QT5201U wiki - User contributions [en]

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-30T05:40:46Z

Jinyidu: /* Silicon Coating Speed Calibrating */

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-30T05:40:22Z

Jinyidu: /* Performance */

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-30T05:39:43Z

Jinyidu: /* Silicon Coating Speed Calibrating */

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-29T16:11:30Z

Jinyidu: /* Temperature Tuning of silicon etalon */

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-29T12:46:08Z

Jinyidu: /* Silicon Coating Speed Calibrating */

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-29T12:36:30Z

Jinyidu: /* Silicon Supttering Speed Calibrating */

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-29T09:23:39Z

Jinyidu: /* Performance */

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-29T09:19:29Z

Jinyidu: /* Temperature Tuning of silicon etalon */

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-29T08:18:39Z

Jinyidu: /* HR Coated Silicon Wafer */

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-29T08:17:24Z

Jinyidu: /* Performance */

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-29T08:13:24Z

Jinyidu: /* Performance */

File:Png Coating.png

2021-04-29T08:08:59Z

Jinyidu:

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-29T06:26:04Z

Jinyidu: /* Performance */

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-29T03:56:24Z

Jinyidu: /* HR Coated Silicon Wafer */

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-29T03:56:00Z

Jinyidu: /* HR Coated Silicon Wafer */

A temperature-tunable etalon for optical telecommunication wavelength

2021-04-29T03:53:44Z

Jinyidu: /* HR Coated Silicon Wafer */

File:Coating.jpg

2021-03-16T05:43:05Z

Jinyidu: Jinyidu uploaded a new version of File:Coating.jpg

A temperature-tunable etalon for optical telecommunication wavelength

2021-03-16T05:42:32Z

Jinyidu: /* HR Coated Silicon Wafer */

====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 <math>a_1</math>, <math>a_2</math>, <math>a_3</math> are the electrical field intensity of input, oscillating, output light.
[[File:Etalon_principle.jpg]]

The relationship is as follows

<math>a_2=ta_1+r^2a_2e^{-i\phi}</math>

<math>a_3=ta_2</math>

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

<math>\phi=2kd=2\frac{2\pi}{\lambda}d</math>

From the upper two equations, we have

<math>a_2=a_1\frac{t}{1-r^2e^{-i\phi}}</math>

<math>a_3=a_1\frac{t^2}{1-r^2e^{i\phi}}</math>

Then, we can calculate the transmission ratio:

<math>T_R=|\frac{a_3}{a_1}|=|\frac{t^2}{1-r^2e^{i\phi}}|^2=\frac{t^4}{(1-r^2e^{i\phi})^2+(r^2sin\phi)^2}=\frac{t^4}{1-r^2-2rcos\phi}</math>

Here, we have <math>cos\phi=1-2sin^2\frac{\phi}{2}</math>

So, <math>T_R</math> can be simplified as follows

<math>T_R=\frac{t^4}{(1-r^2)^2+4r^2sin^2\frac{\phi}{2}}=\frac{1}{1+\frac{4r^2}{t^4}sin^2\frac{\phi}{2}}</math>

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

So, <math>T_R=\frac{1}{1+Fsin^2\frac{\phi}{2}}</math>

Since we already have the expression of transmission (T), we can also derive some important parameters:

1.Visibility

The interferometric visibility quantifies the contrast of interference in an optical system. The ratio of the amplitude of oscillations to the sum of the powers of the individual waves is defined as the visibility.

Assume <math>I_{max}</math>, <math>I_{min}</math> are the maximum intensity of the oscillations and the minimum intensity of the oscillations, <math>V</math> is the visibility of the interference pattern.

<math>V=\frac{I_{max}-I_{min}}{I_{max}+I_{min}}</math>

Suppose the intensity of incident light of etalon is <math>I</math>,the minimum transmission is <math>T_{min}</math>, the maximum transmission is <math>T_{max}</math>, we can rewrite the visibility

<math>V=I\frac{T_{max}^2-T_{min}^2}{T_{max}^2+T_{min}^2}</math>

<math>T_{min}=\frac{1}{1+0}</math>, <math>T_{max}=\frac{1}{1+F}</math>

<math>V=\frac{(1+F)^2-1}{(1+F)^2+1}</math>

This indicate the visibility of interference pattern is associated with coefficient finesse. When <math>V_{max}=1</math>, <math>F</math> is approximately equal to infinite, get the best interference pattern; when <math>V_{min}=0</math>, <math>F=0</math>, can’t observe the interference pattern.

2.Free spectral range(FSR)

The free spectral range(FSR) of a cavity, in general, is given by

<math>|\Delta \lambda_{FSR}|=\frac{2\pi}{L}|\frac{1}{\frac{\partial \beta}{\partial \lambda}}|</math>

Where <math>\beta</math> is the wavevector of the light inside the cavity,
<math>\beta=\kappa_0n(\lambda)=\frac{2\pi}{\lambda}n(\lambda)</math>. <math>\kappa_0</math> and <math>\lambda</math> are the wavevector and wavelength in vacuum, <math>n</math> is the refractive index of the cavity, <math>L</math> is the length of the cavity(for a standing-wave cavity, <math>L</math> is equal to twice the physical length of the cavity)

<math>|\frac{\partial \beta}{\partial \lambda}|=\frac{2\pi}{\lambda^2}[n(\lambda)-\lambda\frac{\partial n}{\partial \lambda}]=\frac{2\pi}{\lambda^2}n_g</math>

The FSR is <math>\Delta \lambda_{FSR}=\frac{\lambda^2}{n_gL}</math>, <math>n_g</math> is the group index of the media within the cavity.

In etalon, the FSR is <math>\Delta \lambda_{FSR}=\frac{\lambda_0^2}{2nl\cos\theta}</math>

Where <math>\lambda_0</math> is the central wavelength of the nearest transmission peak, <math>n</math> is the index of refraction of the cavity, <math>l</math> is the thickness of the cavity, <math>\theta</math> is the angle of incidence.

3. Full width at half maximum

The full width at half maximum (FWHM) is a parameter commonly used to describe the width of a "bump" on a curve or function. It is given by the distance between points on the curve at which the function reaches half its maximum value.

4.Central wavelength

Central Wavelength, used in defining bandpass filters, describes the midpoint of spectral bandwidth over which the filter transmits.

[[File:FWHM_CENTRAL WAVELENGTH.jpg]]

5.The relationship between FSR and FWHM

The FSR is related to the full-width half-maximum <math>\delta\lambda</math> of any one transmission band by a quantity known as the finesse

<math>\mathcal{F}=\frac{\Delta \lambda}{\delta \lambda}=\frac{\pi}{2\arcsin\frac{1}{\sqrt{F}}}</math>

In a word, If we want to observe more clear interference pattern, we should make <math>F</math> large, or make <math>\Delta\lambda(FSR)</math> large and <math>\delta\lambda (FWHM)</math> small.

==Building an Etalon Out of Silicon Wafer==

=Design=
[[A few photos for now.]]

=Performance=
[[File:Drawing.png|options|caption]]

==Bare Silicon Wafer==
[[File:100um-whole.png|options|Transmission spectrum of a bare silicon wafer of 100μm]]
[[File:100um-zoom.png|options|Zoom in of the spectrum, showing a free spectral range of ~2.3nm (~400GHz)]]

==HR Coated Silicon Wafer==
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:coating.jpg]]
The reflective index of the coating should be as below:
[[File:result2.jpg]]

==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. 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 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 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.

[[File:temperature_shift.png|options|]]
[[File:wavelength_v_temp.png|options|]]

File:Coating.jpg

2021-03-16T05:41:08Z

Jinyidu:

A temperature-tunable etalon for optical telecommunication wavelength

2021-03-16T05:33:52Z

Jinyidu: /* HR Coated Silicon Wafer */

====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 <math>a_1</math>, <math>a_2</math>, <math>a_3</math> are the electrical field intensity of input, oscillating, output light.
[[File:Etalon_principle.jpg]]

The relationship is as follows

<math>a_2=ta_1+r^2a_2e^{-i\phi}</math>

<math>a_3=ta_2</math>

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

<math>\phi=2kd=2\frac{2\pi}{\lambda}d</math>

From the upper two equations, we have

<math>a_2=a_1\frac{t}{1-r^2e^{-i\phi}}</math>

<math>a_3=a_1\frac{t^2}{1-r^2e^{i\phi}}</math>

Then, we can calculate the transmission ratio:

<math>T_R=|\frac{a_3}{a_1}|=|\frac{t^2}{1-r^2e^{i\phi}}|^2=\frac{t^4}{(1-r^2e^{i\phi})^2+(r^2sin\phi)^2}=\frac{t^4}{1-r^2-2rcos\phi}</math>

Here, we have <math>cos\phi=1-2sin^2\frac{\phi}{2}</math>

So, <math>T_R</math> can be simplified as follows

<math>T_R=\frac{t^4}{(1-r^2)^2+4r^2sin^2\frac{\phi}{2}}=\frac{1}{1+\frac{4r^2}{t^4}sin^2\frac{\phi}{2}}</math>

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

So, <math>T_R=\frac{1}{1+Fsin^2\frac{\phi}{2}}</math>

Since we already have the expression of transmission (T), we can also derive some important parameters:

1.Visibility

The interferometric visibility quantifies the contrast of interference in an optical system. The ratio of the amplitude of oscillations to the sum of the powers of the individual waves is defined as the visibility.

Assume <math>I_{max}</math>, <math>I_{min}</math> are the maximum intensity of the oscillations and the minimum intensity of the oscillations, <math>V</math> is the visibility of the interference pattern.

<math>V=\frac{I_{max}-I_{min}}{I_{max}+I_{min}}</math>

Suppose the intensity of incident light of etalon is <math>I</math>,the minimum transmission is <math>T_{min}</math>, the maximum transmission is <math>T_{max}</math>, we can rewrite the visibility

<math>V=I\frac{T_{max}^2-T_{min}^2}{T_{max}^2+T_{min}^2}</math>

<math>T_{min}=\frac{1}{1+0}</math>, <math>T_{max}=\frac{1}{1+F}</math>

<math>V=\frac{(1+F)^2-1}{(1+F)^2+1}</math>

This indicate the visibility of interference pattern is associated with coefficient finesse. When <math>V_{max}=1</math>, <math>F</math> is approximately equal to infinite, get the best interference pattern; when <math>V_{min}=0</math>, <math>F=0</math>, can’t observe the interference pattern.

2.Free spectral range(FSR)

The free spectral range(FSR) of a cavity, in general, is given by

<math>|\Delta \lambda_{FSR}|=\frac{2\pi}{L}|\frac{1}{\frac{\partial \beta}{\partial \lambda}}|</math>

Where <math>\beta</math> is the wavevector of the light inside the cavity,
<math>\beta=\kappa_0n(\lambda)=\frac{2\pi}{\lambda}n(\lambda)</math>. <math>\kappa_0</math> and <math>\lambda</math> are the wavevector and wavelength in vacuum, <math>n</math> is the refractive index of the cavity, <math>L</math> is the length of the cavity(for a standing-wave cavity, <math>L</math> is equal to twice the physical length of the cavity)

<math>|\frac{\partial \beta}{\partial \lambda}|=\frac{2\pi}{\lambda^2}[n(\lambda)-\lambda\frac{\partial n}{\partial \lambda}]=\frac{2\pi}{\lambda^2}n_g</math>

The FSR is <math>\Delta \lambda_{FSR}=\frac{\lambda^2}{n_gL}</math>, <math>n_g</math> is the group index of the media within the cavity.

In etalon, the FSR is <math>\Delta \lambda_{FSR}=\frac{\lambda_0^2}{2nl\cos\theta}</math>

Where <math>\lambda_0</math> is the central wavelength of the nearest transmission peak, <math>n</math> is the index of refraction of the cavity, <math>l</math> is the thickness of the cavity, <math>\theta</math> is the angle of incidence.

3. Full width at half maximum

The full width at half maximum (FWHM) is a parameter commonly used to describe the width of a "bump" on a curve or function. It is given by the distance between points on the curve at which the function reaches half its maximum value.

4.Central wavelength

Central Wavelength, used in defining bandpass filters, describes the midpoint of spectral bandwidth over which the filter transmits.

[[File:FWHM_CENTRAL WAVELENGTH.jpg]]

5.The relationship between FSR and FWHM

The FSR is related to the full-width half-maximum <math>\delta\lambda</math> of any one transmission band by a quantity known as the finesse

<math>\mathcal{F}=\frac{\Delta \lambda}{\delta \lambda}=\frac{\pi}{2\arcsin\frac{1}{\sqrt{F}}}</math>

In a word, If we want to observe more clear interference pattern, we should make <math>F</math> large, or make <math>\Delta\lambda(FSR)</math> large and <math>\delta\lambda (FWHM)</math> small.

==Building an Etalon Out of Silicon Wafer==

=Design=
[[A few photos for now.]]

=Performance=
[[File:Drawing.png|options|caption]]

==Bare Silicon Wafer==
[[File:100um-whole.png|options|Transmission spectrum of a bare silicon wafer of 100μm]]
[[File:100um-zoom.png|options|Zoom in of the spectrum, showing a free spectral range of ~2.3nm (~400GHz)]]

==HR Coated Silicon Wafer==
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). The reflective index of the coating should be as below:
[[File:result2.jpg]]

==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. 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 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 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.

[[File:temperature_shift.png|options|]]
[[File:wavelength_v_temp.png|options|]]

Main Page

2021-03-16T05:27:39Z

Jinyidu: /* A temperature-tunable etalon for optical telecommunication wavelength */

<strong>Project wiki for the Module QT5201U (Quantum control technology) - AY20/21S2</strong>

Welcome to the wiki project page. This will be the place for documenting projects. To be able to write something to this wiki, we need to create a user login manually. If you have not yet created an account, do let me know - Christian.

==Project proposals==
Here, links/short descriptions to projects should be listed.
===[[Example project]]===
This is just a dummy project.
===[[Wavemeter based on interferometer]]===
Basically we are now trying to build a wavemeter which can measure wavelength from 1200nm to 1800nm because the measurement tool for these lasers is not available now in our lab. It is based on Michelson interferometer.
===[[Coincidence Time Measurement of Pulsed Lasers & "Useful" Applications]]===
Proof-of-concept experiment to show how one may use commonly-available materials to measure difference in laser path lengths to sub-millimeter precision with a copper target (TBC). This experiment is done using a 355nm, 120 MHz, 10ps pulsed laser. Upon showing that such a measurement is possible, we shall go on to explore some for-fun applications of this "technology" and see how far and precise we can get.

===[[Saturated Absorption Spectroscopy + Frequency Modulation Locking on the D2 line of Rubidium 87]]===
With a combination of the Saturation Spectroscopy and Frequency Modulation techniques, we aim at stabilizing the wavelength of a Diode Laser at approximately 780.241 nm which corresponds to the transition <math>5S_{1/2} \rightarrow 5P_{3/2}</math> (also known as D2 line) of Rubidium 87. Additionally we will implement in the experiment a Red Pitaya, which is a minicomputer capable of replacing things like an Oscilloscope, Function Generator and PID controller. Therefore reducing the space needed for the experiment.

===[[Control over the atomic spins within certain molecules by NMR technique]]===
NMR has been the workhorse for the experimental implementation of quantum protocols, allowing exquisite control of systems up to seven qubits in size. However, there exists some experimental limitations in terms of the cross-talk, coupled evolution, instrumental errors and so on.
Thanks to the current advanced pulse techniques, we can reduce these influences and extend this technique to a new stage that the experimental limits can be neglected. In this experiment, we try to use composite pulses to compensate RF field strength variations and frequency offsets.

===[[Optical control of qubits built on quantum simulator]]===
Quantum dots or single electron transistors, allow for individual control of single charge or spin. In addition, some semiconductor monolayers possess a sizeable direct bandgap of ≈1.5–2 eV in the optical range allowing electrostatic confinement and optical manipulation of carriers. Therefore, we try to adopt the method of this theoretical paper, and see if we can control single qubit or couple 2 qubits optically.

===[[A temperature-tunable etalon for optical telecommunication wavelength]]===
This project aims to build a Fabry-perot interferometer (also called Etalon) that works at the optical telecommunication wavelengths (1260nm-1625nm). This depicted etalon is made out of a single piece of polished silicon wafer with a thickness of about 100μm. The free spectral range (FSR) of the etalon can be adjusted by changing its thickness through temperature tuning. We will also explore the possibility of applying highly reflective (HR) coatings to the silicon wafer to achieve a high cavity finesse and a narrow transmission line-width.

===[[Microwave control of superconducting cavity and qubit]]===
This project aims to perform a trial pre-experiment based on the cQED architecture including simulation, calibration, microwave control pulse programming, and so on. The 3D superconducting cavity sample is anchored to the MXC flange inside the Bluefors dilution refrigerator to reach a temperature of around 10mK. On the other hand, the generation of microwave control pulses and the acquisition of output signals are handled by a QM quantum control device, connecting the sample via the control lines and the output lines accordingly. Hence, we can realize several bosonic states via cavity driving and qubit control.

===[[Laminar Air Flow-Based Acusto-Optical Modulator]]===
'''Not an active project! Just a random idea, might be fun to try.''' As discussed during the AOM lecture, a media with a slow speed of sound is preferred for construction of AOMs. The most common material through which the speed of sound is very very slow would be air. Unfortunately, atmospheric air by itself is very chaotic and is not optimal for use in the context of an AOM. Given these considerations, is it possible for a small chamber of a laminar flow of air, modulated by some acoustic frequency, act as an effective AOM?

==Material requests==
Please add stuff we should organize one way or the other here:
* more space
* cookies...

==Stuff to be covered in the lecture slots on Mondays (sometimes Tuesdays as well)==
Feel free to add topics or aspects to this list. At the moment, this is just a copy of the tentative syllabus:

{| class="wikitable"
!Date !! Topic !! Description

|-
| 18.1.2021
|[https://youtu.be/vDIOn2SHLJE Paraxial optics, part 1]
| rowspan = "2" | Optical systems often work with Gaussian beams. We cover practical design techniques like the ABCD matrix formalism for simple optical systems.
|-
| 19.1.2021
|[https://youtu.be/yO3JcuCOVoc Paraxial optics, part 2] (only first part of lecture)
|-
| 25.1.2021||[https://youtu.be/nNU1eEOaPdY Optical cavities, part 1] || Many optical techniques require to work with optical cavities. We cover how to design them, and how to couple light into very basic devices. This lecture covered some theory basics.
|-
| 26.1.2021||[https://youtu.be/ekfhUi2JjFM Optical cavities, part 2]|| Some more aspects of optical cavities, and dielectric coatings for mirrors and such

|-
| 1.2.2021||[https://youtu.be/h2LeznCpPTk Optical fiber technology] || Some properties of optical fibers as the most common optical waveguide are covered, including optical mode spectrum, dispersion and transmission properties.

|-
| 8.2.2021||[https://youtu.be/xblN-KzMz0Y Optical modulators, part 1]
| rowspan = "2" | Many optical modulation techniques require rely on devices or materials where optical properties can be changed electrically; we cover accousto-optical and electro-optical devices, as well as liquid crystal systems.
|-
| 9.2.2021||[https://youtu.be/WfP5mahZrWU Optical modulators, part 2]

|-
| 15.2.2021
|[https://youtu.be/m_F4DOHMNeU Homodyne detection techniques] || Measurement of optical fields in many continuous variable scenarios require knowledge of optical homodyning and heterodyning techniques. These techniques, similar to their radiofrequency counterparts, rely on multiplying field amplitudes.

|-
| 1.3.2021
|[https://youtu.be/YkVlxxucLuA Frequency control of laser systems, part 1]
| rowspan="2" |Many laser systems in quantum technologies require to have a well-defined frequency relationship with atomic transitions or solid state qubits. We cover typical techniques how laser systems can be controlled to a high enough accuracy, utilizing spectroscopy techniques and control systems.
|-
| 2.3.2021
|[https://youtu.be/72aVZwI4BHU Frequency control of laser systems, part 2]

|-
| 8.3.2021
|[https://youtu.be/jolUa_EGZEs Interface to computers]
| High level interfacing between computers and electronic hardware: Standard device languages; some serial protocols, some aspects of microcontrollers and FPGAs

|-
| ||Practical aspects of superconducting systems || We cover different materials, transition temperatures, temperature measurement techniques and thermal insulation / conduction techniques.

|-
| ||Generating pulse sequences || Many quantum systems require short control pulses, either in form of optical pulses or radiofrequency pulses. We present a few techniques to generate such control pulses

|-
| ||High voltage techniques || Working with high voltages requires a spectrum of techniques that is differing from more conventional electronics. A few aspects (field emission, dielectric strength, specific components) are covered.

|}

== Getting started ==
Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* Math can be entered in LaTeX style: <code><nowiki><math>r^2=\sqrt{x^2+y^2}</math></nowiki></code> renders as <math>r^2=\sqrt{x^2+y^2}</math>
* Should you miss any module or functionality of this wiki, please contact me (Christian Kurtsiefer).

A temperature-tunable etalon for optical telecommunication wavelength

2021-03-16T05:27:24Z

Jinyidu: /* HR Coated Silicon Wafer */

====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 <math>a_1</math>, <math>a_2</math>, <math>a_3</math> are the electrical field intensity of input, oscillating, output light.
[[File:Etalon_principle.jpg]]

The relationship is as follows

<math>a_2=ta_1+r^2a_2e^{-i\phi}</math>

<math>a_3=ta_2</math>

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

<math>\phi=2kd=2\frac{2\pi}{\lambda}d</math>

From the upper two equations, we have

<math>a_2=a_1\frac{t}{1-r^2e^{-i\phi}}</math>

<math>a_3=a_1\frac{t^2}{1-r^2e^{i\phi}}</math>

Then, we can calculate the transmission ratio:

<math>T_R=|\frac{a_3}{a_1}|=|\frac{t^2}{1-r^2e^{i\phi}}|^2=\frac{t^4}{(1-r^2e^{i\phi})^2+(r^2sin\phi)^2}=\frac{t^4}{1-r^2-2rcos\phi}</math>

Here, we have <math>cos\phi=1-2sin^2\frac{\phi}{2}</math>

So, <math>T_R</math> can be simplified as follows

<math>T_R=\frac{t^4}{(1-r^2)^2+4r^2sin^2\frac{\phi}{2}}=\frac{1}{1+\frac{4r^2}{t^4}sin^2\frac{\phi}{2}}</math>

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

So, <math>T_R=\frac{1}{1+Fsin^2\frac{\phi}{2}}</math>

Since we already have the expression of transmission (T), we can also derive some important parameters:

1.Visibility

The interferometric visibility quantifies the contrast of interference in an optical system. The ratio of the amplitude of oscillations to the sum of the powers of the individual waves is defined as the visibility.

Assume <math>I_{max}</math>, <math>I_{min}</math> are the maximum intensity of the oscillations and the minimum intensity of the oscillations, <math>V</math> is the visibility of the interference pattern.

<math>V=\frac{I_{max}-I_{min}}{I_{max}+I_{min}}</math>

Suppose the intensity of incident light of etalon is <math>I</math>,the minimum transmission is <math>T_{min}</math>, the maximum transmission is <math>T_{max}</math>, we can rewrite the visibility

<math>V=I\frac{T_{max}^2-T_{min}^2}{T_{max}^2+T_{min}^2}</math>

<math>T_{min}=\frac{1}{1+0}</math>, <math>T_{max}=\frac{1}{1+F}</math>

<math>V=\frac{(1+F)^2-1}{(1+F)^2+1}</math>

This indicate the visibility of interference pattern is associated with coefficient finesse. When <math>V_{max}=1</math>, <math>F</math> is approximately equal to infinite, get the best interference pattern; when <math>V_{min}=0</math>, <math>F=0</math>, can’t observe the interference pattern.

2.Free spectral range(FSR)

The free spectral range(FSR) of a cavity, in general, is given by

<math>|\Delta \lambda_{FSR}|=\frac{2\pi}{L}|\frac{1}{\frac{\partial \beta}{\partial \lambda}}|</math>

Where <math>\beta</math> is the wavevector of the light inside the cavity,
<math>\beta=\kappa_0n(\lambda)=\frac{2\pi}{\lambda}n(\lambda)</math>. <math>\kappa_0</math> and <math>\lambda</math> are the wavevector and wavelength in vacuum, <math>n</math> is the refractive index of the cavity, <math>L</math> is the length of the cavity(for a standing-wave cavity, <math>L</math> is equal to twice the physical length of the cavity)

<math>|\frac{\partial \beta}{\partial \lambda}|=\frac{2\pi}{\lambda^2}[n(\lambda)-\lambda\frac{\partial n}{\partial \lambda}]=\frac{2\pi}{\lambda^2}n_g</math>

The FSR is <math>\Delta \lambda_{FSR}=\frac{\lambda^2}{n_gL}</math>, <math>n_g</math> is the group index of the media within the cavity.

In etalon, the FSR is <math>\Delta \lambda_{FSR}=\frac{\lambda_0^2}{2nl\cos\theta}</math>

Where <math>\lambda_0</math> is the central wavelength of the nearest transmission peak, <math>n</math> is the index of refraction of the cavity, <math>l</math> is the thickness of the cavity, <math>\theta</math> is the angle of incidence.

3. Full width at half maximum

The full width at half maximum (FWHM) is a parameter commonly used to describe the width of a "bump" on a curve or function. It is given by the distance between points on the curve at which the function reaches half its maximum value.

4.Central wavelength

Central Wavelength, used in defining bandpass filters, describes the midpoint of spectral bandwidth over which the filter transmits.

[[File:FWHM_CENTRAL WAVELENGTH.jpg]]

5.The relationship between FSR and FWHM

The FSR is related to the full-width half-maximum <math>\delta\lambda</math> of any one transmission band by a quantity known as the finesse

<math>\mathcal{F}=\frac{\Delta \lambda}{\delta \lambda}=\frac{\pi}{2\arcsin\frac{1}{\sqrt{F}}}</math>

In a word, If we want to observe more clear interference pattern, we should make <math>F</math> large, or make <math>\Delta\lambda(FSR)</math> large and <math>\delta\lambda (FWHM)</math> small.

==Building an Etalon Out of Silicon Wafer==

=Design=
[[A few photos for now.]]

=Performance=
[[File:Drawing.png|options|caption]]

==Bare Silicon Wafer==
[[File:100um-whole.png|options|Transmission spectrum of a bare silicon wafer of 100μm]]
[[File:100um-zoom.png|options|Zoom in of the spectrum, showing a free spectral range of ~2.3nm (~400GHz)]]

==HR Coated Silicon Wafer==
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). The reflective index of the coating should be as below:
[[File:result2.jpg|options|Transmission spectrum of a bare silicon wafer of 100μm]]

==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. 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 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 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.

[[File:temperature_shift.png|options|]]
[[File:wavelength_v_temp.png|options|]]

A temperature-tunable etalon for optical telecommunication wavelength

2021-03-16T05:24:51Z

Jinyidu: /* HR Coated Silicon Wafer */

====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 <math>a_1</math>, <math>a_2</math>, <math>a_3</math> are the electrical field intensity of input, oscillating, output light.
[[File:Etalon_principle.jpg]]

The relationship is as follows

<math>a_2=ta_1+r^2a_2e^{-i\phi}</math>

<math>a_3=ta_2</math>

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

<math>\phi=2kd=2\frac{2\pi}{\lambda}d</math>

From the upper two equations, we have

<math>a_2=a_1\frac{t}{1-r^2e^{-i\phi}}</math>

<math>a_3=a_1\frac{t^2}{1-r^2e^{i\phi}}</math>

Then, we can calculate the transmission ratio:

<math>T_R=|\frac{a_3}{a_1}|=|\frac{t^2}{1-r^2e^{i\phi}}|^2=\frac{t^4}{(1-r^2e^{i\phi})^2+(r^2sin\phi)^2}=\frac{t^4}{1-r^2-2rcos\phi}</math>

Here, we have <math>cos\phi=1-2sin^2\frac{\phi}{2}</math>

So, <math>T_R</math> can be simplified as follows

<math>T_R=\frac{t^4}{(1-r^2)^2+4r^2sin^2\frac{\phi}{2}}=\frac{1}{1+\frac{4r^2}{t^4}sin^2\frac{\phi}{2}}</math>

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

So, <math>T_R=\frac{1}{1+Fsin^2\frac{\phi}{2}}</math>

Since we already have the expression of transmission (T), we can also derive some important parameters:

1.Visibility

The interferometric visibility quantifies the contrast of interference in an optical system. The ratio of the amplitude of oscillations to the sum of the powers of the individual waves is defined as the visibility.

Assume <math>I_{max}</math>, <math>I_{min}</math> are the maximum intensity of the oscillations and the minimum intensity of the oscillations, <math>V</math> is the visibility of the interference pattern.

<math>V=\frac{I_{max}-I_{min}}{I_{max}+I_{min}}</math>

Suppose the intensity of incident light of etalon is <math>I</math>,the minimum transmission is <math>T_{min}</math>, the maximum transmission is <math>T_{max}</math>, we can rewrite the visibility

<math>V=I\frac{T_{max}^2-T_{min}^2}{T_{max}^2+T_{min}^2}</math>

<math>T_{min}=\frac{1}{1+0}</math>, <math>T_{max}=\frac{1}{1+F}</math>

<math>V=\frac{(1+F)^2-1}{(1+F)^2+1}</math>

This indicate the visibility of interference pattern is associated with coefficient finesse. When <math>V_{max}=1</math>, <math>F</math> is approximately equal to infinite, get the best interference pattern; when <math>V_{min}=0</math>, <math>F=0</math>, can’t observe the interference pattern.

2.Free spectral range(FSR)

The free spectral range(FSR) of a cavity, in general, is given by

<math>|\Delta \lambda_{FSR}|=\frac{2\pi}{L}|\frac{1}{\frac{\partial \beta}{\partial \lambda}}|</math>

Where <math>\beta</math> is the wavevector of the light inside the cavity,
<math>\beta=\kappa_0n(\lambda)=\frac{2\pi}{\lambda}n(\lambda)</math>. <math>\kappa_0</math> and <math>\lambda</math> are the wavevector and wavelength in vacuum, <math>n</math> is the refractive index of the cavity, <math>L</math> is the length of the cavity(for a standing-wave cavity, <math>L</math> is equal to twice the physical length of the cavity)

<math>|\frac{\partial \beta}{\partial \lambda}|=\frac{2\pi}{\lambda^2}[n(\lambda)-\lambda\frac{\partial n}{\partial \lambda}]=\frac{2\pi}{\lambda^2}n_g</math>

The FSR is <math>\Delta \lambda_{FSR}=\frac{\lambda^2}{n_gL}</math>, <math>n_g</math> is the group index of the media within the cavity.

In etalon, the FSR is <math>\Delta \lambda_{FSR}=\frac{\lambda_0^2}{2nl\cos\theta}</math>

Where <math>\lambda_0</math> is the central wavelength of the nearest transmission peak, <math>n</math> is the index of refraction of the cavity, <math>l</math> is the thickness of the cavity, <math>\theta</math> is the angle of incidence.

3. Full width at half maximum

The full width at half maximum (FWHM) is a parameter commonly used to describe the width of a "bump" on a curve or function. It is given by the distance between points on the curve at which the function reaches half its maximum value.

4.Central wavelength

Central Wavelength, used in defining bandpass filters, describes the midpoint of spectral bandwidth over which the filter transmits.

[[File:FWHM_CENTRAL WAVELENGTH.jpg]]

5.The relationship between FSR and FWHM

The FSR is related to the full-width half-maximum <math>\delta\lambda</math> of any one transmission band by a quantity known as the finesse

<math>\mathcal{F}=\frac{\Delta \lambda}{\delta \lambda}=\frac{\pi}{2\arcsin\frac{1}{\sqrt{F}}}</math>

In a word, If we want to observe more clear interference pattern, we should make <math>F</math> large, or make <math>\Delta\lambda(FSR)</math> large and <math>\delta\lambda (FWHM)</math> small.

==Building an Etalon Out of Silicon Wafer==

=Design=
[[A few photos for now.]]

=Performance=
[[File:Drawing.png|options|caption]]

==Bare Silicon Wafer==
[[File:100um-whole.png|options|Transmission spectrum of a bare silicon wafer of 100μm]]
[[File:100um-zoom.png|options|Zoom in of the spectrum, showing a free spectral range of ~2.3nm (~400GHz)]]

==HR Coated Silicon Wafer==
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). The reflective index of the coating should be as below:

==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. 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 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 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.

[[File:temperature_shift.png|options|]]
[[File:wavelength_v_temp.png|options|]]

File:Result2.jpg

2021-03-16T05:14:01Z

Jinyidu:

A temperature-tunable etalon for optical telecommunication wavelength

2021-03-10T06:47:26Z