IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 26, NO. 13, JULY 1, 2014 1321

Integrated High Sensitivity HybridSilicon Magnetometer

Sudharsanan Srinivasan, Student Member, IEEE, and John E. Bowers, Fellow, IEEE

Abstract— We propose and analyze a novel highly sensitiveoptical magnetometer, using low-loss silicon nitride waveguides.With the recent advances in Ce:YIG pulsed laser deposition onsilicon nitride, we show the possibility of reaching sensitivitieson the order of 20 fT/

√Hz at room temperature in an area

<1 cm2. This letter examines a number of parameters, includingthe dependence of sensitivity on sensor area.

Index Terms— Magnetometers, optical waveguides, Sangacinterferometers.

I. INTRODUCTION

H IGHLY sensitive magnetometers are a key requirementin the fields of geophysical surveying, space science,

nuclear magnetic resonance, and for diagnostic tools likemagnetocardiography (MCG) and magneto-encephalography(MEG) in health care. A superconducting quantum inter-ference device (SQUID) is a common tool used in lowfield magnetic sensing, but requires low temperature oper-ation [1]. Driven by recent technological developments andthe advent of reliable, small, and inexpensive diode lasers,atomic magnetometers have been shown to achieve sensitivi-ties rivaling SQUID based magnetometers [2]. A more recentdemonstration of a micromachined atomic magnetometer hasachieved very low sensitivities in a compact package [3]. This,however, still requires meticulous packaging of optical fibersand alignment of bulk optical elements.

We propose a design for a new fully integrated magne-tometer that can reach very low sensitivity of 20 fT/

√Hz.

The device takes advantage of the non-reciprocal phase shiftexperienced by light guided in a waveguide made of magneto-optic material, such as cerium substituted yttrium irongarnet (Ce:YIG) or other cerium/bismuth substituted iron gar-nets [4]. These waveguide sensors can then be integrated within-plane laser sources, phase modulators and detectors to forma magnetometer that detects changes in magnetic field strengthas changes in photocurrent in the detector via the Sagnacinterferometric effect. A schematic of the photonic circuitintegrated on a common silicon substrate is shown in Fig. 1.

The platform of choice for the integration of all theseelements is the hybrid silicon platform [5] for two main

Manuscript received March 7, 2014; revised April 23, 2014; accepted May 6,2014. Date of publication May 8, 2014; date of current version June 13, 2014.This work was supported by TE Connectivity.

The authors are with the Department of Electrical and Computer Engineer-ing, University of California at Santa Barbara, Santa Barbara, CA 93106 USA(e-mail: sudhas@ece.ucsb.edu; bowers@ece.ucsb.edu).

Color versions of one or more of the figures in this letter are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LPT.2014.2322576

Fig. 1. Schematic of the magnetometer using monolithic waveguides andintegrated photonic devices. PD-photodetector, PM-phase modulator.

reasons. First, the use of silicon substrates enables large scale,robust and inexpensive manufacturing of active opticaldevices, viz. lasers, modulators and detectors, on a single chip.The capability to integrate with complementary metal-oxide-semiconductor (CMOS) electronic devices allows for compactpackaging and lower noise from interference. Second, by inte-grating low propagation loss silicon nitride waveguides [6],several meters of delay can be achieved which increases thesensitivity of the sensor, as described below. The followingdiscussion is divided into three sections: device design, resultsand conclusions.

II. DEVICE DESIGN

The circuit in Fig. 1 is used in rotation sensing because itis reciprocal, and hence robust to vibration, temperature varia-tions, coupler variations and other imperfections [7]. Rotationsensors typically use optical fiber, and hence polarizationrotation is an issue.

Here, we use waveguides that are highly birefringent socoupling between polarizations is minimal. These structuresdescribed here can be applied to rotation sensing, but the focusof the analysis is on magnetic field sensing. The operatingpolarization is transverse electric (TE), and the transverse mag-netic (TM) polarization has much higher bend loss. Eqn. (3) inRef. [8] states that the change in propagation constant (�βTE)for the TE mode is dependent on magnetic field strengthalong y axis. Therefore, the waveguide cross-section, andthe magnetic field orientation that gives maximum reciprocalphase shift are as shown in Fig. 2.

This waveguide design is attractive as a result of the recentdemonstration of growth of high quality YIG films on siliconnitride [9]. These magneto-optic (MO) waveguides can nowbe used in the following configurations to convert changes in

1041-1135 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

1322 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 26, NO. 13, JULY 1, 2014

Fig. 2. Waveguide cross section and external magnetic field direction for thesensor in the magnetometer.

Fig. 3. MO waveguide sensor designs. (a) Waveguide spiral, (b) single ringand (c) cascaded multiple ring resonators. The direction of magnetic fieldis out of the plane of the paper. Red-MO material and grey-silicon nitridewaveguide.

magnetic field strength into differential phase delay for thetwo counter-propagating optical fields in the interferometricsensor. Fig. 3 shows two main sensor designs, one using a longspiral MO waveguide and another using a single or multiplering resonator.

In each design the MO waveguide exhibits a different effec-tive index for each of the counter-propagating optical modesin the presence of an external magnetic field. The differencein accumulated phase increases with interaction length andmagnetic field strength. In the case of ring resonators, theeffective interaction length is enhanced from the circumferenceof the ring by a factor N

(1 + t

γ−t + tγ1−tγ

)where N is the

number of rings, γ and t are the electric field amplitudetransmission factors for one roundtrip propagation and acrossthe coupler respectively. The enhancement factor can be quitelarge when t is designed close to γ . However, the resonatorsare wavelength selective and require a narrow linewidth lasersource, which increases Rayleigh and other scattering relatednoise.

III. RESULTS

The expression for photocurrent at the detector as a functionof the phase shift between the two counter-propagating modescan be derived to be

I = ηP0

8e−αL

(1 + cos

(π

2+ �θ

))(1)

where η is an attenuation factor which includes the respon-sivity of the detector and other fixed losses excluding thecouplers, P is the optical power from the source, α isthe waveguide loss, L is the length of the sensor and �θ is thenon-reciprocal phase shift. The argument of the cosine termhas π /2 term to bias at maximum sensitivity. This can beachieved using a phase modulator and is discussed below.

Fig. 4. Waveguide loss and MO material sensitivity per unit length (change inphase shift for a given change in magnetic field intensity) versus confinementfactor of the optical mode in the MO material.

The most important parameter that provides the merit to anyphysical effect used in a magnetometer is the conversion gainfrom magnetic field changes to the detected signal. In ourcase the gain is the ratio of non-reciprocal phase shift (ordetector current) to the change in magnetic field intensity(∂(�θ)/∂Happlied) per unit length.

Assuming a linear MO effect, from [8], we calculate theMO material sensitivity per unit length and waveguide lossfor various optical mode confinement factor values in Ce:YIG(Fig. 4). The MO material absorption loss is assumed to bethe dominant contribution to waveguide loss. With this asthe starting point we derive expressions for the root-mean-squared (rms) noise in the measured phase shift (�φnet) due tovarious noise sources and calculate the limit to magnetometersensitivity using the following relation.

Sensi tivi ty = �φnet

L ∂(�θ)∂ Happlied

(2)

where Happlied is the external magnetic field strength.We consider four sources of noise, viz. thermal noise, shotnoise, relative intensity noise of the source and thermo-refractive noise. The expression for each phase noise term andthe net phase noise from all contributions can be written as

�φRI N =√

10RI N/10 rad/√

H z (3)

�φthermal = 8

ηP0e−αL

√4kBT

Rrad

/√H z (4)

�φshot =√

16q

ηP0e−αLrad

/√H z (5)

�φthermo−re f ract ive = 4.3 × 10−7

√L

40rad

/√H z (6)

�φnet = �φRI N + �φthermal + �φshot

+ �φthermo−re f ract ive (7)

where RIN is the relative intensity noise in dBc/Hz, kB is theBoltzmann constant, T is temperature, assumed to be 300 K,R is the termination resistance for the detector, assumed to be1 k�, q is the electronic charge, and L is the length in meters.

The value for thermo-refractive noise is obtained fromRef. [10] which is valid for small confinement factors in theMO material as the dneff /dT is roughly the same as that of

SRINIVASAN AND BOWERS: INTEGRATED HIGH SENSITIVITY HYBRID SILICON MAGNETOMETER 1323

Fig. 5. (a) Contributions from various noise sources to the ultimate sensitivityas a function of sensor length for P0 = 100 mW and loss = 20 dB/m, fora receiver load of 1 k�. The earth rate rotation error signal is also plotted.Contours of minimum sensitivity (b), in fT/

√Hz, and optimum length (c),

in meters, as a function of source power and confinement factor in the MOmaterial (which determines waveguide loss).

a fiber. Here neff is the effective refractive index of the MOwaveguide and T is the temperature. Since the constant in(6) is proportional to the square of dneff /dT of the opticalmode and inversely proportional to the square of wavelength,necessary corrections can be incorporated directly into thisterm. The noise from backscattering can be minimized byusing superluminescent laser diodes or a frequency modulatedlaser. On the other hand, broad linewidth sources exhibitpoorer RIN, and hence RIN reduction using feedback controlis required. Of course, rotation causes an error signal. Theerror from earth’s rotation is <2 fT/

√Hz for loop length <2 m

and so is not significant compared to the RIN noise.Fig. 5a shows the contribution from each noise term to the

magnetic field sensitivity for a given source power and MOwaveguide loss. Fig. 5b and 5c show the minimum sensitivityand the optimum length for that sensitivity as a function ofsource power and waveguide loss. The assumed value for RINand η are −140 dBc/Hz and 1 respectively. From Fig. 5a wesee that RIN is a dominant source of noise in this technique.With increasing MO waveguide length, both sensitivity and

Fig. 6. Sagnac signal vs. (a) quiescent phase difference and (b) modulationdepth.

Fig. 7. Chip area (blue), magnetometer phase sensitivity (green) andmodulation frequency (red) required for biasing as a function of length, fora 3 μm wide waveguide with a 30 μm center-to-center spacing, as used forultralow loss 100 nm thick Si3N4 waveguide core. The confinement factor inthe MO material is assumed to be 10%.

loss increases. Reducing RIN and/or improving the receiversensitivity would improve the achievable sensitivity.

As discussed in the beginning of this section, the maximumsensitivity of the Sagnac interferometer is achieved when thephase difference of the two counter-propagating modes is anodd multiple of π/2. The phase modulator provides a differentphase shift to the two counter-propagating modes during onecycle, thereby providing a convenient control to bias thenet phase difference in the Sagnac loop, independent of themagnetic field strength. The phase modulation is essential asthe slope of the photocurrent at zero phase difference is zero.Fig. 6 shows the dependence of Sagnac signal with respectto quiescent phase difference and modulation depth. For apush-pull drive phase modulator the optimum modulationdepth is at 0.92.

To lower the phase modulation frequency, one could addadditional waveguide length without any MO material, whichkeeps the net loss low. However, hybrid silicon modulatorswith bandwidths in excess of 60 GHz have been demon-strated [11], so the modulation frequency for biasing the sensorshould not be an issue. A compromise is to operate at highconfinement for a short sensor length and transition to low lossnitride waveguides to increase the Sagnac loop length to keepthe phase modulation frequency sufficiently low. Fig. 7 showsthe chip area and phase modulation frequency required as afunction of length, for a 3 μm wide waveguide with a 30 μmcenter-to-center spacing, as used for ultralow loss 100 nmthick Si3N4 waveguide core. We also show the magnetometerphase sensitivity as a function of sensor length for a 10%confinement in the MO material. With increasing nitride corethickness, the bend radii becomes smaller, however, the lossalso increases due to scattering from sidewall roughness.

1324 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 26, NO. 13, JULY 1, 2014

IV. CONCLUSION

We propose and analyze a novel magnetic field sensor withexcellent sensitivity, down to 20 fT/

√Hz. All the required

elements can be fully integrated on a chip using the hybridsilicon platform. The sensor area using a two meter longwaveguide is 1 cm2. We derive expressions for rms noisein detected phase shift signal from various noise sources andcompared their respective contributions to the net system sen-sitivity achievable. By using materials with greater sensitivityto magnetic field, like BixCe3−xFe5O12 [12], the minimumachievable sensitivity can be further improved by a factorof two.

ACKNOWLEDGMENT

The authors would like to thank Daryl T. Spencer,Paolo Pintus, Dan Blumenthal and Katya Golovchenko foruseful discussions.

REFERENCES

[1] D. Robbes, “Highly sensitive magnetometers-a review,” Sens. ActuatorsA, Phys., vol. 129, nos. 1–2, pp. 86–93, May 2006.

[2] D. Budker and M. Romalis, “Optical magnetometry,” Nature Phys.,vol. 3, no. 4, pp. 227–234, 2007.

[3] R. Mhaskar, S. Knappe, and J. Kitching, “A low-power, high-sensitivitymicromachined optical magnetometer,” Appl. Phys. Lett., vol. 101,no. 24, pp. 1–4, Dec. 2012.

[4] T. Mizumoto and Y. Naito, “Nonreciprocal propagation characteristicsof YIG thin film,” IEEE Trans. Microw. Theory Techn., vol. 30, no. 6,pp. 922–925, Jun. 1982.

[5] M. J. R. Heck et al., “Hybrid silicon photonic integrated circuittechnology,” IEEE J. Sel. Topics Quantum Electron., vol. 19, no. 4,Jul./Aug. 2013, article 6100117.

[6] J. F. Bauters et al., “Silicon on ultra-low-loss waveguide photonicintegration platform,” Opt. Exp., vol. 21, no. 1, pp. 544–555, Jan. 2013.

[7] R. A. Bergh, H. Lefevre, and H. J. Shaw, “An overview of fiber-opticgyroscopes,” J. Lightw. Technol., vol. 2, no. 2, pp. 91–107, Apr. 1984.

[8] P. Pintus, F. Di Pasquale, and J. E. Bowers, “Integrated TE and TMoptical circulators on ultra-low-loss silicon nitride platform,” Opt. Exp.,vol. 21, no. 4, pp. 5041–5052, Feb. 2013.

[9] M. C. Onbasli, T. Goto, K. Taichi, H. Dong, L. Bi, and C. Ross,“Integration of magneto-optical cerium-doped YIG on silicon nitridefilms for nonreciprocal photonic devices,” in Frontiers Opt., OSA Tech.Dig., 2012, paper FTu1A.4.

[10] K. H. Wanser, “Fundamental phase noise limit in optical fibres dueto temperature fluctuations,” Electron. Lett., vol. 28, no. 1, pp. 53–54,Jan. 1992.

[11] Y. Tang, J. D. Peters, and J. E. Bowers, “Over 67 GHz bandwidthhybrid silicon electroabsorption modulator with asymmetric segmentedelectrode for 1.3 μm transmission,” Opt. Exp., vol. 20, no. 10,pp. 11529–11535, May 2012.

[12] M. Sekhar, M. R. Singh, S. Basu, and S. Pinnepalli, “Giant Faradayrotation in BixCe3−xFe5O12 epitaxial garnet films,” Opt. Exp., vol. 20,no. 9, pp. 9624–9639, Apr. 2012.