Optical frequency comb generation in monolithic microresonator phd thesis

Optical frequency comb generation in monolithic microresonator phd thesis

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Optical frequency comb generation from a monolithic microresonator – arXiv Vanity

Optical frequency combs Udem optical frequency comb generation in monolithic microresonator phd thesis Cundiff ; BookFemto provide equidistant frequency markers in the infrared, visible and ultra-violet Jones ; Gohle and can link an unknown optical frequency to a radio or microwave frequency reference Diddams ; Diddams Since their inception frequency combs have triggered major advances in optical frequency metrology and precision measurements Diddams ; Diddams and in applications such as broadband laser-based gas sensing Thorpe and molecular fingerprinting Diddams Early work generated frequency combs by intra-cavity phase modulation KOUROGI ; Yewhile to date frequency combs are generated utilizing the comb-like mode structure of mode-locked lasers, whose repetition rate and carrier envelope phase can be stabilized Jonesa.

Here, we report an entirely novel approach in which equally spaced frequency markers are generated from a continuous wave CW pump laser of a known frequency interacting with the modes of a monolithic high-Q microresonator Armani via the Kerr nonlinearity Kippenberga ; Savchenkova. Optical-heterodyne-based measurements reveal that cascaded parametric interactions give rise to an optical frequency comb, overcoming passive cavity dispersion. The uniformity of the mode spacing has been verified to within a relative experimental precision of 7.

In contrast to femtosecond mode-locked lasers Steinmeyer the present work represents an enabling step optical frequency comb generation in monolithic microresonator phd thesis a monolithic optical frequency comb generator allowing significant reduction in size, cost and power consumption. Moreover, the present approach can operate at previously unattainable repetition rates Keller exceeding GHz which are useful in applications where the access to individual comb modes is required, such as optical waveform synthesis Weinerhigh capacity telecommunications or astrophysical spectrometer calibration murphyar Optical microcavities Vahala are owing to their long temporal and small spatial light confinement ideally suited for nonlinear frequency conversion, which has led to a dramatic improvement in the threshold of nonlinear optical light conversion Bookchang.

In contrast to stimulated gain, parametric frequency conversion Dunn does not involve coupling to a dissipative reservoir, is broadband as it does not rely on atomic or molecular resonances and constitutes a phase sensitive amplification process, making it uniquely suited for tunable frequency conversion.

In the case of a material with inversion symmetry - such as silica - the non linear optical effects are dominated by the third order non linearity. The process is based on four-wave mixing among two pump photons frequency ν P with a signal ν S and idler photon ν I and results in the emergence of phase coherent signal and idler sidebands from the vacuum fluctuations at the expense of the pump field cf.

The observation of parametric interactions requires two conditions to be satisfied. First momentum conservation has to be obeyed. for four-wave mixing, cf. The second condition that has to be met is energy conservation. Indeed, it has only recently been possible to observe these processes in microcavities made of crystalline Savchenkova CaF 2 and silica Kippenberga ; Carmon Importantly, this mechanism could also be employed to generate optical frequency combs: the initially generated signal and idler sidebands can interact among each other and produce higher order sidebands cf.

This leads to an equidistant spectrum throughout the entire comb. This can be readily seen by noting that e. Thus, provided the cavity exhibits low dispersion, the successive four-wave mixing to higher orders would intrinsically lead to the generation of phase coherent sidebands with equal spacing, i.

an optical frequency comb. Here, we report that microresonators allow realization of this process and generation of optical frequency combs. We employ ultra-high-Q monolithic microresonators in the form of silica toroidal microcavities Armani on a silicon chip, which possess giant photon storage times τ i.

Highly efficient coupling is achieved using tapered optical fibers Spillane Owing to the high circulating power, parametric interactions are readily observed at a threshold of approx. When pumping with a continuous wave CW nm laser source, we observe a massive cascade and multiplication of the parametric sidebands extending to both higher and lower frequencies.

The parametric frequency conversion could extend over more than nm cf, optical frequency comb generation in monolithic microresonator phd thesis.

Fig 1a insetwith the total conversion efficiency being These bright sidebands termed Kerr combs in the remaining discu ssions could be observed in many different samples.

Also, in the largest fabricated samples μ m diameter nm broad Kerr combs comprising modes spaced by GHz could be generated at the expense of slightly higher pump power cf, optical frequency comb generation in monolithic microresonator phd thesis. Supplementary Information, optical frequency comb generation in monolithic microresonator phd thesis. In brief, an external cavity laser at nm was used as pump laser cf.

Fig 2 main panel. The Kerr lines of the microcavity were superimposed with the reference comb in a beat note detection unit BDUconsisting of polarizing optics to combine the reference and Kerr combs and a grating to select the desired region of spectral overlap. Remarkably, from the equidistant spacing of the radio-frequencies, it is found that the generated sidebands are equidistant to within less than 5 kHz as determined by the measurement time of μ s.

To improve the accuracy, we developed an additional experiment where we measured the beat-notes of three Kerr modes with the fiber-reference comb using three separate BDUs cf.

A signal-to-noise ratio exceeding 30 dB in kHz bandwidth was achieved, sufficient to use radio-frequency counters, which were all referenced to a 10 MHz reference signal provided by the MPQ hydrogen Maser. The beat-note measured on BDU1 was used to implement an offset lock between a single reference comb line and the pumping laser by a known offset frequency f 0.

The second third counter measured the N t h M t h mode of the Kerr comb as shown in Fig. The uniformity of the Kerr comb was then checked by comparing the variation in the mode spacing, i. The cavity modes of this measurement span over approx, optical frequency comb generation in monolithic microresonator phd thesis.

Note that the wavelength span that could be used for the measurement is currently limited by the gain bandwidth of an EDFA, which had to be used to amplify the reference comb to have sufficient power to run three BDUs simultaneously.

The results for different gate times and for the two different counting methods are shown in Table 1 the complete list is contained in the supplementary information. The weighted average of these results verifies the uniformity of the comb spacing to a level of 7. Normalized to the bandwidth of the measured Kerr lines 2. This accuracy is on par with measurements for fiber based frequency combs Kubina and confirms that the generated Kerr combs exhibit uniform mode spacing. Next we investigated the role of dispersion underlying the observed comb generation.

supplementary information. Since the GVD of silica is positive for wavelength greater than 1, optical frequency comb generation in monolithic microresonator phd thesis. Indeed we measured a positive dispersion cf. SI which equates to only ca. This low value indicates that the present experiments are carried out close to the zero dispersion wavelength, in agreement with theoretical predictions.

This can be explained in terms of a nonlinear optical mode pulling process as reported in Ref. The strong CW pump laser will induce both self-phase modulation SPM and cross-phase modulation XPM agrawalthe latter being twice as large as the former. The resultant XPM and SPM induced refractive index changes will shift the cavity resonance frequencies by different amounts, thereby causing a net change in the driven cavity dispersion from its passive un-driven value Kippenberga.

This nonlinear mode pulling can optical frequency comb generation in monolithic microresonator phd thesis a mechanism to compensate the residual cavity dispersion.

Regarding future experimental work in light of applications in metrology, optical frequency comb generation in monolithic microresonator phd thesis, we note that absolute referencing can be attained by locking the pump laser to a known atomic transition and locking the mode spacing to a microwave reference such as a Cs atomic clock. The latter requires that the two degrees of freedom of the comb, its repetition rate i. mode spacing, Δ ν and frequency offset, i.

Indeed it could already been shown in a proof of concept experiment that it is possible to lock two modes of the Kerr comb simultaneously to two modes of the reference comb, showing that we are able to control both ν C E O and Δ ν.

The two actuators used for this lock are the detuning of the pump laser from the microcavity resonance and the pump power, which affects the optical pathlength of the cavity via the thermal effect and the nonlinear phase shift. Pertaining to the implications of our work, we note that the present observation of a monolithic frequency comb generator could potentially prove useful for frequency metrology, given however further improvements.

Evidently a readily measurable repetition rate would prove useful when directly referencing the optical field to a microwave signal Cundiff On the other hand, a large mode spacing as demonstrated here could prove useful in several applications, such as line-by-line pulse shaping, calibration of astrophysical spectrometers or direct comb spectroscopy. The high repetition rate from an on chip device may also prove useful for the generation of multiple channels optical frequency comb generation in monolithic microresonator phd thesis high capacity telecommunications spacing GHz and for the generation of low noise microwave signals.

Furthermore, we note that optical frequency comb generation in monolithic microresonator phd thesis interactions do also occur in other types of microcavities - e.

CaF 2 Savchenkova - provided the material exhibits a third order nonlinearity and sufficiently long photon lifetimes. As such the cavity geometry is not conceptually central to the work and the reported phenomena should become equally observable in other types of high-Q microresonators, such as silicon, SOI or crystalline based WGM-resonators.

Indeed the recent observation of net parametric gain Optical frequency comb generation in monolithic microresonator phd thesis on a silicon chip is a promising step in this direction. Acknowledgements: The authors thank T. Hänsch, Th. Udem, K. Vahala and Scott Diddams for critical discussions and suggestions. TJK acknowledges support via an Independent Max Planck Junior Research Group.

This work was funded as part of a Marie Curie Excellence Grant MEXT-CTthe DFG funded Nanoscience Initiative Munich NIM and a Marie Curie Reintegration Grant MIRG-CT The authors gratefully acknowledge J. Kotthaus for access to clean-room facilities for sample fabrication. Figure 5 shows the Kerr comb spectrum at a lower repetition rate mentioned in the optical frequency comb generation in monolithic microresonator phd thesis paper. The repetition rate is G H zcorresponding to a free spectral range of 3 n m.

With larger samples it should be possible to generate repetition rates smaller than G H z which permits the direct measurement of the repetition rate with high-bandwidth photodiodes.

To demonstrate the equidistant nature of the parametric Kerr lines, a reference frequency comb in the form of a mode locked erbium fiber laser is used from Menlo Systems GmbH. The principle underlying the measurement is similar to the concept of multi-heterodyne spectroscopy [ 27 ]. The experimental setup is depicted in Figure 2 of the main paper. A tunable external cavity diode laser ECDL is used to pump a microtoroid resonance as detailed in [ 30 ] and [ 14 ].

Since the cavity resonances are polarization dependent, a in-fiber polarization controller is used to adjust the polarization of the pump laser. The microtoroid is placed in a sealed enclosure containing a nitrogen atmosphere, to avoid the deposition of water on the surface of the silica toroid which has strong absorption bands in the -nm regime, optical frequency comb generation in monolithic microresonator phd thesis.

In the microresonator a spectrum of modes is generated via nonlinear parametric interactions and four-wave mixing see main paper. The output signal of the tapered optical fiber containing the parametric modes that are outcoupled from the microresonator back to the tapered fiber is split by two 3 d B couplers and monitored with a photodiode connected to an oscilloscope and an optical spectrum analyzer.

The BDU consists of quarter wave plates and half wave plates to prepare orthogonal linear polarization in the two input beams, which are subsequently combined using a polarizing beam splitter. To increase the signal-to-noise ratio SNRthe spectral region containing the Kerr comb lines is selected by a grating and finally detected with a PIN InGaAs photodiode Menlo Systems FPD An oscilloscope with a built-in FFT routine is utilized to analyze the radio frequency spectrum.

For rough analysis an electronic spectrum analyzer is used. Since the repetition rate of the reference comb is around M H z the beat note frequencies between a laser line and the reference comb are in the range of 0 M H z to 50 M H z.

To verify the equidistance of the Kerr comb modes it is necessary to know the frequencies of three Kerr comb modes simultaneously. The frequency counting is achieved by using radio frequency counters that are connected to a photodiode in a beat note detection unit cf.

figure 2 in the main paper. To determine the frequencies of three Kerr comb modes at the same time, three beat note detection units BDU have been built. By tuning the grating of the BDUs it is possible to measure the beat note frequency of a single Kerr comb line with a reference comb line.

2021. Optical frequency comb generation in silica microsphere whispering gallery mode resonator.

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Optical Frequency Comb Generation in Monolithic Microresonators

Optical Frequency Comb Generatrion in Monolithic Microresonators PhD Thesis Author: Pascal Del’Haye Duration: July – April Advisors: Prof. Kippenberg, Prof. Hänsch, Prof. Kleineberg: Building an ultra-stable Diode Laser locked to a Reference Cavity for molecular sensing Diploma Thesis Author: Sebastian Karpf Duration: Jan. – Jan. Make sure you leave a few more days if you need the paper revised. You'll get 20 more warranty days Optical Frequency Comb Generation In Monolithic Microresonator Phd Thesis to request any revisions, for free. support@. 39, Zorro drive, Victoria, , Australia. +/10() Optical Frequency Comb Generation In Monolithic Microresonator Phd Thesis, Good Attention Grabbers For Narrative Essay, Text Mining Thesis Paper, Cheap Expository Essay Ghostwriters Site For Mba. Completed Orders: SUBMIT NOW. Read all testimonials >>