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Lidas

By DefenSys

LASER INTERFEROMETRIC DIFFERENTIAL ACOUSTIC SENSOR

Mission

Methods in this document describe the design of a quantum acoustic sensor based on laser interferometric Liffs architecture. The described interferometer, called Lidas, is capable of detecting very faint stationary or moving acoustic sources in the air or underwater. Lidas operates on quantum properties of laser light and the changes in its interference pattern inside an optical cavity when impacted by a sound wave. The resulting interferometry-based sensor can resolve acoustic sources several factors farther away in distance than classical acoustic sensors, in a very large bandwidth covering subsonic, sonic and ultrasonic spectrum. This has enormous benefit in several fields such as acoustic weapons systems detection from a safe distance and defence systems that rely on acoustic sensing such as drone detectors. More specifically, Lidas is sensitive to acoustic vibrations in the range of 1 Hz to 1 GHz with sensitivity 10-7 m/√Hz and 10-14 m/√Hz respectively, with a minimum at 1 MHz with sensitivity 10-16 m/√Hz. Lidas can be used to detect

Introduction

Acoustic sensors are key components in a very diverse array of industries, and military defence is one such key industry. In this draft, we describe the design and principal construction of a military-grade acoustic sensor that functions by leveraging the quantum properties of light. Due to its use of laser light in detecting movements caused by sound waves in carefully placed mirrors, the resolution of the resulting sensor is in the sub-nanometer range; this resolution is trivially at least of the order of the wavelength of the laser source, and in fact several factors below it in practice. This extremely fine resolution of the proposed configuration contributes to remarkable sensitivity of the sensor to acoustic vibrations. This amplified sensitivity naturally results in increased earliness of detecting an approaching target, e.g. a drone or a swarm of drones, at much farther distances than previously possible. Similarly, Lidas can also be used to detect acoustic weapons from a safe distance due to its remarkable sensitivity in the entire acoustic range between 1 Hz - 1 GHz.

The construction of the sensor is based on the classical Michelson interferometer, currently being used in the real world in Metrology, Seismology, Optical Coherence Tomography (OCT), and mega hyper-sensing instruments such as LIGO-Virgo-KAGRA detectors. The Michelson interferometer's ability to measure extremely small changes in distance makes it an essential tool in both fundamental research and practical applications. This document describes the necessary design modifications which allow this miniature version of LIGO detectors to function on a much smaller physical scale that is appropriate for a realistic acoustic sensor.

Principle

The Laser Interferometric Differential Acoustic Sensor (Lidas) is built on Liffs architecture with a Michelson interferometer at its core. A Michelson laser interferometer is a precision instrument that uses the principles of interference to measure small distances and changes in distance with high accuracy. The core setup of a Michelson interferometer consists of a coherent light source, typically a laser, a beam splitter, and two mirrors positioned at right angles to each other.

  1. Light Source: The laser emits a coherent beam of light which travels toward the beam splitter.
  2. Beam Splitter: The beam splitter is a partially reflective mirror that divides the incoming laser beam into two separate beams, directing them along two perpendicular paths toward the mirrors.
  3. Mirrors: The two beams travel to mirrors placed at the ends of these paths and are then reflected back to the beam splitter.
  4. Recombination: Upon returning to the beam splitter, the two beams are recombined. Depending on the difference in the optical path lengths they travelled, they can interfere constructively or destructively.

Figure 1: Concept

The interference pattern created by the recombined beams is observed on a detector or screen. If the lengths of the two paths are exactly equal, the waves will interfere constructively, creating a bright fringe. If they differ by half a wavelength, they will interfere destructively, creating a dark fringe. The Michelson interferometer is highly sensitive to changes in the length of one of the paths. When the position of one mirror is altered, the path length changes, leading to shifts in the interference pattern. This shift can be measured to determine the amount of movement with extremely high precision, often down to fractions of the wavelength of the laser light. In order to reach ultra-precision scales, the power circulating in each arm must be very high; each arm of the interferometer must then be upgraded with a power-amplifying recycling cavity called a Fabry-Pérot resonator with a high Finesse of F = 10.

Technology

The sensor is an L-shaped interferometer with two arms of variable length L each, co-joined by the beam splitter at one end; L is usually in the range of 0.1 - 1 m for a reasonably sized sensor. The co-joined end of the beam splitter acts as a mirror and another mirror is placed on the opposite end of each arm. This results in two Fabry-Pérot cavities co-joined in an L formation by the beam splitter. The L-shaped interferometer is lit by a diode laser of wavelength 590 nm or 1064 nm with nominal power output of 20 mW. The collimated and coherent emission from the laser is passed through:

such that the beam splitter receives a clean laser input of relatively high power. The 50-50 splitting at the beam splitter sends 0.1 W of laser power into each Fabry-Pérot resonator, which then further amplifies the power of the electromagnetic field by a factor of 10 to 1 W. The light spends about 10 round trips in each arm before recombining destructively† at the beam splitter. The recombined light finally arrives at the photodetector which can resolve the transient intensity of electromagnetic radiation.

† arm lengths are slightly offset by half of wavelength

In this construction, the end mirror in one of the Fabry-Pérot cavities is allowed to move freely along the length of the arm using a sophisticated seismically isolated setup, while the other arm is fixed at length L. The arrival of a sound wave moves one of the free mirrors while the other remains fixed, resulting in a small phase difference between recombining beams at the beam splitter. The phase difference is the source of transient intensity of light on the photodetector. The sensitivity of the interferometer to the amplitude of the acoustic signal largely depends on its isolation from the seismic noise sources and the quantum noise inside the Fabry-Pérot resonators. The sensitivity of the interferometer to the frequency of the acoustic signal depends on the arm length L and the Finesse F of Fabry-Pérot cavities, which depends on the reflection and transmission coefficients of both cavity end mirrors. Lastly, the entire apparatus must rotate with a low constant angular velocity to maintain sensitivity to all polarisation angles of the acoustic waves.

Sweet Spot

When L = 0.1 m is used, the sweet spot of the interferometer is a function of L and F, and it lies at 𝑓 ~ 10 MHz. If a bigger sensor of L = 1 m can be afforded, then the sweet spot lies at 1 MHz. On either side of the sweet spot, fundamental noise contribution rises due to inelastic coupling of the suspended mirror with the pole of the Fabry-Pérot cavity.

Sensitivity

The sensitivity S of the interferometer is a function of the suspended end mirror's oscillation frequency 𝑓 (as a result of acoustic interaction) expressed in 1/√Hz, and depends on the positional amplitude spectral density 𝛿x and the accelerational amplitude spectral density 𝛿a.

Figure 2: Sensitivity

Quantum Noise

Positional uncertainty is the main contributor to the noise floor near or above the sweet spot all the way down to 100 Hz. This error is the result of laser shot noise resulting from the uncertainty in the count of photons hitting the mirror surface. 𝛿x is a quantum effect and it is a function of laser wavelength and input power to the Fabry-Pérot cavity, such that 𝛿x ~ 10-30 m2/Hz, and more intuitively amplitude power spectral density √𝛿x ~ 10-15 m/√Hz.

Seismic Noise

Below 100 Hz, acceleration uncertainty arising from seismic motion is the main quantifier of noise floor. The value of this contribution scales as 𝛿a/𝑓2, where 𝛿a ~ 10-12 m2/s4/Hz and √𝛿a ~ 10-6 m/s2/√Hz. The suspended mirror mount as well as the detector mount contribute to this noise floor and limit the sensitivity of the sensor at the lower end of the audible spectrum and in the infrasonic range down to 1 Hz.

The overall sensitivity of the interferometer is such that the sensor is capable of resolving acoustic vibration in the suspended mirror with a resolution of roughly (0.1/L) fm‡ at 𝑓 > 100 Hz, and (0.1/L) μm at 𝑓 < 100 Hz.

‡ fm = femtometer (10-15 m) and μm = micrometer (106 m)

Polarisation

Note that a stationary Michelson interferometer with seismically isolated mounts is only sensitive to acoustic waves which have a non-zero amplitude component along the arm length that contains the suspended mirror due to their longitudinal polarisation. In order to make the sensor sensitive to co-planar perpendicular direction, the apparatus must be rotated at a sufficiently slow and constant angular velocity; other options for bi-directional sensitivity include freeing and suspending the second end mirror or a dual-interferometric setup. Further note that the rotating in horizontal plane doesn't effect the sensitivity to acoustic sources that are located directly above the sensor; this blind spot cannot be removed without adding significant complexity to the apparatus.

Remarks

In this document, we have detailed the design and underlying principles of Laser Interferometric Differential Acoustic Sensor (Lidas). By leveraging the quantum properties of laser light and its interaction with sound waves, Lidas achieves unprecedented sensitivity in detecting faint acoustic sources. This capability extends over a vast frequency range from 1 Hz to 1 GHz, allowing for the detection of various threats, including drones and acoustic weapons, at distances significantly greater than those achievable with conventional acoustic sensors.

The foundation of Lidas lies in the Michelson interferometer, enhanced with Fabry-Pérot resonators to achieve high precision in measuring minute changes in distance caused by acoustic vibrations. The interferometer's design ensures ultra-fine resolution, facilitated by high circulating power and careful isolation from seismic noise. This results in a sensor with exceptional sensitivity, capable of detecting acoustic signals down to the femtometer scale.

The practical implementation of Lidas requires addressing challenges such as quantum noise and seismic noise, which influence its sensitivity across different frequency ranges. By optimising the arm length and the Finesse of the Fabry-Pérot cavities, the sensor's sweet spot can be tailored to specific frequencies, enhancing its performance for targeted applications.

Additionally, the sensor's ability to detect acoustic signals in multiple polarisations can be achieved by rotating the apparatus or adopting a dual-interferometric setup. This versatility ensures comprehensive coverage and detection capabilities in various operational scenarios.

In summary, Lidas represents a significant advancement in acoustic sensing technology. Its quantum-enhanced interferometric approach offers unparalleled sensitivity and resolution, making it a valuable tool for military defense and other fields requiring precise acoustic detection. The successful deployment of Lidas will mark a new era in acoustic sensing, providing early and accurate detection of potential threats from a safe distance.