Dissemination of ultra-stable optical frequencies over commercial fiber network [Elektronische Ressource] / Osama Terra

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Dissemination of ultra-stable opticalfrequencies over commercial fibernetworksVon der Fakult at fur Mathematik und Physik derGottfried Wilhelm Leibniz Universitat Hannoverzur Erlangung des GradesDoktor der NaturwissenschaftenDr. rer. nat.genehmigte DissertationvonM.Sc. Osama Terrageboren am 27.11.1975in Kairo (Agypten)December 1, 2010Referent: Prof. Dr. Wolfgang ErtmerKorreferent: Prof. Dr. Piet SchmidtTag der Promotion: 30. November 2010iiContents1 Introduction 12 Comparison of frequency standards 92.1 Frequency standards . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Femtosecond frequency comb as a transfer oscillator . . . . . . . . . . 112.2.1 Basics of femtosecond frequency combs . . . . . . . . . . . . . 112.2.2 Fiber based frequency combs . . . . . . . . . . . . . . . . . . . 142.2.3 Transferring the stability of a cavity stabilized laser to a berlaser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2.4 Determination of the correct mode number (n) . . . . . . . . . 222.3 Properties of optical bers . . . . . . . . . . . . . . . . . . . . . . . . 232.3.1 Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3.2 Stimulated Brillouin scattering (SBS) . . . . . . . . . . . . . . 252.3.3 Fiber induced phase uctuations . . . . . . . . . . . . . . . . 272.3.4 Chromatic Dispersion (CD) . . . . . . . . . . . . . . . . . . . 282.3.5 Polarization Mode Dispersion(PMD) . . . . . . . . . . . . . .

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Dissemination of ultra-stable optical
frequencies over commercial fiber
networks
Von der Fakult at fur Mathematik und Physik der
Gottfried Wilhelm Leibniz Universitat Hannover
zur Erlangung des Grades
Doktor der Naturwissenschaften
Dr. rer. nat.
genehmigte Dissertation
von
M.Sc. Osama Terra
geboren am 27.11.1975
in Kairo (Agypten)
December 1, 2010Referent: Prof. Dr. Wolfgang Ertmer
Korreferent: Prof. Dr. Piet Schmidt
Tag der Promotion: 30. November 2010
iiContents
1 Introduction 1
2 Comparison of frequency standards 9
2.1 Frequency standards . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Femtosecond frequency comb as a transfer oscillator . . . . . . . . . . 11
2.2.1 Basics of femtosecond frequency combs . . . . . . . . . . . . . 11
2.2.2 Fiber based frequency combs . . . . . . . . . . . . . . . . . . . 14
2.2.3 Transferring the stability of a cavity stabilized laser to a ber
laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.4 Determination of the correct mode number (n) . . . . . . . . . 22
2.3 Properties of optical bers . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.1 Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.2 Stimulated Brillouin scattering (SBS) . . . . . . . . . . . . . . 25
2.3.3 Fiber induced phase uctuations . . . . . . . . . . . . . . . . 27
2.3.4 Chromatic Dispersion (CD) . . . . . . . . . . . . . . . . . . . 28
2.3.5 Polarization Mode Dispersion(PMD) . . . . . . . . . . . . . . 29
3 Phase noise measurement and compensation 33
3.1 Phase noise sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2 Frequency domain measurement . . . . . . . . . . . . . . . . . . . . . 35
3.2.1 Power spectral density of phase uctuations . . . . . . . . . . 36
3.2.2 Phase demodulation . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Time domain measurement . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3.1 -type frequency counters . . . . . . . . . . . . . . . . . . . . 40
3.3.2 -type counters . . . . . . . . . . . . . . . . . . . . 41
3.3.3 Allan deviation (ADEV) . . . . . . . . . . . . . . . . . . . . . 42
3.3.4 Modi ed Allan deviation (ModADEV) . . . . . . . . . . . . . 43
iii3.4 Relation between S and ADEV . . . . . . . . . . . . . . . . . . . . . 45
3.5 Interferometer for phase noise compensation . . . . . . . . . . . . . . 47
3.5.1 Interferometer Design . . . . . . . . . . . . . . . . . . . . . . . 47
3.5.2 In transfer function . . . . . . . . . . . . . . . . . 49
3.5.3 Interferometer phase noise . . . . . . . . . . . . . . . . . . . . 52
4 Optical signal detection and ampli cation 57
4.1 Amplitude noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.1.1 Thermal Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.1.2 Shot noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1.3 Intensity Noise (Laser and ampli er) . . . . . . . . . . . . . . 59
4.2 Optical ampli cation . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.1 Erbium doped ber ampli er (EDFA) . . . . . . . . . . . . . . 62
4.2.2 Fiber Brillouin ampli er (FBA) . . . . . . . . . . . . . . . . . 65
4.2.3 Comparison between FBA and EDFA . . . . . . . . . . . . . . 66
4.2.4 FBA pump laser stabilization . . . . . . . . . . . . . . . . . . 71
5 Optical frequency transfer over 146 km urban ber 73
5.1 Description of the ber link . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 The frequency transmission setup . . . . . . . . . . . . . . . . . . . . 75
5.3 Laser noise and self-heterodyning . . . . . . . . . . . . . . . . . . . . 77
5.4 Frequency transfer stability and accuracy . . . . . . . . . . . . . . . . 79
5.4.1 Frequency transfer stability . . . . . . . . . . . . . . . . . . . 79
5.4.2 Accuracy of the transmitted frequency . . . . . . . . . . . . . 81
6 Remote Measurement of frequency standards using the ber link 83
6.1 Frequency measurement setup . . . . . . . . . . . . . . . . . . . . . . 83
6.2 Short-term stability of the cavity stabilized lasers at IQ . . . . . . . . 85
6.3 Stability of the Mg-frequency standard . . . . . . . . . . . . . . . . . 88
7 Frequency transfer over 480 km ber link using FBA 91
7.1 Description of the ber link . . . . . . . . . . . . . . . . . . . . . . . 92
7.2 The frequency transmission setup . . . . . . . . . . . . . . . . . . . . 93
7.3 Frequency transfer stability and accuracy . . . . . . . . . . . . . . . . 95
iv8 Towards a European ber network for frequency dissemination 99
8.1 Towards a frequency comparison over 900 km (PTB-MPQ) . . . . . . 100
8.1.1 Expected frequency stability of the 900 km link . . . . . . . . 103
8.1.2 Towards a European ber network . . . . . . . . . . . . . . . 104
A Model for phase noise compensation 111
B Phase noise and modulation 119
List of abbreviations 131
vviAbstract
The development of optical frequency standards has a strong impact on metrology,
astronomy and on fundamental physics. Todays optical frequency standards reach
16 15 1=2a relative uncertainty below 10 and a relative instability of 10 /( /s). For
the dissemination of such a stable frequency, an optical ber link provides a promis-
ing technique to avoid degradation of frequency stability and accuracy when used
with a technique that compensates phase noise due to temperature uctuations and
acoustic perturbations of the optical ber.
In this thesis, an all-in- ber interferometer to detect and compensate the phase
noise introduced by the ber link has been developed. In order to measure the lowest
attainable phase noise after compensation, the interferometer is stabilized after being
connected to a short ber. The interferometer reaches a relative instability of ()y
17 20= 210 /(/s) that drops below 10 after about one hour. Even for the free-
18running interferometer the relative instability reaches a icker oor of 1 10 after
a few minutes. This extremely low noise oor is attributed to the careful design of
the interferometer.
This interferometer has been used to investigate the performance of a 146 km
telecommunication ber to transfer ultrastable optical frequencies. The 146 km long
ber consists of two 73 km bers connecting the Physikalisch-Technischen Bunde-
sanstalt (PTB) in Braunschweig to the Leibniz University of Hanover (LUH). The
phase noise introduced by the ber is compensated with a compensation band-
width limited by the time delay introduced by the ber link. The frequency trans-
fer is performed over the 146 km ber link with a relative instability of () =y
15 193.310 /(/s) and a relative uncertainty below 110 .
As an application, the frequency of the Mg frequency standard at the Institute of
Quantum Optics (IQ) in LUH has been remotely measured against that of optical
viifrequency standards at PTB using the frequency stabilized 73 km ber link. A comb has been used to transfer the stability of the frequency standard at
PTB to a ber laser at =1542 nm. At IQ, a second femtosecond frequency comb is
used to compare the transmitted light frequency with that of Mg frequency standard
at =914 nm (which is then frequency doubled to meet the clock transition of Mg
at =457 nm). The ratio between the frequencies of the transfered light from PTB
15and the Mg laser showed a relative short term instability of about = 4 10y
at 0.1 s limited by the instability of the Mg interrogation laser.
Currently, this technique described in this thesis is implemented to enable fre-
quency comparison over a ber link of about 900 km between PTB and the Max-
Planck institute of Quantum Optics (MPQ) in Garching. Here the transmitted sig-
nal has to be ampli ed several times to maintain the required power level and signal
to noise ratio (SNR). Eight bidirectional erbium-doped ber ampli er (BEDFA) sta-
tions are used to amplify the signal about every 100 km. All stations are controlled
remotely using a wavelength of 1.3m and a built-in microcontroller with specially
designed software.
The performance of a ber Brillouin ampli er (FBA) instead of BEDFA has been
additionally studied in order to bridge larger spans in a single step. Unlike BEDFA,
a FBA enables bidirectional ampli cation without su ering from lasing e ects or
saturation in the gain medium. The FBA ampli cation can reach about 50 dB
down to an input signal power of several nW’s. This allows to bridge distances of
about 250 km in a single step. We have tested this technique over a 480 km ber
link using only one intermediate ampli cation station, together with ampli ers at
the remote and the local ends. The relative instability of the frequency transfer is
14 18 ()=210 /(/s) and reaches 210 after about two hours. The mean valuey
of the transmitted frequency is shifted from that of the reference laser by 64Hz with
a statistical uncertainty of 54 Hz. This shift corresponds to fractional frequency
19deviation of 310 . This result demonstrates for the rst time worldwide that,
telecommunication bers with lengths up to about 500 km are suitable to remotely
compare the best available optical clocks within a few seconds.
Keywords: Frequency transfer over optical ber, ber phase noise, optical am-
pli cation, All-in- ber interferometer, comparison of frequency standards.
viiiZusammenfassung
Optische Frequenznormale haben gro es Anwendungspotenzial in der Metrologie,
Astronomie, und fur fundamentale Fragen der Physik. Heutige optische Frequen-
17znormale erreichen relative Unsicherheit von 10 und eine relative Instabilit at von
15 0:510 /( /s). Um dieses Potenzial voll auszusch opfen, ist es erforderlich, auch Fre-
quenznormale an unterschiedlichen Standorten direkt miteinander zu vergleichen.
Ein solcher Vergleich kann durch die Ubertragung optischer Frequenzen ub er eine
Telekommunikationsglasfaser erfolgen. Diese Verfahren wird in dieser Arbeit unter-
sucht.
In dieser Arbeit wurde ein Faserinterferometer aufgebaut, um das Phasenrauschen
der Glasfaser aufgrund von akustischen und thermischen Schwankung hochemp nd-
lich zu detektieren und zu kompensieren. Schlie t man den Messarm des Interferom-
eters mit einem kurzen Stuc k Faser ab,asstl sich das Eigenrauschen des Interferome-
ters und damit seine Nachweisgrenze fur Phasen uktuationen bestimmen. Als Folge
eines sorgf altigen Aufbaus, bei dem insbesondere die L ange unkompensierter Faser
minimiert wurde, erreicht das stabilisierte Interferometer eine relative Instabilit at
17von () = 210 /(/s); nach einer Stunde betr agt die relative Instabilit at bere-y
20its weniger als 10 . Selbst fur das unstabilisierte Interferometer konnte bereits
18nach eine paar Minuten eine relative Instabilit at von 1 10 erreicht werden.
Die Eignung dieses Interferometers, eine optische Frequenz uber eine 146 km
lange, kommerzielle Glasfaserstrecke hochstabil zu ub ertragen, wurde untersucht.
Die 146 km lange Teststrecke besteht aus zwei 73 km langen Fasern, die die Physikalisch-
Technischen Bundesanstalt (PTB) in Braunschweig mit der Leibniz Universit at
Hannover (LUH) verbinden. Auf dieser Ubertragungsstrecke wurde eine relative
15 19Instabilit at von () = 3.310 /(/s) und ein relative Genauigkeit von 110y
erreicht. Dabei wird die erreichbare Instabilit at durch das Phasenrauschen der un-
stabilisierten Faser und durch die Laufzeit des Lichts in der Faser bestimmt.
ix