A temperature-tunable etalon for optical telecommunication wavelength

Members

Shi Yicheng (A0054800R), Du Jinyi (A0227185B), Zhang Qian(A0228752Y)

Rationale

A Fabry-Perot interferometer (or an Etalon), being probably the simplest form of all interferometers, is found useful in a variety of optical applications such as spectral filtering or frequency referencing.

An etalon is typically constructed out of the two parallel reflecting surfaces of a transparent plate. The plate needs to have low absorption loss for the desired working wavelengths to ensure a relatively high finesse of the etalon. The material choice for visible wavelengths is usually fused silica with an absorption coefficient of [bla] and a thermal expansion coefficient of [bla].

For optical telecommunication wavelengths, which range from about 1260nm to 1625nm, pure silicon becomes a more practical choice with an absorption coefficient of [bla] and thermal expansion coefficient of [bla].

Characteristic Parameters of an Etalon

The performance of etalon is characterized by several main parameters: including visibility (V), free spectral range （FSR), full width half maximum (FWHM), and central wavelength.

Suppose that the $a_1$, $a_2$, $a_3$ are the electrical field intensity of input, oscillating, output light.

The relationship is as follows

$a_2=t{a}_1+r^2{a}_2{e}^{-i\varphi }$

$a_3=t{a}_2$

Where \phi means that phase delay in the cavity and the gap between two reflective surfaces is d.

$\varphi =2kd=2\frac{2\pi }{\lambda }d$

From the upper two equations, we have

$a_2=a_1\frac{t}{1-r^2{e}^{-i\varphi }}$

$a_3=a_1\frac{t^2}{1-r^2{e}^{i\varphi }}$

Then, we can calculate the transmission ratio:

$T_R=|\frac{a_3}{a_1}|=|\frac{t^2}{1-r^2{e}^{i\varphi }}{|}^2=\frac{t^4}{(1-r^2{e}^{i\varphi }{)}^2+(r^{2}sin\varphi {)}^2}=\frac{t^4}{1-r^2-2rcos\varphi }$

Here, we have $cos\varphi =1-2si{n}^2\frac{\varphi }{2}$

So, $T_R$ can be simplified as follows

$T_R=\frac{t^4}{(1-r^2{)}^2+4r^{2}si{n}^2\frac{\varphi }{2}}=\frac{1}{1+\frac{4r^2}{t^4}si{n}^2\frac{\varphi }{2}}$

Here, we define a new parameter: $F=\frac{4r^2}{t^4}$, which is called coefficient finesse.

So, $T_R=\frac{1}{1+Fsi{n}^2\frac{\varphi }{2}}$

Design

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Performance

Bare Silicon Wafer

Temperature Tuning of silicon etalon

A small piece of the silicon wafer is mounted on a copper block with a 4mm diameter hole through hole. The copper serves as a thermally conductive mount for the silicon etalon and is placed on top of a Peltier stage. The temperature of this entire stack is adjusted and stabilized with a TEC controller. A few different temperatures were tried.