Processing of optical combs with fiber optic parametric amplifiers

doi:10.1364/OE.20.010059

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Processing of optical combs with fiber optic parametric amplifiers

R. Slavík, J. Kakande, P. Petropoulos, and D. J. Richardson »View Author Affiliations

Optics Express, Vol. 20, Issue 9, pp. 10059-10070 (2012)
http://dx.doi.org/10.1364/OE.20.010059

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Abstract

Low noise optical frequency combs consist of equally spaced narrow-linewidth optical tones. They are useful in many applications including, for example, line-by-line pulse shaping, THz generation, and coherent communications. In such applications the comb spacing, extent of spectral coverage, degree of spectral flatness, optical tone power and tone-to-noise ratio represent key considerations. Simultaneously achieving the level of performance required in each of these parameters is often challenging using existing comb generation technologies. Herein we suggest and demonstrate how fiber optic parametric amplifiers can be used to enhance all of these key comb parameters, allowing frequency span multiplication, low noise amplification with simultaneous comb spectrum flattening, and improvement in optical tone-to-noise ratio through various phase insensitive as well as phase sensitive implementations.

1. Introduction

An optical comb consists of many equally spaced narrow-linewidth frequency tone components. In the time domain such a frequency comb corresponds to a periodic train of low-timing-jitter short optical pulses. Optical combs have attracted considerable recent interest due to both their spectral, as well as temporal properties. In the spectral domain, frequency combs form a frequency ‘ruler’, enabling measurement over bandwidths significantly larger than those achievable using electronics (>>100 GHz). This property enables precise frequency and time measurement at wavelengths where no metrology reference exists [1

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002). [CrossRef] [PubMed]

], and also allows for the precise phase synchronization of spectrally distant signals – as desirable for example for terahertz wave generation [2

S. Fukushima, C. F. C. Silva, Y. Muramoto, and A. J. Seeds, “10 to 110 GHz tunable opto-electronic frequency synthesis using optical frequency comb generator and uni-travelling-carrier photodiode,” Electron. Lett. 37(12), 780–781 (2001). [CrossRef]

]. In principle, we can divide optical combs into two main categories. Into the first category fall the so-called self-referenced combs that typically require an octave spanning spectral bandwidth and employ subsequent carrier-envelope offset (CEO) stabilization through a 1f-2f interferometer [1

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002). [CrossRef] [PubMed]

]. Such combs are usually generated using ultra short pulse mode-locked lasers and the absolute frequency of the comb lines is very accurately defined. In the second category lie combs generated from a continuous wave (cw) master laser using either: a passive or an active (but non-lasing) resonant cavity incorporating an electro-optic modulator [3

S. Bennett, B. Cai, E. Burr, O. Gough, and A. J. Seeds, “1.8-THz bandwidth, zero-frequency error, tunable optical comb generator for DWDM applications,” IEEE Photon. Technol. Lett. 11(5), 551–553 (1999). [CrossRef]

M. Kourogi, T. Enami, and M. Ohtsu, “Monolithic optical frequency comb generator,” IEEE Photon. Technol. Lett. 6(2), 214–217 (1994). [CrossRef]

]; four-wave mixing (FWM) [5

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007). [CrossRef] [PubMed]

]; or a cavity-less configuration consisting of a cascade of modulators [6

T. Healy, F. C. Garcia Gunning, A. D. Ellis, and J. D. Bull, “Multi-wavelength source using low drive-voltage amplitude modulators for optical communications,” Opt. Express 15(6), 2981–2986 (2007). [CrossRef] [PubMed]

]. Although these combs could in principle also be CEO stabilized (provided that their spectrum can be broadened over an octave [7

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett. 107(6), 063901 (2011). [CrossRef] [PubMed]

]), they can be used directly in many applications where the accurate definition of absolute frequency is less critical (e.g., terahertz generation [2

], line-by-line arbitrary pulse shaping [8

Z. Jiang, D. E. Leaird, C. Huang, H. Miao, M. Kourogi, K. Imai, and A. M. Weiner, “Spectral Line-by-Line Pulse Shaping on an Optical Frequency Comb Generator,” IEEE J. Quantum Electron. 43(12), 1163–1174 (2007). [CrossRef]

], optical coherence tomography [9

S. J. Lee, B. Widiyatmoko, M. Kourogi, and M. Ohtsu, “Ultrahigh Scanning Speed Optical Coherence Tomography Using Optical Frequency Comb Generators,” Jpn. J. Appl. Phys. 40(Part 2, No. 8B), L878–L880 (2001). [CrossRef]

], coherent telecommunications [6

], etc). Herein, we are interested predominantly in this latter category of combs and applications. In many of these applications it is important to get a flat comb with adequate (depending on application) bandwidth, power and optical tone-to-noise ratio (OTNR). Unfortunately, this is challenging for all the technologies used, as they generally rely on a cascaded re-distribution of the input cw signal into the comb tones, resulting in a non-uniform power distribution (the comb tones closer to the original cw signal are generally stronger than those further away). When a passive cavity is used, the output power tends to be low and shot noise prevents the attainment of high OTNRs. On the other hand, when a gain mechanism is included in the cavity, the OTNR is compromised by amplified spontaneous emission (ASE). A further effect to mention is the bandwidth limitation imposed by either the intracavity dispersion or gain bandwidth. We give a more comprehensive review later.

The obvious solution to boost the power of the comb is via direct external amplification. Ideally, such amplification should have sufficient gain and bandwidth, as well as a low noise figure. Additionally, the possibility of having an adaptable spectral gain profile to help generate flat(ter) combs would be highly advantageous. Another interesting concept and functionality would be to combine the amplification process with a mechanism that serves to broaden the bandwidth of the input optical comb (e.g., by generating spectral copies).

Here, we show how fiber optic parametric amplifiers (FOPAs) can improve many of the key comb parameters. FOPAs have a number of useful features that make them interesting for processing optical combs. Firstly, they can have a bandwidth surpassing that of an erbium-doped fiber amplifier (EDFA) – moreover, they can double the bandwidth occupied by the input signal, which is a feature that is generally disadvantageous for the amplification of telecommunication signals (requiring auxiliary bandwidth for the data idlers), but which turns out to present interesting opportunities for the processing of optical combs. Secondly, by controlling the dispersive properties of the highly non-linear fiber (HNLF) used in the FOPA, the parametric gain profile can be controlled, thereby allowing for flattening of optical comb specra. The last interesting feature deals with OTNR. FOPAs can be configured to perform phase sensitive amplification in which the optical signal-to-noise ratio (OSNR) can be improved by up to 6 dB as compared to standard phase insensitive amplification (e.g., by EDFA). For optical combs, the tones form the ‘signal’ and thus this OSNR improvement translates directly into an OTNR improvement. This is difficult to exploit in telecommunications, as it requires two temporally identical data streams transmitted simultaneously over the network (besides using twice the data bandwidth, these two data streams forming a signal-idler pair must be precisely phase synchronized) [10

Z. Tong, C. Lundström, P. Andrekson, C. McKinstrie, M. Karlsson, D. Blessing, E. Tipsuwannakul, B. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards the Ultra-Sensitive Optical Link Enabled by Low Noise Phase-Sensitive Amplifiers,” Nat. Photonics 5(7), 430–436 (2011). [CrossRef]

], but is straightforward for optical combs that already contain phase synchronized pairs of comb tones. To summarize, FOPAs are very promising for the processing of optical combs, as they promise tailored gain profiles, wide-bandwidth amplification, multiplication of the comb span and improvement of OTNR – most of these features are not possible using an EDFA. Here, we demonstrate all these key features. Some preliminary results are to be found in [11

J. Kakande, P. Petropoulos, and D. J. Richardson, “Fiber optical parametric amplification of optical combs for enhanced performance and functionality,” 37th European Conference and Exhibition on Optical Communication (ECOC), Geneva, Switzerland, 18–22 Sept. 2011.

2. FOPA for optical combs: principles

A FOPA can be configured to perform phase insensitive (PI-FOPA) or phase sensitive (PS-FOPA) amplification [10

] and, as will be shown here, both these regimes can be useful for the processing of optical frequency combs.

Various possible configurations and comb processing possibilities enabled by PI-FOPAs are shown in Fig. 1 . Using a single-pump configuration, one can amplify and shape the spectral profile of the comb, leading to flatter combs with higher power. The pump can be either phase/frequency synchronized to a comb tone at the edge of the comb spectrum (Fig. 1(a)), allowing for doubling of the comb spectral width, or further away, to obtain a (flattened and amplified) comb copy in another spectral band (Fig. 1(b)). FOPAs can also use two pumps, which allows one to launch two times more pump power (as compared to the single pump equivalent) before the stimulated Brillouin scattering (SBS) threshold of the HNLF is reached. Besides that, it gives more flexibility for flattening of the comb spectrum (e.g., by controlling the power of each pump), tripling of the comb bandwidth (Fig. 1(c)), and further broadening of the comb spectrum via cascaded FWM processes in which new pumps are generated first, followed by the generation of additional comb copies, (Fig. 1(c)) [12

C.-S. Brès, A. Wiberg, B. P. Kuo, N. Alic, and S. Radic, “Wavelength Multicasting of 320-Gb/s Channel in Self-Seeded Parametric Amplifier,” IEEE Photon. Technol. Lett. 21(14), 1002–1004 (2009). [CrossRef]

Fig. 1 Single-pump (a,b) and dual-pump (c) phase insensitive FOPA for processing of an optical comb. A single pump can be (a) used to amplify and shape the comb with simultaneous doubling its spectral width by phase synchronizing the pump with a comb tone at its edge or (b), to generate a comb copy in another spectral band. The dual-pump configuration (c) has several advantages including better parametric gain, better shaping capabilities and the possibility to either triple the spectral width or broaden the comb even further by exploiting cascaded FWM processes in which additional pumps are generated from the original pumps, allowing for subsequent generation of additional comb copies.

A PS-FOPA requires properly phase locked pump(s), signal and idler to be present at the HNLF input [10

]. In conjunction with an optical comb, practical single-pump and dual-pump configurations are suggested in Fig. 2 . For efficient phase sensitive amplification, the signal and idler powers need to be equalized, imposing some limitations on the optical comb to be processed. The main advantage of the PS-FOPA over phase insensitive amplification (PI-FOPA, EDFA) is the potential for a 6 dB improvement in OSNR [10

]. As mentioned previously, the OSNR improvement translates directly to OTNR improvement when an optical comb is used as the signal. Another advantage is the 6 dB higher gain for a PS-FOPA as compared to PI-FOPA for a fixed pump power [10

Fig. 2 Single-pump (a) and dual-pump (b) phase sensitive FOPAs.

Parametric gain in HNLF is achieved via a resonant FWM process, which needs to be phase matched to maximize efficiency. It is therefore possible to tailor the spectral gain profile using both linear (HNLF dispersion) and nonlinear (pump power) mechanisms – indeed phase matching is typically achieved by compensating for one using the other [13

R. H. Stolen and J. E. Bjorkholm, “Parametric ampliﬁcation and frequency conversion in optical ﬁbers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982). [CrossRef]

]. For flat gain, the pump wavelength should be set at the fiber zero dispersion wavelength (ZDW). With the pump below the ZDW (normal dispersion), the gain typically has a sinc-squared profile, with the maximum gain close to the pump. With the pump wavelength higher than the ZDW (anomalous dispersion), gain peaks are observed symmetrically around the pump, but detuned in wavelength from it. As such, it is possible to have flat, negatively or positively sloped gain profiles close to the pump, and the steepness of the slope can be controlled using the pump power.

3. Key components and chosen experimental configurations

Let us first discuss the key components: the optical comb generator and HNLF.

3.1 Optical comb generator

Optical comb generators based on cascaded modulators (e.g., [6

]), high-finesse passive (no gain) Fabry-Perot resonators incorporating a phase modulator [4

M. Kourogi, T. Enami, and M. Ohtsu, “Monolithic optical frequency comb generator,” IEEE Photon. Technol. Lett. 6(2), 214–217 (1994). [CrossRef]

], gain-assisted ring resonators incorporating a phase or amplitude modulator [3

,14

M. Hirano and A. Morimoto, “Generation of flat optical frequency comb by fiber loop modulation,” Opt. Rev. 18(1), 13–18 (2011). [CrossRef]

], and recently also nonlinear micro-resonators [5

] are currently the most promising configurations in terms of noise performance. Table 1 gives a rough comparison of these various technologies – obviously some reports show a wider spectral span at the expense of the flatness, etc., so it is difficult to give truly definitive figures of merit for each approach. However, we consider that the selected data shows the key strengths and weaknesses of the various technologies. In general, all of them suffer either from limited flatness at the comb edges, limited power-per-tone, limited bandwidth, and/or modest to low OTNR.

Table 1 Comparison of Key Parameters of Combs Based on Various Technologies

Comb technology	Bandwidth, nm	Comb mode spacing, GHz	Uniformity, dB	Output power, dB	OTNR, dB /resolution
FWM in µ-resonator [5 P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007). [CrossRef] [PubMed] ]	250	375, 900	<5	>10	30 dB/10pm*
Gain-assisted resonator [13 R. H. Stolen and J. E. Bjorkholm, “Parametric ampliﬁcation and frequency conversion in optical ﬁbers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982). [CrossRef] ]	8	10	<2	0-3	>20 dB/10pm*
Passive resonator (this work)	32 8	25	13 3	-13	40-50 dB/20pm
Two-cascaded modulators [6 T. Healy, F. C. Garcia Gunning, A. D. Ellis, and J. D. Bull, “Multi-wavelength source using low drive-voltage amplitude modulators for optical communications,” Opt. Express 15(6), 2981–2986 (2007). [CrossRef] [PubMed] ]	3-4	42	<2	0-3**	30 dB/0.2 nm**

* an estimate based on analysis of figures in the corresponding references

** these values were kindly supplied by the authors of the referenced article

In the work reported herein, we chose to use a commercial passive resonator-based comb generator (Optical Frequency Comb Generator, OFCG, OptoComb Inc., Japan) since it is compact and provides a high-quality comb [15

S. Xiao, L. Hollberg, N. R. Newbury, and S. A. Diddams, “Toward a low-jitter 10 GHz pulsed source with an optical frequency comb generator,” Opt. Express 16(12), 8498–8508 (2008). [CrossRef] [PubMed]

] spanning an extended spectral region (~4 THz). The spectrum of our comb source is shown in Fig. 3 (the optical resolution used for capturing this trace, as well as all other spectral traces shown in this article, is 20 pm). The spectral profile is seen to be quite symmetric, allowing for efficient phase sensitive amplification due to the signal-idler equalization criteria mentioned previously. The comb is also far from flat – indeed it has a logarithmically triangular spectral shape, which although generally a drawback provides us with the opportunity to demonstrate one of the key advantages of amplification using a FOPA – the ability to flatten the comb by providing a tailored gain profile. Another drawback of this comb is the relatively low output power, which again is a parameter that can be enhanced using a FOPA. The detailed OFCG spectral characteristics are as follows: tone spacing of 25 GHz, tone intensity slope of 0.8 dB/nm, total output power of −13 dB when seeded with 16 dBm of cw power (which is the maximum input power recommended by the manufacturer). The OTNR is slightly compromised by ASE present from the seed source (a saturated EDFA was used to boost the power of the seed laser to 16 dBm). Obviously, this could be straightforwardly improved by placing a narrow-band filter just before the comb generator. To allow comparison with the experimental results shown later, the spectrum in Fig. 3 was obtained with the seed laser operated in a gated mode. The reasons for gating the seed laser are discussed in detail later.

Fig. 3 OFCG spectrum at its output when seeded by 40 mW (max power recommended by the manufacturer) – the seed was a semiconductor laser amplified with an EDFA.

It is worth mentioning that by virtue of the operating mechanism the OFCG generates a comb that has a tone-to-tone phase difference of 0 at the longer wavelength side and π at the shorter wavelength side. In the temporal domain, this corresponds to pulses with alternate phases (pulse-to-pulse phase change of 180 deg) [15

]. The significance of this property will become clear later when dealing with PS-FOPA.

3.2 HNLF

The specific HNLF used in our experiments was a 500-m long Germanium-doped fiber selected primarily by virtue of its dispersion characteristics: zero dispersion wavelength of 1555 nm, and dispersion slope of 0.02 ps/nm²/km. The non-linear coefficient is 11 W⁻¹km⁻¹. In order to obtain the required flattening of our comb we estimated we would require around 31 dBm of cw pump power. This amount of power exceeded the SBS threshold of the fibre (17dBm). Therefore for our demonstration we decided to perform low duty cycle gating of the pump and comb, reducing the SBS interaction length to the spatial length of the gated pulse and thereby boosting the SBS threshold significantly. We used 20% duty-cycle gating and 500 kHz gating frequency, which gives 80 m long pulses. After amplifying the gated pump in an EDFA with an average power at the HNLF input of 24 dBm, a maximum peak pump power of 31 dBm could be generated (constant during the 20% on-time).

To allow cw operation an HNLF with better nonlinearity/SBS ratio and similar level of control of its dispersive properties would be needed. This could be achieved using controlled straining of HNLF with simultaneous control of the zero dispersion wavelength [16

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. Wiberg, C.-S. Brès, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero-dispersion wavelength proﬁles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009). [CrossRef]

], doping using a material other than germanium (e.g. aluminum) [17

L. Grűner-Nielsen, S. Dasgupta, M. D. Mermelstein, D. Jakobsen, S. Herstrm, M. E. V. Pedersen, E. L. Lim, S. Alam, F. Parmigiani, D. Richardson, and B. Pálsdótti, “A silica based highly nonlinear fibre with improved threshold for stimulated Brillouin scattering,” European Conference on Optical Communications (ECOC), paper Tu.4.D., Torino, Italy, 19–23 September, 2010.

], or by using non-silicate fibers (e.g., lead silicate [18

A. Camerlingo, F. Parmigiani, X. Feng, F. Poletti, P. Horak, W. Loh, D. J. Richardson, and P. Petropoulos, “Multichannel wavelength conversion of 40-Gb/s nonreturn-to-zero DPSK signals in a lead–silicate fiber,” IEEE Photon. Technol. Lett. 22(15), 1153–1155 (2010). [CrossRef]

]). Another option would be to use other waveguide-based non-linear media, however further development is needed in their design and fabrication to simultaneously achieve the required level of nonlinearity, dispersion, power handling, and loss.

3.3 Experimental configurations

Let us start with the PS-FOPA as it is the most straightforward to explain. To obtain PS-amplification, the OFCG seed can also be used as the FOPA pump, as it fulfills the two principal requirements. Firstly, its optical frequency is exactly in the middle of the OFCG spectrum – thus, the pairs of comb lines that serve as signal-idler pairs have the same power (which is required for maximally efficient PS-FOPA). Secondly, the seed is inherently frequency locked to the comb lines generated by OFCG. Thus, for the PS-FOPA, we only need to tap off the seed before the OFCG and then combine it with the OFCG output. Our PS-FOPA configuration is shown in Fig. 2(a). In order to allow for direct comparison between PI- and PS-FOPA, we decided to use the following configuration for PI-FOPA. As for the PS-FOPA, we wanted to use the OFCG seed as the pump. This was realized by blocking off one half of the OFCG spectrum (i.e. removing all tones in the spectral region of the idlers) before combining it back with the pump and obtaining PI-FOPA as outlined in Fig. 1(a).

4. Phase insensitive FOPA

The detailed set-up is shown in Fig. 4 . A narrow linewidth cw signal (RIO semiconductor laser from Redfern Inc., USA with linewidth <5 kHz and an output power of 10 mW) emitting at 1558 nm was used as a high-quality seed for our OFCG. As explained previously the seed laser was gated with a duty cycle of 1:5 at a repetition rate of 500 kHz to allow for suppression of SBS in the HNLF. The HNLF parameters are summarized in section 3.2. The gated seed was amplified in a high power EDFA (maximum power used in our experiments was 29 dBm) and split in a 95/5 coupler. The smaller portion was used to seed the OFCG, followed by a 16-nm bandpass filter (with almost square-like filtering characteristics, Alnair Inc., Japan). In the temporal domain, the 16-nm comb formed very short (sub-picosecond) pulses. Although the average power of these pulses was very low (around −20 dBm), the peak power due to their short duration is sufficient to generate unwanted nonlinear processes in the HNLF in which the comb serves as the pump. Thus, we introduced some dispersion (by adding 5 km of SMF-28 fiber) to broaden these pulses and effectively reduce their peak power in the HNLF. The 95% portion of the seed was used as the FOPA pump with ASE from the EDFA suppressed using a 2-nm bandpass filter. The pump and comb were combined in an add-drop multiplexer (ADM) with an insertion loss below 1 dB and an add-port bandwidth of 0.2 nm. Then, the combined output (consisting of the pump and the comb) was launched into the HNLF and the corresponding output was analyzed with an optical spectrum analyzer (OSA). Polarization maintaining components were used wherever possible to reduce the number of polarization controllers required in the system (as shown in Fig. 4).

Fig. 4 Set-up for the phase-insensitive FOPA. The bandpass filter behind the OFCG selects the 1541-1557.5 nm spectral band (one half of the OFCG spectrum).

Figure 5 shows the output spectra for average pump powers of 18, 21, and 24 dBm (measured at the HNLF input). Here we see that variation of the pump power influences the gain profile. At 24 dBm of average pump power, the FOPA gain profile is roughly inverse to that of the comb across over ± 16 nm range about the pump wavelength, resulting in a flat comb at the FOPA output. We also confirm that the comb bandwidth was efficiently doubled. To better appreciate all the critical characteristics of the generated comb, the spectrum captured at an average pump power of 24 dB is also presented in Fig. 6 . Here we see that comb is flattened to within 3 dB peak-to-peak variation over a 4 THz bandwidth (32 nm) with OTNR>21 dB.

Fig. 5 Phase insensitive FOPA for average pump powers of 18, 21, and 24 dBm, respectively.

Fig. 6 Phase insensitive FOPA for an average pump power of 24 dBm showing the key comb parameters.

Figure 7 shows a comparison between the amplification performance obtained with the FOPA and a standard telecom-grade gain-flattened in-line EDFA with a noise figure of 5 dB – for completeness, the unamplified comb spectrum is also shown. To minimize the ASE generated in the EDFA, the comb (which had a total power of about −20 dBm) was combined with a small fraction of the pump to obtain an input signal power of −5 dBm (maximum allowed input power into the EDFA preamplifier). To allow a like-with-like comparison the EDFA output spectrum (Fig. 7(c)) was post-processed to emulate the effect of an idealized gain flattening filter - superimposed spectral plots of the measured FOPA output (Fig. 7(b)) and the ‘numerically flattened’ EDFA output (Fig. 7(c)), are shown in Fig. 7(d). For the gain flattening filter, we assumed that it has no excess insertion loss, fully transmits the weakest comb signal (at 1542 nm), and that it is applied at the EDFA output. (One might consider putting it at the EDFA input or in the middle of a two-stage EDFA, however, for this application, we do not expect any significant advantage from either such an approach in terms of noise, as the overall noise figure is dominated by the first EDFA stage).

Fig. 7 Comb spectrum without amplification (pump OFF) (a), FOPA-amplified with pump power of 24 dBm (b), and amplified only with an EDFA to obtain the same output power as FOPA at 1542 nm (c), EDFA output numerically filtered by an idealized gain flattening filter with zero attenuation at 1542 nm is shown in (d) together with FOPA result shown in (b). The observed OTNR difference of 10 dB should be lowered by 3 dB, as half of the EDFA ASE noise is in an orthogonal polarization as compared to the signal.

Furthermore to allow a fair comparison, we also subtract 3 dB from the EDFA ASE level shown in Fig. 7(c) and 7(d) since the ASE is not polarized in the case of the EDFA whilst a single-pump FOPA generates ASE (fluorescence) predominantly in one polarization [19

R. Tang, P. L. Voss, J. Lasri, P. Devgan, and P. Kumar, “Noise-figure limit of fiber-optical parametric amplifiers and wavelength converters: experimental investigation,” Opt. Lett. 29(20), 2372–2374 (2004). [CrossRef] [PubMed]

]. This feature is included below in the comparison between the PI-FOPA and EDFA.

From Fig. 7(a) it follows that the comb itself has an OTNR of >29 dB. The PI-FOPA and EDFA, Fig. 7(d), give an OTNR of >21 dB and >14 dB, respectively, resulting in OTNR degradation of 7 dB for the EDFA as compared to the PI-FOPA.

Given that both of these amplifiers have the same theoretical noise performance limit, characterized by a minimum noise figure of 3 dB, it is important to clarify the physical origin of the apparent 7 dB noise improvement for the PI-FOPA relative to the EDFA. The EDFA requires an average gain which is significantly higher than that required for the FOPA in order to compensate for the loss provided by the gain flattening filter needed at its output to obtain a comb of the same flatness and power. Consequently, the noise properties are expected to be different as observed. It is worth mentioning that a FOPA may suffer from pump noise transfer that would not be directly observable in the measured OTNR. Thus, a pump with close-to-shot noise limit performance should be used.

5. Phase sensitive FOPA

To obtain a PS-FOPA, we slightly modified the set-up, as shown in Fig. 8 . The most notable difference is the feedback control unit that is needed to maintain the phase relation between the interacting pump, signals and idlers. The phase sensitive amplification of any signal-idler pair (which in our case consists of two comb tones with frequencies symmetrically placed around the pump) depends on their relative phase with respect to the pump phase. As the pump and comb are propagating through different optical paths (between the 95/5 coupler, where the seed is split and the ADM, where the pump and comb are combined again), any differential change in optical path length between these two arms produces a change in the relative phase between the pump and the signal-idler pair when they are combined at the ADM. Such differential phase changes can arise due to temperature variations and also acoustic pick-up in the fibers. To actively compensate for such phase changes, the power of the comb at the HNLF output is suitable tapped and measured and maximum phase sensitive gain is maintained by controlling a PZT-based fiber stretcher in the optical path of the pump. However, as mentioned earlier, the comb tones for one half of the comb spectrum have alternate phases (changing by π), and thus it is only every second comb tone that experiences maximum gain while the rest of comb tones experience maximum de-amplification. In the temporal domain, where the signal consists of pulses with alternate phases (pulse-to-pulse phase difference of π) this means that every other pulse is de-amplified, while the remainder experience maximum phase sensitive gain. Thus, measuring the total power of the amplified comb tones does not give the required feedback signal. To get around this issue, we put a 50-GHz delay-line interferometer-based filter in front of the feedback detector, suppressing every other line, leaving us only with lines of identical phase incident to the detector. In this way, all the comb lines coming to the detector simultaneously experience maximum phase sensitive gain. As opposed to the case of the phase-insensitive FOPA we did not use any filter after the OFCG in order to obtain the highest OTNR values achievable. We also did not use any SMF-28 fiber to help suppress competing nonlinear processes since pulse chirp must be kept at its minimum to obtain optimum phase sensitive gain across the entire comb spectrum [20

R. Tang, J. Lasri, P. S. Devgan, V. Grigoryan, P. Kumar, and M. Vasilyev, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13(26), 10483–10493 (2005). [CrossRef] [PubMed]

]. Indeed, for this reason, we needed to carefully compensate for any fiber dispersion between the Comb and the HNLF. This was performed by inserting a short piece of dispersion compensating fiber in front of the HNLF to compensate the dispersion of the fiber pigtails (of the HNLF, ADM, OFCG, etc.) made of SMF-28. The bias voltage applied to OFCG also changes the dispersion slightly – we optimized this parameter as well, to get as broadband operation as possible.

Fig. 8 Set-up for PS-FOPA (without the programmable filter shown as ‘A’). The programmable filter ‘A’ was inserted to allow ready comparison between the PI-FOPA and the PS-FOPA.

Figure 9 shows results for the optimum pump power of 24 dBm. For comparison, the output when the pump is off is also shown. Here we see that a gain of up to 20 dB (at the edges of the comb) was achieved, the comb flatness is better than 2.5 dB over 4 THz bandwidth and an OTNR>26 dB is obtained. As expected, every other line is suppressed since these lie at the minimum of the phase sensitive gain. The power difference between the neighboring tones (one experiencing gain maximum, whilst the other experiences minimum gain) is between 8 and 14 dB. In theory, the deamplification of every other line (gain minimum) should be equal to the gain of the lines that are at the gain maximum. However, as we see in Fig. 9, there is almost no observable de-amplification (negative gain). Several effects may be responsible for this behavior. Firstly, the two gated signals (pump and comb) may not overlap perfectly leading to a residual contribution from the unprocessed comb. We used another sample of an HNLF with the same length, but with a strain gradient that pushed the SBS threshold up to 25 dBm. This HNLF did not have the right dispersive properties to flatten the comb, but allowed us to see a broadband 6 dB phase sensitive gain with 6 dB deamplification of every other line supporting our hypothesis. Another possibility is the presence of competing nonlinear processes due to the high peak powers due to the short pulse nature of the comb. In the experiment with the gradient-strained HNLF, the gain was perhaps not high enough to observe such effects. Nevertheless, the effective doubling of the comb tones spacing observed here may be useful, as this would require two times lower frequency of the RF signal driving the optical comb. For applications where this feature is undesireable a comb without tone-to-tone alternating phases may be used, which would allow for simultaneous amplification of all comb tones.

Fig. 9 PS-FOPA for pump powers 24 dBm (black) and pump off (red) showing key parameters. Every odd line is suppressed by 8-14 dB.

6. Phase sensitive versus phase insensitive FOPA

As well as higher gain the PS-FOPA should also provide better OTNR performance. To evaluate this feature in our experiment, we used the set-up shown in Fig. 8 with a slight modification. We inserted a programmable filter (Waveshaper, Finisar Inc.) behind the OFCG. It has an insertion loss of about 5 dB and allowed us to block or pass one half of the comb spectrum in the 1547-1570 nm spectral band. In Fig. 10 we focus on the detailed tone spectrum around 4 nm and 11 nm from the centre of the comb (unfortunately, due to the limited bandwidth of the programmable filter, we were not able to evaluate the performance at the edge of the comb (16 nm from the center) as investigated previously). We can see from Fig. 10 that the PS-FOPA has about 5.5 dB higher gain and 4-5 dB better OTNR as compared to the PI-FOPA. This compares with the theoretical limit (derived for shot noise limited signals only) of 6 dB higher gain and 6 dB better OTNR.

Fig. 10 Detail of comparison of phase sensitive (red, solid) and phase insensitive (black, dashed) FOPA at two wavelength being 4 and 11 nm from the comb center. PS-FOPA has about 5.5 dB higher gain.

7. Conclusions

We have highlighted the suitability of FOPAs for improving several key parameters of optical combs. The wavelength dependent gain of the FOPA pumped in the anomalous dispersion regime was used to provide simultaneous low-noise comb amplification and flattening – the original 11-dB difference in the comb tone power was reduced to less that 3 dB. At the same time, the comb spectrum was broadened from 2 THz to 4 THz without any degradation in OTNR or comb flatness. Furthermore, we investigated the possibility of using a phase sensitive FOPA for improvement of the OTNR and gain. We succeeded to obtain phase sensitive interaction over a 4 THz bandwidth and showed that it leads to 5.5 dB higher gain and a 4-5 dB better OTNR as compared to the phase insensitive FOPA. Phase sensitive amplification of a cw signal-seeded comb is very straightforward, as all the comb lines are inherently locked to the seed. Moreover, due to the comb symmetry, it automatically gives the necessary signal-idler pairs of the same power. Thus, it can be realized in a simple and compact configuration.

Acknowledgment

We would like to thank to OFS Denmark for the HNLF. This research has received funding from the European Communities Seventh Framework Program FP/2007-2013 under grant agreement 255368 (TOP CLASS).

References and links

1.	T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002). [CrossRef] [PubMed]
2.	S. Fukushima, C. F. C. Silva, Y. Muramoto, and A. J. Seeds, “10 to 110 GHz tunable opto-electronic frequency synthesis using optical frequency comb generator and uni-travelling-carrier photodiode,” Electron. Lett. 37(12), 780–781 (2001). [CrossRef]
3.	S. Bennett, B. Cai, E. Burr, O. Gough, and A. J. Seeds, “1.8-THz bandwidth, zero-frequency error, tunable optical comb generator for DWDM applications,” IEEE Photon. Technol. Lett. 11(5), 551–553 (1999). [CrossRef]
4.	M. Kourogi, T. Enami, and M. Ohtsu, “Monolithic optical frequency comb generator,” IEEE Photon. Technol. Lett. 6(2), 214–217 (1994). [CrossRef]
5.	P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007). [CrossRef] [PubMed]
6.	T. Healy, F. C. Garcia Gunning, A. D. Ellis, and J. D. Bull, “Multi-wavelength source using low drive-voltage amplitude modulators for optical communications,” Opt. Express 15(6), 2981–2986 (2007). [CrossRef] [PubMed]
7.	P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett. 107(6), 063901 (2011). [CrossRef] [PubMed]
8.	Z. Jiang, D. E. Leaird, C. Huang, H. Miao, M. Kourogi, K. Imai, and A. M. Weiner, “Spectral Line-by-Line Pulse Shaping on an Optical Frequency Comb Generator,” IEEE J. Quantum Electron. 43(12), 1163–1174 (2007). [CrossRef]
9.	S. J. Lee, B. Widiyatmoko, M. Kourogi, and M. Ohtsu, “Ultrahigh Scanning Speed Optical Coherence Tomography Using Optical Frequency Comb Generators,” Jpn. J. Appl. Phys. 40(Part 2, No. 8B), L878–L880 (2001). [CrossRef]
10.	Z. Tong, C. Lundström, P. Andrekson, C. McKinstrie, M. Karlsson, D. Blessing, E. Tipsuwannakul, B. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards the Ultra-Sensitive Optical Link Enabled by Low Noise Phase-Sensitive Amplifiers,” Nat. Photonics 5(7), 430–436 (2011). [CrossRef]
11.	J. Kakande, P. Petropoulos, and D. J. Richardson, “Fiber optical parametric amplification of optical combs for enhanced performance and functionality,” 37th European Conference and Exhibition on Optical Communication (ECOC), Geneva, Switzerland, 18–22 Sept. 2011.
12.	C.-S. Brès, A. Wiberg, B. P. Kuo, N. Alic, and S. Radic, “Wavelength Multicasting of 320-Gb/s Channel in Self-Seeded Parametric Amplifier,” IEEE Photon. Technol. Lett. 21(14), 1002–1004 (2009). [CrossRef]
13.	R. H. Stolen and J. E. Bjorkholm, “Parametric ampliﬁcation and frequency conversion in optical ﬁbers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982). [CrossRef]
14.	M. Hirano and A. Morimoto, “Generation of flat optical frequency comb by fiber loop modulation,” Opt. Rev. 18(1), 13–18 (2011). [CrossRef]
15.	S. Xiao, L. Hollberg, N. R. Newbury, and S. A. Diddams, “Toward a low-jitter 10 GHz pulsed source with an optical frequency comb generator,” Opt. Express 16(12), 8498–8508 (2008). [CrossRef] [PubMed]
16.	E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. Wiberg, C.-S. Brès, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero-dispersion wavelength proﬁles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009). [CrossRef]
17.	L. Grűner-Nielsen, S. Dasgupta, M. D. Mermelstein, D. Jakobsen, S. Herstrm, M. E. V. Pedersen, E. L. Lim, S. Alam, F. Parmigiani, D. Richardson, and B. Pálsdótti, “A silica based highly nonlinear fibre with improved threshold for stimulated Brillouin scattering,” European Conference on Optical Communications (ECOC), paper Tu.4.D., Torino, Italy, 19–23 September, 2010.
18.	A. Camerlingo, F. Parmigiani, X. Feng, F. Poletti, P. Horak, W. Loh, D. J. Richardson, and P. Petropoulos, “Multichannel wavelength conversion of 40-Gb/s nonreturn-to-zero DPSK signals in a lead–silicate fiber,” IEEE Photon. Technol. Lett. 22(15), 1153–1155 (2010). [CrossRef]
19.	R. Tang, P. L. Voss, J. Lasri, P. Devgan, and P. Kumar, “Noise-figure limit of fiber-optical parametric amplifiers and wavelength converters: experimental investigation,” Opt. Lett. 29(20), 2372–2374 (2004). [CrossRef] [PubMed]
20.	R. Tang, J. Lasri, P. S. Devgan, V. Grigoryan, P. Kumar, and M. Vasilyev, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13(26), 10483–10493 (2005). [CrossRef] [PubMed]

OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 23, 2012
Revised Manuscript: March 31, 2012
Manuscript Accepted: April 1, 2012
Published: April 18, 2012

Citation
R. Slavík, J. Kakande, P. Petropoulos, and D. J. Richardson, "Processing of optical combs with fiber optic parametric amplifiers," Opt. Express 20, 10059-10070 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-9-10059

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References

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature416(6877), 233–237 (2002). [CrossRef] [PubMed]
S. Fukushima, C. F. C. Silva, Y. Muramoto, and A. J. Seeds, “10 to 110 GHz tunable opto-electronic frequency synthesis using optical frequency comb generator and uni-travelling-carrier photodiode,” Electron. Lett.37(12), 780–781 (2001). [CrossRef]
S. Bennett, B. Cai, E. Burr, O. Gough, and A. J. Seeds, “1.8-THz bandwidth, zero-frequency error, tunable optical comb generator for DWDM applications,” IEEE Photon. Technol. Lett.11(5), 551–553 (1999). [CrossRef]
M. Kourogi, T. Enami, and M. Ohtsu, “Monolithic optical frequency comb generator,” IEEE Photon. Technol. Lett.6(2), 214–217 (1994). [CrossRef]
P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450(7173), 1214–1217 (2007). [CrossRef] [PubMed]
T. Healy, F. C. Garcia Gunning, A. D. Ellis, and J. D. Bull, “Multi-wavelength source using low drive-voltage amplitude modulators for optical communications,” Opt. Express15(6), 2981–2986 (2007). [CrossRef] [PubMed]
P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett.107(6), 063901 (2011). [CrossRef] [PubMed]
Z. Jiang, D. E. Leaird, C. Huang, H. Miao, M. Kourogi, K. Imai, and A. M. Weiner, “Spectral Line-by-Line Pulse Shaping on an Optical Frequency Comb Generator,” IEEE J. Quantum Electron.43(12), 1163–1174 (2007). [CrossRef]
S. J. Lee, B. Widiyatmoko, M. Kourogi, and M. Ohtsu, “Ultrahigh Scanning Speed Optical Coherence Tomography Using Optical Frequency Comb Generators,” Jpn. J. Appl. Phys.40(Part 2, No. 8B), L878–L880 (2001). [CrossRef]
Z. Tong, C. Lundström, P. Andrekson, C. McKinstrie, M. Karlsson, D. Blessing, E. Tipsuwannakul, B. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards the Ultra-Sensitive Optical Link Enabled by Low Noise Phase-Sensitive Amplifiers,” Nat. Photonics5(7), 430–436 (2011). [CrossRef]
J. Kakande, P. Petropoulos, and D. J. Richardson, “Fiber optical parametric amplification of optical combs for enhanced performance and functionality,” 37th European Conference and Exhibition on Optical Communication (ECOC), Geneva, Switzerland, 18–22 Sept. 2011.
C.-S. Brès, A. Wiberg, B. P. Kuo, N. Alic, and S. Radic, “Wavelength Multicasting of 320-Gb/s Channel in Self-Seeded Parametric Amplifier,” IEEE Photon. Technol. Lett.21(14), 1002–1004 (2009). [CrossRef]
R. H. Stolen and J. E. Bjorkholm, “Parametric ampliﬁcation and frequency conversion in optical ﬁbers,” IEEE J. Quantum Electron.18(7), 1062–1072 (1982). [CrossRef]
M. Hirano and A. Morimoto, “Generation of flat optical frequency comb by fiber loop modulation,” Opt. Rev.18(1), 13–18 (2011). [CrossRef]
S. Xiao, L. Hollberg, N. R. Newbury, and S. A. Diddams, “Toward a low-jitter 10 GHz pulsed source with an optical frequency comb generator,” Opt. Express16(12), 8498–8508 (2008). [CrossRef] [PubMed]
E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. Wiberg, C.-S. Brès, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero-dispersion wavelength proﬁles in nonlinear fibers,” IEEE Photon. Technol. Lett.21(24), 1807–1809 (2009). [CrossRef]
L. Grűner-Nielsen, S. Dasgupta, M. D. Mermelstein, D. Jakobsen, S. Herstrm, M. E. V. Pedersen, E. L. Lim, S. Alam, F. Parmigiani, D. Richardson, and B. Pálsdótti, “A silica based highly nonlinear fibre with improved threshold for stimulated Brillouin scattering,” European Conference on Optical Communications (ECOC), paper Tu.4.D., Torino, Italy, 19–23 September, 2010.
A. Camerlingo, F. Parmigiani, X. Feng, F. Poletti, P. Horak, W. Loh, D. J. Richardson, and P. Petropoulos, “Multichannel wavelength conversion of 40-Gb/s nonreturn-to-zero DPSK signals in a lead–silicate fiber,” IEEE Photon. Technol. Lett.22(15), 1153–1155 (2010). [CrossRef]
R. Tang, P. L. Voss, J. Lasri, P. Devgan, and P. Kumar, “Noise-figure limit of fiber-optical parametric amplifiers and wavelength converters: experimental investigation,” Opt. Lett.29(20), 2372–2374 (2004). [CrossRef] [PubMed]
R. Tang, J. Lasri, P. S. Devgan, V. Grigoryan, P. Kumar, and M. Vasilyev, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express13(26), 10483–10493 (2005). [CrossRef] [PubMed]

Electron. Lett.

S. Fukushima, C. F. C. Silva, Y. Muramoto, and A. J. Seeds, “10 to 110 GHz tunable opto-electronic frequency synthesis using optical frequency comb generator and uni-travelling-carrier photodiode,” Electron. Lett.37(12), 780–781 (2001). [CrossRef]

IEEE J. Quantum Electron.

Z. Jiang, D. E. Leaird, C. Huang, H. Miao, M. Kourogi, K. Imai, and A. M. Weiner, “Spectral Line-by-Line Pulse Shaping on an Optical Frequency Comb Generator,” IEEE J. Quantum Electron.43(12), 1163–1174 (2007). [CrossRef]
R. H. Stolen and J. E. Bjorkholm, “Parametric ampliﬁcation and frequency conversion in optical ﬁbers,” IEEE J. Quantum Electron.18(7), 1062–1072 (1982). [CrossRef]

IEEE Photon. Technol. Lett.

C.-S. Brès, A. Wiberg, B. P. Kuo, N. Alic, and S. Radic, “Wavelength Multicasting of 320-Gb/s Channel in Self-Seeded Parametric Amplifier,” IEEE Photon. Technol. Lett.21(14), 1002–1004 (2009). [CrossRef]
E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. Wiberg, C.-S. Brès, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero-dispersion wavelength proﬁles in nonlinear fibers,” IEEE Photon. Technol. Lett.21(24), 1807–1809 (2009). [CrossRef]
A. Camerlingo, F. Parmigiani, X. Feng, F. Poletti, P. Horak, W. Loh, D. J. Richardson, and P. Petropoulos, “Multichannel wavelength conversion of 40-Gb/s nonreturn-to-zero DPSK signals in a lead–silicate fiber,” IEEE Photon. Technol. Lett.22(15), 1153–1155 (2010). [CrossRef]
S. Bennett, B. Cai, E. Burr, O. Gough, and A. J. Seeds, “1.8-THz bandwidth, zero-frequency error, tunable optical comb generator for DWDM applications,” IEEE Photon. Technol. Lett.11(5), 551–553 (1999). [CrossRef]
M. Kourogi, T. Enami, and M. Ohtsu, “Monolithic optical frequency comb generator,” IEEE Photon. Technol. Lett.6(2), 214–217 (1994). [CrossRef]

Jpn. J. Appl. Phys.

S. J. Lee, B. Widiyatmoko, M. Kourogi, and M. Ohtsu, “Ultrahigh Scanning Speed Optical Coherence Tomography Using Optical Frequency Comb Generators,” Jpn. J. Appl. Phys.40(Part 2, No. 8B), L878–L880 (2001). [CrossRef]

Nat. Photonics

Z. Tong, C. Lundström, P. Andrekson, C. McKinstrie, M. Karlsson, D. Blessing, E. Tipsuwannakul, B. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards the Ultra-Sensitive Optical Link Enabled by Low Noise Phase-Sensitive Amplifiers,” Nat. Photonics5(7), 430–436 (2011). [CrossRef]

Nature

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450(7173), 1214–1217 (2007). [CrossRef] [PubMed]
T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature416(6877), 233–237 (2002). [CrossRef] [PubMed]

Opt. Express

Opt. Lett.

R. Tang, P. L. Voss, J. Lasri, P. Devgan, and P. Kumar, “Noise-figure limit of fiber-optical parametric amplifiers and wavelength converters: experimental investigation,” Opt. Lett.29(20), 2372–2374 (2004). [CrossRef] [PubMed]

Opt. Rev.

M. Hirano and A. Morimoto, “Generation of flat optical frequency comb by fiber loop modulation,” Opt. Rev.18(1), 13–18 (2011). [CrossRef]

Phys. Rev. Lett.

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett.107(6), 063901 (2011). [CrossRef] [PubMed]

Other

J. Kakande, P. Petropoulos, and D. J. Richardson, “Fiber optical parametric amplification of optical combs for enhanced performance and functionality,” 37th European Conference and Exhibition on Optical Communication (ECOC), Geneva, Switzerland, 18–22 Sept. 2011.
L. Grűner-Nielsen, S. Dasgupta, M. D. Mermelstein, D. Jakobsen, S. Herstrm, M. E. V. Pedersen, E. L. Lim, S. Alam, F. Parmigiani, D. Richardson, and B. Pálsdótti, “A silica based highly nonlinear fibre with improved threshold for stimulated Brillouin scattering,” European Conference on Optical Communications (ECOC), paper Tu.4.D., Torino, Italy, 19–23 September, 2010.

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