TDF) as an ultra-narrow bandwidth filter. A high optical signal-to-noise ratio (OSNR) of over 60 dB is obtained and a high power of over 400 mW is achieved with a high slope-efficiency (~45.8%) thulium-doped fiber amplifier (TDFA).

We proposed and experimentally demonstrated a novel sensing scheme by using high order stimulated Brillouin scattering effect in a recirculating fiber ring to improve the sensitivity Temperature sensing using this scheme has been implemented in the experiment for demonstration. By measuring the frequency shift of the beat signal, temperature variation can be monitored. The sensitivity of monitoring the second-order beat signal is estimated to ~2.2 MHz/° in the experiment, which is twice of that of first order, and by using higher-order beat signal, higher sensitivity can be achieved.

We demonstrate a femtosecond fiber laser incorporating a ReSe2/PVA-based saturable absorber (SA). Using a ReSe2/PVA-based SA, stable ~862-fs pulses are shown to be readily obtained from an erbium-doped fiber ring cavity at 1561.2 nm.

We present algorithms for the computation of the Castelnuovo-Mumford regularity of the Rees algebra and of the fiber ring of equigenerated m -primary ideals in two variables. Applying these algorithms, we find a counter-example to a conjecture of Eisenbud and Ulrich which states that these regularities are equal.

We investigated the behavior of a fiber-ring polarization-maintaining passively modelocked ytterbium-doped laser in a broad range of dispersion values; i.e., from highly net-normal to net-anomalous, with a special emphasis near the zero of chromatic dispersion. Different lengths of an ad hoc polarization-maintaining photonic crystal fiber were used as intracavity dispersion compensator to shift the operation of this laser from net-normal to the net-anomalous regime. The laser generated the shortest light pulses around the zero of dispersion: 6 ps / 7ps for −0.023 ps2 / 0.045 ps2 ; in both cases, pulses were not transform-limited, being theoretically possible an out-of-cavity recompression down to 170 fs / 220 fs, respectively. In the net-normal regime, we obtained a stable, ultra-low frequency, emission at 1.19 MHz, with pulses with a FWHM of 162 ps and pulse energy of 115 pJ. This laser presents a somewhat symmetrical behavior at both sides of the zero of dispersion thanks to its simple filter-free configuration. The laser is also environmentally robust, insensitive against temperature variations and mechanical vibrations, due to its integrated all-polarization-maintaining design.

A tunable dual-wavelength fiber ring-cavity laser based on a fiber Bragg grating (FBG) and an external-injected distributed feedback (DFB) laser is proposed and experimentally demonstrated. The wavelength spacing can be tuned by adjusting the operating temperature of the DFB laser. When the FBG works at 40℃ and the injected DFB laser operates at 10℃, a stable dual-wavelength simultaneous oscillation at 1550.32 nm and 1552.40 nm with a wavelength spacing of 2.08 nm is achieved, and a tuning range from 2.08 nm to 5.34 nm is obtained. Our experimental results demonstrate the new concept of dual-wavelength fiber ring-cavity laser with a DFB laser injection and the technical feasibility.

Temporal cavity solitons (CS) are optical pulses that can persist in passive resonators, and they play a key role in the generation of coherent microresonator frequency combs. In resonators made of amorphous materials, such as fused silica, they can exhibit a spectral red-shift due to stimulated Raman scattering. Here we show that this Raman-induced self-frequency-shift imposes a fundamental limit on the duration and bandwidth of temporal CSs. Specifically, we theoretically predict that stimulated Raman scattering introduces a previously unidentified Hopf bifurcation that leads to destabilization of CSs at large pump-cavity detunings, limiting the range of detunings over which they can exist. We have confirmed our theoretical predictions by performing extensive experiments in several different synchronously-driven fiber ring resonators, obtaining results in excellent agreement with numerical simulations. Our results could have significant implications for the future design of Kerr frequency comb systems based on amorphous microresonators., Comment: 9 pages, 7 figures

A compact and robust mode-locked fiber laser with a locked repetition rate is demonstrated in a polarization-maintain fiber ring cavity. The repetition rate is locked at 108 MHz and the standard deviation of the controlled signal is 0.997 mHz in a 10-hours test.

We numerically and experimentally investigate the asymmetrically phase-detuned dual pumping of a passive inhomogeneous fiber ring cavity. This configuration originates from the fine control of frequency mismatch between the frequency spacing of the bichromatic pump and the free spectral range of the cavity. Multicomb states at offset frequencies can be selectively generated by means of the mismatch parameter and the coexistence of Turing and Faraday instabilities.

We provide a clear demonstration of a period-doubling phenomenon associated to the modulation instability in dispersion oscillating fiber cavities. This has been done by performing roundtrip-to-roundtrip measurements of the temporal pattern generated through the instability.

We present the first demonstration of carbon nanoparticles (CNP) as an optical modulator to generate short laser pulses. An ytterbium-doped fiber ring cavity is successfully Q-switched with CNPs prepared in-house via a simple flame synthesis.