**May 2024 Issue,**

**Volume 92, No. 5**

An in-fiber Mach–Zehnder strain sensor for studying multimode interference of light

Multimode interference of light is an optical interference phenomenon based on waveguides, which has broad applications in optical communication, lasers, and optical fiber sensing. Since optical fiber has become the most widely used optical waveguide in modern society, multimode interference in optical fibers is an ideal candidate for projects in university teaching laboratories. Here, we implement an in-fiber Mach–Zehnder strain sensor-based experiment to study multimode interference in optical fibers. The sensor is fabricated by fusion splicing a piece of thin core fiber between two single mode fibers. One end of the thin core fiber is spliced without a core offset, while the other end is spliced with a core offset. Due to the mode field diameter mismatch and core offset, cladding modes are excited and interfere with the core mode in thin core fiber. Students can observe the sensor fabrication demonstration and perform a strain test with an optical spectrum analyzer. The wavelength spectra captured by the optical spectrum analyzer under different strains are analyzed with the signal processing tools of fast Fourier transform and fast Fourier transform filter. Students then find characteristics of the multimode interference in the sensor from the analysis. The experiment extends undergraduates' knowledge of light interference and is an instructive exercise for them in modern coherence theory.

#### EDITORIAL

In this issue: May 2024 by John Essick; Jesse Kinder; Claire A. Marrache-Kikuchi; Raina Olsen; Beth Parks; Cameron Reed; Donald Salisbury; Todd Springer. DOI: 10.1119/5.0210880

#### LETTERS TO THE EDITOR

J. Robert Oppenheimer, Physicist by Robert N. Cahn; Chris Quigg. DOI: 10.1119/5.0209857

Virtual learning via spreadsheets: Real-time simulation of an RC circuit by Fayzan Ahmed; Majid Iqbal; Iqbal Tariq; Muhammad Talat. DOI: 10.1119/5.0199004

#### PAPERS

Whose work matters? A tool for identifying and developing more inclusive physics textbooks by Tai Xiang; William Gray; Janice Hudgings. DOI: 10.1119/5.0148649

Motivated by a desire for textbooks to describe the work of scientists from more diverse backgrounds, the authors of this paper developed a simple tool to characterize the backgrounds of scientists whose work appears in textbooks. The paper describes the methodology and algorithm, as well as the results from testing a range of textbooks. The tool is freely available, with the goal of helping authors develop more representative textbooks as well as helping students and instructors analyze existing textbooks.

Labor-based grading practices in the physics classroom by Jeremy M. Wachter. DOI: 10.1119/5.0121625

Essentially anyone who has attended college or worked in an academic setting will recognize assessment as a central component of a course. Instructors will also be familiar with the variety of ways in which traditional assessments can actually impede learning. Alternative assessment frameworks are becoming more popular, and this article presents one such approach where students' labor determines their grade. We hope that this article leads readers to critically examine the role assessment plays in their courses.

A modern interpretation of Newton's theorem of revolving orbits by Nolan Samboy; Joseph Gallant. DOI: 10.1119/5.0166698

It is commonly known that Newton derived the Kepler orbits that result from an inverse square central force in his famous work Principia. But fewer people know that Newton also considered precessing orbits in Principia, showing that they are produced by an inverse cubed central force. Subsequent texts on precessing orbits explored the problem with such technical detail that the simplicity of the original problem was often lost. This paper presents the derivation using modern techniques, while also frequently referring back to Newton's original derivation to provide context, providing a nice introduction to the topic appropriate for undergraduate mechanics students.

Effects of general relativistic post-Newtonian approximations on the configuration space properties of elliptical orbitaltrajectories by Prasenjit Bose. DOI: 10.1119/5.0159075

This straightforward analysis of predicted orbital precession could serve in introductory physics and astronomy courses, particularly in evaluating the likelihood of orbital collisions.

Recovering seldom-used theorems of vector calculus and their application to problems of electromagnetism by A. Pérez-Garrido. DOI: 10.1119/5.0182191

Readers who are familiar with differential forms will enjoy seeing how they can be employed to prove several new vector calculus identities. But even readers who do not follow those derivations will benefit from seeing how these identities can be employed to find forces and torques on current-carrying loops.

Static dielectric response and screening in solid state physics: Why dimensionality matters in dielectrics by Cesar E. P. Villegas; Aider Vasquez-Marcani; Alexandre R. Rocha. DOI: 10.1119/5.0122288

Screening in dielectrics is a measure of the strength of Coulomb interactions. Because of the reduced dimensionality, screening is hampered in 2D or quasi-1D materials, with important consequences in nanometer-scale systems that are currently important to the condensed matter community. This paper explains why reduced dimensionality reduces the screening. The topic is appropriate for undergraduate electromagnetism classes or advanced condensed matter courses.

Magnetic hyperfine interaction made easier by Wayne M. Saslow. DOI: 10.1119/5.0167423

This article describes two classical derivations of the hyperfine interaction in hydrogen. In contrast to familiar derivations, these involve no singularities in the magnetic field of the electron. Instead, the interaction energy of a localized proton magnetic moment in the smooth field of an electron in a 1 s orbital is calculated using both bound magnetic charges and bound currents, and the general equivalence of these two approaches is proved. The analysis is accessible in a junior-level electrodynamics course and connects classical electrodynamics to quantum mechanics, as well as the 21 cm line used in astronomy and astrophysics.

The Born rule: Axiom or result? by Jay Lawrence. DOI: 10.1119/5.0151405

The Born rule predicts the probability of the outcome of a measurement on a quantum system, which depends on the projection of the initial state onto the eigenstates of the observable operator. This article shows that the Born rule can be derived from the other axioms of quantum mechanics theory by assuming non-contextuality: the probability of the outcome only depends on the final observed eigenstate. These derivations do not assume any particular interpretation of the theory and could be used as an exercise for undergraduate or graduate students studying the foundations of quantum mechanics.

Statistical physics of frictional grains: Some simple applications of the Edwards statistics by Eric Bertin. DOI: 10.1119/5.0094141

Since the late 20th century, granular materials have been recognized as forming a distinct state of matter, neither solid nor liquid, but amenable to a statistical description. It turns out that dissipation, through inter-grain friction, governs the large-scale properties of these systems, so that the usual Boltzmann–Gibbs statistics is replaced by the Edwards statistics. These statistics are full of surprises. For instance, model granular systems can exhibit a critical point at infinite-temperature. To know more, you can delve into this paper, which can be used in advanced statistical physics courses, or as a graduate-level introduction to soft matter.

#### INSTRUCTIONAL LABORATORIES AND DEMONSTRATIONS

An in-fiber Mach–Zehnder strain sensor for studying multimode interference of light by Gang Zhang; Linguang Xu; Qiang Ge. DOI: 10.1119/5.0173941

This paper reports the development of an advanced instructional laboratory experiment aimed at teaching undergraduates about the physics and applications of multimode interference effects in optical fibers. The experiment is based on an in-fiber Mach-Zehnder strain sensor, which is fabricated by fusion-splicing a thin core fiber between two single-mode fiber leads. The experiment introduces students to optical fiber sensing in a cost-effective way and applies theoretical concepts they have learned in courses in the areas of wave guides, optical interference, and spectral analysis. Experimental results are presented for the sensor's output optical interference spectrum as well as the spectral response to strain. This experiment will be of interest to advanced laboratory and upper-level optics course instructors.

#### NOTES AND DISCUSSIONS

Arduino cavity controller for LIGO analogy lab [Am. J. Phys. 87, 44 (2019)] by Dennis Ugolini. DOI: 10.1119/5.0193289

The LIGO analogy lab [Am. J. Phys. 87, 44 (2019)] includes advanced experiments in which op-amp-based mixing and feedback circuits are used to lock the length of an optical cavity using heterodyne detection. This Note describes an alternate, Arduino-based controller that implements the heterodyning technique in a significantly less complex and easier to troubleshoot manner. This simplified approach makes the advanced LIGO analog experiments accessible to a wider audience in advanced instructional and optics laboratory courses.

A simple treatment of the trolley paradox by Len Zane. DOI: 10.1119/5.0187579 This is a short resolution of the paradox concerning the motion of a rolling wheel, involving standard Lorentz transformations. It can serve as an insightful application in classroom introductions to the special theory of relativity.

Which is greater: or πe? An unorthodox physical solution to a classic puzzle by Andrés Vallejo; Italo Bove. DOI: 10.1119/5.0188912 No calculator allowed: Which is greater: or πe? If you bet on the former, you win. This brief paper shows how this question can be answered by applying the second law of thermodynamics to a reservoir at absolute temperature e in contact with a finite body of temperature π and evaluating the change in entropy as they come to equilibrium. The argument is then extended to showing that, in general, the inequality also holds. A fun example for all thermodynamics students.

#### BOOK REVIEWS

BOOK REVIEW Am. J. Phys. 92, 399–400 (2024). DOI: https://doi.org/10.1119/5.0209209

#### Additional Resources