Achromatic design of a photonic tricoupler and phase shifter for broadband nulling interferometry Teresa Klinner-Teoabc Marc-Antoine Martinodabc Peter Tuthillabc Simon Grossd_2

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Achromatic design of a photonic tricoupler and phase shifter for

broadband nulling interferometry

Teresa Klinner-Teoa,b,c, Marc-Antoine Martinoda,b,c,*, Peter Tuthilla,b,c, Simon Grossd,

Barnaby Norrisa,b,c, Sergio Leon-Savala,b,c

aSydney Institute for Astronomy, School of Physics, University of Sydney, NSW 2006, Australia

bSydney Astrophotonic Instrumentation Laboratories, University of Sydney, NSW 2006, Australia

cAAO-USyd, School of Physics, University of Sydney, NSW 2006, Australia

dMQ Photonics Research Centre, School of Engineering, Macquarie University, NSW 2006, Australia

Abstract. Nulling interferometry is one of the most promising technologies for imaging exoplanets within stellar

habitable zones. The use of photonics for carrying out nulling interferometry enables the contrast and separation

required for exoplanet detection. So far, two key issues limiting current-generation photonic nullers have been identi-

ﬁed: phase variations and chromaticity within the beam combiner. The use of tricouplers addresses both limitations,

delivering a broadband, achromatic null together with phase measurements for fringe tracking. Here, we present a

derivation of the transfer matrix of the tricoupler, including its chromatic behaviour, and our 3D design of a fully sym-

metric tricoupler, built upon a previous design proposed for the GLINT instrument. It enables a broadband null with

symmetric, baseline-phase-dependent splitting into a pair of bright channels when inputs are in anti-phase. Within

some design trade space, either the science signal or the fringe tracking ability can be prioritised. We also present

a tapered-waveguide 180◦-phase shifter with a phase variation of 0.6◦in the 1.4−1.7µm band, producing a near-

achromatic differential phase between beams for optimal operation of the tricoupler nulling stage. Both devices can

be integrated to deliver a deep, broadband null together with a real-time fringe phase metrology signal.

Keywords: broadband nulling interferometry, integrated-optics, photonics, tricoupler, fringe tracking, high contrast

imaging.

*Email: marc-antoine.martinod@sydney.edu.au

1 Introduction

Methods for exoplanet direct detection and characterisation are often limited by the inherent high

contrast ratio and small angular separation intrinsic to exoplanetary systems, even when found or-

biting the most favorable nearby stars. Unlike indirect detection methods, nulling interferometry

enables direct imaging of dim stellar companions, extincting the bright starlight by arranging a

condition of destructive interference from two (or more) apertures.1Interferometry can also ex-

ploit sparse or separated apertures and is not bound by the formal diffraction limit of conventional

monolithic telescopes, and so can observe companions closer to the host star compared with tech-

niques such as coronagraphy.2The contrast ratios required for exoplanet detection span a range

from 10−4for self-luminous hot exoplanets observed in the mid-infrared3to 10−10 for Earth-like

exoplanets imaged in reﬂected light from their host star.4Performance levels over this range lie

within theoretical limits for nulling interferometers (“nullers” hereafter). While most have hith-

erto been built using bulk optics (for example, the Keck interferometer5and the Large Binocular

Telescope Interferometer6), integrated optics and photonic methods are increasingly becoming the

desired technology for nullers.7The use of photonics provides single-mode waveguides, which

perform modal-ﬁltering (where phase aberrations from the wavefront translate coupling efﬁcien-

cies into single-moded waveguides, in essence converting phase into intensity ﬂuctuations), and

their monolithic designs ensure stability against environmental conditions and compactness for

scalability2.

arXiv:2210.01040v1 [astro-ph.IM] 3 Oct 2022

The Guided-Light Interferometric Nulling Technology (GLINT) instrument2,8is a nuller cur-

rently integrated into the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system at

the Subaru Telescope, and is operated by our team. It is able to combine light in the astronomical

Hband from multiple sub-apertures coupled into separate single-mode waveguides, nulling mul-

tiple baselines simultaneously. In its present conﬁguration, nulling is carried out within a photonic

chip, which is able to combine light channeled from four sub-apertures on the telescope, produc-

ing six non-redundant baselines. Light is combined using directional couplers, with output ﬂux

directed into two channels: (1) the null channel in which on-axis starlight destructively interferes

and is therefore heavily suppressed (potentially, together with off-axis planet-light not similarly ex-

tincted), and (2) the anti-null or “bright” channel which contains constructively interfered starlight.

The aim of the instrument is to tune the interference to maximise destructive interference of the

starlight, extincting it from the null channel and routing it instead into the bright channel. The

most commonly used observable quantity, the null depth, is derived from the ratio of these two

outputs. The GLINT device also features photometric monitoring outputs that give an instanta-

neous measurement of the ﬂux contributions of each input beam to the interference signals. This

conﬁguration of the instrument has been characterised on-sky and demonstrated8to reach a null

depth of 10−3with a precision of 10−4. However, to be truly scientiﬁcally competitive, a nuller

targeting planets in the infrared9will require a signiﬁcantly improved null depth of around 10−6.

The current limitations preventing GLINT from reaching deeper nulls have been identiﬁed: the

chromatic behavior of the directional coupler that induces a wavelength-dependent null depth and

the residual phase ﬂuctuations of light entering the instrument. Replacing the directional coupler

with a symmetric tricoupler, which splits input beams into three outputs, rather than two, has been

shown in simulation to be capable of overcoming these limitations.10 Assuming that the waveg-

uides in the interaction region of the tricoupler are arrayed in an equilateral triangle and that the

injected beams are in perfect anti-phase and with equal ﬂux, the central channel will produce a

completely nulled output, regardless of the wavelength of incoming light. Underlying this power-

ful conﬁguration are arguments based on simple symmetry: anti-symmetric input beams are unable

to couple to an even-symmetry mode ﬁeld required to overlap with the central null channel.11 A

further advantage is provided by the output ﬂuxes from the two bright channels, which can be used

to measure the incoming differential phase thereby providing a signal for active cophasing correc-

tion in real time. Simulations of a tricoupler able to deliver this achromatic null have been shown

to reach a null depth 45 times better than with a single directional coupler.10 The use of a tricoupler

has been previously mooted as a combiner for nulling and stellar interferometry.11,12 To exploit the

equal coupling ratios and phase delays between outputs, early devices made use of three waveg-

uides in a planar, rather than triangular, conﬁguration. In order to produce the desired performance,

waveguides were tapered to adiabatically alter the coupling ratios13. Planar tricouplers following

this methodology have been designed for nulling interferometry14. However, devices with an equi-

lateral triangular conﬁguration in the interaction region are able to exploit further symmetries:

namely, an equal splitting ratio between bright channels10. Early tricouplers made use of fused ﬁ-

bre twisted together to produce this triangular conﬁguration in the central region, which introduced

asymmetries, altering the desired coupling ratio 15. Today, the ultrafast laser inscription (ULI)16–19

process enables efﬁcient and precise inscription of tricouplers and other photonic devices requir-

ing three-dimensional design freedom. The use of tricouplers for space interferometry is currently

being investigated20,21.

Here, we present a full chromatic treatment of a new design for a tricoupler. This design incor-

porates fully symmetric triangular inputs and outputs, unlike the design presented in Ref. 10, which

eliminates slight asymmetries in the splitting ratios and allows for equal splitting between non-null

channels across the band. This greatly simpliﬁes the treatment of interactions using the tricou-

pler’s transfer matrix and offers more ﬂexibility with choice of waveguide injected into, while still

being fully fabricable using the ULI technique. Additionally, we investigate the potential for this

tricoupler to maximise the signal from a faint stellar companion, showing that adjustments to the

physical properties of the device can either maximise science throughput or provide better fringe

tracking. Furthermore, any instrument incorporating a tricoupler for the nulling beam combina-

tion requires a perfect 180◦differential phase between injected beams across the working spectral

band. Therefore, an achromatic phase shift has to be implemented preceding every tricoupler in

the chip to enforce this anti-phase condition between beams. To date, simulations of nulling with

tricouplers have assumed inputs arranged to be in anti-phase using a (chromatic) delay in air: a

simple piston term applied to one beam10 which only meets the ideal anti-phase condition at one

wavelength within the observing band. This limits the maximum number of simultaneously nulled

baselines for any given number of apertures and wastes the signal-to-noise advantages that a truly

achromatic null would deliver over all spectral channels in the band. We introduce an achromatic

180◦photonic phase shifter using tapered waveguides, which can be used in concert with the tri-

coupler to achieve an achromatic null across the working band.

In Section 2, we derive the full transfer matrix for the current proposed tricoupler, taking chro-

matic behaviour into account. We introduce our new proposed completely symmetric equilateral

tricoupler in Section 3, and simulate the throughput of a planet light signal, as well as examine the

effects of changing the design to maximise this signal, in Section 4. In Section 5, we advance our

design for an achromatic phase shifter which can be added at the input side of each tricoupler. The

combination of both devices can be replicated for each combiner in the case of a multi-baseline

nuller, as shown in Section 6. These photonic components can be realistically fabricated using ULI

inside a single integrated-optics chip.

2 Modelling beam combination with transfer matrices

The tricoupler proposed in Ref. 10 exhibits asymmetric coupling ratios. While we expect similar

coupling effects regardless of the waveguide in which the light is injected, some discrepancies arise

depending on which waveguide is fed. These come from the waveguides’ shape, which transitions

from a linear array at both the inputs and outputs to an equilateral triangular conﬁguration in the

central region. These transition areas result in two asymmetrically arranged zones at both ends of

the interaction region, where the waveguides converge on approach to the interaction region, and

again where they diverge (Fig. 1).

The transfer matrix for a tricoupler with symmetry between left and right waveguides, but not

three-fold equilateral symmetry as described above, would have at least two independent coupling

coefﬁcients. Hence mode ﬁeld orthogonality is generally needed, in addition to energy conserva-

tion and symmetry arguments, to determine the phase shift. However, by assuming mode orthogo-

nality principle,22 the transfer matrix can be written as

M=



T1˜

C1˜

T2˜

C2˜

C1˜



,(1)

Fig 1: Top (left) and 3D (right) view of the asymmetric tricoupler. While the interaction region

follows an equilateral triangular pattern, some coupling effects happen in the remapping from

and to a linear array before and after the interaction region, breaking the full symmetry of the

interactions between the waveguides inside the tricoupler. The light enters the device from the

bottom and leaves at the top of the tricoupler.

where ˜

C1,˜

C2,˜

T1and ˜

T2are the complex coupling coefﬁcients from the input waveguide to the

central and outer output waveguides, and transmission coefﬁcients in the outer and central waveg-

uides, respectively (Fig. 2).

Mdescribes the relationship between the input and output beams of the tricoupler, such that if I

is a vector of the complex amplitudes of the input waveguides, then the vector of output waveguide

amplitudes Ois given by O=MI. The transmission and coupling coefﬁcients are treated as

complex phasors which act on the incoming beams ˜

Ein:

Ti=TieiψTi(2)

Ci=CieiψCi(3)

Ti, Ciare deﬁned to be the square modulus of these phasors such that

|˜

Ti|2=|˜

Eout,i|2

|˜

Ein,i|2=T2

i.(4)

A tricoupler with asymmetric coupling or tapered waveguides14,22 requires the treatment of

coupling to the centre and unfed outer waveguides, C1and C2, separately. As a result, expres-

sions for the differential phases between channels become complicated to compute in terms of the

coupling and transmission coefﬁcients, which in turn makes the transfer matrix complicated and

potentially impacts the efﬁciency of phase calculations for fringe tracking. Instead, we focus here

on a design of a fully symmetric tricoupler. Equal coupling of light simpliﬁes the transfer matrix

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AchromaticdesignofaphotonictricouplerandphaseshifterforbroadbandnullinginterferometryTeresaKlinner-Teoa,b,c,Marc-AntoineMartinoda,b,c,*,PeterTuthilla,b,c,SimonGrossd,BarnabyNorrisa,b,c,SergioLeon-Savala,b,caSydneyInstituteforAstronomy,SchoolofPhysics,UniversityofSydney,NSW2006,AustraliabSydneyAstrop...

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Achromatic design of a photonic tricoupler and phase shifter for broadband nulling interferometry Teresa Klinner-Teoabc Marc-Antoine Martinodabc Peter Tuthillabc Simon Grossd_2

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