Parametric amplification and frequency conversion in optical fibers

Stolen, R. H.; Bjorkholm, J. E.

doi:10.1109/jqe.1982.1071660

Cited by 568 publications

(214 citation statements)

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“…which is inversely proportional to the parametric gain bandwidth [22] can be calculated by integrating the numerical solution over the toroidal cross section plane (here, E is the electrical field and D the electric flux density). These results are depicted in Figure 4b,c and d, respectively.…”

Section: Figmentioning

confidence: 99%

“…In addition to fused silica microtoroids [9,10], this method of comb generation has already been demonstrated in a variety of systems, including crystalline calcium fluoride resonators [11,12], silicon nitride microresonators[14] as * Electronic address: tobias.kippenberg@epfl.ch well as compact fibre cavities [21] and silica glass ring on chip microresonators [15]. In a first step, the continuous wave light of a pump laser at frequency ν P is converted into signal ν S and idler ν I sidebands via degenerate fourwave mixing [9,22,23,24] (cf. Figure 1f).…”

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Octave Spanning Tunable Frequency Comb from a Microresonator

et al. 2011

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Optical frequency combs [1,2,3] have revolutionized the field of frequency metrology within the last decade and have become enabling tools for atomic clocks [4], gas sensing [5,6] and astrophysical spectrometer calibration [7,8]. The rapidly increasing number of applications has heightened interest in more compact comb generators. Optical microresonator based comb generators bear promise in this regard. allow deriving an optical frequency comb directly from a continuous wave laser source and have been demonstrated in a number of optical microresonator geometries [9,10,11,12,13,14,15]. Critical to their future use as 'frequency markers', is however the absolute frequency stabilization of the optical comb spectrum [16]. A powerful technique for this stabilization is self-referencing [16,17], which requires a spectrum that spans a full octave, i.e. a factor of two in frequency. In the case of mode locked lasers, overcoming the limited bandwidth has become possible only with the advent of photonic crystal fibres for supercontinuum generation [18,19]. Here, we report for the first time the generation of an octave-spanning frequency comb directly from a toroidal microresonator on a silicon chip. The comb spectrum covers the wavelength range from 990 nm to 2170 nm and is retrieved from a continuous wave laser interacting with the modes of an ultra high Q microresonator, without relying on external broadening. Full tunability of the generated frequency comb over a bandwidth exceeding an entire free spectral range is demonstrated. This allows positioning of a frequency comb mode to any desired frequency within the comb bandwidth. The ability to derive octave spanning spectra from microresonator comb generators represents a key step towards achieving a radio-frequency to optical link on a chip, which could unify the fields of metrology with micro-and nano-photonics and enable entirely new devices that bring frequency metrology into a chip scale setting for compact applications such as space based optical clocks.In addition to the advantage of compact integration, microresonator based frequency combs have high power per comb line, which is a result of the smaller resonator size and the correspondingly higher repetition rate. This high power per comb line enables direct comb spectroscopy [20] and is advantageous for many applications, and critical for high capacity telecommunication. On the other hand, the high repetition rate of micro-combs results in a smaller peak power of the optical pulses that are underlying the generated frequency comb. This renders spectral broadening using nonlinear fibres [1,18] inefficient. Spectral broadening is a method which allowed for the first broadening of mode locked lasers to octave spanning combs ten years ago [19], leading to a breakthrough of the optical frequency comb technology.Here we show that the high power enhancement in a microresonator itself is sufficient for direct octave spanning frequency comb synthesis without the need for any additional spectral broadening. Optical freq...

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confidence: 99%

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Octave Spanning Tunable Frequency Comb from a Microresonator

et al. 2011

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“…I ) photons [2,4]. In order for parametric oscillations to occur, both energy and momentum must be conserved in this process [4,15]. In whispering-gallery-type resonators, such as microtoroids, momentum is intrinsically conserved when signal and idler angular mode numbers (') are symmetrically located with respect to the pump mode (i.e., ' S;I ' p N) [16].…”

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“…I , which effectively gives the degree to which the cavity modes violate strict energy conservation. It can be shown that the existence of parametric gain requires that this detuning be less than the parametric gain bandwidth [15] 4 c n P ! c n 2…”

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Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-QToroid Microcavity

2004

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Kerr-nonlinearity induced optical parametric oscillation in a microcavity is reported for the first time. Geometrical control of toroid microcavities enables a transition from stimulated Raman to optical parametric-oscillation regimes. Optical parametric oscillation is observed at record low threshold levels (174 micro-Watts of launched power) more than 2 orders of magnitude lower than for optical-fiberbased optical parametric oscillation. In addition to their microscopic size (typically tens of microns), these oscillators are wafer based, exhibit high conversion efficiency (36%), and are operating in a highly ideal ''two photon'' emission regime, with near-unity (0:97 0:03) idler-to-signal ratio.

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“…The parametric gain bandwidth ⍀ gives the amount by which energy conservation can be relaxed in the process. 3,5 This bandwidth which scales linearly with the pump power and the nonlinear coefficient is also progressively broadened by compressing the minor diameter d ͑i.e., increasing the aspect ratio D p / d where D p is the principal diameter͒ of the toroidal microcavity, and thereby, in turn, the effective cross-sectional area of the mode. Empirically, D p / d Ͼ 15 has been proven sufficient to enable parametric oscillation.…”

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Controlled transition between parametric and Raman oscillations in ultrahigh-Q silica toroidal microcavities

Min¹,

Yang²,

Vahala³

2005

Applied Physics Letters

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A controllable and reversible transition between parametric and Raman oscillations in an ultrahigh-Q silica toroidal microcavity is experimentally demonstrated and theoretically analyzed. By direct change of cavity loading and indirect adjustment of frequency detuning, parametric and/or Raman oscillation can be accessed selectively without modification of cavity geometry in a toroidal microcavity with a large enough aspect ratio. Based on an effective cavity gain theory, this transition is analyzed in terms of cavity loading and frequency detuning leading to a better understanding of the combined effects of parametric and Raman processes in silica microcavities. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.2120921͔ Toroidal microcavity resonators 1 have extended the performance of well-known microsphere resonators ͑including liquid microdroplets͒ by providing both a simplified resonator spectrum and ultrahigh-Q performance on a silicon microelectronic chip. Like microspheres they provide a combination of an effectively long-interaction length ͑high-quality factor͒ and a microscale mode volume so that even weak nonlinear mechanisms, such as stimulated Raman scattering, are observable at only tens of microwatts of input power, which is orders of magnitude lower than corresponding threshold powers for fiber-based Raman lasers. 2 However, in contrast to microsphere resonators, microtoroids have been proven to be more versatile by recently enabling the first demonstration of a Kerr-nonlinearity optical parametric micro-oscillator ͑micro-OPO͒ 3 ͓note: a polariton-based micro-OPO in strongly coupled vertical cavity surfaceemitting laser ͑VCSEL͒ microcavities has also been reported previously͔. 4 Micro-OPOs are more challenging to realize than their stimulated counterparts as they require both ultrahigh-Q performance and phase matching of the underlying nonlinear process. Of the two requirements for matching ͑momentum and energy conservations͒, momentum conservation is intrinsically satisfied in microcavities for symmetrically located signal and idler modes with respect to the pump mode. This is a natural consequence of the rotational symmetry which yields a propagation constant ␤ m =2m / D eff , where m is an azimuthal mode number and D eff is an effective diameter of the light path in the cavity. Strict energy conservation, which is not satisfied automatically due to material and cavity mode dispersions, is relaxed by cross-phase modulation ͑and in part by self-phase modulation͒. The parametric gain bandwidth ⍀ gives the amount by which energy conservation can be relaxed in the process. 3,5 This bandwidth which scales linearly with the pump power and the nonlinear coefficient is also progressively broadened by compressing the minor diameter d ͑i.e., increasing the aspect ratio D p / d where D p is the principal diameter͒ of the toroidal microcavity, and thereby, in turn, the effective cross-sectional area of the mode. Empirically, D p / d Ͼ 15 has been proven sufficient to enable parametric oscillation. Howev...

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Parametric amplification and frequency conversion in optical fibers

Cited by 568 publications

References 33 publications

Octave Spanning Tunable Frequency Comb from a Microresonator

Octave Spanning Tunable Frequency Comb from a Microresonator

Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-QToroid Microcavity

Controlled transition between parametric and Raman oscillations in ultrahigh-Q silica toroidal microcavities

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