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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 16 — Aug. 1, 2011
  • pp: 14763–14778
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Noise reduction of supercontinua via optical feedback

Nicoletta Brauckmann, Michael Kues, Petra Groß, and Carsten Fallnich  »View Author Affiliations


Optics Express, Vol. 19, Issue 16, pp. 14763-14778 (2011)
http://dx.doi.org/10.1364/OE.19.014763


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Abstract

The impact of delayed optical feedback on the supercontinuum noise properties is investigated numerically and experimentally. The supercontinuum is generated by coupling femtosecond laser pulses into a microstructured fiber within a ring resonator, which introduces the optical feedback. The power noise and spectral amplitude noise properties of this feedback system are numerically and experimentally compared with single-pass supercontinuum generation. In a demonstrative experiment via optical feedback the power noise could be reduced by 15 dB and the spectral amplitude noise could be reduced by up to 28 dB.

© 2011 OSA

1. Introduction

Optical fibers with small core diameter allow high peak intensities in combination with relatively long interaction lengths, resulting in strong nonlinear effects. Thus, the propagation of ultrashort laser pulses in fibers near the zero-dispersion wavelength is suitable for broadband supercontinuum (SC) generation [1

1. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]

].

Supercontinua are usable for many applications, e.g., optical coherence tomography [2

2. I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,” Opt. Lett. 26, 608–610 (2001). [CrossRef]

, 3

3. A. D. Aguirre, N. Nishizawa, J. G. Fujimoto, W. Seitz, M. Lederer, and D. Kopf, “Continuum generation in a novel photonic crystal fiber for ultrahigh resolution optical coherence tomography at 800 nm and 1300 nm,” Opt. Express 14, 1145–1160 (2006). [CrossRef] [PubMed]

], fluorescence microscopy [4

4. J. H. Frank, A. D. Elder, J. Swartling, A. R. Venkitaraman, A. D. Jeyasekharan, and C. F. Kaminski, “A white light confocal microscope for spectrally resolved multidimensional imaging,” J. Microsc. 227, 203–215 (2007). [CrossRef] [PubMed]

] or optical frequency metrology [5

5. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000). [CrossRef] [PubMed]

, 6

6. T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002). [CrossRef] [PubMed]

]. These applications require special SC properties, for instance a special spectral composition is required for optical coherence tomography, or a high degree of pulse-to-pulse stability for frequency metrology. To meet these demands, on the one hand SC can be modified by input pulse [1

1. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]

, 7

7. H. Zhang, S. Yu, J. Zhang, and W. Gu, “Effect of frequency chirp on supercontinuum generation in photonic crystal fibers with two zero-dispersion wavelengths,” Opt. Express 15, 1147–1152 (2007). [CrossRef] [PubMed]

, 8

8. M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003). [CrossRef]

] and fiber parameters [9

9. M. H. Frosz, P. M. Moselund, P. D. Rasmussen, C. L. Thomsen, and O. Bang, “Increasing the blue-shift of a supercontinuum by modifying the fiber glass composition,” Opt. Express 16, 21076–21086 (2008). [CrossRef] [PubMed]

11

11. P. Falk, M. H. Frosz, and O. Bang, “Supercontinuum generation in a photonic crystal fiber with two zero-dispersion wavelengths tapered to normal dispersion at all wavelengths,” Opt. Express 13, 7535–7540 (2005). [CrossRef] [PubMed]

]. On the other hand the coherence properties were for example improved by modulating the input pulse [12

12. G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009). [CrossRef]

], and the spectrum was shaped by two-color pumping [13

13. E. Räikkönen, G. Genty, O. Kimmelma, M. Kaivola, K. P. Hansen, and S. C. Buchter, “Supercontinuum generation by nanosecond dual-wavelength pumping in microstructured optical fibers,” Opt. Express 14, 7914–7923 (2006). [CrossRef] [PubMed]

], by using fiber cascades [14

14. J. C. Travers, S. V. Popov, and J. R. Taylor, “Extended blue supercontinuum generation in cascaded holey fibers,” Opt. Lett. 30, 3132–3134 (2005). [CrossRef] [PubMed]

], or by fiber Bragg gratings [15

15. P. S. Westbrook, J. W. Nicholson, and K. S. Feder, “Grating phase matching beyond a continuum edge,” Opt. Lett. 32, 2629–2631 (2007). [CrossRef] [PubMed]

].

While these approaches mostly improve one specific feature of the SC, the introduction of an optical feedback was demonstrated to lead to a number of different effects, such as the manipulation of the optical spectrum or the manipulation of the nonlinear dynamics with its characteristic temporal evolution of the SC pulse train. The influence on the SC spectral shape was demonstrated for optical feedback systems pumped with picosecond pulses [16

16. P. M. Moselund, M. H. Frosz, C. L. Thomsen, and O. Bang, “Back-seeding of higher order gain processes in picosecond supercontinuum generation,” Opt. Express 16, 11954–11968 (2008). [CrossRef] [PubMed]

,17

17. Y. Deng, Q. Lin, F. Lu, G. P. Agrawal, and W. H. Knox, “Broadly tunable femtosecond parametric oscillator using a photonic crystal fiber,” Opt. Lett. 30, 1234–1236 (2005). [CrossRef] [PubMed]

], where SC generation relies on seeded four-wave mixing, as well as for femtosecond systems [18

18. N. Brauckmann, M. Kues, P. Groß, and C. Fallnich, “Adjustment of supercontinua via the optical feedback phase - numerical investigations,” Opt. Express 18, 20667–20672 (2010). [CrossRef] [PubMed]

, 19

19. N. Brauckmann, M. Kues, P. Groß, and C. Fallnich, “Adjustment of supercontinua via the optical feedback phase - experimental verifications,” Opt. Express 18, 24611–24618 (2010). [CrossRef] [PubMed]

], where self-phase modulation and higher order dispersion are the dominant effects leading to the spectral broadening. Furthermore, the occurrence of nonlinear dynamics due to optical feedback was shown for femtosecond SC feedback systems [20

20. M. Kues, N. Brauckmann, T. Walbaum, P. Groß, and C. Fallnich, “Nonlinear dynamics of femtosecond super-continuum generation with feedback,” Opt. Express 17, 15827–15841 (2009). [CrossRef] [PubMed]

, 21

21. N. Brauckmann, M. Kues, T. Walbaum, P. Groß, and C. Fallnich, “Experimental investigations on nonlinear dynamics in supercontinuum generation with feedback,” Opt. Express 18, 7190–7202 (2010). [CrossRef] [PubMed]

], as well as for the case of feedback systems with the weaker effective nonlinearity of a conventional single mode fiber [22

22. G. Steinmeyer, A. Buchholz, M. Hänsel, M. Heuer, A. Schwache, and F. Mitschke, “Dynamical pulse shaping in a nonlinear resonator,” Phys. Rev. A 52, 830–838 (1995). [CrossRef] [PubMed]

, 23

23. G. Sucha, D. S. Chemla, and S. R. Bolton, “Effects of cavity topology on the nonlinear dynamics of additive-pulse mode-locked lasers,” J. Opt. Soc. Am. B 15, 2847–2853 (1998). [CrossRef]

]. By adjusting different regimes of nonlinear dynamics it is possible to change the pulse train evolution, e.g., to generate SC pulse trains with alternating spectral shapes, as fast as the laser’s repetition rate [18

18. N. Brauckmann, M. Kues, P. Groß, and C. Fallnich, “Adjustment of supercontinua via the optical feedback phase - numerical investigations,” Opt. Express 18, 20667–20672 (2010). [CrossRef] [PubMed]

, 19

19. N. Brauckmann, M. Kues, P. Groß, and C. Fallnich, “Adjustment of supercontinua via the optical feedback phase - experimental verifications,” Opt. Express 18, 24611–24618 (2010). [CrossRef] [PubMed]

].

Beside the spectral composition and the pulse train evolution, the stability of SC light sources especially for frequency metrology is an important topic, because fluctuations of the SC lead to a reduced signal-to-noise ratio and thus to a limited applicability of supercontinua. SC stability in dependence on the input pulse parameters has extensively been investigated, considering technical, i.e., low-frequency amplitude noise [24

24. N. R. Newbury, B. R. Washburn, K. L. Corwin, and R. S. Windeler, “Noise amplification during supercontinuum generation in microstructure fiber,” Opt. Lett. 28, 944–946 (2003). [CrossRef] [PubMed]

] and quantum shot noise [25

25. K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, “Fundamental noise limitations to supercontinuum generation in microstructure fiber,” Phys. Rev. Lett. 90, 113904 (2003). [CrossRef] [PubMed]

, 26

26. B. R. Washburn and N. R. Newbury, “Phase, timing, and amplitude noise on supercontinuum generation in microstructure fiber,” Opt. Express 12, 2166–2175 (2004). [CrossRef] [PubMed]

] as well as coherence properties [27

27. G. Genty, S. Coen, and J. M. Dudley, “Fiber supercontinuum sources,” J. Opt. Soc. Am. B 24, 1771–1785 (2007). [CrossRef]

]. As a result a rule of thumb was proposed: for high-stability SC generation, short input pulses (≈ 50 fs) with relatively low peak power (a few kW) should be used in combination with a relatively short (some cm), anomalously dispersive fiber.

In this work, the suitability of using the optical feedback to improve the SC noise properties is analyzed. The impact of an optical feedback on the technical SC noise properties is investigated numerically and experimentally by comparing the feedback system’s characteristics with those of a single-pass SC generating system, i.e., without feedback. Technical noise is typically the dominant noise source in the low frequency range of up to a few 100 kHz. Especially residual relaxation oscillations, that can hardly be avoided even with highly stable pumping conditions, lead to slow amplitude modulations of the pulse train of a mode-locked laser which can result in Q-switched mode-locked operation. Thus, in order to demonstrate the noise reduction method presented in this work, the laser was adjusted to the Q-switched mode locking regime, resulting in a pulse train modulated with a frequency of 450 kHz. In a first step, noise reduction of relatively high amplitude noise in the order of 1% to 10% of the pulse amplitude for this specific noise frequency is demonstrated numerically and experimentally. In a second step, the suitability of the presented noise reduction technique for lower amplitude noise and for other noise frequencies is discussed. In the following, the noise reduction of the power fluctuations as well as the noise reduction of the spectral amplitude fluctuations of individual frequency components will be presented.

2. Experimental setup

The experimental setup is sketched in Fig. 1. The laser system together with the SC generating setup including the feedback cavity are illustrated in part A. The analysis setup of the power noise is illustrated in part B and the spectral amplitude noise measurement setup in part C.

Fig. 1 Experimental setup; part A: laser system and feedback cavity, part B: power noise measurements, part C: spectral amplitude noise measurements. BS: beam splitter, MSF: microstructured fiber, MO: 40x microscope objective, GS: uncoated glass substrate, F: spectral bandpass filter, PD: photodiode, M: mirror only used for option B, for more details see text.

The laser system consisted of a Titanium:Sapphire laser (Tsunami by Spectra-Physics) followed by a Faraday isolator to avoid reflections back into the laser resonator, and a prism compressor to compensate the material dispersion especially of the Faraday isolator. After passing this prism compressor, a pulse duration of 54±6 fs (full width at half maximum, FWHM, and assuming a sech2 intensity profile) was measured with an autocorrelator (model Mini by APE) at 775 nm central wavelength and 82 MHz repetition rate. In order to create a signal with a defined modulation frequency the laser was adjusted to operate in the Q-switched mode-locked regime [28

28. C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16, 46–56 (1999). [CrossRef]

], and with this technique an amplitude modulation of the laser’s 82 MHz output pulse train with a frequency of 450 kHz was achieved.

The feedback efficiency was measured by recording the power at the output port with and without feedback and yielded values between 15% and 20%. Due to the material dispersion, the feedback resonator was normally dispersive for the SC wavelength range with a dominant quadratic phase term of 0.9 · 10−3ps2 · (ωω 0)2 for the laser’s central frequency ω 0 = 2π · c/775 nm. Thus, the feedback resonator was not synchronously resonant for all SC wavelengths, and by tuning the resonator length, i.e., the delay, different wavelengths could be chosen to be resonant (this was investigated in detail in [18

18. N. Brauckmann, M. Kues, P. Groß, and C. Fallnich, “Adjustment of supercontinua via the optical feedback phase - numerical investigations,” Opt. Express 18, 20667–20672 (2010). [CrossRef] [PubMed]

, 19

19. N. Brauckmann, M. Kues, P. Groß, and C. Fallnich, “Adjustment of supercontinua via the optical feedback phase - experimental verifications,” Opt. Express 18, 24611–24618 (2010). [CrossRef] [PubMed]

]).

For analysis of the system characteristics the partially reflected beam from an uncoated glass substrate (GS) was used. For the results presented in section 4.2 concerning the power noise reduction, the signal was detected with a silicon photodiode (PD 0) connected to a radio frequency spectrum analyzer (Advantest, TR 4131/E), as is shown in Fig. 1 part B. In order to measure the effect of spectral amplitude noise reduction presented in section 5.2, a spectral bandpass filter (F) was incorporated into the feedback cavity, so that only spectral components between 750 nm and 800 nm were fed back. Furthermore, the beam was split into four partial beams, as is shown in part C of Fig. 1, in order to enable spectrally resolved measurements of fast fluctuations: First, the beam was divided into two parts with a 50:50 beam splitter (BS), where one part was directly detected with a photodiode (PD 1) as a measure of the average SC power. The second part was dispersed using a prism, and three spectral ranges of 10 nm bandwidth (FWHM) with central wavelengths at 730 nm, 775 nm, and 830 nm were filtered with slits, and the according power values were separately measured with three photodiodes (PD 2, PD 3, PD 4). The photodiodes were chosen to have a response time between 0.1 μs and 1 μs, which was much longer then the laser’s repetition rate (12 ns) to average over the laser pulses, but which was fast enough to resolve the amplitude modulations of interest at a frequency around 450 kHz (≙ 2.2 μs). Time series of all four generated signals were measured simultaneously with a four-channel oscilloscope (Tektronix, DPO7000).

3. Numerical implementation

Fig. 2 Schematic sketch of the program blocks performed within the numerical simulations of the SC feedback system. Path A: procedure for feeding back the whole SC spectral bandwidth for analyzing the average power noise. Path B: procedure for feeding back the spectrally filtered SC for analyzing the spectral amplitude noise. For a detailed explanation see text.

4. Power noise reduction

4.1. Numerical results

In order to illustrate the phase and intensity dependence of the SC generating feedback system and to find parameter settings, where noise reduction can be expected, we numerically calculated the feedback system intra-cavity power for different pump power values. The results are shown in Fig. 3(a), where the feedback system intra-cavity power was calculated for pump powers from 1 mW to 10 mW in dependence on the feedback delay from 0 fs to 5 fs, which corresponds to a phase shift from 0 to 3.88π (= 2πc· 5 fs/λ 0, where λ 0 = 775 nm is the central wavelength and c is the velocity of light in vacuum).

Fig. 3 Numerical results: feedback system output power as a function of the feedback phase for pump powers from 1 mW to 10 mW in steps of 1 mW. The feedback system showed a phase and intensity dependent behavior. Regions with approached proximate curves (one example is marked with the blue circle) indicate noise reduction; regions with far separated proximate curves (one example is marked with the red ellipse) indicate noise amplification. a) exact calculations; b) calculations with adapted wavelength-dependent response function of the photodiode that was used in the experiments.

Each of the curves in Fig. 3(a) shows the combination of a delay dependence and an intensity dependence. The delay dependence can be seen from the power not being constant for different delay positions. The intensity dependence is reflected by the fact that the curves are not only offset by a value corresponding to the pump power, but that they also differ in shape. The deformation of the curves led to a varying distance between proximate curves as a function of the delay and the pump power. In regions where proximate curves approached each other closely (see for example the region marked by the blue circle), the feedback system intra-cavity power is nearly the same for different values of the pump power. For the example marked with the blue circle the intra-cavity power variations were reduced to 8.9% of the pump power variations of 1 mW, indicating power noise reduction. However, the feedback did not necessarily lead to a noise reduction; with other parameter settings, the input variations could also be amplified. For example, with a slightly changed delay position (1.8 fs instead of 1.4 fs), the distance between the proximate curves increased drastically, and the intra-cavity power fluctuations were amplified to 197.9% of the pump power variations (see the red ellipse in Fig. 3(a)).

Figure 3(b) shows the same results as Fig. 3(a) but with considering the wavelength-dependent response function of the photodiode that was used in the experiments for signal detection. Thus it shows how the graph would be measured under realistic experimental conditions, which was used to estimate the measurement error. Up to a pump power of around 5 mW no significant differences were observed, and thus a relatively low error of ±1 dB could be estimated in this power range. For increased pump power the bandwidth of the SC optical spectrum further increased resulting in a more significant impact of the response function of the photodiode. The evolution of each curve did not significantly change, but the detected power decreased. As a result proximate curves approached, suggesting an improved measured noise reduction. Thus the measurement error depended on the pump power and was estimated for each particular experimental case from those numerical investigations.

Fig. 4 Numerical results: a) evolution of the pump power varied in the range from 6.8 mW to 6.9 mW; b) according evolution of the resulting feedback system output power.

In comparison to the presented dynamical perturbation, for the stationary case, i.e., without considering the system’s dynamical response as was illustrated in Fig. 3, a considerably better noise reduction of 20.44 dB was calculated. This difference results from the increased impact of the dynamical system response as a function of the perturbation frequency, which leads to changed system behavior. Thus, for perturbation frequencies of up to 450 kHz a noise reduction between 11.5 dB and 20.44 dB can be estimated for the investigated parameter setting.

Considering that the influence of the system’s dynamical response increases with increasing perturbation frequencies, the noise reduction of 11.5 dB for a perturbation frequency of 450 kHz can be estimated as lower noise reduction limit for perturbation frequencies of up to 450 kHz for the investigated parameter setting.

4.2. Experimental results

In order to experimentally verify the numerically predicted effects of pulse noise reduction qualitatively, we used the setup in Fig. 1 part A without the spectral bandpass filter. For analysis a photodiode connected to a radio frequency spectrum analyzer was used as shown in part B of Fig. 1. The parameters were not exactly matched to the ones used in the simulations. Without the exact knowledge of all parameters, quantitative predictions of the system behavior seem unrealistic for the complex system under consideration. However, the presented results showed good qualitative agreement between experiments and simulations. The radio frequency spectrum of the feedback system was measured up to a frequency of 1 MHz at a pump power of 8.5 mW, while the delay was detuned by up to four wavelengths (8π) of the laser’s central wavelength of 775 nm. The result of this phase dependent delay scan is shown in Fig. 5(a). Note, that the stated values for the feedback phase are only relative with respect to the start position of the measurement. Each line in the graph corresponds to one radio frequency spectrum, where the spectral power is color-coded on a logarithmic scale. The radio frequency spectra were normalized to the average power for each single measurement. This was necessary because the system output power varied in dependence on the delay due to interferometric effects as was predicted by the numerical simulations (see Fig. 3(b)).

Fig. 5 Power noise measurement at a pump power of 8.5 mW with perturbations at a frequency of 450 kHz; a) normalized phase dependent evolution of the radio frequency spectrum at the feedback system output; b) corresponding evolution of the noise peak amplitude, where the red curve indicates the peak amplitude of the single-pass system.

Figure 5(a) shows that the frequency peak at 450 kHz, which was introduced by the amplitude modulation of the pump laser pulses, was clearly visible in the radio frequency spectrum of the feedback system during the whole delay scan, but that the magnitude of the frequency peak varied as a function of the feedback phase. For a better illustration of the quantity of the peak amplitude variation in the radio frequency spectra, the evolution of the peak amplitude is plotted as a function of the delay in Fig. 5(b). The normalized peak amplitude of the single-pass reference measurement is plotted as the red line in the same graph for comparison. Note, that a silicon photodiode was used for the measurements, which showed a wavelength-dependent response function for the broadband spectral range of some hundreds of nanometers which was typical for the measured supercontinua. With the help of the simulations and considering the wavelength-dependent response function of the photodiode (see Fig. 3), an error of ±5 dB for the noise reduction was evaluated for the presented power range. It was observed, that with considering the characteristics of the photodiode typically an improved noise reduction was suggested. Thus, in order to include this inaccuracy, the measured noise reduction values have to be reduced by 5 dB, which resulted in a demonstrated power noise reduction of 15 dB. However, the effect of power noise reduction crucially depended on the feedback phase: when the feedback phase was shifted by half a wavelength (π), the power noise reduction was transformed into power noise amplification. Hence, the experimental results verify the numerically predicted effects, that a power noise reduction can be realized by introducing an optical feedback, and that this effect is strongly phase dependent.

5. Spectral amplitude noise reduction

5.1. Numerical results

For investigations on the spectral amplitude stability not only the power has to be considered, but also the variations of each single spectral component of the generated SC. As a first step, the numerical data of the previously generated time series (see section 4.1) were analyzed regarding their spectral contents, and the results are plotted in Fig. 6. The optical spectra that were calculated when the pump power was varied between 6.8 mW and 6.9 mW, are plotted for the single-pass system in Fig. 6(a) and for the feedback system in Fig. 6(b).

Fig. 6 Numerical results without filter: optical spectra for varying pump power between 6.8 mW and 6.9 mW (180 spectra are plotted on top of each other) a) without and b) with feedback; c) corresponding spectral variations without (red dashed line) and with (black solid line) feedback; d) corresponding relative spectral variations without (red dashed line) and with (black solid line) feedback.

One can see, that the spectra that were calculated with feedback were more strongly modulated than those without feedback, which is the result of spectral interference effects in combination with the cavity dispersion.

For both the single-pass and the feedback system the spectral variations were calculated from the difference of the minimum and the maximum spectral intensity for each spectral component that was reached when the pump power was varied. The results are plotted in Fig. 6(c), which clearly shows that the variations of the feedback system (black solid line) were higher than those of the single-pass system (red dashed line) for most spectral components. However, for some spectral regions (around 800 nm, 830 nm, and 850 nm) the variations were suppressed via feedback. Because of the big difference of the spectral shapes for the single-pass and the feedback system the spectral variations have to be normalized to the according spectral intensities for a significant comparison, as is shown in Fig. 6(d) (with feedback: black solid line, single-pass: red dashed line). Also the normalized spectral variations were amplified via optical feedback for almost all spectral components. In addition to the reduction of the power noise, as was reported in section 4, the spectral amplitude fluctuations could only be reduced in a small wavelength interval from 791 nm to 803 nm via optical feedback. Due to the increased spectral amplitude fluctuations a power noise reduction seems not intuitive. But despite of high spectral amplitude fluctuations the power fluctuations can be reduced, if different spectral components fluctuate out of phase, i.e., if the spectral amplitude is increased for some spectral components while it is simultaneously decreased for others. Integrated over the whole optical spectrum in order to calculate the power fluctuations, this led to power noise reduction.

Due to the nonlinear effects, the generated supercontinua strongly depended on the exact form and amplitude of the input pulses and thus, in order to further improve the spectral amplitude noise characteristics for more wavelength components, the influence of feedback on the input pulses has to be evaluated in more detail. Therefore, the impact of feedback on the input pulses E input is illustrated in Fig. 7(a), where the input pulses of the feedback system after the transient phase are plotted for constructive (blue dotted line) and destructive (black solid line) interference conditions as well as the pump pulse (red dashed line) at a power of 7 mW. The amplitude of E input was increased and reduced for constructive and destructive interference conditions, respectively, which can be used to compensate the pulse amplitude fluctuations of the pump pulse and, therefore, is highly welcome. But beside the amplitude fluctuations also the pulse shape especially in the rising edge of the pulse was changed considerably, which is unwanted, because fluctuations of the pulse form do not help to compensate pump pulse amplitude fluctuations, but they result in fluctuations of the spectrum of the generated supercontinua. Note, that the main interference effects that are responsible for pulse amplitude fluctuations are due to the feedback of spectral components of the SC in the same wavelength range as the pump pulse spectrum. All other wavelength components do not interfere with the pump pulse, but they still influence the shape of the input pulse. By considering an additional spectral bandpass filter in the feedback cavity with a transmittance range around the pump pulse central wavelength of 775 nm, it was possible to reduce the fluctuations of the input pulse shape, thereby creating better controlled experimental conditions (see Fig. 7(b)). On the one hand, the input pulse form nearly stayed unchanged and was not affected by the feedback. On the other hand, the interference effects were preserved, and thus this modified setup provided optimized conditions for the compensation of pump pulse fluctuations, such that the input pulse E input in front of the fiber was effectively stabilized.

Fig. 7 Feedback system input pulses for constructive (blue dotted line) and destructive interference (black solid line) conditions and pump pulse (red dashed line) at a pump power of 7ṁW a) without any filter and b) with spectral bandpass filter. c) Numerical results with spectral filtering: resulting feedback system output power in dependence on the feedback phase, when the pump power was varied from 1 mW to 10 mW in steps of 1 mW. The feedback system showed a phase and intensity dependent behavior. Regions with approached proximate curves (one example is marked with the blue circle) indicate noise reduction.

The impact of the additional spectral filter on the SC feedback system without considering the dynamical system response was investigated by numerically calculating the intra-cavity power in front of the filter of the modified feedback system for the same pump power values as in Fig. 3 (from 1 mW to 10 mW). The results are depicted in Fig. 7(c), where the response of the feedback system again shows a complex dependence on feedback phase and pump power. Between 5 mW and 6 mW at a delay position of 1.2 fs two curves approach each other, i.e., this parameter range is expected to show noise reduction via feedback, and detailed numerical calculations including the dynamical system response to analyze the reduction of power variations were performed within this parameter range. The feedback system power was calculated for a pump power variation between 5.7 mW and 5.8 mW following the same routine as in Fig. 4. While the pump power was varied by 0.1 mW (Fig. 8(a)) the feedback system output power variations (Fig. 8(b)) were reduced by more than a factor of two to 0.042 mW. For this example a reduction of the relative noise of 3.54 dB was found for the perturbation frequency of 450 kHz.

Fig. 8 Numerical results with introduced spectral filter: a) evolution of the pump power varied sinusoidally in the range from 5.7 mW to 5.8 mW; b) according evolution of the resulting feedback system power.

The optical spectra as well as the spectral amplitude variations for the pump power region from 5.7 mW to 5.8 mW for the single-pass system and the feedback system are plotted in Fig. 9. For this case, the spectrum of the feedback system (Fig. 9(b)) was very similar to the spectrum of the single-pass system (Fig. 9(a)), because spectral interference effects were suppressed by the spectral filter. The spectral amplitude variations and the spectral amplitude variations normalized to the corresponding mean spectra are plotted in Fig. 9(c) and Fig. 9(d), respectively. In both figures the spectral variations for the single-pass system are plotted as a red dashed line and those for the feedback system as a black solid line. The shape of the curves for the single-pass system and the feedback system look very similar. However, the black solid curve is below the red dashed curve, which shows that the spectral amplitude variations could be reduced for almost all spectral components. Nevertheless, the noise reduction was a function of wavelength. In average the noise was reduced by 2.37 dB in the wavelength region between 640 nm and 900 nm. Note, that the normalized spectral power density around 763 nm and 780 nm was very low (≪ 1) (see Fig. 9(a) and (b)), and thus the variation function was divided by a value ≪ 1 at these spectral components in order to calculate the normalized spectral amplitude variations. This resulted in very high relative variations for those wavelength components (see Fig. 9(d)), that were not representative and, therefore, should not be taken into account for physical interpretations.

Fig. 9 Numerical results with introduced spectral filter: optical spectra for varying system input power between 5.7 mW and 5.8 mW (180 spectra are plotted on top of each other) a) without and b) with feedback; c) corresponding spectral variations without (red dashed line) and with (black solid line) feedback and d) normalized spectral variations.

The bandwidth of the spectral filter was chosen to be in the range of the bandwidth of the pump pulse. If it was too narrow, the feedback efficiency was reduced, and interference effects were not used optimally. If the bandwidth was too wide, the input pulse shape started to get distorted by the feedback and perturbations were introduced to the SC generation.

Beside the fluctuations of the optical SC spectrum, we verified that also the fluctuations of the SC pulse form were simultaneously reduced, which indicated that not only the spectral amplitude but also the spectral phase was stabilized synchronously. Our investigations showed, that noise reduction of the spectral amplitude over the whole SC spectrum via optical feedback is possible in principle.

5.2. Experimental results

In order to qualitatively verify the numerically found predictions concerning the spectral amplitude stability, an additional spectral bandpass filter with a transmission window with a FWHM of approx. 20 nm around the central wavelength of the pump pulse was inserted into the experimental setup. An experimental verification measurement by directly extracting the spectral amplitude variations from the recorded optical spectra was not possible, because the variations were too fast (≈ 450 kHz) to be measured with a spectrometer. Instead, we used the analysis setup described in section 2 and shown in part C of Fig. 1, where the power of three filtered spectral regions as well as the power of the whole SC spectrum were simultaneously recorded with four photodiodes connected to the four ports of a digital oscilloscope.

Fig. 10 Spectrally resolved analysis of the SC noise properties; a) generated optical spectrum without feedback. The spectral ranges that were recorded are shown as bars and labeled with PD 1 to PD 4; b) phase dependent noise peak amplitude with feedback (black solid line) and reference noise peak amplitude for single-pass SC generation (red dashed line) integrated over the whole pulse; c–e) phase dependent noise peak amplitudes for the spectral regions around 730 nm, 775 nm, and 830 nm.

The best simultaneous noise reduction of all four signals was found at a delay position of 7.7π, where the noise peak for the total SC spectrum was reduced by 3.3 dB (considering the measurement error), while the noise level of the individual spectral regions were reduced by 26.2 dB (730 nm), 5.4 dB (775 nm), and by 11.4 dB (830 nm). The simultaneous noise reduction for all measured signals within certain delay regions was in good agreement with our numerical prediction (see Fig. 9(d)).

6. Perspectives of reducing low amplitude noise

In the presented examples the impact on relatively high input fluctuations in the order of 1% to 10% of the average pump power were discussed. These examples were chosen to realize a comparison to our experiments, where relatively high fluctuations were introduced for systematic analysis. For the simulations, however, we carefully checked that the principles of our noise reduction technique are still suitable for smaller fluctuations (< 1%) by reducing the fluctuations stepswise. The results for the static feedback response for the parameter range marked with the blue cycle in Fig. 3 are listed in the following table.

Table 1. Power Reduction Results for Different Amplitude Values of Input Noise

table-icon
View This Table

The variation amplitude was reduced stepwise from 1 mW via 0.1 mW and 0.01 mW finally to 0.001 mW. This corresponds to a relative input noise of 7.69%, 0.73%, 0.075%, and 0.0073%, respectively. In this example the relative noise reduction could even be continuously improved from 11.15 dB to 35.86 dB by reducing the input variations. The tendency of improved noise reduction as a function of the variation amplitude was not universal for all parameter ranges. However, these findings clearly demonstrate that beside relatively high fluctuations also very small fluctuations can considerably be suppressed. This shows that our noise reduction technique can in principle be used to reduce a wide amplitude range of power fluctuations and a combination with other active noise reduction techniques of the pump source should be possible in order to achieve highly stable SC generation.

7. Summary and conclusions

Power noise reduction as well as spectral amplitude noise reduction of supercontinua via optical feedback were demonstrated numerically and experimentally. The supercontinua were generated within a highly nonlinear, microstructured fiber, which was incorporated into a ring cavity. It was shown, that the SC noise characteristics could be influenced via optical feedback based on the interplay of the fiber nonlinearity and the interference of the pulses in the ring cavity. Both effects could be balanced by adjusting the pump power and the feedback phase with the result of noise reduction.

Two different setups of optical feedback were investigated. Firstly, the whole SC spectrum was fed back without any filter within the feedback loop. With this setup a considerable noise reduction of the power could be achieved numerically (of 11.5 dB) as well as experimentally (in the order of 15 dB). The spectral amplitude noise, however, was only reduced for a narrow spectral region around 800 nm. Secondly, in order to improve the spectral amplitude noise characteristics, the complexity of the SC pulse shape in front of the MSF was reduced by adding a spectral filter to the feedback cavity. With this setup the input pulses in front of the MSF were effectively stabilized and beside the noise reduction of the power, additionally spectral amplitude noise reduction over the whole optical spectrum could be demonstrated in our simulations and was experimentally verified.

This second noise reduction method would allow for a stabilization specific to an application: depending on the requirements, a SC with stabilized spectrum regarding all wavelength components could be realized, or at the cost of increased noise at unused wavelength regions, certain wavelength regions could be stabilized with an even better noise reduction. In order to find parameter ranges with low noise at a certain wavelength for low perturbation frequencies, a road map very similar to the ones shown in Figs. 3 and 7(c) could be prepared. From the intensity of the desired wavelength component at the system output measured as a function of the pump power and the feedback phase one could extract parameter ranges, within which the intensity of this wavelength component can be expected to be insensitive to pump power variations.

Additionally, we proved with our numerical simulations that noise reduction via optical feedback can be used for the reduction of a wide amplitude range of power fluctuations within SC generation. The advantage of the presented passive, all-optical stabilization technique in comparison to active methods is that in principle it is relatively fast. Furthermore, it would also allow for reducing perturbations, for example with very low amplitude fluctuations that would hardly be possible to measure, so that active methods would fail. Thus, a combination of the presented passive noise reduction method with active methods should provide SC generation with outstanding high stability.

Acknowledgments

We acknowledge support by Deutsche Forschungsgemeinschaft and Open Access Publication Fond of University of Muenster.

References and links

1.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]

2.

I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,” Opt. Lett. 26, 608–610 (2001). [CrossRef]

3.

A. D. Aguirre, N. Nishizawa, J. G. Fujimoto, W. Seitz, M. Lederer, and D. Kopf, “Continuum generation in a novel photonic crystal fiber for ultrahigh resolution optical coherence tomography at 800 nm and 1300 nm,” Opt. Express 14, 1145–1160 (2006). [CrossRef] [PubMed]

4.

J. H. Frank, A. D. Elder, J. Swartling, A. R. Venkitaraman, A. D. Jeyasekharan, and C. F. Kaminski, “A white light confocal microscope for spectrally resolved multidimensional imaging,” J. Microsc. 227, 203–215 (2007). [CrossRef] [PubMed]

5.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000). [CrossRef] [PubMed]

6.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002). [CrossRef] [PubMed]

7.

H. Zhang, S. Yu, J. Zhang, and W. Gu, “Effect of frequency chirp on supercontinuum generation in photonic crystal fibers with two zero-dispersion wavelengths,” Opt. Express 15, 1147–1152 (2007). [CrossRef] [PubMed]

8.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003). [CrossRef]

9.

M. H. Frosz, P. M. Moselund, P. D. Rasmussen, C. L. Thomsen, and O. Bang, “Increasing the blue-shift of a supercontinuum by modifying the fiber glass composition,” Opt. Express 16, 21076–21086 (2008). [CrossRef] [PubMed]

10.

F. Lu, Y. Deng, and W. H. Knox, “Generation of broadband femtosecond visible pulses in dispersion-micromanaged holey fibers,” Opt. Lett. 30, 1566–1568 (2005). [CrossRef] [PubMed]

11.

P. Falk, M. H. Frosz, and O. Bang, “Supercontinuum generation in a photonic crystal fiber with two zero-dispersion wavelengths tapered to normal dispersion at all wavelengths,” Opt. Express 13, 7535–7540 (2005). [CrossRef] [PubMed]

12.

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009). [CrossRef]

13.

E. Räikkönen, G. Genty, O. Kimmelma, M. Kaivola, K. P. Hansen, and S. C. Buchter, “Supercontinuum generation by nanosecond dual-wavelength pumping in microstructured optical fibers,” Opt. Express 14, 7914–7923 (2006). [CrossRef] [PubMed]

14.

J. C. Travers, S. V. Popov, and J. R. Taylor, “Extended blue supercontinuum generation in cascaded holey fibers,” Opt. Lett. 30, 3132–3134 (2005). [CrossRef] [PubMed]

15.

P. S. Westbrook, J. W. Nicholson, and K. S. Feder, “Grating phase matching beyond a continuum edge,” Opt. Lett. 32, 2629–2631 (2007). [CrossRef] [PubMed]

16.

P. M. Moselund, M. H. Frosz, C. L. Thomsen, and O. Bang, “Back-seeding of higher order gain processes in picosecond supercontinuum generation,” Opt. Express 16, 11954–11968 (2008). [CrossRef] [PubMed]

17.

Y. Deng, Q. Lin, F. Lu, G. P. Agrawal, and W. H. Knox, “Broadly tunable femtosecond parametric oscillator using a photonic crystal fiber,” Opt. Lett. 30, 1234–1236 (2005). [CrossRef] [PubMed]

18.

N. Brauckmann, M. Kues, P. Groß, and C. Fallnich, “Adjustment of supercontinua via the optical feedback phase - numerical investigations,” Opt. Express 18, 20667–20672 (2010). [CrossRef] [PubMed]

19.

N. Brauckmann, M. Kues, P. Groß, and C. Fallnich, “Adjustment of supercontinua via the optical feedback phase - experimental verifications,” Opt. Express 18, 24611–24618 (2010). [CrossRef] [PubMed]

20.

M. Kues, N. Brauckmann, T. Walbaum, P. Groß, and C. Fallnich, “Nonlinear dynamics of femtosecond super-continuum generation with feedback,” Opt. Express 17, 15827–15841 (2009). [CrossRef] [PubMed]

21.

N. Brauckmann, M. Kues, T. Walbaum, P. Groß, and C. Fallnich, “Experimental investigations on nonlinear dynamics in supercontinuum generation with feedback,” Opt. Express 18, 7190–7202 (2010). [CrossRef] [PubMed]

22.

G. Steinmeyer, A. Buchholz, M. Hänsel, M. Heuer, A. Schwache, and F. Mitschke, “Dynamical pulse shaping in a nonlinear resonator,” Phys. Rev. A 52, 830–838 (1995). [CrossRef] [PubMed]

23.

G. Sucha, D. S. Chemla, and S. R. Bolton, “Effects of cavity topology on the nonlinear dynamics of additive-pulse mode-locked lasers,” J. Opt. Soc. Am. B 15, 2847–2853 (1998). [CrossRef]

24.

N. R. Newbury, B. R. Washburn, K. L. Corwin, and R. S. Windeler, “Noise amplification during supercontinuum generation in microstructure fiber,” Opt. Lett. 28, 944–946 (2003). [CrossRef] [PubMed]

25.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, “Fundamental noise limitations to supercontinuum generation in microstructure fiber,” Phys. Rev. Lett. 90, 113904 (2003). [CrossRef] [PubMed]

26.

B. R. Washburn and N. R. Newbury, “Phase, timing, and amplitude noise on supercontinuum generation in microstructure fiber,” Opt. Express 12, 2166–2175 (2004). [CrossRef] [PubMed]

27.

G. Genty, S. Coen, and J. M. Dudley, “Fiber supercontinuum sources,” J. Opt. Soc. Am. B 24, 1771–1785 (2007). [CrossRef]

28.

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16, 46–56 (1999). [CrossRef]

29.

NKT Photonics, “NL-PM-750 data sheet,” http://www.nktphotonics.com/files/files/datasheet_nl-pm-750.pdf.

OCIS Codes
(320.7110) Ultrafast optics : Ultrafast nonlinear optics
(320.7140) Ultrafast optics : Ultrafast processes in fibers
(320.6629) Ultrafast optics : Supercontinuum generation

ToC Category:
Ultrafast Optics

History
Original Manuscript: March 21, 2011
Revised Manuscript: April 29, 2011
Manuscript Accepted: June 2, 2011
Published: July 18, 2011

Citation
Nicoletta Brauckmann, Michael Kues, Petra Groß, and Carsten Fallnich, "Noise reduction of supercontinua via optical feedback," Opt. Express 19, 14763-14778 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-16-14763


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References

  1. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]
  2. I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,” Opt. Lett. 26, 608–610 (2001). [CrossRef]
  3. A. D. Aguirre, N. Nishizawa, J. G. Fujimoto, W. Seitz, M. Lederer, and D. Kopf, “Continuum generation in a novel photonic crystal fiber for ultrahigh resolution optical coherence tomography at 800 nm and 1300 nm,” Opt. Express 14, 1145–1160 (2006). [CrossRef] [PubMed]
  4. J. H. Frank, A. D. Elder, J. Swartling, A. R. Venkitaraman, A. D. Jeyasekharan, and C. F. Kaminski, “A white light confocal microscope for spectrally resolved multidimensional imaging,” J. Microsc. 227, 203–215 (2007). [CrossRef] [PubMed]
  5. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000). [CrossRef] [PubMed]
  6. T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002). [CrossRef] [PubMed]
  7. H. Zhang, S. Yu, J. Zhang, and W. Gu, “Effect of frequency chirp on supercontinuum generation in photonic crystal fibers with two zero-dispersion wavelengths,” Opt. Express 15, 1147–1152 (2007). [CrossRef] [PubMed]
  8. M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003). [CrossRef]
  9. M. H. Frosz, P. M. Moselund, P. D. Rasmussen, C. L. Thomsen, and O. Bang, “Increasing the blue-shift of a supercontinuum by modifying the fiber glass composition,” Opt. Express 16, 21076–21086 (2008). [CrossRef] [PubMed]
  10. F. Lu, Y. Deng, and W. H. Knox, “Generation of broadband femtosecond visible pulses in dispersion-micromanaged holey fibers,” Opt. Lett. 30, 1566–1568 (2005). [CrossRef] [PubMed]
  11. P. Falk, M. H. Frosz, and O. Bang, “Supercontinuum generation in a photonic crystal fiber with two zero-dispersion wavelengths tapered to normal dispersion at all wavelengths,” Opt. Express 13, 7535–7540 (2005). [CrossRef] [PubMed]
  12. G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009). [CrossRef]
  13. E. Räikkönen, G. Genty, O. Kimmelma, M. Kaivola, K. P. Hansen, and S. C. Buchter, “Supercontinuum generation by nanosecond dual-wavelength pumping in microstructured optical fibers,” Opt. Express 14, 7914–7923 (2006). [CrossRef] [PubMed]
  14. J. C. Travers, S. V. Popov, and J. R. Taylor, “Extended blue supercontinuum generation in cascaded holey fibers,” Opt. Lett. 30, 3132–3134 (2005). [CrossRef] [PubMed]
  15. P. S. Westbrook, J. W. Nicholson, and K. S. Feder, “Grating phase matching beyond a continuum edge,” Opt. Lett. 32, 2629–2631 (2007). [CrossRef] [PubMed]
  16. P. M. Moselund, M. H. Frosz, C. L. Thomsen, and O. Bang, “Back-seeding of higher order gain processes in picosecond supercontinuum generation,” Opt. Express 16, 11954–11968 (2008). [CrossRef] [PubMed]
  17. Y. Deng, Q. Lin, F. Lu, G. P. Agrawal, and W. H. Knox, “Broadly tunable femtosecond parametric oscillator using a photonic crystal fiber,” Opt. Lett. 30, 1234–1236 (2005). [CrossRef] [PubMed]
  18. N. Brauckmann, M. Kues, P. Groß, and C. Fallnich, “Adjustment of supercontinua via the optical feedback phase - numerical investigations,” Opt. Express 18, 20667–20672 (2010). [CrossRef] [PubMed]
  19. N. Brauckmann, M. Kues, P. Groß, and C. Fallnich, “Adjustment of supercontinua via the optical feedback phase - experimental verifications,” Opt. Express 18, 24611–24618 (2010). [CrossRef] [PubMed]
  20. M. Kues, N. Brauckmann, T. Walbaum, P. Groß, and C. Fallnich, “Nonlinear dynamics of femtosecond super-continuum generation with feedback,” Opt. Express 17, 15827–15841 (2009). [CrossRef] [PubMed]
  21. N. Brauckmann, M. Kues, T. Walbaum, P. Groß, and C. Fallnich, “Experimental investigations on nonlinear dynamics in supercontinuum generation with feedback,” Opt. Express 18, 7190–7202 (2010). [CrossRef] [PubMed]
  22. G. Steinmeyer, A. Buchholz, M. Hänsel, M. Heuer, A. Schwache, and F. Mitschke, “Dynamical pulse shaping in a nonlinear resonator,” Phys. Rev. A 52, 830–838 (1995). [CrossRef] [PubMed]
  23. G. Sucha, D. S. Chemla, and S. R. Bolton, “Effects of cavity topology on the nonlinear dynamics of additive-pulse mode-locked lasers,” J. Opt. Soc. Am. B 15, 2847–2853 (1998). [CrossRef]
  24. N. R. Newbury, B. R. Washburn, K. L. Corwin, and R. S. Windeler, “Noise amplification during supercontinuum generation in microstructure fiber,” Opt. Lett. 28, 944–946 (2003). [CrossRef] [PubMed]
  25. K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, “Fundamental noise limitations to supercontinuum generation in microstructure fiber,” Phys. Rev. Lett. 90, 113904 (2003). [CrossRef] [PubMed]
  26. B. R. Washburn and N. R. Newbury, “Phase, timing, and amplitude noise on supercontinuum generation in microstructure fiber,” Opt. Express 12, 2166–2175 (2004). [CrossRef] [PubMed]
  27. G. Genty, S. Coen, and J. M. Dudley, “Fiber supercontinuum sources,” J. Opt. Soc. Am. B 24, 1771–1785 (2007). [CrossRef]
  28. C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16, 46–56 (1999). [CrossRef]
  29. NKT Photonics, “NL-PM-750 data sheet,” http://www.nktphotonics.com/files/files/datasheet_nl-pm-750.pdf .

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