A temperature-tunable etalon for optical telecommunication wavelength: Difference between revisions

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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.  
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 with a relatively low absorption coefficient of [bla] and a thermal expansion coefficient of [bla].  
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 <math>6 \times 10^{-5}</math>/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.
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 <math>6 \times 10^{-5}</math>/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.
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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 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==
==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===
===Setup===
A double-side polished silicon wafer acts as the etalon in the setup.<ref>https://order.universitywafer.com/default.aspx?cat=Silicon&diam=76.2mm</ref> The wafer has a thickness of <math>L=100</math>μm, which corresponds to a free spectral range of <math> \Delta \lambda = \frac{{\lambda}^2}{2nL} \approx 2.45</math>nm at 1310nm.  
A double-side polished silicon wafer acts as the etalon in the setup.<ref>https://order.universitywafer.com/default.aspx?cat=Silicon&diam=76.2mm</ref> The wafer has a thickness of <math>L=100</math>μm, which corresponds to a free spectral range of <math> \Delta \lambda = \frac{{\lambda}^2}{2nL} \approx 2.45</math>nm at 1310nm.  
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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 <math>\pm </math>4mK.
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 <math>\pm </math>4mK.


[[File:Drawing.png|600px|caption]]   **    [[File:20210427 154330.jpg|400px|caption]]
[[File:Drawing.png|600px|caption]]       [[File:20210427 154330.jpg|400px|caption]]


To measure the transmission spectrum of the silicon etalon, we prepared a Super-luminescence LED to provide a wide-band light of 1320<math>\pm</math>50nm. The optical beam propagates through the etalon and the transmitted light spectrum is measured with a wave-meter (2GHz spectral resolution).<ref>https://www.bristol-inst.com/bristol-instruments-products/spectrum-analyzers/771-series-laser-spectrum-analyzer/</ref>
To measure the transmission spectrum of the silicon etalon, we prepared a Super-luminescence LED to provide a wide-band light of 1320<math>\pm</math>50nm. The optical beam propagates through the etalon and the transmitted light spectrum is measured with a wave-meter (2GHz spectral resolution).<ref>https://www.bristol-inst.com/bristol-instruments-products/spectrum-analyzers/771-series-laser-spectrum-analyzer/</ref>


==Bare Silicon Wafer==
===Bare Silicon Wafer: Transmission Spectrum===
[[File:100um-whole.png|600px|Transmission spectrum of a bare silicon wafer of 100μm]]
The measured transmitted spectrum together with a zoom-in view are shown below.
[[File:100um-zoom.png|600px|Zoom in of the spectrum, showing a free spectral range of ~2.3nm (~400GHz)]]


==Temperature Tuning of silicon etalon==
[[File:100um-whole.png|500px|Transmission spectrum of a bare silicon wafer of 100μm]]    [[File:100um-zoom.png|500px|Zoom in of the spectrum, showing a free spectral range of ~2.3nm (~400GHz)]]
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. Just to quickly note that the thermal expansion coefficient of silicon is <math>\frac{1}{l} \frac{dl}{dT} \approx 2.6\times 10^{-6} {\text{K}}^{-1}</math> ([http://www.ioffe.ru/SVA/NSM/Semicond/Si/thermal.html]).


Besides the thermal expansion of the etalon, the refractive index of silicon also changes with varying temperature. One report of the thermal-optic coefficient <math>\frac{dn}{dT}</math> of silicon can be found here([https://arxiv.org/pdf/physics/0606168.pdf]), which states a coefficient <math>\frac{dn}{dT}\approx 2\times 10^{-4}\text{K}^{-1}</math>. 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 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.


The shift of transmission center wavelength of a fringe can be expressed as: <math>\frac{d\lambda}{dT}=\lambda(\frac{1}{n} \frac{dn}{dT} + \frac{1}{l} \frac{dl}{dT}) \approx 0.079 \text{nm/K}</math> for 1310nm.
===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.
 
[[File:temperature_shift.png|500px]]      [[File:wavelength_v_temp.png|500px]]
 
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.  


[[File:temperature_shift.png|620px]]
[[File:wavelength_v_temp.png|620px]]</p><p>
We adjusted the temperature finer, taking 15 transmission intensities under different temperature between 25 and 55. We have linearly fitted the shift of the central wavelength with temperature and find that they are perfectly linearly. The result shows that the central wavelength will shift 0.1nm when the temperature changes by 1 celsius degree. </p><p>
[[File:Temperature-tuning.png|1000px]]
[[File:Temperature-tuning.png|1000px]]


==HR Coated Silicon Wafer==
Just to quickly note again the thermal expansion coefficient of silicon is <math>\frac{1}{l} \frac{dl}{dT} \approx 2.6\times 10^{-6} {\text{K}}^{-1}</math>.<ref>http://www.ioffe.ru/SVA/NSM/Semicond/Si/thermal.html</ref> Besides the thermal expansion of the etalon, the refractive index of silicon also changes with varying temperature. One report of the thermal-optic coefficient <math>\frac{dn}{dT}</math> of silicon can be found here, <ref>https://arxiv.org/pdf/physics/0606168.pdf</ref> which states a coefficient <math>\frac{dn}{dT}\approx 2\times 10^{-4}\text{K}^{-1}</math>.  
We wrote some MATLAB codes to simulate the performance of high reflection coating. Here, we are using a six-layer coating. The first layer from the air is the Si3N4, 163nm for thickness. After that, is the SiO2 layer, 226nm for thickness. Then the Si3N4 (163nm), SiO2 (226nm), Si3N4 (163nm), SiO2 (226nm).  
 
[[File:png_Coating.png|620px]] </p><p>
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: <math>\frac{d\lambda}{dT}=\lambda(\frac{1}{n} \frac{dn}{dT} + \frac{1}{l} \frac{dl}{dT}) \approx 0.08 \text{nm/K}</math> for 1310nm. This roughly agrees with the 0.1nm/K rate that we observed.
The reflective index of the coating should be as below:
 
[[File:simulation_result.png|620px]] </p><p>
===Highly Reflective (HR) Coating on Silicon Surface===
When the thickness of all the layers is correct, the reflection spectrum should have a peak at a wavelength around 1310nm. The reflection peak should reach 90%. If so, our etalon would have high finesse and can act as a very useful filter for high bandwidth lasers.  
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 <math>\lambda_n/4</math>, where <math>\lambda_n</math> is the corresponding wavelength in the coating medium.
==Silicon Coating Speed Calibrating==
 
Sputtering speed depends not only on the input RF power but also related to the distance between the target and the sample. and the surface area of the sample. We have to calibrate the sputtering speed to make sure the thickness of the film we coated is correctly equal to a quarter lambda or a half lambda. We sputtered silicon film on the optical window to measure the thickness of different sputtering time. In this calibration experiment, we are using 100w power for RF signal, and the distance between the target and the sample is about 8cm, while the diameter of the glass (Optical Window) is 25.4mm. We tried for 6000s, 8000s, 10000s, 12000s, 20000s. </p><p>
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.
 
[[File:png_Coating.png|500px]]       [[File:simulation_result.png|500px]]  
 
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==


[[File:Silicon-thickness.png|1000px]] </p><p>
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.


The estimated speed is drawn in the graph with dashed lines.</p><p>
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.
[[File:Substrate-BK7.png|1000px]]

Latest revision as of 07:12, 1 May 2021

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 6×10−5/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 2.6×10−6/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 dndT≈2×10−4/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.[1] The wafer has a thickness of L=100μm, which corresponds to a free spectral range of Δλ=λ22nL≈2.45nm 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 ±4mK.

caption caption

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

Bare Silicon Wafer: Transmission Spectrum

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

Transmission spectrum of a bare silicon wafer of 100μm Zoom in of the spectrum, showing a free spectral range of ~2.3nm (~400GHz)

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 1ldldT≈2.6×10−6K−1.[3] Besides the thermal expansion of the etalon, the refractive index of silicon also changes with varying temperature. One report of the thermal-optic coefficient dndT of silicon can be found here, [4] which states a coefficient dndT≈2×10−4K−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: dλdT=λ(1ndndT+1ldldT)≈0.08nm/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 λn/4, where λn 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.

  1. ↑ https://order.universitywafer.com/default.aspx?cat=Silicon&diam=76.2mm
  2. ↑ https://www.bristol-inst.com/bristol-instruments-products/spectrum-analyzers/771-series-laser-spectrum-analyzer/
  3. ↑ http://www.ioffe.ru/SVA/NSM/Semicond/Si/thermal.html
  4. ↑ https://arxiv.org/pdf/physics/0606168.pdf
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