Search with multi-worker firms

We present a generalization of the standard random-search model of unemployment in which firms hire multiple workers and in which the hiring process is time-consuming as well as costly. We follow Stole and Zwiebel (1996a, 1996b) and assume that wages are determined by continuous bargaining between the firm and its employees. The model generates a nontrivial dispersion of firm sizes; when firms' production technologies exhibit decreasing returns to labor, it also generates wage dispersion, even when all firms and all workers are ex ante identical. We characterize the steady-state equilibrium and show that, with a suitably chosen distribution of ex ante heterogeneity across firms, it is consistent with several important stylized facts about the joint distribution of firm size, firm growth, and wages in the U.S. economy. We also conduct a numerical investigation of the out-of-steady-state dynamics of our model. We find that the responses of unemployment and of the vacancy-to-unemployment ratio to a shock to labor productivity can be somewhat more persistent than in the Mortensen–Pissarides benchmark where each firm employs a single worker

Are we Dialogical or Sociomaterial in Our Written Corrective Feedback? A Reflection by Two Academic Writing Instructors

Despite the growing movement to embrace sociomaterial approaches to feedback practices (e.g. Gravett, 2020), dialogicity remains the prominent and dominant approach, especially in the teaching of introductory or compulsory writing courses at the tertiary level. To examine this in our own practice, we reflected on and compared our written corrective feedback (WCF) provided to our students. Based on our WCF practices, we contend that feedback practices may range from dialogic to sociomaterial. The former aims to ensure students’ learning of expected academic skills or objectives of a module, while the latter promotes students’ pursuit of content knowledge. These observations are noteworthy for other higher education instructors, whether subject experts or academic literacy instructors. In particular, we recommend that instructors need to carefully identify temporal and spatial contexts where either or both dialogic and sociomaterial feedback practices can be utilized to enhance students’ learning experiences

Stably accessing octave-spanning microresonator frequency combs in the soliton regime

Microresonator frequency combs can be an enabling technology for optical frequency synthesis and timekeeping in low size, weight, and power architectures. Such systems require comb operation in low-noise, phase-coherent states such as solitons, with broad spectral bandwidths (e.g., octave-spanning) for self-referencing to detect the carrier-envelope offset frequency. However, stably accessing such states is complicated by thermo-optic dispersion. For example, in the Si3N4 platform, precisely dispersion-engineered structures can support broadband operation, but microsecond thermal time constants have necessitated fast pump power or frequency control to stabilize the solitons. In contrast, here we consider how broadband soliton states can be accessed with simple pump laser frequency tuning, at a rate much slower than the thermal dynamics. We demonstrate octave-spanning soliton frequency combs in Si3N4 microresonators, including the generation of a multi-soliton state with a pump power near 40 mW and a single-soliton state with a pump power near 120 mW. We also develop a simplified two-step analysis to explain how these states are accessed in a thermally stable way without fast control of the pump laser, and outline the required thermal properties for such operation. Our model agrees with experimental results as well as numerical simulations based on a Lugiato-Lefever equation that incorporates thermo-optic dispersion. Moreover, it also explains an experimental observation that a member of an adjacent mode family on the red-detuned side of the pump mode can mitigate the thermal requirements for accessing soliton states

A Kerr-microresonator optical clockwork

Kerr microresonators generate interesting and useful fundamental states of electromagnetic radiation through nonlinear interactions of continuous-wave (CW) laser light. Using photonic-integration techniques, functional devices with low noise, small size, low-power consumption, scalable fabrication, and heterogeneous combinations of photonics and electronics can be realized. Kerr solitons, which stably circulate in a Kerr microresonator, have emerged as a source of coherent, ultrafast pulse trains and ultra-broadband optical-frequency combs. Using the f-2f technique, Kerr combs support carrier-envelope-offset phase stabilization for optical synthesis and metrology. In this paper, we introduce a Kerr-microresonator optical clockwork based on optical-frequency division (OFD), which is a powerful technique to transfer the fractional-frequency stability of an optical clock to a lower frequency electronic clock signal. The clockwork presented here is based on a silicon-nitride (Si$_3$N$_4$) microresonator that supports an optical-frequency comb composed of soliton pulses at 1 THz repetition rate. By electro-optic phase modulation of the entire Si$_3$N$_4$ comb, we arbitrarily generate additional CW modes between the Si$_3$N$_4$ comb modes; operationally, this reduces the pulse train repetition frequency and can be used to implement OFD to the microwave domain. Our experiments characterize the residual frequency noise of this Kerr-microresonator clockwork to one part in $10^{17}$, which opens the possibility of using Kerr combs with high performance optical clocks. In addition, the photonic integration and 1 THz resolution of the Si$_3$N$_4$ frequency comb makes it appealing for broadband, low-resolution liquid-phase absorption spectroscopy, which we demonstrate with near infrared measurements of water, lipids, and organic solvents