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Liffs

By DefenSys

LASER INTERFEROMETRIC FORCE FIELD SENSOR

Mission

Methods in this document describe the design of a quantum sensor based on laser interferometry capable of coupling to an arbitrary force field such as an electric field, magnetic field, or fluid field. The described interferometer, called Liffs, can act as a voltmeter, magnetometer, acoustic sensor, and altimeter, among other detector types. Liffs operates on quantum properties of laser light and the changes in its interference pattern inside an optical cavity when interacted with a physical disturbance due to a force field. These physical vibrations result from force fields interacting with the interferometer through uniquely designed and highly efficient coupling agents. The resulting interferometry-based sensor can resolve physical targets several factors farther away in distance than classical sensors, in a very large bandwidth covering sub, ultra, and hyper ranges of the force field's frequency spectrum. This has enormous benefit in several fields such as:

  1. Acoustic Sensing : Acoustic weapons systems detection from a safe distance and defence systems that rely on acoustic sensing such as drone detectors. Liffs can be used to detect:

    • Drones by sensing and localising their acoustic emissions in the audible spectrum between 100 - 5,000 Hz, and
    • Infrasonic 1 - 20 Hz, sonic 20 - 20,000 Hz and ultrasonic > 20,000 Hz weapons systems.

  2. Magnetometers : Magnetometers with very high sensitivity to Earth's magnetic field used in MagNav and Magnetic Anomaly Detection (MAD).

  3. Inertial Sensors : Inertial sensors similar to Ring Laser Gyroscopes (RLG) capable of detecting minor changes in tilts of bodies.

  4. Gravitometers : Gravitometers with very high sensitivity to Earth's gravitational field, with possible use in GravNav and Gravitational Anomaly Detection (GAD). Gravitational channel is potentially a better resolver of local position than magnetic channel due to Earth's gravitational field being significantly more stable over all relevant scales.

More specifically, a Liffs sensor of size 1 m is sensitive to physical vibrations in the range of 1 Hz to 1 GHz with sensitivity 10-7 m/√Hz and 10-15 m/√Hz respectively. In the sub-Hz range, the sensitivity diminishes quickly for fixed detector size but this can be compensated with a combination of higher grade Fabry-Pérot resonators, larger size and balloon-mounted airborne carrier. By rotating the apparatus at slow and fixed angular velocities, sensitivity to multiple polarisations in all directions can be trivially achieved. Liffs represents a significant advancement in force field sensing technology, making it a valuable tool for military defense and other fields requiring precise sensing.

Introduction

Force field 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 force field sensor that functions by leveraging the quantum properties of light. Due to its use of laser light in detecting movements caused by force fields in efficiently coupled and carefully placed mirrors, the resolution of the resulting sensor is in the sub-nanometre 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. Each sensor type is adapted to the target force field through an efficient coupling agent which converts the field energy to physical vibrations.

This extremely fine resolution of the proposed configuration contributes to remarkable sensitivity of the sensor to force field vibrations. This amplified sensitivity naturally results in increased earliness of detecting an approaching target, e.g. a drone or a swarm of drones in the case of acoustic sensors, at much farther distances than previously possible. Similarly, Liffs can also be used to sense force fields from a safe distance due to its remarkable sensitivity in the entire spectral range between sub-Hz and 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.

Principle

The Laser Interferometric Force Field Sensor (Liffs) is built on the concept of Michelson interferometer. 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 occurance of a physical disturbance 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 force field vibration 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 force field vibration 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 propagating force field.

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 force field 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 spectrum near 1 Hz and in the sub-Hz range below 1 Hz.

The overall sensitivity of the interferometer is such that the sensor is capable of resolving the induced 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)

If sensitivity is desired in the sub-Hz range, then the most optimal way to seismically isolate the apparatus is through balloon-mounted airborne carriers, in which case the frequency dependence of noise floor in the sub-Hz range scales as 1/𝑓 instead of 1/𝑓2.

Polarisation

Note that a stationary Michelson interferometer with seismically isolated mounts is only sensitive to a propagating force field which has a non-zero amplitude component along the arm that contains the suspended mirror. In order to allow for sensitivity in all directions, the apparatus must be rotated at a sufficiently slow and constant angular velocity; other options for multi-directional sensitivity include freeing and suspending the second end mirror or a multi-interferometric setup.

Coupling Agent

Each sensor type built on Liffs core must implement a unique mount for the suspended end mirror of Fabry-Pérot resonator that can couple with the force field that it is trying to detect. This mount should take into consideration the directions in which the sensor needs to be sensitive as well as the polarisation of the force field. For instance, an acoustic sensor should (perhaps) use a diaphragm-like mount for its suspended mirror which can respond to acoustic waves with a non-zero component along its arm due to their longitudinal polarisation. A magnetometer implementation of Liffs should instead suspend the mirror on a seismically isolated bench and coat the backside of the mirror with a substance of high magnetic susceptibility. A voltmeter should implement a similar method as the magnetometer but instead use a coating substance of high electric susceptibility.

Liffs Sensors

Lidas

Lidas is an example of a hyper-sensitive acoustic sensor built on the Liffs core. Lidas mounts the suspended end mirror of the Fabry-Pérot resonator in two formations: one on a taut diaphragm capable of coupling with pressure waves in a fluid in all directions for airborne carriers, and the second for ground-based sensors that use seismically isolating suspensions. These ground-based sensors have decreasing sensitivity with increasing azimuth and a blind spot vertically above them. The Indranet network is designed to use Lidas as the ground-based acoustic sensor in its mesh.

Remarks

In this document, we have detailed the design and underlying principles of the Laser Interferometric Force Field Sensor (Liffs). By leveraging the quantum properties of laser light and its interaction with the force field oscillations, Liffs achieves unprecedented sensitivity in detecting faint oscillations in the force fields. This capability extends over a vast frequency range from 1 mHz 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. Through its use of modular coupling agents, Liffs also forms the core of hyper-sensitive magnetometers and inertial sensors.

The foundation of Liffs lies in the Michelson interferometer, enhanced with Fabry-Pérot resonators to achieve high precision in measuring minute changes in distance caused by force field 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 oscillations down to the femtometer scale.

The practical implementation of Liffs 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 propagating force fields 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, Liffs represents a significant advancement in force field 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 sensing. The successful deployment of Liffs will mark a new era in hyper-sensing infrastructure, providing early and accurate detection of potential threats from a safe distance.