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 various 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 given its low absorption and thermal expansion.

For optical telecommunication wavelengths, which range from about 1260nm to 1625nm, pure silicon becomes a more practical choice. Polished silicon wafers can be easily purchased at different thickness (100μm to a few mm), which allows for various free spectral ranges. The absorption coefficient of silicon is about $6\times 10^{-5}$/cm at 1310nm. Given this low absorption loss at the telecom wavelength, it is possible in principle to build etalons with high finesse by applying Highly Reflective coatings to the two surfaces of a silicon wafer.

The thermal expansion coefficient of silicon is $2.6\times 10^{-6}$/K, which translates to a thickness change of merely 0.26nm/K for a 100μm wafer. On the other hand, the refractive index of silicon has a temperature dependence of ${\frac {dn}{dT}}\approx 2\times 10^{-4}$/K, which is two orders of magnitude higher than the thermal expansion coefficient. It is also independent of the thickness which suggests that the transmission wavelengths of the etalon is tunable even for a very thin piece.

Characteristic Parameters of an Etalon

A very quick intro to Fabry-Perot interferometer is here: How does an etalon work?. Alternatively one can turn to literally any text books on interferometry.

A Bare Silicon Wafer as an Etalon

Even without any coatings on the surfaces, a silicon-air interface has about 30% reflectance, hence one should be able to observe the etalon effect of the wafer. We hence proceed to test the transmission spectrum as well as the temperature tunability of such a bare piece of silicon wafer.

Setup

A double-side polished silicon wafer acts as the etalon in the setup. The wafer has a thickness of $L=100$μm, which corresponds to a free spectral range of $\Delta \lambda ={\frac {{\lambda }^{2}}{2nL}}\approx 2.45$nm at 1310nm.

The silicon wafer is cut into a small rectangular piece of about 5mmx10mm, and is UV-glued onto the surface of a copper block. A through-hole was drilled in advance to allow passage of an optical beam. Thermal compound is applied between the wafer piece and the copper block to ensure a good thermal transfer. The copper block is mounted on a peltier stage with a thermistor attached. Enclosed in an acrylic box, the temperature of the silicon wafer can be adjusted between 25°C and 50°C and stabilized to about $\pm$4mK.

To measure the transmission spectrum of the silicon etalon, we prepared a Super-luminescence LED to provide a wide-band light of 1320$\pm$50nm. The optical beam propagates through the etalon and the transmitted light spectrum is measured with a wave-meter (2GHz spectral resolution).

Bare Silicon Wafer: Transmission Spectrum

The measured transmitted spectrum together with a zoom-in view are shown below.

The observed free spectral range is about 2.3nm as opposed to the estimated value of 2.45nm for a wafer with 100μm thickness. The cause of this 0.1nm difference is yet unclear, but could be attributed to the thickness variation of the wafer itself, or the possibility that the wafer is tilted against the incidence beam. As anticipated, the reflectance of the silicon-air interface is only about 30%, which causes a low visibility (~0.44) of the transmitted spectrum. The finesse of this etalon is estimated to be about 2.6, which is considered low for typical etalon performances.

Bare Silicon Wafer: Temperature Tuning

The temperature of the setup is adjusted and stabilized with a TEC controller. A few different temperatures were tried. The two graphs below shows the position of different transmission peaks around 1320nm at 4 different temperatures.

Similar measurements are repeated over more temperature settings. Shown below is a heat map that summarize the results at 15 different temperatures. The position of high transmission peaks (white) shifts linearly with temperature at a rate of 0.1nm/K.

Just to quickly note again the thermal expansion coefficient of silicon is ${\frac {1}{l}}{\frac {dl}{dT}}\approx 2.6\times 10^{-6}{\text{K}}^{-1}$. Besides the thermal expansion of the etalon, the refractive index of silicon also changes with varying temperature. One report of the thermal-optic coefficient ${\frac {dn}{dT}}$ of silicon can be found here, which states a coefficient ${\frac {dn}{dT}}\approx 2\times 10^{-4}{\text{K}}^{-1}$.

Do note that the thermal-optical coefficient is two orders of magnitude larger than the thermal expansion coefficient, which suggest that the change in refractive index is the main contribution towards wavelength tuning of this etalon. The shift of transmission center wavelength of a fringe can be expressed as: ${\frac {d\lambda }{dT}}=\lambda ({\frac {1}{n}}{\frac {dn}{dT}}+{\frac {1}{l}}{\frac {dl}{dT}})\approx 0.08{\text{nm/K}}$ for 1310nm. This roughly agrees with the 0.1nm/K rate that we observed.

Highly Reflective (HR) Coating on Silicon Surface

An etalon, in its true sense, should come with two highly reflective surfaces to achieve high finesse. HR coatings usually consists of interleaved layers with different refractive indices with thickness equals to $\lambda _{n}/4$, where $\lambda _{n}$ is the corresponding wavelength in the coating medium.

For HR coating materials on silicon at telecom wavelength, typical choices are Silicon Dioxide (SiO2), Silicon Nitride (Si3N4) or even just use silicon itself. An example of a six-layer coating is shown below using Si3N4 and SiO2, with layer thickness of 163nm and 226nm respectively. This can in theory achieve about 90% reflectance centered at 1310nm over a bandwidth of about 200nm.

One can also use layers of Si3N4 (163nm) and Si (93nm) to achieve similar reflection behavior. The usage of silicon is slightly more preferable as its much higher refractive index (n=3.5) corresponds to much thinner coating layers, thus making it easier for manufacturing.

Unfortunately this small project stops at this stage where creating HR coatings on silicon surface becomes a problem. We have in fact, gotten access to a RF sputtering machine is capable of creating such coatings. However, this particular machine needs certain amount of calibration work to ensure an accurate deposition rate such that one can create coated layers with the correct thickness. Some efforts have been made towards this direction and is briefly documented here.

Stage Summary for the Project

In summary, we show that a thin piece of polished silicon wafer can behave as an etalon with low finesse at telecom wavelength. One can quite easily tune the transmission wavelengths of this etalon by simply varying the temperature. This wavelength tuning has a temperature dependence of about 0.1nm/K, and this effect is mainly due to the change in refractive index of the silicon material itself.

In principle, one can increase the finesse of the silicon etalon by applying HR coatings to the surfaces. This temperature tunable silicon etalon can be used as a variable spectral filter or frequency reference for telecom wavelength.