UMEA UNIVERSITY

Implementation of continuous

filtering frequency comb Vernier

spectroscopy for continuous

acquisition of spectra in a flame

by

Adam Edlund

Master’s thesis in Engineering Physics

Faculty of Science and Technology

Department of Physics

November 2017

This thesis is written as a requirement for the Master’s degree in EngineeringPhysics.

Master’s degree in Engineering Physics, 30.0 ECTS. Department of Physics, UmeaUniversity, Sweden.

Author: Adam Edlund, adam92edlund@gmail.comSupervisor: Alexandra Johansson,

Department of Physics, Umea UniversityExaminer: Aleksandra Foltynowicz Matyba,

Department of Physics, Umea University

To my father

ii

Abstract

In this project laser absorption spectroscopy was performed on a flame in a Fabry-Perot cavity, using an optical frequency comb. Optical frequency comb spec-troscopy is a technique that allows broadband ultra-sensitive detection of molec-ular species in gas phase. Optical frequency combs are generated by femtosecondmode-locked lasers, which generate short pulses and whose spectrum consists of acomb of sharp laser lines covering a broad spectral range. Doing spectroscopy withoptical frequency combs can hence be compared to measurements with thousandof synchronised continuous wave lasers simultaneously, which enables broadbandsensitive measurements in short acquisition times. A Vernier spectrometer usesthe filtering ability of the cavity to allow sequential transmission of parts of thefrequency comb spectrum. Its technical simplicity and robustness make it a goodcandidate for measuring in turbulent environments.

The aim of the project was to implement continuous-filtering Vernier spec-troscopy in a setup for measuring absorption spectra in air and in a flame. Thiswas done by using an Er:fiber femtosecond laser emitting in the near-infraredwavelength range and a Fabry-Perot cavity containing the flame. The cavity,which consists of two highly reflective mirrors, lets the light of the comb inter-act with the molecules in the flame for each of the many round-trips it perform;thus increasing the sensitivity to absorption. An active locking mechanism wasimplemented to stabilize the coupling of the optical frequency comb to the cavity.The locking allowed multiple measurements to be averaged which reduced noise.A galvanometer scanner was added to the system which was used to measure abroad part of the comb spectrum. Hot water absorption lines were detected inthe swept comb spectrum and a candidate absorption peak for OH absorption wasrecorded.

The spectrometer today has opportunities for improvements. A frequencycalibration should be implemented which is essential for making estimates of re-actant/product concentrations in combustion processes.

Popularvetenskaplig Sammanfattning

Spektroskopi med optiska frekvenskammar anvands som ett medel att detekteramolekylara amnen i gasfas med mycket hog kanslighet. Optiska frekvenskammargenereras av femtosekund modlasta lasrar som ger korta pulser. I frekvensdomanger detta en kamlik struktur med skarpa linjer over ett brett spektrum. Optiskfrekvenskamspektroskopi har ett brett optiskt frekvensomrade med en hog spektralupplosning som gor det mojligt att mata flera molekylara amnen samtidigt underkort mattid. Detta kan jamforas med att mata med flera tusen synkroniseradelasrar samtidigt. Dessa egenskaper gor optiska frekvenskammar eftertraktade inomindustriell processkontroll, medicinsk diagnostisering och inom miljovervakning.

I detta projekt anvandes frekvenskamspektroskopi for att mata absorption-slinjer fran hett vatten och OH i en eldslaga. Tekniken bygger pa att fanga innara infrarott ljus fran laserkammen i en resonator bestaende av tva speglar ochen brannare. Speglarna later ljuset fran kammen interagera med molekylerna ilagan over en langre stracka nar ljuset passerat gasen vid varje runda vilket okarabsorptionskansligheten.

En Vernierspektrometer ar en tillampning pa frekvenskamsspektroskopi. Denanvander sig av resonatorn for att filtrera frekvenskamsspektrumet. Dess teknisktsimpla konstruktion och robusthet gor den lamplig att anvanda vid turbulentamiljoer.

Malet med detta projekt var att aterstalla en tidigare uppstallning av spek-trometern samt att utoka med en aktiv lasning av lasern till resonatorn med hjalpav reglerteknik. Den nya lasningen gjorde det mojligt att mata flera matserieroch medelvardesbilda signalen. Ett vridspoleinstrument gjorde det mojligt attvrida ett gitter for att mata ett bredare spektrum an vad som var tidigare mojligt.Absorptionslinjer av hett vatten samt OH kunde detekteras med spektrometern.

Spektrometern har utrymme for forbattringar. Ett nasta steg ar att kallibrerafrekvensen pa det matta spektrumet vilket ar en vasentlig del i att kunna matakoncentrationen av produkt och reaktanter vid forbranningsprocesser.

iv

AcknowledgementsI would like to thank Aleksandra Foltynowicz for the opportunity to work on thisproject and the insightful advice you have brought me. My sincerest thanks toAlexandra Johansson my supervisor for your kind support and patience helpingme with technical questions during these weeks. Your kindness and cheerfulnessseem to know no bounds.

I would like to thank my mother and father for supporting me during mystudies, for whom without I would never have made it this far. Thank you foryour unconditional love and support during all these years. A big thank you tomy beloved brother Noa who’s creativeness keeps me inspired. Last but not least,thanks to my best friend and wife Angelica for all the joy you have brought to mylife.

v

Contents

Abstract iii

Popularvetenskaplig Sammanfattning iv

Acknowledgements v

List of Figures viii

Nomenclature x

Abbreviations xii

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Scope of the project . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Theory 3

2.1 Laser absorption spectroscopy . . . . . . . . . . . . . . . . . . . . . 3

2.2 Fabry-Perot cavities . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.1 Cavity parameters . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Optical frequency combs . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4 Continuous filtering Vernier spectroscopy . . . . . . . . . . . . . . . 8

2.4.1 Perfect match . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4.2 Continuous filtering . . . . . . . . . . . . . . . . . . . . . . . 9

2.5 Stabilising the laser frequency . . . . . . . . . . . . . . . . . . . . . 10

2.5.1 Block diagrams and transfer functions . . . . . . . . . . . . 10

2.5.2 Basic control theory . . . . . . . . . . . . . . . . . . . . . . 11

2.5.3 PI controller . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Setup of the spectrometer and measurement procedures 14

3.1 Building the high finesse Cavity . . . . . . . . . . . . . . . . . . . . 15

3.2 Mode-matching the laser to the cavity . . . . . . . . . . . . . . . . 17

3.3 Laser actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

vi

CONTENTS vii

3.4 Locking the comb to the cavity . . . . . . . . . . . . . . . . . . . . 19

3.5 Measuring in air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.6 Measuring with a flame . . . . . . . . . . . . . . . . . . . . . . . . 22

4 Results 23

4.1 One sweep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2 Averaging multiple spectra . . . . . . . . . . . . . . . . . . . . . . . 25

4.3 Normalising and scaling . . . . . . . . . . . . . . . . . . . . . . . . 27

5 Discussion 30

6 Summary and conclusions 33

References 34

A Voltage vs. Vernier Orders 36

B CO2 absorption lines in air 37

C Position sensing detector 38

List of Figures

2.1 A schematic of a simple direct laser absorption spectrometer. Thelight from the laser source is partially absorbed by the sample andthe transmitted light is recorded by a photodetector. . . . . . . . . 3

2.2 A schematic illustration of the Fabry-Perot cavity with intracavityindex of refraction nr. . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Three consequtive modes transmitted through the cavity. . . . . . . 6

2.4 (a) Time representation of an optical frequency comb. (b) Fre-quency domain representation . . . . . . . . . . . . . . . . . . . . . 7

2.5 A schematic illustration showing the perfect matching between thecomb modes (red bars and cavity modes (black curve). Each combmode is matched to a cavity mode. . . . . . . . . . . . . . . . . . . 9

2.6 A schematic illustration of the continuous-filtering Vernier scheme.There is a small mismatch between the cavity and comb. Severalgroups of comb modes are transmitted. . . . . . . . . . . . . . . . . 9

2.7 A simple negative feedback control loop is shown in the block diagram. 11

2.8 The block diagram of the PI controller. . . . . . . . . . . . . . . . . 12

2.9 The amplitude of the transfer function of the PI controller. . . . . . 13

3.1 Illustration of the continuous-filtering Vernier spectrometer setup,where BS is the 50:50 beamspliter, f1-f4 are the lenses, M1-M5 aremirrors, TS are translation stages, Mcav

1 -Mcav2 are the wedged cavity

mirrors, PD1-PD2 are two photo detectors, Ph is a phase shifter andHVA is a high voltage amplifier. Note that the beam has to enterthe cavity at an angle due to the wedge which is not shown in theillustration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Simplified schematic of the internal parts in the comb laser. Theactuators of the comb laser are labeled in blue [16]. . . . . . . . . . 18

3.3 Schematic of the frep controller. The servo controllers are coupledin series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4 Open-loop error signal for three consequtive Vernier orders aroundk = −19. The signal was recorded as the cavity length was scannedlinearly with the grating position fixed. . . . . . . . . . . . . . . . . 20

3.5 Open-loop error signal for a single Vernier order. The signal wasrecorded with a fixed position of the grating. The sweep of thecavity length was decreased to resolve only one VO. . . . . . . . . . 20

viii

LIST OF FIGURES ix

3.6 a) Open-loop error signal for VO k = −19, recorded as the cavitylength and the grating position was scanned simultaneously. Thesweep of the cavity length and grating position are slightly out ofsynchronisation and the left side of the signal is close to the unlinearturning point of the sweep. b) The corresponding closed-loop errorsignal recorded with the integrators on. . . . . . . . . . . . . . . . . 21

4.1 A single measurement of the spectra when the flame is off, in air(blue curve) and with the flame on (red curve). The HAB was 2 mm 24

4.2 Air spectrum (flame off) in blue and spectrum when the flame ison in red HAB = 2 mm. . . . . . . . . . . . . . . . . . . . . . . . . 24

4.3 a) The recorded signal for air, b) measured signal for three differentheights when the flame is on, HAB= 2, 2,5 and 5 mm. The signalshows an average of 100 measured spectra. . . . . . . . . . . . . . . 25

4.4 Flame spectra for number of averages, N = 1 (black), N = 20 (red),N = 100 (blue). The signal to noise ratio is greatly improved bythe averaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.5 Averaged comb spectrum with the flame on at HAB = 2 mm fornumber of averages N = 100 (blue) and N = 5 (red). The averagedrecording of the comb spectrum in air for N = 100 sample (black)is also plotted, showing an etalon fringe pattern. . . . . . . . . . . . 27

4.6 Normalised intensity signal of the comb spectrum in the flame forHAB = 2 mm (blue), HAB = 2,5 mm (red) and HAB = 5 mm(black). All are averaged N = 100 times. . . . . . . . . . . . . . . . 28

4.7 Normalised intensity signal of the comb spectrum with the flame fordifferent HAB, scaled to get an overlap. A suspected OH absorptionline is seen to the right. . . . . . . . . . . . . . . . . . . . . . . . . . 28

A.1 The peak intensity of the Vernier signal is shown as it drops whenshortening the cavity length with integer numbers of k. . . . . . . 36

B.1 Suspected CO2 absorption lines atmospheric air. . . . . . . . . . . . 37

C.1 The active sensing area of the position detector divided into fourquadrants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Nomenclature

Roman symbols

IT transmitted intensity W/m2

I0 intensity of incident light W/m2

Nabs population density of absorbing molecules molecules/cm−3

S integrated molecular line strength cm−1/molecule/cm−2

nr index of refraction inside the cavity dimensionless

L cavity length m

ti transmission coefficient dimensionless

ri reflection coefficient dimensionless

li loss coefficient dimensionless

IR reflected intensity W/m2

Ic intra cavity intensity W/m2

FSR free spectral range Hz

E0 incident electric field Vm−1

ER reflected electric field Vm−1

ET transmitted electric field Vm−1

F cavity finesse dimensionless

OPL optical path length m

f0 laser offset frequency Hz

frep laser repetition rate Hz

r distance from the optical axis m

z0 Rayleigh range m

R(z) radius of curvature m

LPM perfect match length m

x

NOMENCLATURE xi

k Vernier order dimensionless

FSRV Vernier free spectral range dimensionless

Greek symbols

ν frequency Hz

α(ν) frequency dependent absorption coefficient cm−1

χabs area normalised absorption lineshape function cm

ω angular frequency rads−1

λ0 wavelength of incident light m

νq cavity resonant frequency Hz

Γc cavity mode-width Hz

∆φce phase shift dimensionless

ω0 beam waist radius m

ΓV Vernier resolution Hz

Abbreviations

OFC Optical Frequency Comb

NIR Near-Infrared

DAS Direct Absorption Spectroscopy

EM Electro Magnetic

FSR Free Spectral Range

FWHM Full Width Half Maximum

OPL Optical Path Lenght

TEM Transverse Electric Mode

CF-VS Continuous Filtering Vernier Spectroscopy

PZT Piezo Electric Transducer

PM Perfect Match

PML Perfect Match Length

VO Vernier Order

PI Proportional Integral

DAQ Data Acquisition

SG Signal Generator

CW Continuous Wave

EOM Electro-Optic Modulator

HAB Height-Above Burner

SNR Signal to Noise Ratio

xii

Chapter 1

Introduction

1.1 Background

Spectroscopy is the science of studying the interaction between electromagneticwaves and matter. In this project a special type of spectroscopy technique calledVernier spectroscopy was used to detect molecular species in gas phase. Theproject was ordered by Optical Frequency Comb Spectroscopy Group at the De-partment of Physics at Umea University. The group works with development ofoptical frequency comb spectroscopy which can be used for broadband highly sen-sitive detection of trace gases [1]. The optical frequency combs are produced byfemto-second mode-locked lasers whose spectrum consists of a comb like struc-ture of sharp laser lines. The spectrum covers a broad spectral range and allowssensitive detection of many molecular species in short acquisition times. Doingspectroscopy with optical frequency combs is equivalent to measuring with thou-sand of synchronised continuous wave lasers simultaneously. The technique hastherefore a chance of becoming an industry standard for process control or medicaldiagnostics such as breath analysis.

In the work for this thesis optical frequency comb absorption spectroscopy isused to detect broadband absorption spectrum of water and OH in a flame. Atechnique called continuous-filtering Vernier spectroscopy (CF-VS) was used torecord a broad spectrum of an optical frequency comb in short acquisition time.Its technical simplicity and robustness make it a good candidate for measuring inturbulent environments.

1.2 Scope of the project

The aim of the project was to improve on a previously built Vernier spectrometer,by adding an active locking and a grating sweep to enable fast continuous mea-surements and averaging of recorded comb spectra. The goal of the project wasto build a continuous-filtering Vernier spectrometer capable of measuring multi-ple spectra in a flame. The project did not include analysis of reactant/productconcentrations in the reaction in the flame.

1

Chapter 1 Introduction 2

1.3 Outline of this thesis

The disposition of this thesis is as follows: Chapter 1 gives an introduction to thesubject of this thesis and the background of the project. Chapter 2 covers thegeneral theory of laser absorption spectroscopy. The theory section has a largeemphasis on the cavity and how light interacts with it, it plays a central role ofunderstanding the concepts of the Vernier technique. The theory section thuscovers a large portion of this thesis. Chapter 3 presents the experimental setupand procedures. In Chapter 4 are the results of the measurements done with thespectrometer. Chapter 5 discusses the result and the reasoning behind some of themeasurements. Chapter 6 gives a brief conclusion to the work done in this projectand the results presented in the thesis. This thesis assumes some knowledge ofoptics and laser physics for which reference [2] covers the basics.

Chapter 2

Theory

The theory in this chapter starts with a short introduction to laser absorptionspectroscopy and continues with how light interacts with cavities. A large portionis spent on describing optical cavities, namely the Fabry-Perot cavity. Furthermorethere is an introduction to optical frequency combs, the continuous filtering Vernierspectroscopy technique and the chapter is concluded with a brief mentioning ofthe basics of control theory.

2.1 Laser absorption spectroscopy

Spectroscopy is a science of studying how electromagnetic waves interact withmatter. Three interactions commonly studied in spectroscopy include absorption,emission and scattering. In absorption spectroscopy the absorption of incidentradiation is measured as its frequency is varied [3]. The irradiated matter, com-monly referred to as a sample, is in this case a sample of molecules in gas phase.When a laser is used as a source of electromagnetic-radiation (EM-radiation), it isreferred to as laser absorption spectroscopy or laser absorption spectrometry (AS).The simplest form of laser based AS is direct absorption spectrometry (DAS). InDAS the sample is put directly in the path of a laser beam. FIGURE 2.1 shows aset-up where the absorbing sample has a length L.

Figure 2.1: A schematic of a simple direct laser absorption spectrometer.The light from the laser source is partially absorbed by the sample and the

transmitted light is recorded by a photodetector.

According to the Lambert-Beer law, the intensity IT (W/m2) of light transmittedthrough an absorbing sample is

3

Chapter 2 Theory 4

IT = I0e−α(ν)L, (2.1)

where α(ν) is the frequency dependent absorption coefficient (cm−1) and I0 is theincident intensity [4]. The absorption coefficient of the sample α(ν) is given by

α(ν) = SNabsχabs(ν), (2.2)

where S is the integrated molecular line strength (cm−1/molecule/cm−2), Nabs

is the population density of absorbing molecules (molecules/cm−3) and χabs(ν) isthe area normalised absorption lineshape function (cm) [1]. The sensitivity toabsorption is increased by increasing the interaction length. [1]. We can alsoincrease the sensitivity by choosing a strong absorption line (that is choosing aproper wavelength range for a specific atom or molecule) or using noise reductionmethods (such as modulation techniques [1]).

The absorption coefficient can be calculated from the interaction length andthe intensities of the incident and transmitted light

α(ν) =1

Lln

I0

IT (ν), (2.3)

We may also define the relative (or normalised) absorption as ∆I(ν)/I0 [1], where∆I(ν) = I0 − IT (ν) is the change in intensity due to the absorption. If theabsorption is small [α(ν)L � 1], we can Taylor expand the exponential functionin (2.2) and get

IT (ν) ≈ I0[1− α(ν)L], (2.4)

and by simple algebra we have

∆I(ν)

I0

≈ α(ν)L. (2.5)

Hence according to the Lambert-Beer law (equation (2.1)) the transmitted lightis to first approximation (and for small absorption) proportional to the integratedmolecular line strength, the density and the cavity length. We can increase theoptical pathlength through the sample by introducing multipass cells or resonantcavities. This is the topic of the following section 2.2.

2.2 Fabry-Perot cavities

A Fabry-Perot cavity is an arrangement of mirrors that allows EM-radiation toresonate. Resonance cavities are commonly used to increase the interaction lengthof the EM-radiation between the light source and the sample, referred to as a cavityenhancement [5].

One commonly used cavity design is the Fabry-Perot cavity shown in FIGURE

2.2 below.

Chapter 2 Theory 5

Figure 2.2: A schematic illustration of the Fabry-Perot cavity with intracavityindex of refraction nr.

The cavity is built from two concave mirrors separated by L, where the index ofrefraction of the medium inside the cavity is nr. Each mirror has an associatedtransmission, reflection and loss coefficient (defined for the intensity of light) ti, ri,li, respectively. By the principle of energy conservation ti+ri+ li = 1. The opticalintensities of the incident, reflected and transmitted light are denoted by I0, IRand IT . The incident, reflected and transmitted electric fields are given by E0, ER

and ET respectively. The intensity inside the cavity is denoted by Ic. In depthcalculations of the electrical fields and intensities and cavity transmission functionscan be found in [4]. When light enters the cavity it gets partially reflected by thecavity mirrors. The waves that are reflected interfere constructively if a multipleinteger q times the wavelength of the incident light, λ0, is equal to the round-tripoptical length of the cavity, qλ0 = 2nrL. What follows is an increased intracavityintensity, Ic. Moreover the effective interaction length is longer than the physicallength of the cavity, L, as for each round-trip the light passes the sample multipletimes. The electrical field will resonate at cavity resonant frequencies, νq that is

νq =qc

2nrL, (2.6)

where, c is the speed of light. The frequency spacing between two resonant fre-quencies is what is known as the free spectral range (FSR) of the cavity and isgiven by

FSR =c

2nrL. (2.7)

Some of the electric field inside the cavity leaks out through the cavity mirrorsat each round-trip. The results of the constructive interference is a repetitivestructure in the transmitted intensity at the resonating frequencies νq. This isknown as cavity modes [6] and is depicted in FIGURE 2.3.

Chapter 2 Theory 6

Figure 2.3: Three consequtive modes transmitted through the cavity.

2.2.1 Cavity parameters

There are some important parameters describing the cavity such as the cavity res-onant frequencies, νq and FSR described earlier. Two other important parametersare the cavity finesse, F , and the full width at half maximum (FWHM) of thecavity modes, Γc. The FWHM (also known as the cavity mode-width) is given by[4]

Γc =(1−√r1r2)FSR

π 4√r1r2

, (2.8)

where the width of the cavity modes is assumed to fulfil Γc � FSR. The finesse,F , of the cavity is defined as

F =FSR

Γc=

π 4√r1r2

1−√r1r2

. (2.9)

For two identical mirrors (r1 = r2 = r), equation (2.9) simplifies to F = π√r/(1−

r).

2.3 Optical frequency combs

Optical frequency combs (OFCs) can be produced by various laser sources suchas mode-locked lasers, indirect comb sources and continuous wave (cw) lasers.Common mode-locked lasers for comb spectroscopy are Ti:sapphire laser, Yb:fiberlaser and Er:fiber laser. They generate pulses with a duration of femtoseconds [7].In FIGURE 2.4(a) is an illustration of a pulse train in time domain generated bya mode-locked laser and (b), the frequency representation of the OFC.

Chapter 2 Theory 7

Figure 2.4: (a) Time representation of an optical frequency comb. (b) Fre-quency domain representation

In the frequency domain there are many equidistant narrow modes. Theseparation of these modes are given by the repetition rate of the laser frep = 1/τrep.The comb has an offset f0 from an multiple integer of frep. Due to intracavitydispersion the pulses are not completely identical. The electric field oscillation hasa phase shift ∆φce with respect to its envelope [7]. The offset frequency is

f0 = frep∆φce2π

. (2.10)

By performing a Fourier transform of the time series of the pulses we get anexpression for the frequency, νn, of the nth line of the frequency comb as

νn = nfrep + f0, (2.11)

where n typically is in the order of 105− 106(for mode-locked femtosecond lasers)[1].

The mode-locked Er:fiber lasers generate combs around a wavelenght of 1.55 µm[8]. Since this is the main telecommunication wavelength, they use relative inex-pensive and accessible technologies.

Chapter 2 Theory 8

2.4 Continuous filtering Vernier spectroscopy

The previous sections defined the general terms and the fundamental equationsregarding optical cavities and optical frequency combs. This section presents theconcept of CF-VS. The CF-VS technique is relatively new [9]. It allows acquisitionof broadband and cavity-enhanced comb spectra with medium to high resolution.A measurement can be performed in tens of ms using a robust and compactdetection system. But first we need to address the principle of frequency matchingthe comb modes to the cavity.

2.4.1 Perfect match

The modes of the cavity and the modes of the OFC share a similar structure.Hence to transmit the comb through the cavity, the optical frequencies of thecomb need to match the resonance frequencies of the cavity. An intuitive wayof coupling two comb structures together is to match them by adjusting theirfrequency spacing and offset. With the actuators on the OFC source it is possibleto tune the frep and f0. Even though the frep of the comb is constant over thewhole bandwidth of the laser, the FSR of the cavity changes with frequency due tothe dispersion inside the cavity. This limits the bandwidth of effective matchingbetween the cavity and the OFC [1].

In general we have a perfect match (PM) locally when

mfrep = q FSR, (2.12)

where m and q are positive integers and when f0 is tuned to match the offset ofthe cavity modes. The length of the cavity at perfect match is called the perfectmatching length (PML). A trivial case of perfect matching occurs when m = q = 1.FIGURE 2.5 illustrates perfect matching for m and q = 1 while not consideringdispersion. Here the comb modes are shown with vertical bars in red as the widthof the comb modes is typically a lot thinner than the widths of the cavity modesshown in black.

Chapter 2 Theory 9

Figure 2.5: A schematic illustration showing the perfect matching betweenthe comb modes (red bars and cavity modes (black curve). Each comb mode is

matched to a cavity mode.

2.4.2 Continuous filtering

The Vernier filtering scheme uses the cavity to filter the comb. The filtering alsoenables sequential detection of the entire bandwidth using a photodiode. Thefiltering of the comb modes is produced by mismatching the cavity modes andcomb modes from PM by a slight detuning of the frep of the comb from the FSR.It transmits groups of comb lines, each group is called a Vernier order (VO) [10].FIGURE 2.6 shows two consecutive Vernier orders resulting from the groups ofcomb modes that are transmitted.

Figure 2.6: A schematic illustration of the continuous-filtering Vernier scheme.There is a small mismatch between the cavity and comb. Several groups of comb

modes are transmitted.

Let us assume that we have an OFC and an enhancement cavity at perfectmatching FSRPM = frep such that n = 1 and q = 1 in equation (2.12), whereFSRPM = c/2nrLPM and LPM is the perfect match length (PML) of the cavity.Now the cavity length, L is detuned from the PML by a value |∆L| < LPM/F ,

Chapter 2 Theory 10

such that L = LPM + ∆L, where ∆L can be either positive or negative. Thecavity FSR is then changed to

FSR =c

2nr(LPM + ∆L)=

frep1 + ∆L/LPM

, (2.13)

and the created Vernier orders are centred at frequencies νk [10] given by

νk =c(k − δf0/frep)

2nr|∆L|, (2.14)

where k is an integer number of the order and δf0 is the mismatch between thecavity and the comb offset frequencies. For high Vernier orders (k � 1) the centerfrequencies can be simplified to νk ≈ ck/2nr|∆L|.

Consecutive Vernier orders are separated in the frequency domain. This sep-aration is given by the Vernier free spectral range,

FSRV =c

2nr|∆L|, (2.15)

and their width (resolution) is

ΓV =FSRV

F=

c

2nrF |∆L|. (2.16)

To acquire a spectrum the Vernier orders needs to be separated spatially. Theintegrated intensity of a selected Vernier order is tuned over the comb spectrum byscanning the length of the cavity with ∆L. An alternative is to scan the frep of thecomb. Scanning the length is usually preferred in practise as it can usually be doneover a greater range than the frep [10]. Detuning by shortening is also the typicalchoice as it results in a higher contrast in the normalised transmitted intensityspectrum [11]. Being able to adjust the frep and ∆L allows for stabilisation of theVernier order frequency by controlling them both.

2.5 Stabilising the laser frequency

In order to keep the matching between the cavity and the comb an active lockingis needed in order to compensate for thermal drift and vibrations. This lockingis a stabilisation process that requires some form of error signal to tell when andhow to correct the eventual mismatch [12]. This section will go through the basicterminology and concepts of control theory.

2.5.1 Block diagrams and transfer functions

Block diagrams are schematic illustrations representing a complex system withoutgoing into the specific details of how the different parts operate. Block diagramsare used as a visualisation tool for understanding transfer functions. A transferfunction is in this context a function that connects the input and output signalin a system. If we denote the input signal with Xin and let Xout be the output

Chapter 2 Theory 11

signal, then the transfer function H relates the two by Xout = HXin. The transferfunction represents the gain or loss of the system and may be unit-less. A blockin the block diagram depicts how the output from the block is related to its inputand the diagram itself shows how it is all linked together.

2.5.2 Basic control theory

In control theory there is typically a system that needs to be controlled for theprocess to work properly. This requires negative feedback. When using negativefeedback the output signal, X, of the system is compared to a reference signal,Xref by subtraction. The resulting error signal, Xerr is fed through a controllerand back into the system under control. FIGURE 2.7 shows a schematic diagramof the system where G(f) is the transfer function of the controlled system, H(f)is the transfer function of the controller, Xcorr is the correction signal and Xdist isa disturbance signal [12].

Figure 2.7: A simple negative feedback control loop is shown in the blockdiagram.

The output of the system in a closed loop configuration can be expressed as [4]

X = G(f)(Xdist −Xcorr), (2.17)

where the correction signal is

Xcorr = H(f)(X −Xref ) = H(f)Xerr. (2.18)

We can therefore express X in terms of the reference signal and disturbance

X =G(f)H(f)

1 +G(f)H(f)Xref +

G(f)

1 +G(f)H(f)Xdist. (2.19)

The factor that occurs in front of the reference signal is the closed loop transferand the factor in front of the disturbance is the disturbance propagation function[4]. This can be rewritten as

X =1

1 +1

G(f)H(f)

(Xref +

1

H(f)Xdist

), (2.20)

Chapter 2 Theory 12

which means that if the open loop transfer function, Hopen = G(f)H(f), is muchlarger than 1, then X is close to the reference Xref , and any disturbance is de-creased by the inverse of the transfer function controller namely 1/H(f). So if wedesign a control loop we should aim for as high open loop gain and controller gainas possible.

The control loop is unstable if the open loop transfer function Hopen(f) isequal to −1, as seen from equation (2.20) the denominator approaches infinityand the system starts to oscillate. The open loop transfer function can generallybe written as [12]

Hopen(f) = A(f)eiΦ(f), (2.21)

where A(f) is a frequency dependent amplitude and Φ(f) is the phase shift be-tween the input and output signals. When the phase in equation (2.21) is −180◦,Hopen(f) is close to −1 for unity gain amplitude A(f). In order to keep the systemfrom oscillating a margin is implemented called a phase margin of at least 30◦ atthe point of unity gain (0 dB). Another thing is to keep a gain margin of at least3 dB for when the phase angle inevitably passes −180◦.

2.5.3 PI controller

A Proportional Integral (PI) controller can be used to control a system throughnegative feedback [13]. The proportional part in the PI controller has constantgain. In order to handle slow drift in the system an integrator part is used. FIGURE

2.8 shows a block diagram showing a model of the PI controller. Signals in thetime domain are denoted by small letters whilst their capital counterpart is theirLaplace transform. Here xerr(t) is the error signal and xcorr(t) is the correctionsignal.

Figure 2.8: The block diagram of the PI controller.

Chapter 2 Theory 13

In time domain the proportional block act on the input signal as

xpcorr(t) = Kpxerr(t), (2.22)

where Kp is a constant, and the integral block is

xicorr(t) = Ki

∫ t

0

xerr(t′)dt′ (2.23)

where Ki too is a constant. If we take the Laplace transform of equations (2.22)and (2.23), where s is the complex frequency, we get

Xpcorr(s) = L{Kpxerr(t)}(s) = KpXerr(s), (2.24)

and

X icorr(s) = L

{Ki

∫ t

0

xerr(t′)dt′

}(s) =

1

sKiXerr(s). (2.25)

If we add together the results of equations (2.24) and (2.25) we get

Xcorr(s) = Xpcorr(s) +X i

corr(s) =

(Kp +

Ki

s

)Xerr(s) = H(s)Xerr(s), (2.26)

where H(s) is the collective transfer function. If we look at the transfer functionin complex frequency domain such that s→ i2πf we get

H(f) = Kp +Ki

i2πf. (2.27)

FIGURE 2.9 shows a schematic illustration of the amplitude of the transfer functionin frequency domain. In the illustration the PI corner is marked as a transfer regionbetween where the proportional term dominates over the integral term.

Figure 2.9: The amplitude of the transfer function of the PI controller.

Chapter 3

Setup of the spectrometer andmeasurement procedures

A schematic illustration of the experimental setup is shown in FIGURE 3.1. Theexperimental setup was a recreation and expansion of the setup done perviouslyby [14]. For the experiment an Er:fiber femtosecond laser (Menlo Systems) wasused with a repetition rate of 250 MHz and a power of 20 mW. The laser spectrumcovered 100 nm between 1.5 and 1.6 µm with a bandwidth of 12000 GHz. Thebeam was sent through a polarisation maintaining optical fiber to an open-airoptical cavity with a finesse of 1000. Two mode matching lenses with focal lengthsf1 = 35 mm and f2 = 50 mm were used to couple the Gaussian laser beam to thecavity transverse electric modes (TEM). The second mode matching lens f2 wasmounted on a horizontal translation stage TS. The cavity mirrors M cav

1 and M cav2

were mounted on two horizontal translation stages. The latter translation stageallowed the back mirror M cav

2 to be moved with a 10 µm precision. A piezoelectrictransducer (PZT) was mounted on the former translation stage holding the frontcavity mirror M cav

1 . This PZT was used to scan the cavity length. The PZTwas fed a signal from a signal generator that was amplified by a high voltageamplifier (HVA). See section 3.1 for more details on the cavity and section 3.2 forthe alignment procedure.

Betweeen the two cavity mirrors, below the laser beam, was a premixedair/methane flat flame burner based on the design of [15]. The burner itself wasmounted on a multi-directional translation stage to allow adjustments with 10 µmprecision. The burner was operating at a stoichiometric ratio of 1 and 10 l/minfor methane and air flow, respectively.

Three flat adjustable mirrors M1, M2, and M3 were used to align the beamto the cavity. Two similar mirrors M4 and M5 were mounted behind the cav-ity to align the transmitted beam onto a ruled diffraction grating (Thorlabs,600 grooves/mm). The grating was used to separate the Vernier orders spatially.The grating was designed for a wavelength of 1600 µm. It was mounted on agalvanometer scanner (Thorlabs, GVS001), which made it possible to sweep thegrating to scan across the comb spectrum. The beam diffracted by the gratingwas split by a 50:50 beam splitter. Half of the beam was focused by a lens withf3 = 25 mm onto a position sensitive detector PD1 (Thorlabs, PDQ30C InGaAsquadrant photodiode). The difference signal from PD1 was used as an error signal.

14

Chapter 3 Setup of the spectrometer and measurement procedures 15

The difference signal is calculated as the difference between the sum of two quad-rants on opposite sides of the y-axis from the sensing areas of PD1 (see AppendixC). The other half of the split beam, was sent through a focusing lens f4 = 50 mmonto a photo detector PD2 (Thorlabs, PDA 10CS-EC InGaAs) with adjustablegain. The signal from PD2 was then recorded on a PC using a data acquisition(DAQ) card and yielded the Vernier signal.

The signal from the positioning detector PD1 was used as the error signalto create negative feedback for stabilizing the laser (see section 2.5). The controlsegment is labelled frep controller in the figure. The signal from PD1 was sentto a servo controller (New Focus, LB1005). The output of the servo was fed toa second identical servo controller. The two servos were controlling the currentand PZT actuators of the laser. Section 3.3 further below goes into more detail ofthese laser actuators.

Two apertures Iris1 and Iris2 were placed to help with the alignment of thebeam to the cavity. Another pair of apertures Iris3 and Iris4 were used to selectone Vernier order out of the many orders diffracted by the grating. Aperture Iris3

and Iris4 blocked unwanted VOs from reaching PD1 and PD2 respectively.Finally a signal generator (SG, Agilent 33210A) was used to simultaneously

scan the grating and the cavity PZT with a 20 Hz sine wave. The signal to thecavity PZT was adjusted with a phase shifter and amplification to match the sweepof the grating. These components were used to get a good starting point for thelocking by letting the signal be imaged by the grating over a longer period of time(for further details of the synchronised simultaneous scan see section 3.4).

3.1 Building the high finesse Cavity

To achieve sufficient enhancement of the absorption to study OH and water spectrain the flame the cavity was designed using concave mirrors with reflectivity of99,70 ± 0,10% and radius of curvature R = 5 m. The finesse was approximately1000 using equation (2.9). The mirrors are coated with alternating dielectricmaterials and have a wedge of 3.0 ± 0.1◦ on the outside of the cavity mirrors toavoid interference within the substrate of the mirror [14]. To get the appropriatelength of the cavity equation (2.7) was used together with the perfect matchcondition equation (2.12). The PML is L = 60 cm for frep = 250 MHz.

Chapter 3 Setup of the spectrometer and measurement procedures 16

Figure 3.1: Illustration of the continuous-filtering Vernier spectrometer setup,where BS is the 50:50 beamspliter, f1-f4 are the lenses, M1-M5 are mirrors, TSare translation stages, Mcav

1 -Mcav2 are the wedged cavity mirrors, PD1-PD2 are

two photo detectors, Ph is a phase shifter and HVA is a high voltage amplifier.Note that the beam has to enter the cavity at an angle due to the wedge which

is not shown in the illustration.

Chapter 3 Setup of the spectrometer and measurement procedures 17

3.2 Mode-matching the laser to the cavity

Careful positioning and alignment of the mirrors were needed to couple the lasercomb to the cavity spatially. The positions of the collimator, M1, M2, f1, f2 andthe optical length to the first cavity mirror were reused from the previous setup[14]. A mobile pinhole was used to get the correct alignment of the mirrors. Therequirement for transmitting the comb through the cavity is to have completelyparallel beams inside the cavity. The length of the cavity L, and thereby the FSR,can be coarse tuned with the translation stage. It can be fine tuned via the PZTattached to the front cavity mirror M cav

1 to match the cavity resonance frequenciesto the comb lines. Furthermore the PD2 was temporarily placed directly behindM cav

2 to capture the light of a continuous wave (CW) laser (1550 nm) sent throughthe same polarisation maintaining fibre and collimator. The CW laser was usedfirst in place of the OFC to more easily see modes when the cavity length is closeto but not at PML. By walking the beam by adjusting the rotation of mirrors M2,M3, M cav

1 and M cav2 and tuning L, the higher order transverse modes were reduced

until their peaks were below 1% of the TEM00 signal.

3.3 Laser actuators

The OFC used in this setup was an Er3+ fiber laser that was pumped by a CWdiode laser. The comb laser consisted of a number of parts shown here in aschematic illustration FIGURE 3.2 [16]. The three actuators controlling the repe-tition rate are the current actuator, the PZT actuator and the electro-optic mod-ulator (EOM). Two actuators were used to lock the comb to the cavity; the pumpdiode laser current and the PZT. The current actuator controlled f0 and frep witha bandwidth of approximately 200 kHz. The PZT changes the frep by changingthe laser cavity length. The PZT is limited by it’s response time to a bandwidthof approximately 10 kHz [12]. FIGURE 3.3 shows the two servo controllers wherethe correction signal of the first servo (Current cotroller) is fed to the secondservo (PZT controller) as an input error signal. The control signals from the servocontrollers are sent to the actuators of the laser.

Chapter 3 Setup of the spectrometer and measurement procedures 18

Figure 3.2: Simplified schematic of the internal parts in the comb laser. Theactuators of the comb laser are labeled in blue [16].

Figure 3.3: Schematic of the frep controller. The servo controllers are coupledin series.

Chapter 3 Setup of the spectrometer and measurement procedures 19

3.4 Locking the comb to the cavity

To lock the OFC modes to the cavity, L was shortened from PML until Vernierorder k = −19 was visible which corresponds to a ∆L of −15 µm. The cavitylength and grating position were swept simultaneously with the sine wave from thesignal generator. The error signal was measured by the position sensitive detectorPD1 as a difference signal between two sides of the detector. The difference signalis zero when light hits the detector equally on both sides of the detector. AppendixC shows in detail how this difference signal is measured on the detector. The errorsignal from PD1 was monitored with an oscilloscope. The sweeping angle and offsetof the grating; the alignment of M4 and M5, together with the irises and lenses f3

and f4 were adjusted such that only a single VO hit the detectors. The sweep ofthe cavity length was tuned in phase and amplitude until the width of the errorsignal was maximised in time duration. This ensured a good initial stability sothat the servos mainly correct for small deviations in the sweep. The gain transferfunctions of the open and closed loops for the servos were simulated in MATLABto get a starting point for the settings of the PI-controllers. The grating andcavity length were scanned simultaneously. The servo controllers were set to ”lowfrequency gain limit”, corresponding to proportional correction, which locked thecomb to the cavity. Finally the integrators of the servo controllers were turned on.The settings of the PI-controller gain, PI-corner and gain limits were tested untilthe servos could maintain a stable locking. The PI corner of the current servo wasset to 100 kHz. The low frequency gain limit was set to 50 dB. The gain of thecurrent servo was 4.4 dB. For the PZT servo the PI corner was set to 1 kHz. Thelow frequency gain limit was set to 40 dB and the gain was 3.8 dB.

FIGURE 3.4 shows the open-loop error signal for three consequtive Vernierorders around k = −19 measured in air. The signal was recorded with the gratingfixed and while scanning the cavity length with the PZT. The grating resolvesthe successive Vernier orders but does not resolve their width ΓV . The zero-crossings of the open loop signals from the orders are seperated by FSRV = 10THz, according to equation (2.15). The separation between the extrema of oneVO is determined by the size of the beam hitting the position detector PD1 andthe grating dispersion. By assuming a linear relationship between the time andfrequency domains one can calculate the slope of the error signal in time domain[10], by dividing the difference in the extrema divided by the time separation. Theslope of the middle VO is here 2.3 kV/s which is recalculated to 1.1 µV/MHz byusing the separation of the zero-crossings of the error signals in the time domain,that is 4.8 ms which corresponds to FSRV = 10 THz.

Chapter 3 Setup of the spectrometer and measurement procedures 20

Figure 3.4: Open-loop error signal for three consequtive Vernier orders aroundk = −19. The signal was recorded as the cavity length was scanned linearly

with the grating position fixed.

FIGURE 3.5 shows the open-loop error signal for one Vernier order with fixedgrating position. The sweep of the cavity length was decreased until only one VOwas imaged on the detector.

Figure 3.5: Open-loop error signal for a single Vernier order. The signal wasrecorded with a fixed position of the grating. The sweep of the cavity length

was decreased to resolve only one VO.

FIGURE 3.6 a) shows the open- and closed-loop error signals when the positionof the grating was swept simultaneously with the cavity length. The open loop

Chapter 3 Setup of the spectrometer and measurement procedures 21

error signal is widened in time domain compared to FIGURE 3.5. This suggest thatthe Vernier order is kept on the detector over a longer period of time. FIGURE

3.6 b) shows the closed-loop error signal. The standard deviation of the noise onthe signal is 280 µV. This gives a frequency stability of 252 MHz, calculated bydividing with the slope of the error signal [10]. The frequency stability is thusequal to 2.5% of its resolution (ΓV = 10 GHz) which is slightly worse than theresult achieved by [10].

Figure 3.6: a) Open-loop error signal for VO k = −19, recorded as the cavitylength and the grating position was scanned simultaneously. The sweep of thecavity length and grating position are slightly out of synchronisation and theleft side of the signal is close to the unlinear turning point of the sweep. b) The

corresponding closed-loop error signal recorded with the integrators on.

3.5 Measuring in air

The Vernier signal was measured with PD2. FIGURE A.1 in Appendix A showsthe results of the decrease in peak intensity when the order is increased. Thelength of the cavity was purposefully mismatched from PML by ∆L = −15 µmin order to look for CO2 absorption in air. The expected resolution accordingto equation (2.16) was approximately 10 GHz corresponding to k = −19. Thedata was recorded by using a DAQ card (National Instrument) and a LabViewprogram. The number of data points were 40000 recorded with a sampling rate of1 Msamples/s with 1 MOhm impedance. An external trigger sent from the signalgenerator was used to trigger at 1.8 V. A hundred samples were recorded. Therecorded data was then averaged in MATLAB. The measurement for air was usedas a baseline to normalise the spectrum for the measurement in the flame. Eachmeasured data lacks a proper frequency scale as implementing such lay outside

Chapter 3 Setup of the spectrometer and measurement procedures 22

the scope of this project. The measurement is instead presented as a function oftime.

3.6 Measuring with a flame

The burner was equipped with a cooling flow of water and a co-flow of nitrogenthat kept the flame stable. The flow rates of the methane and air were controlledwith two flow controllers. The flow rate of methane was 1 l/min and the flowrate for air was 10 l/min. When the flame was on a lot of heat is added to thecavity which changes the index of refraction. The alignment of the back cavitymirror was tweaked by adjusting the vertical alignment slightly to compensate forthe change of the optical path length (OPL). The flame was placed in the centerof the cavity using a multi-directional TS. The height above the burner (HAB)was adjusted to record data for HAB = 2, 2,5 and 5 mm. Due to the change inindex of refraction inside the cavity when the flame is on, the Vernier order waschanged with respect to when the flame was off. In order to change the VO ∆L wastweaked by a slight adjustment of the offset on the HVA feeding the cavity PZT.The correct Vernier order (k = −19) was found by looking for the same intensityfor when k = −19 ± 1 without the flame. The measured data was analysed inMATLAB. The data was normalised to the air spectrum to look at the relativeabsorption lines of the products when methane reacts with oxygen. The productsare H2O, CO2 and OH. Finally the data was scaled in amplitude to look for OHabsorption lines in hot water absorption lines spectrum similar to [17].

Chapter 4

Results

The data presented in this section is all measured for the Vernier order numberk = −19±1. The VO corresponds to a detuning from PML by ∆L = −15 µm anda resolution of 10 GHz. The recorded signal is for measurements in atmosphericpressure air and in a flame with different HAB. When the data is not referred toas air it denotes the use of the burner to record the absorption spectrum of theproducts of the combustion: hot water and OH.

4.1 One sweep

FIGURE 4.1 shows the result of one recorded sample for measurements in air (bluecurve) and in a flame with a HAB of 2 mm (red curve). The figure displaysthe intensity (V) of the Vernier signal versus time (ms). The swept spectrum isrecorded two times; one on the way up and one on the way back down. FIGURE 4.1shows the Vernier signal recorded in one direction of the sweep with the turningpoint of the grating sweep at 13 ms. The second turning point of the sweep isoccurs after 35 ms. The signal peaks near 160 mV.

If one compares the recordings of the two spectra in FIGURE 4.1 one can seesome hot water absorption lines present in the sample when the flame is on (HAB= 2 mm, red dots). The signal near the turning point (at 13 ms) is oscillatingslightly. The peaks located between 20 ms and 35 ms are recorded at the mostlinear part of the scan of the grating and cavity.

23

Chapter 4 Results 24

14 16 18 20 22 24 26 28 30 32 34

Time [ms]

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Inte

nsity

[V]

AirFlame

Figure 4.1: A single measurement of the spectra when the flame is off, in air(blue curve) and with the flame on (red curve). The HAB was 2 mm

FIGURE 4.2 shows a zoomed version of the previous figure between 20 ms and 35ms.

20 25 30 35

Time [ms]

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Inte

nsity

[V]

AirFlame

Figure 4.2: Air spectrum (flame off) in blue and spectrum when the flame ison in red HAB = 2 mm.

Chapter 4 Results 25

There are visible hot water absorption lines in Figure 4.2. The signal is oscillat-ing slightly around 25 ms, indicating issues with the stability of the gain of thecontrollers when locking the laser comb to the cavity modes.

4.2 Averaging multiple spectra

A set of N = 100 recorded spectra were averaged. FIGURE 4.3 shows the recordedaveraged signal of air and with the flame on at different heights above the burner.The Vernier signals were averaged 100 times.

14 16 18 20 22 24 26 28 30 32 34

Time [ms]

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Inte

nsity

[V]

Air k=19HAB 2 mmHAB 2.5 mmHAB 5 mm

Figure 4.3: a) The recorded signal for air, b) measured signal for three differentheights when the flame is on, HAB= 2, 2,5 and 5 mm. The signal shows an

average of 100 measured spectra.

The spectra taken at different HAB have a slight difference in intensity, mainlycaused by small changes in the OPL inside the cavity when the HAB is varied.The difference at the peak is approximately −8 mV between the HAB = 2 mmand HAB = 5 mm.

The flame spectrum measured at HAB = 2 mm was studied in more detailby varying the number of averaged samples. FIGURE 4.4 shows 1000 data pointsrecorded over 1 ms between 27 and 28 ms. The measured data points in the figureare connected by lines to make the peaks more distinguishable.

Chapter 4 Results 26

27 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8 27.9 28

Time [ms]

0.057

0.058

0.059

0.06

0.061

0.062

0.063

0.064

0.065

0.066

0.067In

tens

ity [V

]N=1N=20N=100

Figure 4.4: Flame spectra for number of averages, N = 1 (black), N = 20(red), N = 100 (blue). The signal to noise ratio is greatly improved by the

averaging.

The recorded Vernier signals shows three absorption lines for a single sweep (blackcurve) and signals averaged 20 times (red curve) and 100 times (blue curve). Thesignals for a single sweep have a lot of noise. The signal to noise ratio is improvedas the number of averages are increased. For N = 100 in blue the noise is stronglyreduced.

The comb spectrum for the flame with HAB = 2 mm, with N = 100 (bluecurve) and N = 5 (red curve) were plotted together with the recorded averagedN = 100 samples of the comb spectrum in air. The result of the recorded signalcan be seen in FIGURE 4.5 recorded between 25 to 35 ms.

Chapter 4 Results 27

25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30

Time [ms]

0.045

0.05

0.055

0.06

0.065

0.07

0.075

0.08

Inte

nsity

[V]

HAB 2 mm, N=5HAB 2 mm, N=100Air, N=100

Etalon fringes

Figure 4.5: Averaged comb spectrum with the flame on at HAB = 2 mm fornumber of averages N = 100 (blue) and N = 5 (red). The averaged recordingof the comb spectrum in air for N = 100 sample (black) is also plotted, showing

an etalon fringe pattern.

The two spectra in FIGURE 4.5 in the flame with N = 100 and N = 5 are plottedtogether. The recorded signal for air is showing the etalon fringes which are notdistinguishable in the recorded signal with the flame. The absorption lines are ontop of the etalon fringes.

4.3 Normalising and scaling

For three different HAB, the averaged signal of 100 samples with the flame on wasnormalised to the recorded averaged signal of the comb spectrum in air. The resultcan be seen in FIGURE 4.6 which shows a part of the spectrum between 20 and 30ms. The relative intensity is calculated by using the intensity of the air spectrumas the background reference. The normalisation improves the readability of theabsorption lines.

Chapter 4 Results 28

20 25 30 35

Time [ms]

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

Rel

ativ

e in

tens

ity

HAB 2 mmHAB 2.5 mmHAB 5 mm

Figure 4.6: Normalised intensity signal of the comb spectrum in the flame forHAB = 2 mm (blue), HAB = 2,5 mm (red) and HAB = 5 mm (black). All are

averaged N = 100 times.

In order to reduce the noise to a level where the absorption peaks can be comparedin relative intensity difference an averaging of N = 100 is needed. The values of therelative intensity for HAB = 2,5 mm and HAB = 5 mm in FIGURE 4.6 are scaledin amplitude by multiplying with two arbitrary constants until the lines overlapvertically. FIGURE 4.7 shows the spectra measured at different HAB, when theyhave been multiplied with arbitrary constants to make them overlap.

20 25 30 350.86

0.88

0.9

0.92

0.94

0.96

0.98

1

Rel

ativ

e In

tens

ity

HAB 2 mmHAB 2.5 mmHAB 5 mm

OH-absorption

Figure 4.7: Normalised intensity signal of the comb spectrum with the flamefor different HAB, scaled to get an overlap. A suspected OH absorption line is

seen to the right.

Chapter 4 Results 29

At the fourth peak from the right in the figure (at 33 ms) the normalised intensitydiffers noticeably between HAB = 2 mm (blue dots) and HAB = 5 mm (blackdots). This result is similar to the result presented in [17]. This is a suspected OHabsorption line. The relative absorption of H2O is expected to stay fairly constantwith a small increase of the HAB. The absorption of OH is expected to decreasewith increased HAB according to the results of [17].

Chapter 5

Discussion

From the results of the single sweep presented in FIGURE 4.1 it is clear that thereare some oscillations near the endpoints of the sweep. This is due to the fact thatthe gain limit of the servo controllers are reached. Near the peak of the combspectrum there are large amplitude changes in the spectrum. It is difficult to lockthe spectrum if there is nearly no light on the detector. At the turning points ofthe grating sweep the movement is the least linear stemming from the use of asine wave for the sweep. Therefore the most valuable region of study is expectedto be the region in the center of the scan.

The noise on the error signal is estimated by looking at flat part of the airspectrum and taking the standard deviation over a few data points. It was mea-sured to 1.8 mV where the peak signal of the spectrum was 160 mV for the sumsignal of the PD2. The signal to noise ratio (SNR) was roughly estimated to about100 for one average N = 1. The estimate is crude but gives an indication that thesignal to noise ratio is slightly lower than what was previously achieved in [14]. Itis possible to lock the comb to the cavity to scan over a wider region of the combspectrum than what was previously possible.

FIGURE 4.2 shows data for the most linear region of the scan and thus theone of most interest. The absorption lines are visible, however the details of thelines are not clear, due to low signal to noise ratio and oscillations. The spectraover the whole range is interesting as it shows there are water absorption in theentire swept range. In an earlier testing phase the Vernier signal was recordedwith the position detector PD1 by using the sum signal that it provides. Thiswas the originally planned to be used exclusively for both the Vernier and errorsignal. However there was a travelling noise spike picked up in the sum signalof the position detector. The travelling noise spike repeated itself with a regularinterval. As a solution the beamsplitter was introduced to pick up half the signal.This improved the signal to noise ratio from 67 to 100. The error signal wasrecorded after some capacitors were introduced acting as a low pass noise filter.The SNR of the error signal for the open loop was 578. The closed-loop errorsignal reaches 20 mV at the peak of the comb spectrum. The frequency stabilityof 2.5% of the Vernier resolution is close to the results by [10].

FIGURE 4.3 shows the flame spectra for different HAB. The signal for theflame when the HAB was 5 mm is lower by 8 mV compared to the signal for HAB= 2 mm. A hypothesis is that it was recorded at a higher VO k = −20. This

30

Chapter 5 Discussion 31

agrees with the measured intensity drop between Vernier order k = −19 and −20.If the hypothesis is correct the spectrum was recorded with a slightly differentresolution. This is not of great concern when looking at the recorded spectrum ofthe relative intensity as the difference in resolution is small. When measuring atdifferent heights, turning the servos on and off would often lock to another VO.Locking anew in the flame and assuring that the same VO was used was somewhatdifficult. The lock could differ up to 2 VO from VO k = −19.

FIGURE 4.4 shows the recorded flame spectra for different number of averagedsamples. What is interesting is how the system is stable enough to allow foraveraging with a great number of averages. The improvement on the SNR byincreasing the number of averages can not be made indefinitely. At some point theabsorption lines are expected to be broadened by the averaging due to frequencyinstability. At N = 100 samples the peaks are visible and broadening can not beseen clearly. The averaging seems to reduce the noise by a good degree. Thereis a trade off between low noise (many averaged spectra) and broadening of theabsorption lines. If the frequency stability of the locking is improved, and ifthe signal was recorded at a higher VO (higher resolution): sharper peaks andless broadening is to be expected. In order to make good averages a frequencycalibration is needed.

Visible in FIGURE 4.5 is the measurements for both air and in a flame with aHAB of 2 mm. In the figure there are visible etalon fringes in the spectrum of air.The fringe pattern is produced by some optical component. The absorption linesare on top of the fringe pattern and can not be seen in the flame spectra. In order tomore easily see the effect of the absorption the normalised intensity is calculatedand plotted. The result seen in FIGURE 4.6 shows that the absorption peaksoccur at the same sample time. However the relative intensity differs betweenthe different HABs. The noise is low thanks to the averaging. The normalisationagainst the air spectrum allows the relative absorption peaks to be seen. Thechosen region has a relative constant trend over the range between 20 and 35ms. This is expected to be the most linear region of the sweep of cavity andgrating. The intensity was scaled in FIGURE 4.7 to make the curves overlapvertically. According to the results presented in [17] the hot water absorptionlines are expected to stay constant with a slight increase of the HAB. The OHabsorption is expected to decrease with increased HAB. This seems to be thecase for the fourth rightmost peak in FIGURE 4.7. The work on the Vernierspectrometer was deemed finished at this point as the initial goals had been met.

It is difficult to make good use of the data without a proper frequency cal-ibration. One way to further develop the instrument is to add a Fabry Perotetalon with a known FSR and another detector to make a frequency callibrationof the recorded spectrum, similar to the works of [10][11]. The source of the etalonfringes visible in FIGURE 4.5 and their FSR are unknown. There is noise from theposition signal PD1. Improvements to the SNR could be made if the noise of thedetector were lower. One suggestion is to check the expected noise level of thedetector to see if the device is malfunctioning. At the time of writing this thesisthe expected noise level is not specified by the producer.

Measuring the whole comb spectrum is not possible with this setup. Theservos can not lock the comb laser modes to the cavity modes if the amplitude of

Chapter 5 Discussion 32

the error signal is too small. To keep a robust lock with the servos the spectrumswept with the grating was limited to assure that there would always be lighthitting the position detector.

In the combustion process when methane reacts with oxygen it produces waterand CO2. The absorption lines of CO2 are not identified in recorded signal of thecomb spectrum with the flame. The expected relative absorption of CO2 is small[14]. In Appendix B in FIGURE B.1 are measurements done in air averaged over5 samples in an attempt to find carbon dioxide absorption.

The built Vernier spectrometer is stable enough to allow many samples tobe averaged. It can continuously acquire more of the spectrum than what waspreviously possible. One sweep back and forth is recorded in 25 ms.

Chapter 6

Summary and conclusions

The main task of this project was to implement a continuous filtering Vernier spec-trometer to measure absorption spectra in air and in a flame. A spectrometer witha 60 cm cavity with a finesse of 1000 was built using an 1.5 µm Er:fibre femtosecondlaser; a diffraction grating on a galvanometer scanner; two InGaAs photodiodes;two servo controllers and a premixed air/methane flat flame burner. The Vernierorder of the optical frequency comb was locked to the cavity modes with a fre-quency stability of 252 MHz. The demonstrated near-infrared continuous-filteringVernier spectrometer is capable of acquiring a large section of the comb signalspectrum with a resolution of 10 GHz in 25 ms. The Vernier spectrometer hasbeen shown capable of performing multiple measurements in a flame. The sta-bilisation of the lock between the OFC and the open air cavity is good enoughto allow for averaged samples to be made. Hot water absorption lines and OHabsorption were detected in a flame. The averaging reduces the noise considerably.The spectrometer in its current state is not yet ready to measure concentrationof reactant and product. A frequency calibration needs to be implemented tomeasure this.

33

References

[1] A. Khodabakhsh. Fourier transform and Vernier spectroscopy us-ing optical frequency combs. PhD thesis, Umea University, 2017.URL http://www.diva-portal.org/smash/record.jsf?pid=diva2%

3A1093488&dswid=-4670#sthash.1qPHlHwe.dpbs. (Visited 2017-07-24).

[2] P. W. Milonni and J. H. Eberly. Laser Physics. chapter 3. John Wiley &Sons, 2010.

[3] P. Atkins and J. de Paula. Physical Chemistry. chapter 12. Oxford UniversityPress, 10th edition, 2014.

[4] A. Foltynowicz Matyba. Fiber-laser-based Noise-Immune Cavity-EnhancedOptical Heterodyne Molecular Spectrometry. PhD thesis, Umea University,2009. URL http://umu.diva-portal.org/smash/record.jsf?pid=diva2%

3A214195&dswid=4615#sthash.RWmhkwIJ.dpbs. (Visited 2017-07-24).

[5] R. Paschotta. Enhancement Cavities. URL https://www.rp-photonics.

com/enhancement_cavities.html. (Visited 2017-11-06).

[6] P. W. Milonni and J. H. Eberly. Laser Physics, chapter 1, pages 8–10. JohnWiley & Sons, 2010.

[7] K. C. Cossel F. Adler, M. J. Thorpe and J. Ye. Cavity-enhanced direct fre-quency comb spectroscopy: Technology and applications. Annual Reviewof Analytical Chemistry, (3):175–205, February 2010. URL http://www.

annualreviews.org/doi/10.1146/annurev-anchem-060908-155248. (Vis-ited 2017-11-14).

[8] J. Rauschenberger, T. M. Fortier, D. J. Jones, J. Ye, and S. T. Cundiff. Con-trol of the frequency comb from a mode-locked erbium-doped fiber laser. Op-tics Express, 10(24):1404–1410, 2002. URL https://www.osapublishing.

org/oe/abstract.cfm?uri=oe-10-24-1404. (Visited 2017-11-14).

[9] L. Rutkowski and J. Morville. Broadband cavity-enhanced molecular spectrafrom Vernier filtering of a complete frequency comb. Opt. Lett., 39(23):6664–6667, Dec 2014. doi: 10.1364/OL.39.006664. URL http://ol.osa.org/

abstract.cfm?URI=ol-39-23-6664. (Visited 2017-11-14).

[10] A. Khodabakhsh, L. Rutkowski, J. Morville, and A. Foltynowicz. Mid-infrared continuous-filtering Vernier spectroscopy using a doubly reso-nant optical parametric oscillator. Applied Physics B, 123(7):210, Jul

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REFERENCES 35

2017. doi: 10.1007/s00340-017-6781-0. URL https://doi.org/10.1007/

s00340-017-6781-0. (Visited 2017-10-16).

[11] L. Rutkowski and J. Morville. Continuous Vernier filtering of an optical fre-quency comb for broadband cavity-enhanced molecular spectroscopy. Jour-nal of Quantitative Spectroscopy and Radiative Transfer, 187(SupplementC):204 – 214, 2017. ISSN 0022-4073. doi: https://doi.org/10.1016/j.jqsrt.2016.09.021. URL http://www.sciencedirect.com/science/article/

pii/S0022407316301984. (Visited 2017-11-14).

[12] O.Rydberg. Stabilization of an optical frequency comb to an external cavity.Master’s thesis, Umea University, Faculty of Science and Technology, Depart-ment of Physics, 2014. URL http://urn.kb.se/resolve?urn=urn:nbn:se:

umu:diva-93439. (Visited 2017-11-14).

[13] R. A. Paz. The design of the pid controller. 01 2001. URLhttps://www.researchgate.net/publication/237528809_The_Design_

of_the_PID_Controller. (Visited 2017-11-13).

[14] M.Fakhri. Near-infrared optical frequency comb Vernier spectroscopy in airand in a flame. Master’s thesis, Umea University, Faculty of Science andTechnology, Department of Physics, 2017.

[15] G. Hartung, J. Hult, and C.F. Kaminski. Detection of oh in an atmosphericflame at 1.5 micro m using optical frequency comb spectroscopy. Meas. Sci.Technol., 17(9):2485–2493, 2006.

[16] Menlo Systems GmbH. User Manual - FC1500 Optical Frequency Synthesizer.Menlo Systems GmbH, Munich, Germany, October 2010. Version [1.6.3].

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Appendix A

Voltage vs. Vernier Orders

In FIGURE A.1 is the result of measuring the peak intensity of the Vernier signal(PD2) when stepping over the Vernier orders k. In the figure are two linear fittingsto the slope. The first fitting was centred around k = −20 and has a difference ofapproximately 8 mV between the neighbouring Vernier orders. The second fit wasfitted for around VO number k = −40. The difference between the five nearestVernier orders are 2 mV.

0 10 20 30 40 50 60 70

Vernier Order -k

0

0.5

1

1.5

2

2.5

3

Inte

nsity

[V]

Peak signallinear fit y = -0.0081*x+0.2902linear fit y = -0.0019*x+0.1454

Figure A.1: The peak intensity of the Vernier signal is shown as it drops whenshortening the cavity length with integer numbers of k.

36

Appendix B

CO2 absorption lines in air

In FIGURE B.1 is the result of an averaged 5 samples of the spectra in air. Theintensity of the signal is plotted against sample point number. In the figure thesuspected CO2 absorption lines are marked in red. Etalon fringes are present inthe spectrum.

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Data points

0.03

0.031

0.032

0.033

0.034

0.035

0.036

0.037

0.038

Inte

nsity

[V]

Air

Figure B.1: Suspected CO2 absorption lines atmospheric air.

37

Appendix C

Position sensing detector

In FIGURE C.1 is a schematic of the sensing area of the position detector. Theposition detector consists of four quadrants of active sensing area. The positionalong the x-axis is measured as the difference between the quadrants (Q2 +Q3)−(Q1 +Q4).

Figure C.1: The active sensing area of the position detector divided into fourquadrants.

38