Laser Gyroscope

Some Description

Team members

Darren e0303300@u.nus.edu

Wen Xin e0309271@u.nus.edu

Idea

This project aims to measure some rotation by using the Sagnac effect, by using a loop of fiber as a ring interferometer.

Sagnac effect

When two beams of light are sent into the two ports of a ring interferometer, they travel clockwise (CW) and counter-clockwise (CCW) paths respectively. For a stationary ring interferometer, since the path length traversed by each beam is the same, this leads to complete constructive interference at the output port.

Now let's say the interferometer is spinning in the CW direction with rotation rate $\mathrm{\Omega }$. Then there will be a difference in path length:

$\mathrm{\Delta }L=R\mathrm{\Omega }{t}_{CW}$

which results in a timing difference of:

$t_{CW}=\frac{2\pi nR+R\mathrm{\Omega }{t}_{CW}}{c},t_{CCW}=\frac{2\pi nR-R\mathrm{\Omega }{t}_{CCW}}{c}$

where n is the refractive index of the medium. Simplifying,

$t_{CW}=\frac{L_0}{c-R\mathrm{\Omega }},t_{CCW}=\frac{L_0}{c+R\mathrm{\Omega }},\mathrm{\Delta }t=t_{CW}-t_{CCW}=\frac{L_0\cdot 2R\mathrm{\Omega }}{c^2}\cdot \frac{1}{1+{\left(\frac{R\mathrm{\Omega }}{c}\right)}^2}$

as $R\mathrm{\Omega }<<c$,

$\mathrm{\Delta }t\approx \frac{2R{L}_0}{c^2}\cdot \mathrm{\Omega }$

For a fiber loop with radius R and number of loops N,

$\mathrm{\Delta }t=\frac{4N\pi n{R}^2}{c^2}\cdot \mathrm{\Omega }$

Thus, for light of frequency f, we can calculate the Sagnac phase shift:

$\mathrm{\Delta }{\varphi }_S=2\pi f\cdot \mathrm{\Delta }t=\frac{8\pi nNA}{\lambda c}\cdot \mathrm{\Omega }$

Parts

1550nm fiber loops

2x 1550nm detectors

2x fiber circulator

1550nm diode

Setup

The main setup will be a fiber based sagnac intereferometer with detection of the output done using photodiodes. We are aiming to build everything in the 1550nm wavelength range.

Measurements

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