Cancelation of optical phase noiseinduced by an optical fiber

Term Project, in the group of Prof. J. P. Home at theInstitute for Quantum Electronics, ETH Zurich

Supervised by D. Kienzler

N. Darkwah Oppong

08/06/2015

Abstract

We present an optical set-up, electronic hardware, and a lock-scheme to accurately can-cel optical phase noise induced by an optical fiber. We use a double-pass hetereodynemeasurement and an AOM for phase-compensation as described in [1] to achieve noisesuppression of 23.9 dB averaged over a 2 kHz span around the carrier frequency.

1. Introduction

Narrow linewidth lasers are crucial for applications that require long coherence time e.g.in trapped ion experiments. Today, laser sources with Hz-level linewidth can be achievedby locking to commercially available high finesse cavities.However, the phase written onto light by an optical fiber is very sensitive to pressureand temperature changes [2]. Acoustic noise (100Hz – 2 kHz) from the lab environmentmediated by an optical fiber leads to broadening of the laser light to kHz-level andultimately limits coherence time. This poses a problem where long optical fibers arerequired. This project develops the electronics to cancel optical phase noise using themethod described in [1].The report gives a short introduction into phase noise induced by an optical fiber insection 2.1 and explains a cancelation scheme for slow phase noise in section 2.2. Thefull experimental setup including optics is described in section 3 and the results arepresented in section 4.

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2. Theory

In this section the theoretical background to phase noise induced by an optical fiber andcancelation of slow phase noise is briefly explained. This identifies the requirements andlimits of the experimental setup described in section 3. The interested reader shouldconsult [1, 2, 3] for more details.

2.1. Phase Noise Induced by An Optical Fiber

The optical path length (OPL) of a fiber is given by the refractive index n(r) and theexact path γ that light takes through the fiber [4]:

OPL =

∫γds n(r) (2.1)

Light which travels through the fiber arrives with the same phase shift ϕ as light thathas travelled the distance OPL in vacuum.

If we assume that at r, t = 0 the phase of the electric field is zero, then the field behindthe fiber is given by:

E(t) = E0 cos [ωt+ ϕ (OPL)] (2.2)

If the optical path length of the fiber is changing over time, e.g. due to pressure ortemperature changes, OPL is time dependent and we introduce a time dependent phaseshift ϕε(t) ≡ ϕ (OPL (t)):

E(t) = E0 cos [ωt+ ϕε (t)] (2.3)

ϕε(t) describes the optical phase noise introduced by the fiber. The spectrum of thephase noise mainly depends on the acoustic noise spectrum in the environment since theresponse of an optical fiber is approximately flat across the 100Hz – 2 kHz band [2].

2.2. Cancelation of Slow Optical Phase Noise

We describe a two-step process to cancel optical phase noise. First, the current phaseerror ϕε(t0) due to transit through the optical fiber is measured using hetereodyne detec-tion. Second, an AOM is used to write the negative phase error ϕAOM = −ϕε(t0) onto

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φ0 + φε

φ0 +2 φε

φ0

Figure 1: Optical step-index fiber with counterpropagating beams (solid and dashed line). ϕ0 isthe initial fixed phase and ϕε is the phase error picked up during transit [4].

the light prior transit which compensates for the phase noise at the output of the opticalfiber.

Assume that we overlap two laser beams (A and B) onto a photodiode. The meanphotocurrent i is then given by [4]:

i = iA + iB + 2 (iAiB)1/2

cos ω∆t+ (ϕA − ϕB) (2.4)

iA, iB is the photocurrent that is generated by each beam individually. ϕA, ϕB denotesthe optical phase of each beam and ω∆ = ωA − ωB denotes the frequency difference ofboth beams. Let ω∆ ≡ 0, ϕA ≡ 2ϕε, and ϕB ≡ −2ϕAOM. Then, discarding the constantterms, the photocurrent is given by:

i ∝ cos 2ϕε + 2ϕAOM ≈ 2ϕε + 2ϕAOM (2.5)

This is the desired error signal required for the cancelation scheme. It vanishes forϕAOM = −ϕε. This condition is fulfilled if the AOM phase cancels the phase erroracquired by light during transit through the fiber.

The cancelation scheme can only be effective if the acoustic phase noise in the band100Hz – 2 kHz is much slower than the transit time of light in the fiber:

τtransit = Lfibernfiberc≈ 25m

1.5

c= 0.125µs (2.6)

And:

τnoise = min100Hz≤fnoise≤2 kHz

1

fnoise=

1

2 kHz= 500µs (2.7)

Thus, the optical path length does not change significantly during transit. Light thatis retro-reflected through the same fiber as depicted in Fig. 1 simply carries the phaseerror ϕε twice [2]. Additionally, the phase/frequency modulation (FM) bandwidth of the

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To Spectrum Analyzer

729 nmTA Diode Laser

f=200 mm

φAOM

PowerSetpoint

AOM

+1st orderφ0 + φAOM

φ0 + φAOM+ φε

0th Orderφ0-1st Order

φ0 - φAOM

0th Orderφ0 + φAOM +2φε

Window

Mirror

ND Filter

To Experiment

f=125 mm

FreuqencySetpoint

VCO

Level-3 MixerDC Error

Signal

Var.Attn.

RF Amplifier

RF Amplifier

LO

RFDETECTOR

LO

FREQ ERR IN

ERR OUT

INT ERR IN

AOM

IF

Photodiode2 φAOM+2φε

DigitalPI-Controller

DDS

-10 dB

Directionalcoupler

Figure 2: Experimental setup: RF/DC signal lines are shown in black and the laser beam is shownin red where dashed lines denote retro-reflections. Main electronics can be found inthe gray box and are explained in section 3.2.

AOM must be larger than the bandwidth of the phase noise. This results in requirementsfor the electronics that control the AOM phase.

3. Experimental Setup

The full experimental setup - including optics and electronics as shown in Fig. 2 - isexplained in this section. Most of the experimental setup is located on a single tablewith only the window for retro-reflection from the fiber located on a second table.Section 3.1 describes the optical setup and section 3.2 describes the electronics board.

3.1. Optics

The coherent light source used for this experiment is a tapered amplifier (TA) diodelaser tuned to 729 nm and locked to a high finesse cavity. Light from the laser is focusedinto an 200 MHz AOMa and the 0th order is retro-reflected using a mirror. We use an

aThe setup works equivalently for AOMs at different frequencies. The desired AOM frequency is onlylimited by the availability of suitable voltage controlled oscillator (VCO) and a photodiode that can

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Attenuator

VCO

Mixer

Figure 3: Top layer of the printed circuit board used for phase noise cancelation. The bottomlayer is a continous ground plane with few short traces. RF components and transmis-sion lines are shown in red.The corresponding schematics can be found in Fig. 4.

attenuator (ND filter) in front of the mirror to reduce the power of the retro-reflectedlight to prevent saturation of the photodiode.The 1st order is coupled into a fiber (blue coiled line in Fig. 2) and taken to the mainexperiment where a window right after the outcoupler is used to reflect a small portion(≈ 4 %) back into the fiber.Light from the retro-reflection is then refracted again by the AOM and the 0th order ofthe retro-reflection from the fiber (short-dashed line in Fig. 2) follows the same path asthe -1st order of the retro-reflection from the mirror (long-dashed line in Fig. 2). Thebeat frequency of the two beams which carries the phase 2ϕAOM− 2ϕε is then measuredwith a fast photodiode and the amplified signal is fed into the DETECTOR port of theelectronics board.

3.2. Electronics

The main electronic components inside the gray box in Fig. 2 are all mounted to a singleprinted circuit board (PCB). The top layer of the PCB can be found in Fig. 3 and the

detect a signal at twice the VCO frequency.

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electronic schematic can be found in Fig. 4. Properties of components mentioned in thissection are not directly measured but taken from data provided by the manufacturer.

There are two seperate circuits on the PCB, which share the power supply. The firstcircuit is used to detect the phase error (ports DETECTOR, LO, ERR OUT in Fig. 2).The second circuit is used to drive the VCO (ports FREQ ERR IN, INT ERR IN, AOMin Fig. 2) with a fixed setpoint (i.e. frequency) and an offset given by the FREQ ERR INport.

The phase detector circuit uses a mixer (MIX1) to mix down the signal from the pho-todiode to DC. The operational amplifier (U100, 10MHz unity gain bandwidth) onthe IF port of the mixer serves as a buffer and a low pass filter, which filters the fastfrequency components from the error signal. The direct digital synthesizer (DDS) is astable frequency reference with less phase noise than the VCO (kHz-level phase noise).The maximal output power of the DDS is 0 dBm, but the mixer requires a power levelof ≥ 3 dBm for minimal conversion loss. We use a broad-band 10 dB RF amplifier (U101)on the LO port of the mixer to meet the power requirement.

The VCO driving circuit consists of two low noise voltage source circuits, one for thetuning voltage of the VCO and the other for the control voltage of the variable RFattenuator. The low noise voltage source circuit consists of three stages. The firststage is a precision 2.5V voltage reference (U1) with low temperature dependence of2 – 10 ppm/K respectively 5 – 25µV/K. The second and third stage use a low noise(3 nV/

√Hz, 33 nV/

√Hz incl. Johnson noise) operational amplifier (U2). The second

stage is a negative amplifier with a gain of −R3/VR2 + R2. The third stage adds thereference voltage to the voltage from the port FREQ ERR IN and inverts the result.The output voltage Vout of the three stage circuit is then given by:

Vout = 2.5VR3

VR2 + R2− VFREQ ERR IN (3.1)

VR2 is a variable resistor (potentiometer) and allows tuning the setpoint of the outputvoltage (i.e. the VCO frequency).The same low noise voltage source circuit is used for the variable attenuator for whichthe port INT ERR IN can be used to lock the laser intensity by controlling the RF powerthat drives the AOM.

A custom FPGA-based digital PI-Controller developed by the group (EVIL) is used toset the correcting voltage VFREQ ERR IN, i.e. the corresponding phase on the VCO. The

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controller is connected to the ports FREQ ERR IN and ERR OUT of the electronicsboard.

The PCB is made of FR-4 laminate with a thickness of 0.81mm (0.032 in) and has two35µm copper layers. The bottom layer is a continous ground plane. RF signal linesare 50Ω transmission lines to minimize losses (0.022 dB/cm). The transmission linesfollow a coplanar waveguide design with a continous ground plane on the top that isconnected to the bottom ground plane with multiple vias (stitching). All components forvoltage regulation are located on one end of the board to maximize thermal resistance totemperature sensitive components, such as the VCO, variable attenuator, and precisionvoltage circuit.

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−120

−110

−100

−90

−80

−70

−60

−50

−40

Pow

er(L

ock

off)P

off

[dB

m]

−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0

Detuning ∆f [kHz]

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−90

−80

−70

−60

−50

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−30

−20

−10Po

wer

(Loc

kon

)Pon

[dB

m]

Lock onLock off

−4 −2 0 2 4

−20

−40

−60

−80

Figure 5: Frequency spectrum of the signal from the photodiode for the Lock on (red line, powerlevel on the left axis) and Lock off (black line, power level on the right axis) mea-surements. The x-axis shows the detuning from the beat frequency (399.999642MHz,400.000102MHz) and the white area denotes the 2 kHz span used for the average noisesuppression calculation. The inset shows the Lock on signal over a 10 kHz span.

4. Results

We make two measurements to evaluate the effective noise suppression. For both mea-surements we record the spectrum of the beat-note signal on the photodiode using thedirectional coupler at the DETECTOR port and a spectrum analyzer as shown in Fig. 2.The two resulting spectra are plotted in Fig. 5.

The first measurement (Lock on in Fig. 5) is taken with the setup shown in Fig. 2 andthe PI-Controller locked.The second measurement (Lock off in Fig. 5) is taken with a modified setup: The DDS isdirectly connected to the AOM and the electronics board is not used. This modificationis neccessary because the spectrum does not only contain optical phase noise induced bythe fiber, but also phase noise from the (unlocked) VCO.

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102 103

Frequency offset from carrier f [Hz]

−90

−80

−70

−60

−50

−40

−30

−20

−10P

hase

nois

eL

(f)

[dB

c/H

z]

Lock onLock off

Figure 6: Phase noise L (f) (f = 25Hz . . . 1 kHz) of the spectra shown in Fig. 5.

The phase noise is plotted in Fig. 6 using the following definition adapted from [3]:

L (f) =average sideband noise power in1Hz bandwidth

carrier power(4.1)

[L ] = dBc/Hz and f denotes the offset of the sideband from the carrier frequency. Thesideband noise power is averaged over the left and right sideband because the spectraare asymmetric. The phase noise is rescaled to a 1Hz bandwidth using an offset of10 log10 1/25 = −13.98 dB because the spectra are recorded with 25Hz bandwidth.

The method to evaluate the phase noise suppression is adapted from previous work doneby the group. We use a Lorentzian fit of the spectrum over a 30 kHz span to estimate thenoise floor (−87.8 dBm, −113.4 dBm) and the beat frequency carrier (399.999642MHz,400.000102MHz) of both spectra in Fig. 5. The power level difference of the Lock onand Lock off spectrum is calculated and averaged over a 2 kHz span around the carrier.We find an average phase noise suppression of 23.9 dB using this method.b

5. Summary

We have built an electronis board to accurately cancel optical phase noise induced byan optical fiber. Further, we have quantified the noise suppression with the methodsdescribed in section 4. We are able to suppress phase noise by 23.9 dB averaged over a2 kHz span around the carrier frequency.

bThe electronics previously used by the group achieved an average noise suppression of 10 – 15 dB.

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References

[1] L.-S. Ma et al. “Delivering the same optical frequency at two places: accurate can-cellation of phase noise introduced by an optical fiber or other time-varying path”.In: Optics Letter 19.21 (Nov. 1994), p. 1777.

[2] L.-S. Ma et al. “Accurate cancellation (to milliHertz levels) of optical phase noisedue to vibration or insertion phase in fiber transmitted light”. In: Proceedings ofSPIE 2378 (1995), p. 165.

[3] E. Rubiola. Phase Noise and Frequency Stability in Oscillators. Cambridge Univer-sity Press, 2008.

[4] B. E. A. Saleh and M. C. Teich. Fundamentals of Photonics. Second Edition. Wiley,2009.

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