Near-infrared optical frequency comb Vernier spectroscopy in air and in a flame

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Near-infrared optical frequency comb Vernier spectroscopy

in air and in a flame

Maryam Fakhri

Department of Physics University of Umeå

This thesis is submitted for the degree of Master of Science in physics

Supervisor: Alexandra Johansson

March 2017

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I would like to dedicate this thesis to my love, Anders . . .

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Declaration

I hereby declare that except where specific reference is made to the work of others, the contents of this dissertation are original and have not been submitted in whole or in part for consideration for any other degree or qualification in this, or any other university. This thesis is my own work and contains nothing which is the outcome of work done in collaboration with others, except as specified in the text and Acknowledgments. This thesis contains 9,109 words including headers and captions and it has 15 equations and 26 figures.

Maryam Fakhri

March 2017

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Acknowledgements

First and foremost, I would like to express my sincere gratitude to my supervisor Alexandra Johansson for her patience and motivation during this project. Her guidance helped me in all the time of doing and writing this thesis. She was always very fast to answer my questions whenever I ran into her room or send email. I could not wish for a better or friendlier supervisor.

My sincere thanks also goes to Aleksandra Foltynowicz-Matyba the head of Optical Fre- quency Comb Spectroscopy Group. Firstly, her teaching style made a strong impression on me to know more about this field. I have always carried positive memories of her lectures with me. Secondly, she provided me an opportunity to join her group and learn more.

Besides, I would like to thank other members of Optical Frequency Comb Spectroscopy Group: Amir Khodabakhsh and Lucile Rutkowski. I am thankful for your aspiring guidance and advise I received for my lab related issues, and of course your friendship.

I also take this opportunity to express my sincere thanks to Umeå university for provid- ing me the opportunity to continue my study after years by granting the scholarship. I am extremely thankful and indebted and I wish I can do the same in the future for another person.

I also wish to express gratitude to all of the physics department members for their help and support during these five month. I have many, many people to thank for but I can not bring all the names. Michael Bradley, thank you for your care and attention and listening to me when I experienced hard moments to overcome obstacles I have been facing during this thesis. Alagappan Annamalai, Eduardo Gracia, Narges Mortezaei, Nicolas Boulanger:

thanks for memorable an fun times that I had with you around the round lunch table with

infinite seats. I would also like to thank Tiva Sharifi, who opened her heart to me when I first

arrived in Umeå. How can I give back a little of the kindness and hospitality I received from

you since the first meet! Thanks for everything.

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viii

To all my friends in umeå: Azadeh, Farahnaz, Sherry, Zohre, Mehdi, Ramin, Sebastian, Khanh, Menglin and Wenqing. Thank you for your friendship, encouragement, help and understanding in my many moment of crisis. You are always in my mind.

Massive credits goes to my parents Azam and Mohammad for giving birth to me at the first place and their continuous encouragement throughout my study and my life in general.

Thank you so much. I would also like to thank my dear Sisters: Akram, you are always my best role model in my life, and lighten my way with your guidance. Mitra, Mehri and Vida, my wholehearted thanks to you for being always there when I need your help. I would also like to say thank to Emelie, whom I consider my best friend-sister. Thank you for your precious existence and all the positive wave I receive from you.

Most importantly, none of this could have happened without unconditional love, encourage-

ment and support which I received since I started the course of this thesis from my loved

ones, Anders. Thank you älskling, I would be grateful forever for your love.

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Abstract

A Vernier spectrometer is built with a near-infrared mode-locked Er:doped fiber laser, a

Fabry-Perot cavity with finesse of 1000, a diffraction grating and a photo detector. The optical

cavity provides high sensitivity in absorption detection by enhancing the interaction length

of the light with molecular species contained in the cavity. Coupling an optical frequency

comb to the cavity provided a broadband spectral bandwidth with high precision to measure

the absorption of several molecular species simultaneously. Also, by using the optical cavity

as a filter, transmission of some bunch comb lines was achieved. This comb filtering together

with a simple grating and a photodiode formed the Vernier detection technique to provide

very fast measurements while it kept the setup very simple and compact. The system allows

to detect carbon dioxide in the air and water vapor and OH radicals in the flame in a spectrum

spanning from 1550 nm to 1590 nm, approximately. The retrieved spectrum has a resolution

of 9.3 GHz being acquired in 0.05 s.

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List of figures

2.1 Direct absorption spectroscopy . . . . 5

2.2 Fabry-Perot cavity . . . . 7

2.3 Cavity modes . . . . 8

2.4 Change in the optical length of the cavity . . . . 8

2.5 A comb of light . . . . 10

2.6 Alignment and mode-matching condition of OFC to optical cavity . . . . . 11

2.7 Perfect matching condition . . . . 12

2.8 Comb filtering with Vernier technique . . . . 14

3.1 Experimental setup . . . . 17

3.2 Spectral profile of the Er:fiber laser . . . . 18

3.3 Simulated CO 2 absorption spectra based on HITRAN database by MATLAB code . . . . 20

4.1 General view of four Vernier order in air . . . . 23

4.2 CO 2 absorption detection . . . . 24

4.3 General view of four Vernier order with the flame in HAB 2 mm . . . . 24

4.4 Water and OH radical absorption lines in the flame at HAB of 2 mm . . . . 25

4.5 Air and flame absorption spectrum comparison . . . . 26

4.6 Four shot to shot air and flame absorption spectrum comparison . . . . 26

4.7 Labeling water absorption lines . . . . 27

4.8 Labeling OH absorption lines . . . . 28

A.1 Setup photo . . . . 33

A.2 Burner photo . . . . 34

B.1 Simulation of water and OH concentration and flame temperature as a func- tion of HAB . . . . 35

B.2 Normalized cavity transmission at different HABs . . . . 36

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xiv List of figures

B.3 Magnification of Normalized cavity transmission at different HABs . . . . 36 B.4 Magnification of normalized cavity transmission to identify water absorption

lines . . . . 37 B.5 Magnification of normalized cavity transmission to identify OH absorption

lines . . . . 37

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Nomenclature

Symbols

a(ν) Absorption coefficient c Speed of light

d Laser cavity length

∆ν c Full width at half maximum of the cavity mode

∆φ Carrier-envelope phase shift in two subsequent pulse

F Finesse

f ₀ Offset frequency of the comb laser f _rep Laser repetition rate

Γ _v Full width at half maximum of Vernier order I ₀ Intensity of the incident light

I _A Intensity of the transmitted light through the sample k Integer and k>1

L Optical cavity length

l The length of the gas sample

L ^′ Length of the cavity after adding molecular species with refractive index n’

l ^′ Length of the added molecular species with refractive index n’

N Density of the gas sample

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xvi Nomenclature

n Index of refraction

n ^′ Refractive index of added molecular species to the open air cavity ν _q Frequency of the optical cavity modes

q Integer

R ₁ Reflection coefficient of the cavity front mirror R ₂ Reflection coefficient of the cavity back mirror σ (ν ) Absorption cross section

τ Laser cavity round trip time Acronyms / Abbreviations

AS Absorption spectroscopy

CE − OFCS Cavity enhanced optical frequency comb spectroscopy CW Continuous wave

DAS Direct absorption spectroscopy EM Electromagnetic

FSR Free Spectral Range

FT S Fourier transform spectrometer FW HM Full width half maximum HAB Heigth above the burner OFC Optical Frequency Comb OPL Optical path length PD Photo detector PM Perfect match

PZT Piezoelectric Transducer

T DLAS Tunable diode laser absorption spectroscopy

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Nomenclature xvii

T S Translation stage

CE − OFCS Virtually-imaged phased array

V O Vernier Order

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Chapter 1 Introduction

Laser based spectroscopy is a non-invasive and fast tool which can be used for selective detection of molecular species, since all molecular species have a particular absorption line in specific wavelength region (molecule’s fingerprint). This technique, which works based on continuous wave lasers (CW-lasers), is widely used in industry and environmental monitoring but it is limited by the working range of the laser. CW-lasers only emit light with one frequency, therefore to detect particular transition, one needs to tune this frequency to that transition. In this way, one laser can detect only one particular species. But when multispecies detection is required, having a broadband laser source would be very desirable.

Optical frequency comb (OFC), which is produced by a femtosecond mode-locked laser, is a solution to this problem. OFC emits very broad spectrum consisting of thousands of discrete frequencies working as thousands of synchronized CW-lasers. In this way, detec- tion of several molecular species is possible simultaneously which solves the problem of time-consuming process of frequency scanning in laser absorption spectroscopy based on CW-lasers. If this broadband laser source is coupled into an optical cavity containing the molecular species under study, the interaction length of the light with the sample would also be increased according to Lambert-Beer law. The result which have a high sensitivity in detection of absorption is called cavity enhanced optical frequency comb spectroscopy (CE-OFCS) [1].

The broadband and precise spectrum being obtained by CE-OFCS needs to be detected

with a broadband detection method covering the entire spectrum to allow analyzing its

information quickly. There are several broadband detection techniques which are used in

different areas like air quality control, human breath analysis, production process monitoring

and biologically hazardous material detection [2]. The initial technique uses a photodetector

array to acquire data from a dispersing grating placed after the optical cavity [3]. This

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2 Introduction

technique is fast and reliable since it uses the advantage of swept coupling scheme to solve FM-to-AM noise conversion which is the result of using the optical cavity. Also it even reaches shot-noise limitation by employing a higher finesse cavity and active feedback to the cavity length [4][5]. But there was two disadvantages in this technique. First, the transmitted power was reduced due to the swept coupling scheme and tight coupling was not applicable also, since it causes amplitude noise. Second, there was limitation in spectral resolution due to the grating [1]

By applying another detection technique which reads the cavity ringdown signals, FM- to-Am noise was decreased significantly without any coupling techniques. But data was acquired by a two dimensional detector array that its horizontal axis corresponds to wave- length being provided by a dispersing grating placed after the cavity [6]. Therefore, the spectral resolution was again limited by the grating. To address this issue, virtually-imaged phased array (VIPA) based spectroscopy came to the picture [7]. The resolution of 1 GHz was achieved with this technique [1]. Fourier transform spectrometer (FTS) is another technique which works based on Michelson interferometer [8] or dual comb spectroscopy [9][10] and allows doing measurement in the spectral range that is not covered by VIPA [11]. Vernier technique which is very compact, robust and even faster than FTS in the last method [12]. In this technique the optical cavity is used for filtering some of the comb lines and transmitting groups of other combs, named Vernier orders (VO), with equal pe- riodicity. These VOs, which are different in resolution, scan the entire OFC spectrum and after being physically separated by a grating, will be monitored selectively on a photodetector.

The aim of this thesis was to built a Vernier spectrometer based on a CE-OFCS in near- infrared region to do measurement in two environments, air and flame. By comparing the stability and quality of the acquired spectra in the flame, which is sort of turbulent environ- ment, with that of in air, the performance of this detection technique was evaluated.

This thesis consists of four main parts: Theory (chapter 2), experimental setup and pro- cedure (chapter 3), result and discussion (chapter 4) and summary and conclusion (chapter 5). In theory part, first laser absorption spectroscopy is introduced and then the theory of the optical cavity and optical frequency comb (OFC) are treated. After that, coupling the OFC into the optical cavity and Vernier spectroscopy technique are explained. This section is ended with a short introductory of the methane combustion products as the target sample.

In experimental setup and procedure part, the instrument being used in the setup as well as

experimental work are explained. In result and discussion part, the results being obtained by

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3 experimental work are presented. In summary and conclusion part, the content of the whole

report is summarized. There are also two additional sections at the end of this thesis which

contain photos of the setup (Appendix A) and literature result for the same sample target

acquired with FTS (Appendix B).

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Chapter 2 Theory

2.1 Absorption spectroscopy

Spectroscopy is a technique that relies on the interaction of electromagnetic radiation (EM- radiation) with matter. When the amount of EM-radiation being absorbed by the molecules of a sample is studied, then this analysis would be classified as absorption spectroscopy (AS)[13].

2.1.1 Laser absorption spectroscopy

When a laser beam is used to provide EM-radiation in AS, the technique is called laser ab- sorption spectroscopy. The simplest kind of laser based AS is direct absorption spectroscopy (DAS). It is based on sending a continuous wave laser (CW-laser) beam directly into the sample with length of l and then measuring the intensity of transmitted light (Fig. 2.1).

Fig. 2.1 Schematic of direct absorption spectroscopy. The intensity of the laser light, I ₀ , will be decreased to I _A after passing a sample with absorption coefficient, a(ν) and length, l.

This technique, which is mostly used for absorption measurement of the gaseous samples,

has a number of advantages. The most important one is that it is non-invasive, meaning

that it does not have destructive effect on the sample. Secondly, it is quantitative, since

the intensities of incident light, I 0 and transmitted light, I _A are related to each other by

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6 Theory

Lambert-Beer law [13]:

I _A = I ₀ exp[−a(ν)l], (2.1)

where a(ν) is absorption coefficient, being determined by equation [14]:

a (ν) = Nσ (ν), (2.2)

where N is the density of the absorbers and σ (ν) is the absorption cross section. In this way, knowing the length of the gas sample and measuring the intensities I ₀ and I _A , the density of the gas can quantitatively be determined if the absorption cross section is known. Finally, since individual molecular species have their unique set of allowed transitions and spectrum, they can be identified and labeled by knowing the frequency at which the light is absorbed during the measurement [13]

Tunable diode laser absorption spectroscopy (TDLAS) is kind of DAS which has been widely used in industry and environmental monitoring for many years [15], but there are some problems that limit its application. One of them is that it is not sensitive enough to detect very small absorption since its sensitivity is limited by the poor signal to noise ratio being the result of measuring the small absorption signal on top of a large background. To address this issue, one can stabilize the intensity of the light propagating through the sample and reduce the noise in the system. In this way, the only changes in the intensity come from the fact that the light is being absorbed. Also, one can increase the absorption signal, by increasing the interaction length of light passing through the sample [13].

Another issue is that this technique is based on CW-lasers, which are limited in frequency to

their tuning range. Therefore, it cannot be used for broadband detection of entire absorption

bands and is also usually limited to single molecular species detection. To address this issue,

an optical frequency comb (OFC), which emits very broad spectrum containing a series of

discrete frequencies, came into the picture [2].

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2.2 Optical Cavity 7

2.2 Optical Cavity

2.2.1 Cavity enhancement

If the laser beam enters an external cavity, then the light will travel back and forth several times between mirrors of the cavity in spatially overlapping beam path, creating very huge intensity comparing to the intensity of the incident laser beam and interacting with molecules inside the cavity in a longer distance. Therefore, very small absorption can be measured which would not be possible to be detected without this external cavity [16]. The most common type of enhancement cavities is the linear Fabry-Perot cavity, which is shown in figure 2.2.

Fig. 2.2 Fabry-Perot cavity with two curved mirrors having a wedge to avoid constructive interference of back reflection

2.2.2 Modes of the cavity

Besides the fact that the external cavity enhances the sensitivity of the absorption spec- troscopy technique by increasing the interaction length, it also allows for particular resonance frequencies. These frequencies of the transmitted light would be achieved when standing wave forms inside the cavity. This will be done by adjusting the physical parameters of the cavity, like the length [16]. These transmission frequencies, which are known as cavity modes, can be determined as:

ν _q = q c

2nL , (2.3)

where c is speed of light, n is index of refraction, L is length of the cavity and q is an integer.

These modes are equally spaced and the cavity mode separation, being known as free spectral range (FSR) (Fig. 2.3), can be calculated as:

FSR _c = c

2nL . (2.4)

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8 Theory

There is another important parameter in all cavities which determines their enhancement factor [16]. This entity is called finesse, F, and is determined by [13]:

F = FSR _c

∆ν c

= π

⁴

√ R ₁ R ₂ (1 − √

R ₁ R ₂ ) , (2.5)

where ∆ν _c is full width at half maximum (FWHM) of the cavity modes (Fig. 2.3) and R ₁ and R ₂ are reflection coefficients of the front and back mirrors of the optical cavity, respectively.

Fig. 2.3 Cavity modes with width ∆ν c and their equal mode spacing FSR _c

2.2.3 Cavity modes fluctuation

The frequencies of the cavity will be changed by any change in the length of the cavity or refractive index, n, according to equation 2.3. Beside manual adjustment of the cavity length, its length can also be changed with adding heat to the system which is known as thermal drift. This thermal drift have to be compensated, otherwise there would be lots of fluctuation in the modes of the cavity by time.

Besides, optical path length (OPL) of the cavity will also be changed by any change in the refractive index, since:

OPL = Ln (2.6)

Figure 2.4 describes the situation that the OPL is changed by adding another molecular species with refractive index, n ^′ in length l ^′ to the system.

Fig. 2.4 Change in the optical length of the cavity due to refractive index alteration

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2.3 Optical frequency comb 9

Under these circumstances, the new OPL of the cavity can easily be determined as:

(OPL) ^′ = (L − l ^′ )n + l ^′ n ^′ (2.7)

In this way, if l ^′ and n ^′ fluctuate by rapid changes of temperature or pressure in the system, OPL would also fluctuate and unstable mode of the cavity would be observed [14].

2.3 Optical frequency comb

A mode locked laser can create very short and regular pulses of light which are separated by the laser cavity round trip time τ. This regular time separation is usually in the scale of nanoseconds and is given by the cavity round trip as:

τ = 2d

c , (2.8)

where d is length of the laser cavity. These narrow pulses, which have a duration in the order of femtoseconds, consist of a series of wave crest and troughs with different amplitudes.

These crest and troughs, which are known as carrier wave, all travel together while they are centered at the carrier frequency. The outer line that covers all these rise and fall of the carrier wave is called its envelope (Fig. 2.5-a).

Because of the interference of this train of pulses, the spectrum of the laser in frequency domain is very broad and contains thousands of narrow laser lines. They are equally spaced in the entire spectrum and the mode separation is called repetition rate of the laser being inversely proportional to the time separation of pulses:

f _rep = 1

τ . (2.9)

If one plots this broad spectrum, it looks like the teeth of a hair comb, therefore it is known as optical frequency comb (OFC) (Fig. 2.5-b).

As also can be seen in Fig. 2.5-b, the comb lines have offset from the zero frequency. This is

due to the fact that the group and phase velocities of the pulse propagating in the laser cavity

are different.Therefore, they are evolving inside the laser cavity all the time and stop evolving

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10 Theory

Fig. 2.5 Time and frequency domain of an OFC. (a) The time domain represen- tation of an OFC, shows train of pulses with separation of τ and phase shift of ∆φ between carrier and envelope in two subsequent pulses. (b) The frequency domain representation of an OFC, shows the mode separation of f _rep and offset frequency of f ₀ . Equally spaced dashed lines represent comb teeth in the absence of f ₀ .

when the pulse leaks out of the laser. In this way, if the crest of the carrier is coincided with the peak of pulse envelope in one transmitted pulse, the carrier will have a phase shift of ∆φ in the subsequent transmitted pulse with respect to its envelope (Fig. 2.5-a) [17]. Therefore, to determine the optical frequency of mth mode of the comb (ν _m ), one needs to measure both

f ₀ and f _rep :

ν _m = f ₀ + m f _rep , (2.10)

where m is a large integer and f ₀ is the frequency offset of the comb laser, given by [18]:

f ₀ = ∆φ · f rep

2π . (2.11)

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2.4 Coupling the laser comb to the optical cavity 11

If OFC couples properly to the optical cavity, the entire absorption spectrum can be measured with high sensitivity [2].

2.4 Coupling the laser comb to the optical cavity

Employing a high finesse cavity in absorption spectroscopy enhances the interaction length of the laser light with the molecular species under study. Coupling an OFC into this cavity, allows for very precise and broadband measurement of the optical losses, since each fre- quency of the comb measures a point of the broad absorption spectrum independently. Also, the amount of absorption of several molecular species can be measured simultaneously.[18]

To couple the OFC to the optical cavity, the modes of OFC should be matched to the longitudinal modes of the cavity. For this to be achieved, first of all the input Gaussian laser beam should be completely aligned and mode-matched with Gaussian electric field propagating inside the cavity. For perfect alignment, the axis of input Gaussian beam should completely coincide with the axis of Gaussian electric field inside the cavity. Cavity axis is defined as the line that connected the center of the curvature of cavity mirrors. If there would be a transverse displacement (Fig. 2.6-a) or rotation (Fig. 2.6-b) between input axis and cavity axis, then the OFC will couple with cavity modes of higher order. For having proper mode-matching, the waist positions and waist sizes of the input Gaussian beam and the Gaussian electric field of the cavity should exactly be the same. In case of difference between the waist sizes (Fig. 2.6-c) or waist positions (Fig. 2.6-d), coupling to the first and second higher order modes of the cavity will be occurred [19]. This would be achieved with placing optical lenses with appropriate focal lens and position in the way of comb beam to the optical cavity.

Fig. 2.6 Possible misalignments of the OFC and the optical cavity (drawing similar to [19])

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12 Theory

Another condition to couple the OFC to the optical cavity is that FSR _c should be matched to f _rep of the comb laser. According to equation 2.4, this can be achieved by precise adjustment of cavity length. But in reality it is not easy to adjust the cavity length with enough precision as it is calculated with equations 2.4 (under condition FSR _c = f _rep ) [14]. In order to adjust the length of the cavity to have a perfect coupling of the cavity modes and laser combs, one needs to sweep the cavity length slightly while detecting the transmitted light through the cavity. One way for this to be achieved is by using a piezoelectric transducer (PZT) . PZTs are piece of polarized material, usually made of quartz, whose physical length can be changed by applying a voltage. In this way, if a PZT is mounted to one of the cavity mirrors, the length of the cavity would be modulated by applying a sine wave with amplitude V to the PZT. The correct length of the cavity would be find at one point of the sweep [18].

Sweeping the cavity length with the PZT allows coupling of OFC modes into the lon- gitudinal modes of the optical cavity for a very short time when the FSR _c is equal to f _rep . Therefore, transmitted light would have a sharp peak with highest intensity when all the OFC modes satisfy the resonance condition of the optical cavity at the correct length of the cavity (Peak ’a’ in Fig. 2.7) and would develop some other set of wide peaks with less intensity when the length of the cavity is changed again (Peaks ’b’ and ’c’ in Fig. 2.7). These wide peaks with less intensity will also be monitored beside of the highest peak on the detector when the sweeping rate is very fast. If f ₀ was adjusted correctly, every two side peaks with the same width and height should have the same distance from the middle peak with highest intensity. This coupling is known as perfect match (PM) [18].

Fig. 2.7 Transmitted light through the optical

cavity being monitored on the detector while

scanning the cavity length. Peak (a), perfect

matching of OFC to the optical cavity when

FSR= f _rep at correct length of the cavity. Peaks

(b) and (c), deviation from perfect matching

when FSR> f _rep .

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2.5 Vernier spectroscopy technique 13

2.5 Vernier spectroscopy technique

The transmitted light from the optical cavity contains absorption spectrum of the molecular species which are under study in the optical cavity. This spectrum should be recorded in order to be used for further studies. For some application, a fast, broadband, compact and robust detection system is desirable. Here, one can use the optical cavity as a tool to filter some of the comb lines as well as enhancing the interaction length. In this way, only some of the comb lines will be resonant with cavity modes and be transmitted through the cavity.

It allows for the measurement of the entire broadband absorption spectrum, using a simple dispersion grating and a detector. This detection technique is called Vernier spectroscopy[12].

To filter the comb lines, they should be mismatched with respect to the optical cavity modes. Figure (2.8-a, peak I) shows the intensity of transmitted light through the cavity in PM condition. As can be seen in the schematic of the mentioned peak in the right hand side of the figure, all the cavity and comb modes are precisely matched as Nth comb line is coincided at the peak of Mth cavity mode and it is the same for all the comb and cavity modes. But by either changing f _rep or FSR _c , comb lines will gradually walk away from the corresponding cavity mode peaks. Since ∆ν _c is much larger than linewidth of oFC teeth comb, still some portion of each comb teeth resonates with corresponding cavity mode and will be transmitted through the cavity. But the sum of these intensities which comes out from the cavity as Peak II (2.8-a), will be lower than that of in PM condition. With the same reasoning, the transmitted peak is wider. This peak is illustrated schematically in the right hand side of the figure again. As can be seen, after a large spectral gap, Nth comb line will be matched with (M-1)th cavity mode peak again and be transmitted at maximum intensity [12].

If increasing the FSR _c would be the case, it would be achieved by decreasing of the cavity

length, according to equation 2.4. For ∆L = −λ _c (λ _c , center frequency of the comb laser)

(Fig. 2.8-b), every Nth comb line will be matched with every (M-1)th cavity modes and be

transmitted completely. But there are also some comb teeth that will be transmitted partially

and some others which will be filtered totally. Therefore, the transmitted light through

the cavity consists of groups of partially transmitted comb lines which are centered on a

completely transmitted comb tooth with a fixed periodicity. The filtered combs are the source

of this periodicity and equal separation between these groups. Each group of transmitted

comb lines is called a Vernier order (VO) and their spacing is known as Vernier FSR (FSR _v ),

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14 Theory

Fig. 2.8 Mismatching comb lines and cavity modes from PM (peak I). By changing the length of the cavity by ∆L, higher Vernier orders will appear. For ∆L= −λ c and ∆L = −2λ c , first (k=-1, Peak II) and second (k=-2, Peak III) Vernier orders will appear, respectively.

being determined as [12]:

FSR _v = c

∆L . (2.12)

By changing ∆L by kλ _c (k is an integer and determines the number of VO), the number of partially transmitted comb lines in each VOs would be decreased and therefore the VO width would be narrower and FSR _v would be decreased. In this way, equation 2.12 can be rewritten as [12]:

FSR _v = c

kλ _c . (2.13)

The width of the VO, Γ _v , determines its resolution which can be calculated as [12]:

Γ v = 1 F · c

∆L . (2.14)

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2.6 Methane combustion products as target sample 15

Although better resolution of measurement would be achieved by making Γ _v as narrow as possible, less intensity of the transmitted light and less sensitivity in detection of small absorption would also be unavoidable. Therefore, there would be always a limitation for having better resolution [12].

For any Vernier resolution, by dividing the width of the entire OFC to FSR _v , the num- ber of transmitted VOs can be calculated. In order to acquire data from each VO individually, they need to be separated in space. It can be achieved by a diffraction grating. In this way, each transmitted VO can be projected on the detector surface in turn by tilting the grating [12].

2.6 Methane combustion products as target sample

Measurement of the combustion product is essential to improve the quality of combustion [20]. Since the measurement should be done close to the burning fuel, which is counted as turbulent and unstable environment, a fast and calibration free technique with high precision and limited optical component would be desirable. In this way, Vernier detection technique would be one of the best options.

Combustion would have the best quality when all the fuel is burnt in oxygen and pro- duces specific products. This is known as a complete combustion which has a chemical equation as 2.15 for combustion of methane as a fuel in air [21]:

CH ₄ + 2(O ₂ + 3.76 N ₂ ) −→ CO ₂ + 2 H ₂ O + 7.52 N ₂ (2.15) As can be seen, carbon dioxide and water vapor are the products of the complete reaction.

When both sides of the reaction are balanced, then the air/methane ratio 2:1 coming out from the reaction would be considered as the ratio at which the complete combustion happens.

This ratio is called stoichiometric air/fuel ratio [21]. But since 21% oxygen is contained in the air, then to have a stoichiometric air/methane, one liter of methane should be mixed with 10.5 liter of air.

Besides the main products of the complete combustion, a great variety of intermediate

products will also be formed in combustion of methane. OH radical is one of these intermedi-

ate products which is short-lived but very reactive [22]. It is also detectable in near infrared

region while it has a huge overlap with water absorption lines as the main product. However,

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16 Theory

the amount of this side product, OH, is not constant and changes with the temperature while

water concentration as a main product is constant and does not change in measurements in

different height above the combustion process [23] (see Appendix B, Fig. B.1).

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Chapter 3 Experimental setup and procedure

3.1 Experimental setup

A schematic of the experimental setup is shown in Fig 3.1.

Fig. 3.1 Setup with comb laser beam which is coupled to an optical cavity with curved mirrors by using 3

flat mirrors M _1,2,3 and 2 mode-matching lenses f _1,2 . The length of the cavity is adjustable by a PZT which is

mounted under a horizontal translation stage of the cavity front mirror. The transmitted light from the cavity

is diffracted by a grating after being reflected by mirror M ₄ . The diffracted light is focused by lens f ₃ to a

photo detector which is connected to a PC. Photos of the setup can be seen in Appendix A, Fig. A.1 and A.2

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18 Experimental setup and procedure

The setup consists of a mode-locked Er:fiber laser with repetition rate of 250 MHz and power of 20 mW which provides 100 nm spectrum from 1.5 to 1.6 µm with 12000 GHz width (Fig.

3.2)

Wavelength [nm]

1500 1520 1540 1560 1580 1600 1620

Amplitude

0 100 200 300 400 500 600 700

Fig. 3.2 Spectral profile of the optical Er:fiber laser spectrum radiation spanning from 1500 to 1600 nm, acquired with Fourier transform spectroscopy technique.

This broad spectrum was sent via a polarization maintaining fiber to an open-air optical cavity with finesse of 1000. Input mirror of the cavity was attached to a PZT and mounted on a horizontal translation stage (TS) in order to make the adjustment of the cavity length possible with precision of 0.01 mm. The cavity contains a premixed methane/air flame which has a diameter of 3.8 mm and operates at a stoichiometric ratio of one with flow rates of 0.95 and 9.05 l/min for methane and air respectively. The flame was mounted inside the cavity between the mirrors on a vertical TS. This vertical TS makes position adjustment of the burner possible for different height above the burner (HAB) with precision of 0.01 mm.

Three adjusting flat mirrors (M _1,2.3 ), two optical lenses (f _1,2 ) with focal lengths of 35 mm and

50 mm, respectively and 2 irises (Iris _1,2 ) were used to couple the comb laser to the optical

cavity. The transmitted light from the optical cavity is sent to a diffraction grating with

600 grooves/mm after being reflected by flat mirror, M ₄ . The grating has a relatively sharp

efficiency peak to diffract the light with wavelength of 1600 nm. One part of the diffracted

light, corresponding to one Vernier order, is selected by an iris (Iris ₃ ) to be sent to a photo

detector (PD) after passing a lens with focal length of 25.4 mm (f ₃ ). The signal of the PD is

acquired using a computer with a LabView program.

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3.2 Experimental procedure 19

3.2 Experimental procedure

3.2.1 Creating a cavity with high finesse

For creating a cavity with finesse of 1000, two concave mirrors (M _5,6 ) with radius of curvature of 5 m and reflectivity of 99.70 ± 0.10% in the wavelength range of the laser comb were employed. Appropriate reflectivity of mirrors was calculated according to the equation 2.5 for the required finesse. Also, the mirrors have a wedge of 3.0 ± 0.1 ^◦ to prevent creating fringes on the spectrum which are a result of constructive interference of back reflection.

Using PM condition and equation 2.4, the length of 60 cm was calculated for the cavity.

3.2.2 Coupling the OFC into the cavity

For coupling the OFC into the cavity, alignment and mode-matching of the comb laser to the optical cavity as well as cavity length adjustment were required. Mode-matching calculation to find the appropriate lenses in the correct position were done before for the same comb laser and an optical cavity with the same length and radius of the curvature of the mirrors but different finesse in [20]. Changing the cavity mirrors in the existing setup, required realignment of the input and cavity axes. To correct the possible transverse displacement and rotation of the two axes, mirrors M ₂ and M ₃ together with cavity mirrors were tilted in order to overlap the reflected beam to the incident beam path all the way. This was controlled and adjusted with the help of a mobile pin hole. The amplitude of the sine wave applied to the PZT was also changed till the transmitted light from the cavity had a sharp peak at PM on the PD.

3.2.3 Demonstration of Vernier technique for measurement in air

In this stage, first a MATLAB code was use to estimate the percentage of absorption of carbon dioxide contained in the ambient air (400 ppm). The MATLAB code which works based on the HITRAN database [24], estimated the detection of 3% absorption of carbon dioxide for cavity with finesse of 1000 (Fig. 3.3). As can be seen in the figure, strongest absorption should be detected at wavelength 1573 nm and 1578 nm corresponding to wave number 6357 and 6337 cm ⁻¹ .

In order to demonstrate the Vernier detection technique with appropriate resolution to detect

these small absorption lines, the PM condition was intentionally mismatched by changing

the length of the cavity, and FSR c consequently, by ∆L. This was done by moving the front

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20 Experimental setup and procedure

1565 1570 1575 1580 1585 1590

Wavelength [nm]

0.97 0.975 0.98 0.985 0.99 0.995 1

Cavity transmission [%]

Fig. 3.3 Simulated CO ₂ absorption spectrum spanning from 1565 to 1590 nm. It is calculated using HITRAN database [24] at experimental conditions (finesse 1000, OFC spectrum spanning from 1.5 to 1.6 nm and 400 ppm CO ₂ in ambient air) with MATLAB code.

cavity mirror with the TS. Using PM condition and reading f _rep of the laser, the length of 59.96 cm were calculated for the cavity by using equation 2.4. By decreasing this length by

∆L = -30 µ m, carbon dioxide absorption lines were monitored with resolution of 9.3 GHz according to the equation 2.14. This resolution corresponds to VO of k= -21 which gives Vernier mode separation of 9300 GHz according equation 2.13. In this way, one full VO is within the whole absorption spectrum because the number of VOs was calculated as 1.29. By tilting the grating, this VO would scan OFC spectrum and a spectrum profile similar to Fig.

3.2 would appear on the PD. Since strong absorption lines of carbon dioxide were predicted to be seen at wavelength about 1573 nm and 1578 nm using the MATLAB code model, the grating was adjusted in a way that the VO only projected data from the above mentioned region to the PD. The part of other VO was blocked by an iris after being diffracted by the grating.

But there was an issue in this stage: Although the grating was fixed, the cavity length

was dithered by the PZT and consequently the cavity modes were changing. Therefore, the

physical position of the chosen VO was changing. In order to collect and send all the light

from the selected VO to the PD, a collecting lens was used after the iris. But this movement in

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3.2 Experimental procedure 21

physical position happens for other VOs too, so it seemed that many VOs were sweeping over comb modes. Therefore, projection of other VOs close to the selected VO was unavoidable.

In this way, four VOs were monitored on the PD and data was recorded while the length of the cavity was scanned by voltage V applied to PZT. By choosing the record length of 100k points in LabView program and taking 2M sample/time, almost 15 nm of the spectrum was recorded in 0.05 s. A trigger control was also used to stabilize the repetitive data and make them look static.

3.2.4 Employing the demonstrated Vernier technique in a turbulent environment

In order to compare the performance of this detection technique in a turbulent environment,

this procedure was repeated with the flame on, in the open air cavity. Two flow controllers

were used to keep the flow rates of methane and air at 0.95 and 9.05 l/min, respectively

during the measurement. Therefore, only the main products of the combustion, like carbon

dioxide and water, and some short-lived radicals, like OH, existed in the cavity. The burner

body was cooled with flow of water. Nitrogen flow was also used to isolate the flame from

the ambient and to stabilize it. Since for HAB greater than 2 mm, homogeneous close

to adiabatic condition is expected [23], HABs 2 mm and 5 mm were selected to acquire

data. The different behavior of water and OH, in terms of concentration change with HAB,

was the motivation to do measurement in the above mentioned HABs (see Appendix B,

Fig.B.1). Strong absorption lines of water vapor and OH were monitored in the same spectral

window as in measurements in air while the length of the cavity was scanned by PZT. Data

were acquired with the same adjustment of Labview program as explained in air spectrum

measurement.

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Chapter 4 Result and Discussion

4.1 Air spectrum

Figure 4.1 shows four VOs recorded with the Vernier spectrometer for a cavity filled with air.

Sample points _×10⁴

5 5.5 6 6.5 7

Intensity [au]

×10^-3

4 6 8 10 12 14

Fig. 4.1 The general view of four VOs in detection of CO ₂ absorption in air. The length of the cavity was scanned by the PZT. The narrowest peak corresponds to the most linear part of the sweeping sine wave applied to the PZT.

As it is explained in subsection 3.2.3, finding the selected VO of k= -21 among the recorded

VOs was difficult. On the other hand, the strength of the carbon dioxide absorption lines was

almost equal in these four VOs. Therefore, the narrowest peak which corresponds to the VO

acquired in the most linear part of the sine wave applied to the PZT to dither the length of

the cavity was selected for further studies. It is magnified in Fig. 4.2.

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24 Result and Discussion

6.04 6.06 6.08 6.1 6.12 6.14 6.16 6.18 6.2 6.22 6.24

Sample points 10⁴

0.008 0.009 0.01 0.011 0.012 0.013 0.014

Intensity [au]

6.115 6.12 6.125 6.13 10⁴ 0.012

0.0122 0.0124 0.0126 0.0128 0.013

C CO CO C CCO

Fig. 4.2 Detection of 3% absorption of CO ₂ in ambient air with resolution of 9.3 GHz. These small absorption lines are marked with arrows in the inset figure.

Since there was not any frequency scale in the measurements, sample points around 6.15 · 10 ⁴ were estimated as the region related to the target wavelength which was predicted by the MATLAB code. As can be seen in the magnified view shown in Fig.4.2, very week absorption lines of CO 2 was successfully observed.

4.2 Flame spectrum

Figure 4.4 shows the data acquired by the demonstrated Vernier spectrometer when the flame was on inside the cavity at HAB of 2 mm. Again three other VOs were simultaneously recorded beside the selected VO in the adjusted resolution.

5 5.5 6 6.5 7

Intensity [au]

×10^-3

3 4 5 6 7 8 9 10 11 12 13

Fig. 4.3 The general view of four VOs with the flame on in the cavity at HAB

of 2 mm. The length of the cavity was scanned by the PZT. The narrowest peak

corresponds to the most linear part of the sweeping sine wave applied to the PZT.

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4.3 Air and flame spectrum comparison in terms of intensity and frequency stability 25

Again the narrowest peak was selected and magnified to enable further comparisons between the acquired data in the air and in the flame (Fig.4.4)

Sample points ×10⁴

5.94 5.96 5.98 6 6.02 6.04 6.06 6.08

Intensity [au]

0.0095 0.01 0.0105 0.011 0.0115 0.012 0.0125 0.013

Fig. 4.4 Detection of water and OH absorption lines in the flame with resolution of 9.3 GHz at HAB of 2 mm. To distinguish these two molecular species, these strong absorption lines should be compared with that measured at HAB of 5 mm.

As can be seen, very strong absorption lines appeared in the spectrum which correspond to water and OH radical. But in order to identify the absorption lines of these two molecular species, this spectrum should be compared with the spectrum acquired at HAB of 5 mm.

4.3 Air and flame spectrum comparison in terms of inten- sity and frequency stability

Figure 4.5 compares magnified views of the selected VO in the air (blue line) with that of in the flame at HAB of 2 mm (black line). As can be seen, the overall structure of the VOs are similar although there is a shift in the position of the spectrum. But since they are two different series of data in different time with different trigger function, therefore they are shift in time and can be neglected.

But there are some discrepancies in the intensity of the flame spectrum with that of the

air. It is due to misalignment of the cavity when the flame is on inside the cavity. As it is

explained in subsection 2.2.3, adding heat into the system or any huge change in refractive

index causes change in the physical and optical length of the cavity which leads to cavity

mode alteration.

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26 Result and Discussion

5.9 5.95 6 6.05 6.1 6.15 6.2 6.25

Intensity [au]

0.007 0.008 0.009 0.01 0.011 0.012 0.013 0.014

Fig. 4.5 Comparison between absorption spectrum of air (blue line) and flame at HAB of 2 mm (black line). The flame peak has less intensity due to misalignment of the cavity length.

But by recording four series of data for both air and flame, in the same way as explained in section 4.1, then frequency fluctuation would be observed in the selected VO of the flame (Fig. 4.6). This is also because of cavity modes alteration which is explained in subsection 2.2.3.

5.9 5.95 6 6.05 6.1 6.15 6.2 6.25

Intensity [au]

0.0095 0.01 0.0105 0.011 0.0115 0.012 0.0125 0.013

Fig. 4.6 Comparison between four shot to shot absorption spectrum of air (right peaks) and flame (left peaks). The flame Vernier order has frequency fluctuation.

It can be concluded that although the structure of the spectrum is not changed by having

the flame on inside the cavity but there are some frequency fluctuations in the retrieved

flame spectrum. It does not cause total drift in the acquired spectrum for the flame, but it is

still crucial to investigate the frequency stability of the acquired spectrum to prove that it is

sufficient enough to do precise and fast measurements simultaneously.

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4.3 Air and flame spectrum comparison in terms of intensity and frequency stability 27

For this to be achieved, two series of data were gathered with the flame at HABs of 2 mm and 5 mm and plotted simultaneously. The water concentration is constant between HABs of 2 mm and 5 mm (see Appendix B, Fig.B.1), therefore the water absorption lines in the acquired spectrum at these two HABs should be completely coincided in the region that they are expected to be detected. Figure B.4 (Appendix B) shows that the water absorption lines are detectable in the region between 1577 nm and 1578 nm, for example. But since there was a difference in the intensity of the spectrum at HAB of 2 mm with that of at HAB of 5 mm and also shift in time scale between these two series of data due the function of the trigger, only the same structure of the peaks in these two series of data can be seen by zooming around the above mentioned region. Therefore, MATLAB program was used to select one point on the absorption spectrum at HAB of 2 mm around 1578 nm and make it to be coincided to the corresponding point in the absorption spectrum at HAB of 5 mm by shifting it by a factor in intensity and time scale.

The result is plotted in figure 4.7-(a). The applied shift made the selected peak at HAB of 2 mm to be completely coincided with the corresponding peak at HAB of 5 mm. This confirms water absorption lines are detectable with the demonstrated Vernier spectrometer.

But as can be seen in the figure, the other peaks do not still overlap. In figure 4.7-(b), this shift was applied to overlap a neighboring peak. The new peaks were completely coincided again, therefore they can be labeled as another water absorption line but still other peaks do not overlap. Therefore, to label other water absorption lines, the shift should be applied for all the peaks individually. It is the result of the frequency fluctuation of the spectrum in the above mentioned HABs which causes the width of absorption peaks at HAB of 5 mm be larger than that of at HAB of 2 mm.

Sample points ×10⁴

6.185 6.19 6.195 6.2 6.205 6.21

Intensity [au]

0.85 0.9 0.95 1 1.05

(a)

Sample points ×10⁴

6.185 6.19 6.195 6.2 6.205

Intensity [au]

0.85 0.9 0.95 1 1.05

(b)

Fig. 4.7 Water absorption lines detected around 1578 nm. MATLAB program was used for two

strong peaks in this region at HAB 2 mm (black line) to shift them by a factor in intensity and

time scale and make them to be coincided to the corresponding peaks at HAB 5 mm (red line).

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28 Result and Discussion

Also the difference in concentration OH radical in different HABs can be used (see Appendix B, Fig.B.1) to investigate the precision of the measurements. OH absorption lines in the acquired spectrum at HAB of 2 mm should be stronger than that of at HAB of 5 mm. Figure B.5 (Appendix B) shows that the OH absorption lines are detectable in the region between 1572 nm and 1573 nm, for example. With the same reasoning as for water, MATLAB program was used in the same way to shift an absorption line at HAB of 2 mm around 1573 nm to the corresponding absorption line at HAB of 5 mm. The result is plotted in figure 4.8. As can be seen, there is difference between the height of the peaks. Therefore, this peak can be labeled as OH absorption line.

6.162 6.164 6.166 6.168 6.17 6.172 6.174 6.176 6.178

Intensity [au]

0.85 0.9 0.95 1 1.05

Fig. 4.8 OH absorption line detected around a peak at 1573 nm. MATLAB program was used for a strong peak in this region at HAB 2 mm (black line) to shift it by a factor in intensity and time scale and make it to be coincided to the corresponding peaks at HAB 5 mm (red line).

Overall, although individually peak shift is required to analyze the retrieved data due to

the frequency fluctuation of the flame spectrum acquired in two above mentioned HABs,

sufficient precision of doing fast measurements in turbulent environment was approved.

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Chapter 5 Summary and conclusions

A broadband cavity enhanced absorption spectrometer, together with a near-infrared OFC has been successfully demonstrated to study the performance of Vernier detection technique by doing comparison between the retrieved spectrum in air and in a laminar flame, as a turbulent environment. The simple and compact experimental setup consisting of a mode- locked Er:fiber laser, a Fabry-Perot cavity with finesse of 1000, a diffraction grating, a photo detector and some standard optical component which can be found in all optical laboratories, enables measurement of very week absorption lines of CO ₂ contained in the ambient air with resolution of 9.3 GHz in wavelength region between 1573 nm and 1578 nm in 0.05 s. By repeating the measurement when a premixed methane/air flame was on inside the optical cavity and water and OH radicals were major products of combustion, stability of intensity and frequency of the spectrum were compared with that of in air.

By comparing the plotted data acquired in these two environment, similar structure of air VO was observed for the flame VO. But the intensity of the flame Vo was lower than that of in air which was the result of cavity length misalignment. Since detection of combustion products were possible, the intensity stability of the flame VO would be in the acceptable scale of measurements.

Also there were frequency fluctuations in shot to shot flame VO which was again the result of

cavity length misalignment and cavity mode fluctuation phenomena. Therefore comparison

between two series of data for HABs of 2 mm and 5 mm was done to find out if the frequency

stability of the flame VO is sufficient enough to do fast and precise measurements. This was

done by investigating the possibility of labeling water and OH absorption line in the acquired

spectrum. For this to be achieved, peak to peak shift of individual absorption line around

1578 nm and 1573 nm at HAB of 2 mm to the corresponding absorption lines at HAB of

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30 Summary and conclusions

5 mm was done by MATLAB program. Water and OH absorption lines were successfully distinguished from each other.

In conclusion, Intensity and frequency stability of the spectrum is reliable to do fast measure-

ment with the demonstrated Vernier spectrometer in turbulent environments.

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References

[1] P. Maslowski, K.C. Cossel, A. Foltynowicz, and J. Ye. Cavity-Enhanced Spec- troscopy and Sensing: Chapters 8- Cavity-enhanced direct frequency comb spec- troscopy. Springer Heidelberg, New York, Dordrecht, London, 2013.

[2] M. Thorpe and J. Ye. Cavity-enhanced direct frequency comb spectroscopy. Applied Physics B, 91:397–414, 2008.

[3] T. Gherman and D. Romanini. Mode-locked cavity-enhancement absorption spec- troscopy. Optics Express, 19(10):1033–1042, 2002.

[4] G. Mejean, S. Kassi, and D. Romanini. Measurement of reactive atmospheric species by ultraviolet cavity-enhanced spectroscopy with a mode-locked femtosecond laser.

Optics Letter, 11(33):1231–1233, 2008.

[5] R. Grilli, G. Méjean, S. Kassi, I. Ventrillard, C. Abd-Alrahman, E. Fasci, and D. Ro- manini. Trace measurement of bro at the ppl level by a transportable mode-locked frequency-doubled cavity-enhanced spectrometer. Applied Physics B, Laser and optics, 1(107):205–212, 2012.

[6] Michael J. Thorpe, Kevin D. Moll, R. Jason Jones, Benjamin Safdi, and Jun Ye.

Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection.

Science, 5767(311):1595–1599, 2006.

[7] M. Shirasaki. Large angular dispersion by a virtually imaged phased array and its application to a wavelength demultiplexer. Optics Letter, 5(21):366–368, 1996.

[8] J. Mandom, G Guelachvili, and N. Picque. Fourier transform spectroscopy with a laser frequency comb. Nature Photonics, 2(3):99–102, 2009.

[9] S. Schiller. Spectroscopy with frequency combs. Optics Letter, 9(27):766–768, 2002.

[10] Ian Coddington, William C. Swann, and Nathan R. Newbury. Coherent multiheterodyne spectroscopy using stabilized optical frequency combs. Review Letter, 1(100):013902, 2008.

[11] Birgitta Bernhardt, Akira Ozawa1, Patrick Jacquet, Marion Jacquey, Yohei Kobayashi, Thomas Udem, Ronald Holzwarth, Guy Guelachvili, Theodor W. Hänsch, and Nathalie Picqué. Cavity enhanced dual comb spectroscopy. Nature Photonics, 1(4):55–57, 2010.

[12] Lucile Rutkowski and Jerome Morville. Broadband cavity-enhanced molecular spectra

from vernier filtering of a complete frequency comb. Optics Letters, 39(23):6664–6667,

2014.

(50)

32 References

[13] Aleksandra Foltynowicz. Fiber-laser-based Noise-Immune Cavity-Enhanced Optical Heterodyne Molecular Spectrometry. PhD thesis, Umeå University, Department of Physics, Sweden, 2009.

[14] Peter W. Miloni and Josef H. Eberly. Laser physics (Chapters 3,5). John Wiley and Sons, Inc., Hoboken, New Jersey, 2010.

[15] Zhechao Qu, Erik Steinvall, Ramin Ghorbani, and Florian Schmidt. Tunable diode laser atomic absorption spectroscopy for detection of potasium under optically thick condition. Analytical Chemistry, 88:3754–3760, 2016.

[16] Daniel Romanini, Irene Ventrillard, Gullaume Mejean, Jerome Morville, and Erik Kerstel. Cavity-Enhanced Spectroscopy and Sensing: Chapters 1- Intoduction to cavity enhanced absorption spectroscopy. Springer Heidelberg, New York, Dordrecht, London, 2013.

[17] Steven Cundiff, Jun Ye, and John Hall. Rulers of light. Scientific American, 298:74–81, 2008.

[18] Florian Adler, Michael J. Thorpe, Kevin C. Cossel, and Jun Ye. Cavity-enhanced direct frequency comb spectroscopy: Technology and applications. Annual Review of Analytical Chemistry, (3):175–205, 2010.

[19] Dana Z. Anderson. Alignment of resonant optical cavities. Applied Optics, 23(17):2944–

2949, 1984.

[20] Chadi Abd Alrahman, Amir Khodabakhsh, Florian M. Schmidt, Qu, and Aleksandra Flo- tynowicz. Cavity-enhanced optical frequency comb spectroscopy of high-temperature H 2 O in a flame. Optical Express, 22(11):13889–13895, 2014.

[21] Peter Atkins and Julio De Paula. Atkins’ Physical Chemistry (Chapter 1). W.H. Freeman and Company, 2010.

[22] Jenny A.M. Sidey and Epaminondas Mastorakos. Simulations of laminar non-premixed flames of methane with hot combustion products as oxidiser. Combustion and Flame, 163:1–11, 2016.

[23] Lucile Rutkowski, Alexandra C. Johansson, Damir Valiev, Amir Khodabakhsh, Florian M. Schmidt Arkadiusz Tkacz, and Aleksanra Foltynowicz. Detection of OH in an atmospheric flame at 1.5 µm using optical frequency comb spectroscopy. Photonics Letters of Poland, 8(4):110–112, 2016.

[24] L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. E. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J. P Champion, K. Chance, L. <h. Coudert, V. Dana, V. M.

Devi, S. Fally, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner,

N. Lacome, W.J. Lafferty, Mandin J. Y, S.T. Massie, S. N. Perrin, A. Predoi-Cross,

C. P. Rinsland, M. Rotger, M. Simekova, M. A. H. Smith, K. Sung, S. A. Tashkun,

J. Tennyson, R.A Toth, A.C. Vandaele, and J. Vander Auwera. The HITRAN 2008

molecular spectroscopic database. Journal of Quantitative Spectroscopy and Radiative

Transfer, 110(9–10):533–572, 2009.

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Appendix A Setup photos

Fig. A.1 (1) Beam blocker which blocks the Er:fiber laser beam being send via the polarizer fiber, (2) Flat

mirror M ₁ , (3) Iris ₁ , (4) Mode-matching lens f ₁ , (5) Mode-matching lens f ₂ , (6) Flat mirror M ₂ , (7) Iris ₂ , (8)

Flat mirror M 3 , (9) Cavity front curved mirror M ₅ , (10) Horizontal transition stage, (11) Burner, (12) Vertical

transition stage, (13) Cavity back curved mirror M ₆ , (14) Flat mirror M ₄ , (15) Grating, (16) Iris ₃ , (17) focusing

lens f ₃ , (18) Photo detector

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34 Setup photos

The burner (item 11) in a closer view:

Fig. A.2 The flame was mounted inside the cavity between the mirrors on a vertical translation stage. Methane

(CH ₄ ) and air were mixed with a stoichiometric ratio of one with flow rates of 0.95 l/min and 9.05 l/min

respectively. Turning on the flame, detection of CO ₂ , water vapor and OH were predicted. The flame was

stabilized with a flow of nitrogen and the burner was cool down with water flow during the process.

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Appendix B

Literature results in detection of Methane/air combustion products

B.1 Variation of water and OH concentration and flame temperature at different HABs

Fig. B.1 Simulation of water and OH concentration and flame temperature as a function of

HAB. The flame temperature is homogeneous for HABs greater than 2 mm. Concentration

of water is constant for HABs greater than 2 mm. Concentraton of OH is not constant and

is greater for HAB of 2 mm comparing with that of 5 mm (Figure is copied from [23])

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36 Literature results in detection of Methane/air combustion products

B.2 Normalized cavity transmission at different HABs

Before I have started my project, the following data was acquired with Fourier transform spectrometer demonstrated with the same optical frequency comb coupled into a cavity with finesse of 150. These data is used in this thesis report with the permission of one the authors of paper [23], Alexandra Johansson.

6250 6300 6350 6400 6450 6500 6550 6600 6650 6700

Wavenumber [cm^-1] 0.65

0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15

Normalized cavity transmission

HAB = 2.5 mm HAB = 3.5 mm HAB = 5 mm

Fig. B.2 Normalized cavity transmission at different HABs in the region of 1500 to 1600 nm corresponding to wave number 6250 to 6650 cm ⁻¹ , respectively [23].

6338 6340 6342 6344 6346 6348 6350 6352 6354 6356

0.9 0.92 0.94 0.96 0.98 1

Fig. B.3 Magnification of normalized cavity transmission at different HABs in the region

of 1578 to 1573 nm corresponding to wave number 6358 to 6336 cm ⁻¹ , respectively [23].

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B.2 Normalized cavity transmission at different HABs 37

6336 6336.5 6337 6337.5 6338 6338.5 6339 6339.5 6340 6340.5

0.92 0.94 0.96 0.98 1

Fig. B.4 Magnification of normalized cavity transmission to identify water absorption lines in the region of 1577 to 1578 nm corresponding to wave number 6340 to 6336 cm ⁻¹ , respectively [23].

6356 6356.5 6357 6357.5 6358 6358.5 6359 6359.5 6360 6360.5

0.92 0.94 0.96 0.98 1

Fig. B.5 Magnification of normalized cavity transmission to identify OH absorption lines in the

region of 1572 to 1573 nm corresponding to wave number 6360 to 6356 cm ⁻¹ , respectively [23].

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Near-infrared optical frequency comb Vernier spectroscopy in air and in a flame