cherenkov radiation photonic chip–based optical frequency ......2015/12/29 · cherenkov...

Cite as: V. Brasch et al., Science 10.1126/science.aad4811 (2015).

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First release: 31 December 2015 www.sciencemag.org (Page numbers not final at time of first release) 1

Optical solitons are propagating pulses of light that retain their temporal and spectral shape due to a balance of non-linearity and dispersion (1). In the presence of higher order dispersion optical solitons can emit soliton Cherenkov radi-ation (2, 3). This process, also known as dispersive wave generation, is one of the key nonlinear frequency conversion mechanisms of coherent supercontinuum generation (4), which allows substantially increasing the spectral band-width of pulsed laser sources. The generation of a coherent supercontinuum from a pulsed laser propagating through an photonic crystal fiber has enabled the first self-referenced optical frequency combs (5, 6) and has given ac-cess to coherent broadband spectra for frequency combs with repetition rates up to approximately 10 GHz.

One route to higher repetition rate and broadband fre-quency combs was established with the discovery of micro-resonator (Kerr) frequency combs (7, 8). Since then the field of microresonator frequency combs has made substantial advances (9–11) including frequency comb generation in CMOS compatible silicon nitride (SiN) photonic chips (12, 13) and a detailed understanding of the comb formation process (14–17). However, achieving with this process broadband frequency combs that are coherent, has been challenging (18, 19). Recently, temporal dissipative Kerr soli-tons (DKS) (analogous to dissipative cavity solitons (20, 21) in fiber loop cavities) have been observed in crystalline mi-croresonators (19), leading to coherent frequency combs. These solitons, which balance dispersion and loss via the Kerr nonlinearity, can be generated spontaneously from

chaotic Kerr frequency combs, when tuning the pump laser through the cavity resonance (19).

Recent numerical simulations (16, 17, 19) have predicted that such solitons in the presence of soliton Cherenkov ra-diation (3, 16, 22) can provide a path to the reliable genera-tion of broadband and coherent frequency combs, which can even span a full octave.

The resonance frequencies of one mode family in a mi-croresonator can be approximated around ω0 as a Taylor series

μ 01

μω ω

!

jj

j

Dj=

= +∑ (1)

where µ ∈ Z is the relative mode number. Here D1/2π is the free spectral range of the resonator, D2 is related to the group velocity dispersion (GVD) parameter β2 by

( ) 22 1 2 βD c n D=− and D3, D4, … are relate to higher-order dis-persion. Figure 1E shows the integrated dispersion Dint(µ) relative to the pump mode at µ = 0; i.e.

( )32

32int μ 0 1

μμμ) ω ω μ! 3!

( +2

DDD D≡ − + = +… (2)

When pumping a microresonator with a continuous wave (CW) laser with frequency ωP near ω0 the dynamics of this system can be described by a master equation (14, 17, 22)

( )21 in0 P2 0 0

κηκ1 ω ω! ω 2 ω

jj

j

D iD PA i A ig A A i At j i=

∂ ∂ ∂ + − + =− + − + ∂ ∂ ∂ ∑

φ φ

(3)

Photonic chip–based optical frequency comb using soliton Cherenkov radiation V. Brasch,1 M. Geiselmann,1 T. Herr,1* G. Lihachev,2,3 M. H. P. Pfeiffer,1 M. L. Gorodetsky,2,3 T. J. Kippenberg1† 1École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland. 2Russian Quantum Center, Skolkovo 143025, Russia. 3Faculty of Physics, M. V.

Lomonosov Moscow State University, Moscow 119991, Russia.

*Present address: Centre Suisse d’Electronique et Microtechnique SA (CSEM), CH-2002 Neuchâtel, Switzerland.

†Corresponding author. E-mail: [email protected]

Optical solitons are propagating pulses of light that retain their shape due to a balance of nonlinearity and dispersion. In the presence of higher order dispersion optical solitons can emit dispersive waves via the process of soliton Cherenkov radiation. This process underlies supercontinuum generation and is of critical importance in frequency metrology. Using a continuous wave pumped, dispersion engineered, integrated silicon nitride microresonator we generate continuously circulating temporal dissipative Kerr solitons. The presence of higher order dispersion leads to the emission of red-shifted soliton Cherenkov radiation. The output corresponds to a fully coherent optical frequency comb that spans 2/3 of an octave, which we phase-stabilize to the sub-Hertz level. By preserving coherence over a broad spectral bandwidth our device offers the opportunity to develop compact on-chip frequency combs for frequency metrology or spectroscopy.

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where

( ) ( )μ μ 0μ

exp μ, ω ωA t A i i t − − = ∑φ φ (4)

is the slowly varying field amplitude, φ is the azimuthal an-gular coordinate inside the resonator, co-rotating with a

soliton, 2 20 2 effωg cn n V= the nonlinear (per photon) Kerr

coupling coefficient with c the speed of light in vacuum, n and n2 the linear and nonlinear (Kerr) refractive indices of the material, Veff = AeffL the effective nonlinear mode volume with Aeff the effective nonlinear mode area and L the cavity length, κ the cavity decay rate, η the coupling efficiency and with Pin the pump power inside the bus waveguide. Formal-ly, this equation is identical to the Lugiato-Lefever equation (16, 17) (a damped, driven nonlinear Schrödinger equation). For anomalous GVD and in the absence of third and higher order dispersion approximate solutions can correspond to bright temporal solitons superimposed on a CW back-ground:

( ) ( ) ( ) ( )0 PCW 1 01 2

2 ω ωsech exp ψN

jj

A iA AD=

−≈ + −

∑φ φ φ

(5) with φj corresponding to the relative angular position of the jth soliton. Amplitude A1, phase ψ0 and background ACW are determined by the system’s parameters. The minimal pulse duration is given by (19)

23dB 2

1 in

Δ 2γ

1nc

DtD P

≈ (6)

with the resonator finesse and γ = ωn2/cAeff. These tem-poral dissipative Kerr solitons have been generated in fiber cavities (21) and have been observed in crystalline microres-onators recently (19). When higher order dispersion terms are present, the shape and velocity of the stationary solitons changes as it develops a radiative tail (3, 23, 24). The spec-trum of such a perturbed soliton becomes asymmetric with its maximum shifted away from the pump frequency and an additional, local maximum (Fig. 1E) is generated (also called a dispersive wave). Since the radiative tail is emitted from the soliton an analogy to Cherenkov radiation can be drawn (3).

The spectral position of the Cherenkov radiation is ap-proximately given by the linear phase matching condition (2, 25) Dint(µDW) = 0 at µDW = (–3D2/D3) for D4 = 0. In the presence of D4 two peaks of Cherenkov radiation may occur at

2

3 3 2DW

4 4 4

2 2 12μ D D DD D D

−= ± −

(7) Our experimental platform is based on silicon nitride opti-cal microresonators which are very suitable for nonlinear optical applications (26). We utilize 800 nm thick silicon

nitride (Si3N4 or SiN in short) ring resonators with 238 m diameter embedded in SiO2 (Fig. 1, A to D) resulting in anomalous GVD for wavelengths around 1.5 m. The micro-resonator fabrication was optimized in order to mitigate avoided crossings of different mode families that can locally alter dispersion (27, 28). Measurements of the dispersion (28) reveal that around the pump wavelength the mode structure closely approaches a purely anomalous GVD (Fig. 2B and fig. S2), with a measured D2/2π = 2.4 ± 0.1 MHz in close agreement with finite element models (FEM) that yield D2/2π = 2.6 MHz (28). When pumping the resonator’s TM00 mode family at 1560 nm via the bus waveguide we ob-serve discontinuities in the cavity transmission and convert-ed frequency comb light (figs. S1 and S5A) as well as a narrowing of the repetition rate beat note (fig. S1, C and D), signatures previously associated with dissipative Kerr soli-ton formation (19).

To access the soliton states in a steady state, we devel-oped a laser tuning technique to overcome instabilities as-sociated with the discontinuous transitions of the soliton states (28), allowing stable soliton operation for hours (fig. S7). The optical single soliton spectrum with Pin ≈ 2W shown in Fig. 2A has several salient features. First, it covers a bandwidth of 2/3 of an octave. Second, it exhibits the char-acteristic sech2 spectral envelope near the pump that is as-sociated with temporal solitons. The 3-dB bandwidth of 10.8 THz corresponds to 29 fs optical pulses. Third, the sharp feature around 1930 nm (155 THz) corresponds to the soli-ton Cherenkov radiation (16, 22). Figure 2B shows the measured and simulated dispersion. The spectral position of the Cherenkov radiation at = –195 is in good agreement with the linear phase matching condition that occurs for Dint(DW) = 0 at DW = –200 with the simulated parameters D2/2π = 2.6 MHz, D3/2π = 24.5 kHz, D4/2π = –290 Hz (fig. S8).

In Fig. 2A also a numerically simulated spectrum is in-cluded (based on coupled mode equations (28)). It shows only small deviations from the experimental spectrum which are caused by effects that are not included in the simulations (28). In particular, the absence of the soliton recoil (Fig. 1E), that is associated with the formation of a dispersive wave (23, 24), is attributed to the cancellation via the soliton Raman self-frequency shift (28, 29). The good agreement with the experimental data establishes numerical simulations as a powerful predictive tool for soliton dynam-ics in microresonators.

To investigate a key property of a frequency comb, its coherence, we first measure the repetition rate beat note of 189.2 GHz on a photodiode using amplitude modulation down mixing (28, 30) (fig. S5B). Figure 2C shows the result-ing beat note which exhibits a narrow linewidth and a sig-nal to noise ratio (SNR) of 40 dB in 100 kHz bandwidth,

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demonstrating the coherent nature of the spectrum. We also record the low frequency amplitude noise of the soliton state and find no excess noise compared to the pump laser noise (fig. S4). To locally investigate the coherence of the Cherenkov radiation we carry out additional CW heterodyne beat note measurements at 1907 nm which exhibit a narrow linewidth ~1 MHz (Fig. 2E). Simultaneously to the beat at 1907 nm we measure the beat with a laser at 1552 nm. The resulting beat note is similar in width to the in-loop beat of the frequency stabilized pump laser (~300 kHz). These measurements prove that the entire spectrum is coherent in contrast to earlier reports (18). It is insightful to contrast the single soliton state to the incoherent high noise state. We observe in the high noise case a spectrum that markedly deviates from the single soliton spectrum in terms of the shape of the Cherenkov radiation peak and the shape of the spectrum around the pump (fig. S4K).

Our system also allows to access states with multiple sol-itons in the resonator. Figure 3, A to C, shows the optical spectra of three multi-soliton states, which are coherent (fig. S3) and stable for hours (fig. S7). The generated spectra show pronounced variations in the spectral envelope that arise from the interference of the Fourier components of the individual solitons as described by the spectral envelope function:

( ) ( )2

1μ exp μ

N

jj

I i=

= ∑ φ (8)

The insets of Fig. 3, A to C, show the reconstructed relative positions of the solitons inside the resonator for the differ-ent spectra (28). Figure 3B shows the case where two soli-tons are almost perfectly opposite to each other in the resonator, resulting in an effectively doubled line spacing. Figure 3C shows that a higher number of cavity solitons (N = 3) results in a spectrum with more complex spectral mod-ulations.

To prove the usability of our system for metrological ap-plications we implement a full phase stabilization of the spectrum by phase locking the pump laser and the repeti-tion rate of the SiN comb to a common radio frequency (RF) reference. For the absolute frequency stabilization of the pump laser we use an offset lock to a self-referenced fiber laser frequency comb (28, 31). In Fig. 4B we show the modi-fied Allan deviation of the in-loop signals and an out-of-loop signal which consist of the beat of one comb tooth of the SiN comb (mode number –18) with one tooth of the refer-ence comb. For all three signals the modified Allan devia-tion averages down with increasing gate time.

The out-of-loop measurement also allows to compare the absolute frequency accuracy of the soliton Cherenkov radia-tion based comb state with the fiber laser reference comb. Taking into account all locked frequencies as shown in Fig.

4C and extracting the center frequency of the out-of-loop signal from counter measurements shown in Fig. 4A, we derive a frequency difference of Δ = 18·frep – 13613· frep,fc – foff + fol = 25 ± 558 mHz for the 1000 s long measurement. We therefore validate the accuracy of the SiN soliton frequency comb to sub-Hz level and verify the relative accuracy (with respect to the optical carrier) to 3·10−15.

The observation of soliton Cherenkov radiation in a pho-tonic chip based microresonator demonstrates a novel in-gredient to realize on chip frequency combs. It provides a path to numerically predictable, fully coherent frequency comb spectra, with increased bandwidth that extends into the normal GVD regime. The presently achieved coherent 2/3 of an octave can be self-referenced with the 2f-3f tech-nique and can be extended to a full octave with modified dispersion designs.

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ACKNOWLEDGMENTS

This publication was supported by the European Space Agency (ESA) under contract numbers ESTEC CN 4000108280/12/NL/PA and ESTEC CN 4000105962/12/NL/PA and the Swiss National Science Foundation (SNSF). This publication was supported by Contract W911NF-11-1-0202 from the Defense Ad-vanced Research Projects Agency (DARPA), Defense Sciences Office (DSO). This material is based upon work supported by the Air Force Office of Scientific Research, Air Force Material Command, USAF under Award No. FA9550-15-1-0099. M.G. and G.L. acknowledge support from the RFBR 13-02-00271 grant.

SUPPLEMENTARY MATERIALS www.sciencemag.org/cgi/content/full/science.aad4811/DC1 Materials and Methods Supplementary Text Figs. S1 to S8 References (32–41) 18 September 2015; accepted 3 December 2015 Published online 31 December 2015 10.1126/science.aad4811

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Fig. 1. Temporal soliton generation and soliton Cherenkov radiation in a planar SiN microresonator on a photonic chip. (A) Colored scanning electron microscopy images of a SiN optical microresonator with the same geometry as the one used but without the SiO2 encapsulation. Shown in blue, magenta and orange are the silicon substrate, the SiO2 pedestal and the SiN waveguide respectively. (B) An image of resonators at lower magnification. (C) A close-up of the coupling region between bus waveguide and resonator (similar geometry as used). (D) A cross section of a device that also shows the top cladding (SiO2, colored purple). (E) A schematic of the integrated dispersion Dint(μ) and the associated soliton dynamics with the Cherenkov radiation at Dint = 0. Regions with positive (negative) curvature have anomalous (normal) group velocity dispersion (GVD). Around the pump Dint(μ) can be approximated by a parabola (red dashed line) as it is dominated by quadratic, anomalous GVD.

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Fig. 2. Single optical dissipative Kerr soliton and soliton Cherenkov radiation in a SiN chip based optical microresonator. (A) The optical spectrum shows the sech2 shape of a single soliton (with a 3-dB width of 10.8 THz) and the soliton Cherenkov radiation at 155 THz. The green dashed lines mark a span of 2/3 of an octave. The green solid line denotes the simulated spectral envelope. The different blue colors indicate measurements done with two different optical spectrum analyzers. (B) The integrated dispersion Dint from FEM simulations for the measured resonator geometry (grey solid line). The grey dashed line indicates the zero dispersion point. The blue dots around 0 (inset shows a zoom-in) are measured positions of around 80 resonances which show good agreement with the simulated dispersion. (C) The repetition rate beat note of the frequency comb at the line spacing of 189.22 GHz shows a narrow linewidth of around 1 kHz. (D and E) The measured beat note of the generated frequency comb with a narrow linewidth reference laser positioned at 1552.0 nm [(D), orange line in (A)] and at 1907.1nm [(E), red line in (A)]. (F) The intensity profile of the soliton pulse inside the resonator estimated from the measured spectrum (blue) and taken directly from the numerical simulation with FWHM of below 30 fs. The red profile shows a small asymmetry due to the effect of the Cherenkov radiation.

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Fig. 3. Multi-soliton states in a planar SiN microresonator on a photonic chip. (A to C) Spectra for multi-soliton states and the relative phase position of the solitons inside the microresonator shown in the insets according to the field autocorrelation (Fourier transform of the intensity spectrum). (A), (B) Two soliton states and (C) three soliton state with the derived single soliton spectral envelope (solid green line).

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Fig. 4. Full phase stabilization and absolute frequency accuracy measurement of dissipative Kerr solitons in a SiN microresonator. (A) Histogram of the counter measurement for the out-of-loop beat of the stabilized microresonator frequency comb with a commercial fiber laser frequency comb. Gate time is 1 s. The Gaussian fit gives the exact frequency of the beat (fol). The stabilized state shown here is a two soliton state. (B) The modified Allan deviation of the out-of-loop beat as well as the in-loop signals for the two locks of the repetition rate and the pump laser offset of the microresonator frequency comb. All signals average down over the gate time as expected for coherent signals. (C) A scheme highlighting the principle of the frequency accuracy measurement referenced to a self-referenced fiber frequency comb. The out-of-loop beat is between the 18th line on the red side of the pump of the microresonator frequency comb and the 13613th line of the reference comb counted from the line that the pump laser is locked to.

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based optical frequency comb using soliton Cherenkov radiation−Photonic chipV. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky and T. J. Kippenberg

published online December 31, 2015

ARTICLE TOOLS http://science.sciencemag.org/content/early/2015/12/29/science.aad4811

MATERIALSSUPPLEMENTARY http://science.sciencemag.org/content/suppl/2015/12/29/science.aad4811.DC1

CONTENTRELATED http://science.sciencemag.org/content/sci/351/6271/340.full

REFERENCES

http://science.sciencemag.org/content/early/2015/12/29/science.aad4811#BIBLThis article cites 36 articles, 2 of which you can access for free

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Copyright © 2015, American Association for the Advancement of Science

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