Dissipative Kerr soliton photonic terahertz oscillator referenced to a molecule James Greenbergy Brendan M. Heffernany Tomohiro Tetsumoto

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Dissipative Kerr soliton photonic terahertz oscillator

referenced to a molecule

James Greenberg†,∗, Brendan M. Heffernan†, Tomohiro Tetsumoto

and Antoine Rolland∗

IMRA America, Inc., Boulder Research Labs, Longmont, CO 80501, USA

†These authors contributed equally.

∗To whom correspondence should be addressed; E-mail: jgreenbe@imra.com, arolland@imra.com.

Controlling the coherence between light and matter has enabled the radiation

of electromagnetic waves with spectral purity and stability that deﬁnes the

Syst`

eme International (SI) second. While transitions between hyperﬁne levels

in atoms are accessible in the microwave and optical domains, faithfully trans-

ferring such stability to other frequency ranges of interest is not trivial. Such

stability is speciﬁcally sought after for the terahertz domain to improve the res-

olution in very long baseline interferometry and molecular spectroscopy, and

advance the technological development of high-speed, high data rate wireless

communications. However, there is an evident lack of native frequency ref-

erences in this spectral range, essential for the consistency of measurements

and traceability. To mitigate the frequency drift encompassed in such waves,

we experimentally demonstrate that using rotational spectroscopy of nitrous

oxide (N2O) can lead to linewidth reduction up to a thousandfold. A pair of

diode lasers, optically injected with a low-noise, chip-based dissipative Kerr

soliton, were incident upon a uni-travelling-carrier photodiode. We frequency-

locked the emitted terahertz wave to the center of a rotational transition of

arXiv:2210.10850v1 [physics.optics] 19 Oct 2022

N2O through phase modulation spectroscopy. A terahertz wave with a 6 Hz

linewidth was achieved (fractional frequency stability of 2×10−11 at 1 second

averaging time) while circumventing the need of frequency multiplication or

division of frequency standards.

The scientiﬁc community has recently focused on efforts to ﬁll the so-called terahertz gap1–3.

The gap refers to a lack of mature and convenient technologies for generating, manipulating,

and detecting terahertz radiation. The terahertz band exists on the electromagnetic spectrum

between microwaves and infrared light, both of which have well developed libraries of compo-

nents for commercial and scientiﬁc use. Much of the motivation for bridging the gap is driven

by a number of critical applications. For example, proposals for the sixth-generation wireless

technology standard, 6G, call for carrier frequencies from 300 GHz to many terahertz4. These

larger frequencies are required to facilitate wider bandwidths for faster data rates and relieve

congestion in currently deployed communication channels. Low noise and long-term stable

THz oscillators are required to improve bit error rate and error vector magnitude for wireless

data in order to realize this spectral band’s full potential5;6. Another important application is

very long baseline interferometry for radioastronomy where the coherence length of the local

oscillator is needed to maintain constructive interference in the phased array antennae7.

Generating terahertz radiation via photomixing two or more continuous wave (CW) optical

frequencies on an ultra-fast diode offers many advantages8–11. This approach enables the use

of widely available and high performance photonic technologies, including broadly tunable low

noise lasers, optical frequency combs, fast modulators and photodiodes12. The technique can

leverage advanced photonic integrated chip technology, like dissipative Kerr solitons (DKS)

generated by micro ring resonators13, providing a path for low size, weight, power, and cost

(SWAPc) terahertz devices. Importantly, photomixing currently provides the most spectrally

pure THz waves. It was recently demonstrated that a pair of highly-coherent continuous wave

lasers, divided down to the terahertz domain using DKS technology, led to the implementa-

tion of a compact 0.3 THz oscillator with a phase noise that out-preforms direct generation or

multiplication of microwave references (for Fourier frequency above 100 Hz)14.

Maintaining frequency stability in the long-term of such high performance terahertz oscil-

lators remains a challenge. A terahertz wave generated via photomixing has a stability given by

the quadratic sum of the optical waves’ stability, which fractionally is seen from the terahertz

spectral range as relatively mediocre. For example, beating two telecom lasers with ∼10 kHz

linewidth (roughly corresponding to fractional stability in the order of 10−9) on a fast photo-

diode would lead to a ∼10 kHz linewidth as well, but at hundreds of GHz. At 0.3 THz, it

corresponds to a fractional frequency stability of 10−6. While it is possible to improve this

stability by phase locking the frequency difference of the two lasers to a microwave reference,

this comes with costly and complex down-conversion schemes through electro-optic combs or

sub-harmonic mixers15–17. Additionally, the stability of the microwave reference can be cor-

rupted in the process of converting it to the terahertz domain. To avoid the use of spectral purity

transfer between disparate frequency ranges, we propose stabilizing a terahertz oscillator to a

native terahertz reference through phase modulation spectroscopy of a gas18.

In the terahertz domain, many polar gas molecules (e.g., HCN, OCS, and N2O) possess

distinct transitions between quantized rotational states19. These levels are populated at room

temperature by blackbody radiation. The dipole moments of such molecules give rise to ab-

sorption coefﬁcients strong enough to perform absorption spectroscopy through a modest path

length (<1m). Precise measurements of these molecular energy levels and lineshapes can

reveal details of molecular structure as well as interactions between molecules and their en-

vironment. The most common practice is to probe a molecule with a terahertz source that is

referenced to a microwave frequency standard20;21. While many improvements to precision

rotational spectroscopy techniques have been pioneered over the years22–29, probing rotational

transitions and using them to stabilize a DKS-based, photonic terahertz source is a fundamen-

tally new approach.

Here, we constructed an oscillator consisting of a pair of diode lasers, separated in fre-

quency by 301.442 GHz, which were simultaneously incident on a uni-travelling-carrier pho-

todiode (UTC-PD). The resulting beat note was emitted by a horn antenna. To enable preci-

sion spectroscopy, the differential phase noise between the two diode lasers was minimized by

optically-injecting two modes of a low noise DKS, respectively, in each diode. The frequency

difference between the two laser diodes was locked to the center of a rotational transition via

phase modulation spectroscopy of nitrous oxide (N2O). This led to a 301.442 GHz oscillator

with a sub-10 Hz linewidth and a fractional frequency stability of 2×10−11 at 1 second averag-

ing time, which corresponds to an unprecedented level of stability using a rotational transition

in the terahertz domain.

Phase modulation spectroscopy relies on three core elements: a phase-modulated local oscil-

lator, a gas cell, and a feedback mechanism that guarantees the local oscillator to be referenced

to the gas. A conceptual overview of the system is shown in Fig. 1. In this experiment, the

local oscillator was implemented with photonic technologies. DKS enable the generation of

optical pulse trains with high repetition rates, usually on the order of a hundreds of GHz. Here,

we generated a 301.442 GHz optical soliton with a microring on a silicon nitride (Si3N4) chip

(methods on how a soliton is generated are provided in the supplementary materials). While

the phase noise properties and timing jitter of an optical soliton are attractive30–32, using it di-

rectly for spectroscopy is not practical due to dispersive elements prior to photodetection, that

inevitably destroy a spectroscopic signal. To entirely overcome dispersion engineering of an

optical soliton, we transferred its spectral purity to a pair of diode lasers, separated by the same

frequency of the optical soliton repetition rate. This was accomplished through optical injection

locking33;34, realized by ﬁrst splitting the DKS comb into two paths. In this case, two neigh-

boring comb lines at 1550 nm and 1552.42 nm were selected and each was sent to the input of

the corresponding LD through a three-port ﬁber circulator. The optical spectrum of the output

after ﬁltering using a waveshaper is shown in Fig 1(b). The injection-locked LD’s show a 40 dB

improvement in signal to noise ratio (SNR) compared to the DKS.

When attempting to transfer the spectral purity of an oscillator to another, a fundamental

assessment is the residual noise measurement, i.e., verifying that the transfer process does not

hinder the noise properties being transferred. We have measured the ability of two injection-

locked LD’s to reliably reproduce the phase noise properties of the DKS, as well as its stability

(see the supplementary information for more experimental details). The phase noise of the DKS

repetition rate and the residual phase noise of the injection process is shown on Fig. 1 (c) (black

and red curve, respectively). For Fourier frequencies below 100 kHz, one can observe that the

additive noise of injection-locking is well below the DKS repetition rate which indicates that

the spectral purity transfer is successful. The bump above 100 kHz is due to the measurement

noise ﬂoor (explanation given in the supplementary material). Additionally, we have evaluated

the precision of the stability transfer in terms of Allan deviation. The residual fractional in-

stability of injection-locking at 301.442 GHz reaches 8×10−14 at 1 second averaging time.

This corresponds to a linewidth transfer that is 25 mHz at 301.442 GHz while the free-running

linewidth of the DKS repetition rate is larger than 1 kHz. Therefore, the spectral purity of the

DKS repetition rate is faithfully transferred to a pair of LDs.

Prior to interfering the LDs on a UTC-PD, they were modulated by two optical modulators

each serving a singular purpose. To perform phase modulation spectroscopy, one laser line

was phase modulated with an electro-optic modulator (EOM) at the frequency fmto generate

sidebands of the same frequency fmin the terahertz domain. The other laser line propagated

through a deﬂecting acousto-optic modulator (AOM) shifting the laser frequency by fAO for

ﬁne frequency correction of the two lasers’ frequency difference. This frequency difference,

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DissipativeKerrsolitonphotonicterahertzoscillatorreferencedtoamoleculeJamesGreenbergy;,BrendanM.Heffernany,TomohiroTetsumotoandAntoineRollandIMRAAmerica,Inc.,BoulderResearchLabs,Longmont,CO80501,USAyTheseauthorscontributedequally.Towhomcorrespondenceshouldbeaddressed;E-mail:jgreenbe@imra.com,arol...

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Dissipative Kerr soliton photonic terahertz oscillator referenced to a molecule James Greenbergy Brendan M. Heffernany Tomohiro Tetsumoto

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