Abstract

The noise figure (NF) of a phase sensitive amplifier (PSA) based on a periodically poled LiNbO3 (PPLN) waveguide was evaluated in the optical and electrical domains. Phase sensitive amplification was realized using degenerate parametric amplification in the PPLN waveguide, which was pumped by the second harmonic frequency of the signal. Second harmonic pumping enables direct observation of the intrinsic amplified spontaneous emission (ASE), which determined the NF of the PSA. An NF below the 3 dB quantum limit was obtained by observing the intrinsic ASE. The low NF was also confirmed via the noise floor measurement of a cascaded PSA and erbium doped fiber amplifier in the electrical domain. The PSA was used as a preamplifier for detecting a 40 Gbit/s phase shift keying signal. The low noise characteristics were confirmed by the improved sensitivity.

© 2012 OSA

1. Introduction

Optical amplifiers are playing an important role in modern optical communication systems. Laser amplifiers such as erbium doped fiber amplifiers (EDFA) and semiconductor optical amplifiers (SOA), or Raman optical amplifiers are now being used. The noise figure (NF) of these phase insensitive amplifiers (PIA) utilizing stimulated emission (or scattering) cannot be improved to below the 3 dB quantum limit [1]. On the other hand, phase sensitive amplifiers (PSA) are attracting a lot of interest because their ideal NF is 0 dB [2]. The signal to noise ratio (SNR) is an essential quantity that determines the maximum spectral efficiency according to Shannon’s theory [3]. Therefore, realizing an optical amplifier with a low NF is vital if we are to achieve future high-capacity communication.

To date most PSAs that have been demonstrated employ four-wave mixing (FWM) in optical fiber. A long interaction length is required because of the small nonlinearity of the fiber. Although, in principle, the spacing between the pump, signal, and idler can exceed 100 nm, rather closely spaced interactive waves in the 1.55 μm band have been used for the experimental demonstration of fiber-based PSAs and so separating the pump and signal is problematic. A single pumped fiber-based degenerate PSA requires an interferometric configuration to separate the pump and signal because the pump and signal wavelengths are the same [2]. This configuration induces noise due to guided acoustic wave Brillouin scattering (GAWBS). Although the GAWBS noise can be avoided by using a dual pumped fiber-based degenerate PSA [4], it appears to be difficult to exclude the extrinsic amplified spontaneous emission (ASE) noise caused by the EDFA because all interaction waves are amplified by using an EDFA. Recently, an improved SNR was demonstrated in an optical link using a fiber-based non-degenerate PSA [5]. In such a single-pumped non-degenerate configuration, extrinsic ASE can be suppressed by using a high contrast band pass filter. However, in such fiber-based non-degenerate PSAs wide guard band between the pump, signal and idler might be required or the signal power should be smaller than the pump power to avoid unwanted crosstalk due to additional FWM, because of the wide phase matching bandwidth for the pump due to the longitudinal distribution of the zero dispersion wavelength. Although the stimulated Brillouin scattering (SBS) threshold can be improved by applying distributed tension to the fiber [6] or by using Al/Ge doping [7], additional phase modulation on a high power pump has been used to suppress SBS in an experimental demonstration of fiber based PSA [5,8].

On the other hand, a χ(2) based PSA can be implemented by using a short nonlinear optical crystal because of its higher nonlinearity, and therefore we can expect the integration of several functions on a chip without the need for SBS suppression. In addition, a χ(2) based PSA utilizes second harmonic (SH) light as a pump [9], and thus high contrast separation can be realized between the pump and signal even for a degenerate PSA by using a conventional dichromatic mirror. However, there have been few demonstrations of χ(2) based PSAs for optical communication where CW operation is mandatory. Recent advances on periodically poled LiNbO3 (PPLN) waveguides technology enable us to explore χ(2) based PSAs for optical communication. A non-degenerate PSA was demonstrated that employed cascaded second-harmonic generation (SHG) and optical parametric amplification (OPA) in a single PPLN waveguide [10], and cascaded SHG and difference frequency generation (DFG) and cascaded SHG and OPA in two PPLN waveguides [11]. This cascaded SHG/OPA approach can simplify the device structure, because SH waves were generated and used only in a PPLN waveguide. However, the drawbacks of the approach are a small gain, the need for a guard band to achieve separation between the pump, signal and idler, and its inability to perform a degenerate operation.

Recently, we have reported a CW pumped degenerate PSA that employs two individual highly efficient periodically poled LiNbO3 (PPLN) waveguides for SHG and OPA [12]. In this configuration the extrinsic ASE caused by the EDFA can be effectively eliminated. This enables us to observe the intrinsic ASE or parametric fluorescence that determines the NF of the PSA. In addition a narrow phase matching bandwidth for the pump in PPLN enables us to handle high power signals without secondary wavelength conversion.

In this work, we evaluated the NF of a PSA based on a PPLN waveguide in the optical and electrical domains. We observed an extremely low intrinsic ASE for the PSA compared with that of an EDFA. An NF below the 3 dB quantum limit was obtained by observing the intrinsic ASE. We also confirmed the low NF by performing a noise floor measurement in the electrical domain. Finally, we demonstrated that the receiver sensitivity can be improved by using a low noise PSA as a preamplifier.

2. Theoretical comparison of PSA and EDFA

Before describing the experimental results, we compare the PSA and conventional EDFA in terms of ASE power. A PSA amplifies only the in-phase component and deamplifies the quadrature phase component, while a PIA such as an EDFA amplifies two orthogonal quadrature phase components equally. The phase sensitive operation of the PSA results in less ASE induced excess noise than with a PIA [2]. If we assume an ideal PSA and laser amplifier, the average number of output photons can be expressed using the following equations [2,13]:

PSA:nout=Gnin+14{(G1)+(1G1)},
PIA:nout=Gnin+(G1)nspm,
where, G is gain, <nin> is the input photon number, nsp is the spontaneous emission coefficient (ideally 1) and m is the mode number, which is 2 for the EDFA. The first term denotes an amplified signal and the second term denotes ASE or parametric fluorescence. It is known that the ASE photon number of the PSA is a quarter that of the PIA in one polarization [2]. The ASE in the PIA contains an equal quantity of in-phase and quadrature phase components, whereas the quadrature phase component is deamplified to a trivial power in a PSA with a large gain. Thus if we compare the number of in-phase ASE photons in one polarization, the PSA generates half the number generated by the PIA. The smaller in-phase ASE photon number is the origin of the 3 dB difference between the NFs of the PSA and PIA. A PPLN-based PSA amplifies only one polarization mode, whereas an EDFA amplifies two polarization modes. This comparison indicates that the total ASE power of an ideal PSA is 9 dB smaller than that of an ideal EDFA.

3. Experiment

We conducted an experiment to investigate the noise characteristics of a PSA based on a PPLN waveguide. The experimental setup is shown in Fig. 1 . We used two PPLN waveguides fabricated using a direct bonding and dry etching technique to obtain a high power tolerance and a large parametric gain [14]. The PPLN waveguides were assembled in a four-port fiber pigtail module, which enabled us to input 1.54 μm band fundamental light and 0.77 μm band second harmonic light into the waveguide through polarization maintaining fibers (PMF) and a dichromatic mirror [15]. The pump and signal lights were generated from an external cavity laser diode (ECL) and split by a polarization maintaining fiber coupler. The wavelength was set at 1537.6 nm. The pump light was amplified with a polarization maintaining EDFA, converted to an SH pump light by a PPLN module and then injected into the other PPLN module for optical parametric amplification (OPA). The signal was modulated using a chirpless Mach-Zehnder modulator with a 15 GHz sinusoidal wave or a 40 Gbit/s non-return to zero differential phase shift keying (NRZ-DPSK) 211-1 pseudo random bit stream (PRBS) and an attenuated signal was injected into the PPLN module for OPA. The relative phase between the pump and signal was maintained by using a phase locked loop (PLL) based on a phase modulator and a piezoelectric fiber stretcher. A small dither was applied to the phase modulator. The PSA output was tapped with a 10 dB fiber coupler, detected with a PD and fed into a PLL circuit. The error signal from the PLL was fed back to both the phase modulator bias voltage and PZT driving voltage with different time constants. The PSA output was analyzed with an optical spectrum analyzer (OSA). Next, the PSA output was amplified with an EDFA and passed through a 1 nm band pass filter (BPF) to minimize the ASE-ASE beat noise. The BPF output was analyzed by using an electrical spectrum analyzer (ESA) with an OE converter. The DPSK signal was demodulated with a delay interferometer (D.I.) and detected with a balanced PD. The bit error rate was measured with a pulse pattern generator (PPG) and an error detector (ED). The phase matching bandwidth of the PPLN waveguide was approximately 0.2 nm for SHG, and 60 nm for OPA at the fundamental wavelength. So the OPA bandwidth is wide enough to amplify a 40 Gbit/s NRZ-DPSK signal.

 

Fig. 1 Experimental setup.

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4. Results

Although we employed an EDFA for pump generation in our experimental setup, we could suppress the extrinsic ASE caused by the EDFA. This was because we converted the pump to an SH pump, we filtered out 1.54 μm band light including ASE with dichromatic mirrors and PMF for the 0.77 μm band, and we injected SH pump light into the PPLN waveguide for the OPA. This enabled us to observe the intrinsic ASE generated by the PPLN waveguide using an OSA. Figure 2 shows the output spectra of the PPLN based PSA and a conventional EDFA.

 

Fig. 2 Optical spectra of the EDFA and the PSA.

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For this comparison, the OPA module and tap coupler for PLL were simply replaced with an EDFA whose gain was controlled by changing the driving current of the pump laser diode (LD). We compare output spectra with the same external gain of 6.6 dB in Fig. 2. The gain of the PSA includes the insertion loss of the PPLN module (−5.0 dB), the internal parametric gain of the PPLN waveguide (+12.6 dB) and the insertion loss of the tap coupler (−1.0 dB) for the PLL. As shown in Fig. 2, the ASE power generated by the PSA was much lower than that of the EDFA. In this case the ASE power difference between the PSA and EDFA was 10 dB. We determined the gain of the amplifiers by comparing input and output optical spectra. Using the measured gain, the measured ASE power and the theoretically calculated ASE power, we can obtain the NFs of the EDFA and the PSA.

Figure 3 shows the measured ASE power as a function of the input power. Here, we kept the external gain ate 6.69 ± 0.1 dB for the PSA and 6.63 ± 0.2 dB for the EDFA. As shown in Fig. 3 the ASE power remains almost constant with the same external gain. The measured ASE power can be expressed as follows [2]:

PSA:PASE=14ηout(G1)(1+D(αL))eαLhνΔν,
EDFA:PASE=2ηout(G1)nsphνΔν,
where
D(αL)=1(αL)2(eαL1αL12(αL)2),
Here, ηout is the coupling loss between the gain media and the output fiber, which includes the insertion loss of tap coupler for the PLL, h is Planck's constant, ν is the optical frequency and Δν is the resolution of the OSA, α is the propagation loss of the PPLN waveguide, and L is the waveguide length. The factor DL) indicates the ASE from the “vacuum” field of distributed loss [2]. We neglected the propagation loss in the EDFA NF estimation. Note that the PSA amplifies only one polarization whereas the EDFA amplifies two polarizations. Here we assumed that the quadrature component of the ASE is negligible in the PSA because we obtained an internal gain of +12.6 and a de-amplification of −11.5 dB in this work [12]. The external gain Gext can be expressed as follows:
Gext=ηinGeαLηout,
Here, ηin is the coupling loss between the gain media and the input fiber. We estimated the noise figure based on the assumption that the SNR of the amplified output is dominated by the shot noise of the amplified signal and the beat noise between the amplified signal and the ASE as follow:

 

Fig. 3 ASE power of the EDFA and the PSA.

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PSA:NF=1ηinGeαLηout+1+D(αL)ηinG1G=1Gext+PASE14GexthνΔν,
EDFA:NF=1ηinGηout+2nspηinG1G=1Gext+PASEGexthνΔν,

We neglected the contribution of the ASE shot noise, the ASE-ASE beat noise and the excess noise of the input light. The second terms denote the beat noise between the amplified signal and the ASE. The second terms can be calculated by using the measured ASE power and the external gain. Note that the second term converged to (1 + DL))/ηin for PSA and 2nspin for the EDFA with a large gain. In Fig. 3 as a reference value we also plot the denominators of the second terms, which can be calculated by using the external gain. From the deviation between the measured ASE power and the reference values we can obtain the contribution of the signal-ASE beat noise to the NF. We obtained NF values of 5.3 and 1.2 dB for the EDFA and PSA, respectively. By adding the shot noise term we obtained NF values of 5.6 and 1.8 dB for the EDFA and PSA, respectively. This means that an NF below the 3 dB quantum limit was obtained in a CW pumped PSA using a PPLN waveguide. The coupling loss ηin was estimated to be 1.75 dB, assuming a 1.5 dB transmission loss for the PPLN waveguide. Assuming these losses, we expected the contribution of the signal-ASE beat noise to the NF to be 2.0 dB and the total NF to be 2.5 dB by adding the shot noise term. We believe that the deviation from the experimental result might result from an overestimation of the coupling loss due to the imbalance of ηin and ηout. The experimental result suggests an ηin of around 1.0 dB and a PPLN waveguide loss of around 1.5 dB. Note that the NF degradation induced by waveguide loss is not proportional to the waveguide loss but the factor (1 + D(αL)). We estimated that the NF degradation caused by waveguide loss was as small as 0.5 dB assuming a 1.5 dB waveguide loss. Even with a 1.5 dB waveguide loss and a 1.0 dB input coupling loss ηin, we can expect the contribution of the signal-ASE beat noise to the NF to be 1.2 dB with an internal gain of 12.6 dB.

Unlike rare earth doped laser materials, parametric gain media respond almost instantaneously to the pump intensity. The intensity noise of the pump light is transferred to the intensity noise of the amplified signal. Therefore, it is also important to test the NF in the electrical domain to capture all the noise components. Incidentally, it should be noted that low noise amplification can be realized even when using a noisy pump if the SNR of the pump is much better than that of the input signal [2]. To investigate the intrinsic NF of the PSA, it is desirable to use a relatively small input power. The applicable dynamic range of the ESA method is not as wide as that of the OSA method. To mitigate this limitation, we cascaded the PSA and EDFA and we observed the noise power of the cascaded amplifiers.

In this measurement we could not measure the noise power density of the input directly because the noise level of the input is much lower than the thermal noise floor of the measurement system (−168.7 dBm/Hz) in the 1 to 14 GHz range [16]. So we could not compare the noise power density of the input and amplified output directly as described in reference [5,8]. Therefore, in this experiment we measured the noise power density of the cascaded amplifiers and obtained the NF using an EDFA as a reference.

Figure 4 shows the noise power density in the 1 to 14 GHz range of the cascaded amplifiers and single EDFA. We compared the output noise power densities with the same external gain of 18 dB, which includes insertion loss a 1 nm BPF. The gain was measured using the intensity of a 15 GHz peak caused by sinusoidal modulation. For this comparison, the OPA module and tap coupler for PLL and EDFA are replaced with the same EDFA as used for the OSA measurement. The EDFA gain was controlled to give the same external gain by changing the driving current of the pump LD. Here the input power was –20 dBm. As shown in Fig. 3 the cascaded amplifier exhibits a lower noise level in an all-frequency band within a 1-14 GHz range. The small spike observed at around 3 and 4 GHz might be due to PLL instability.

 

Fig. 4 Electrical noise spectra of the EDFA and the cascaded PSA and EDFA.

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Figure 5 shows the average noise power density as a function of the input power. As shown in Fig. 5, the noise power density is proportional to the input power, showing that the noise power is dominated by the beat noise between the ASE and the amplified signal. As a reference, we estimated the NF of the EDFA with an 18 dB external gain to be 4.4 dB using the OSA method. In this estimation, we include the shot noise term in Eq. (8), and the gross gain was 19.2 dB. The net gain of the EDFA was attenuated to 18 dB with a 1 nm BPF in the ESA measurement.

 

Fig. 5 Average noise power density of the EDFA and the cascaded PSA and EDFA.

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Using the NF of the EDFA as a reference, we also plot the noise power density corresponding to NF = 0 dB in Fig. 5. The cascaded PSA and EDFA exhibited a 1.5 dB smaller noise power than a single EDFA. From these comparisons we determined that the NF of the cascaded amplifier was 2.9 dB. If we assume that the output noise is dominated by the beat noise between the ASE and the amplified signal and the shot noise of the amplified signal, the NF of a cascaded PSA and PIA can be expressed by the following equation, which is analogous to the NF of cascaded electrical amplifiers:

FPSA+PIA=FPSA+FPIA1G1,
Here, G1 is the gain of the PSA. FPSA and FPIA are the NFs of the PSA and PIA. This equation implies that even when using the PSA cascaded with the EDFA, we can take advantage of the low noise characteristics of the PSA. We used Eq. (9) to evaluate the NF of the PSA from the measured NF of the cascaded amplifier. In the cascaded configuration, the EDFA gain was set at 11.4 dB, which includes the loss of the 1 nm BPF. We estimated the NF of the EDFA with 11.4 dB external gain to be 4.7 dB using the OSA method. In this estimation, we include the shot noise term in Eq. (8), and the gross gain was 12.6 dB, which does not include the loss of the 1 nm BPF. Using Eq. (9) and the measured NF of the cascaded amplifier, the NF of the PSA was found to be 1.8 dB. This value is in good agreement with the value of 1.8 dB measured with the OSA method.

We confirmed that an SH pumped PSA using a PPLN waveguide can realize low noise amplification in an all-frequency band within a 1-14 GHz range. To confirm that the low noise characteristics can be utilized with real data in a broader bandwidth, we used the PSA as a preamplifier for the detection of a 40 Gbit/s DPSK signal. Figure 6 shows the bit error rate performance using the cascaded PSA and EDFA, and a single EDFA as a preamplifier. The receiver sensitivities for a bit error rate of 1x10−9 were −34.3 and −32.9 dBm, respectively. By using the PSA as a preamplifier, the receiver sensitivity was improved by a factor of 1.5 dB, which is in good agreement with the NF improvement measured with the ESA method.

 

Fig. 6 Bit error rate performance.

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5. Conclusion

In conclusion, we obtained an NF below the 3 dB quantum limit in a CW pumped PPLN based PSA. Second harmonic pumping enables us to observe extremely low intrinsic ASE in the PSA. From optical and electrical measurements, we determined NF values of 1.8 and 1.8 dB, respectively. We demonstrated improved receiver sensitivity using a PSA as a preamplifier. Throughout this work, the SH pump was generated by the laser used for the signal, and could not propagate through conventional fiber in the 1.55 μm band. Thus a pump preparation technique is required for “in-line” operation [17]. An optical phase locked loop using a pilot tone [18], and injection locking [4,17] might be useful for pump generation, and SHG must be combined with such a technique for the in-line operation of an SH pumped PSA. We are currently studying the in-line operation of a PPLN based PSA and the results will be published elsewhere. The high capacity communications of the future will most probably operate with spectral efficiencies of better than 1 bit/s/Hz, thereby requiring the use of multilevel phase coding and polarization multiplexing. The degenerate PSA reported in this work can amplify only one polarization and one of two quadrature phase components of the signal. So that possibility of the integration of several PPLN waveguides on a chip will play an important role in dealing with such multilevel phase coding and polarization multiplexing. The low noise characteristics reported in this work suggest that the PPLN based PSA will play an important role in achieving a higher SNR in future high capacity optical communications.

References and links

1. C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields 26(8), 1817–1839 (1982). [CrossRef]  

2. W. Imajuku and A. Takada, “Noise figure of phase-sensitive parametric amplifier using a Mach-Zehnder interferometer with lossy Kerr media and noisy pump,” IEEE J. Quantum Electron. 39(6), 799–812 (2003). [CrossRef]  

3. C. E. Shannon, “Communication in the presence of noise,” Proc. Inst. Radio Eng. 37(1), 10–21 (1949). [CrossRef]  

4. R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010). [CrossRef]  

5. Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011). [CrossRef]  

6. E. Myslivets and S. Radic, “Advanced fiber optic parametric synthsis and characterization” in Optical Fiber Communications/ National Fiber Optic Engineers Conference 2011 Paper OWL5 (2011).

7. M.-J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. A. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, and L. A. Zenteno, “Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express 15(13), 8290–8299 (2007). [CrossRef]   [PubMed]  

8. Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of the noise figure of a cascaded non-degenerate phase-sensitive parametric amplifier,” Opt. Express 18(14), 14820–14835 (2010). [CrossRef]   [PubMed]  

9. J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10(11), 2233–2238 (1993). [CrossRef]  

10. K. J. Lee, F. Parmigiani, S. Liu, J. Kakande, P. Petropoulos, K. Gallo, and D. Richardson, “Phase sensitive amplification based on quadratic cascading in a periodically poled lithium niobate waveguide,” Opt. Express 17(22), 20393–20400 (2009). [CrossRef]   [PubMed]  

11. B. J. Puttnam, D. Mazroa, S. Shinada, and N. Wada, “Phase-squeezing properties of non-degenerate PSAs using PPLN waveguides,” Opt. Express 19(26), B131–B139 (2011). [CrossRef]   [PubMed]  

12. T. Umeki, O. Tadanaga, A. Takada, and M. Asobe, “Phase sensitive degenerate parametric amplification using directly-bonded PPLN ridge waveguides,” Opt. Express 19(7), 6326–6332 (2011). [CrossRef]   [PubMed]  

13. K. Shimoda, H. Takahashi, and C. H. Townes, “Fluctuations in amplification of quanta with application to maser amplifiers,” J. Phys. Soc. Jpn. 12, 686–700 (1957). [CrossRef]  

14. T. Umeki, O. Tadanaga, and M. Asobe, “Highly efficient wavelength converter using direct-bonded PPZnLN ridge waveguide,” IEEE J. Quantum Electron. 46(8), 1206–1213 (2010). [CrossRef]  

15. M. Asobe, T. Umeki, O. Tadanaga, K. Yoshino, E. Yamazaki, and A. Takada, “Low crosstalk and variable wavelength conversion using multiple QPM LiNbO3 waveguide module,” Electron. Lett. 45(10), 519–520 (2009). [CrossRef]  

16. W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3-dB noise figure in a high-gain phase-sensitive fiber amplifier,” Electron. Lett. 35(22), 1954–1955 (1999). [CrossRef]  

17. W. Imajuku and A. Takada, “In-line phase-sensitive amplifier with optical-PLL controlled internal pump light source,” Electron. Lett. 33(25), 2155–2156 (1997). [CrossRef]  

18. M. Yoshida, H. Goto, K. Kasai, and M. Nakazawa, “64 and 128 coherent QAM optical transmission over 150 km using frequency-stabilized laser and heterodyne PLL detection,” Opt. Express 16(2), 829–840 (2008). [CrossRef]   [PubMed]  

References

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  1. C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields 26(8), 1817–1839 (1982).
    [CrossRef]
  2. W. Imajuku and A. Takada, “Noise figure of phase-sensitive parametric amplifier using a Mach-Zehnder interferometer with lossy Kerr media and noisy pump,” IEEE J. Quantum Electron. 39(6), 799–812 (2003).
    [CrossRef]
  3. C. E. Shannon, “Communication in the presence of noise,” Proc. Inst. Radio Eng. 37(1), 10–21 (1949).
    [CrossRef]
  4. R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
    [CrossRef]
  5. Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
    [CrossRef]
  6. E. Myslivets and S. Radic, “Advanced fiber optic parametric synthsis and characterization” in Optical Fiber Communications/ National Fiber Optic Engineers Conference 2011 Paper OWL5 (2011).
  7. M.-J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. A. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, and L. A. Zenteno, “Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express 15(13), 8290–8299 (2007).
    [CrossRef] [PubMed]
  8. Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of the noise figure of a cascaded non-degenerate phase-sensitive parametric amplifier,” Opt. Express 18(14), 14820–14835 (2010).
    [CrossRef] [PubMed]
  9. J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10(11), 2233–2238 (1993).
    [CrossRef]
  10. K. J. Lee, F. Parmigiani, S. Liu, J. Kakande, P. Petropoulos, K. Gallo, and D. Richardson, “Phase sensitive amplification based on quadratic cascading in a periodically poled lithium niobate waveguide,” Opt. Express 17(22), 20393–20400 (2009).
    [CrossRef] [PubMed]
  11. B. J. Puttnam, D. Mazroa, S. Shinada, and N. Wada, “Phase-squeezing properties of non-degenerate PSAs using PPLN waveguides,” Opt. Express 19(26), B131–B139 (2011).
    [CrossRef] [PubMed]
  12. T. Umeki, O. Tadanaga, A. Takada, and M. Asobe, “Phase sensitive degenerate parametric amplification using directly-bonded PPLN ridge waveguides,” Opt. Express 19(7), 6326–6332 (2011).
    [CrossRef] [PubMed]
  13. K. Shimoda, H. Takahashi, and C. H. Townes, “Fluctuations in amplification of quanta with application to maser amplifiers,” J. Phys. Soc. Jpn. 12, 686–700 (1957).
    [CrossRef]
  14. T. Umeki, O. Tadanaga, and M. Asobe, “Highly efficient wavelength converter using direct-bonded PPZnLN ridge waveguide,” IEEE J. Quantum Electron. 46(8), 1206–1213 (2010).
    [CrossRef]
  15. M. Asobe, T. Umeki, O. Tadanaga, K. Yoshino, E. Yamazaki, and A. Takada, “Low crosstalk and variable wavelength conversion using multiple QPM LiNbO3 waveguide module,” Electron. Lett. 45(10), 519–520 (2009).
    [CrossRef]
  16. W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3-dB noise figure in a high-gain phase-sensitive fiber amplifier,” Electron. Lett. 35(22), 1954–1955 (1999).
    [CrossRef]
  17. W. Imajuku and A. Takada, “In-line phase-sensitive amplifier with optical-PLL controlled internal pump light source,” Electron. Lett. 33(25), 2155–2156 (1997).
    [CrossRef]
  18. M. Yoshida, H. Goto, K. Kasai, and M. Nakazawa, “64 and 128 coherent QAM optical transmission over 150 km using frequency-stabilized laser and heterodyne PLL detection,” Opt. Express 16(2), 829–840 (2008).
    [CrossRef] [PubMed]

2011 (3)

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

T. Umeki, O. Tadanaga, A. Takada, and M. Asobe, “Phase sensitive degenerate parametric amplification using directly-bonded PPLN ridge waveguides,” Opt. Express 19(7), 6326–6332 (2011).
[CrossRef] [PubMed]

B. J. Puttnam, D. Mazroa, S. Shinada, and N. Wada, “Phase-squeezing properties of non-degenerate PSAs using PPLN waveguides,” Opt. Express 19(26), B131–B139 (2011).
[CrossRef] [PubMed]

2010 (3)

Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of the noise figure of a cascaded non-degenerate phase-sensitive parametric amplifier,” Opt. Express 18(14), 14820–14835 (2010).
[CrossRef] [PubMed]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

T. Umeki, O. Tadanaga, and M. Asobe, “Highly efficient wavelength converter using direct-bonded PPZnLN ridge waveguide,” IEEE J. Quantum Electron. 46(8), 1206–1213 (2010).
[CrossRef]

2009 (2)

M. Asobe, T. Umeki, O. Tadanaga, K. Yoshino, E. Yamazaki, and A. Takada, “Low crosstalk and variable wavelength conversion using multiple QPM LiNbO3 waveguide module,” Electron. Lett. 45(10), 519–520 (2009).
[CrossRef]

K. J. Lee, F. Parmigiani, S. Liu, J. Kakande, P. Petropoulos, K. Gallo, and D. Richardson, “Phase sensitive amplification based on quadratic cascading in a periodically poled lithium niobate waveguide,” Opt. Express 17(22), 20393–20400 (2009).
[CrossRef] [PubMed]

2008 (1)

2007 (1)

2003 (1)

W. Imajuku and A. Takada, “Noise figure of phase-sensitive parametric amplifier using a Mach-Zehnder interferometer with lossy Kerr media and noisy pump,” IEEE J. Quantum Electron. 39(6), 799–812 (2003).
[CrossRef]

1999 (1)

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3-dB noise figure in a high-gain phase-sensitive fiber amplifier,” Electron. Lett. 35(22), 1954–1955 (1999).
[CrossRef]

1997 (1)

W. Imajuku and A. Takada, “In-line phase-sensitive amplifier with optical-PLL controlled internal pump light source,” Electron. Lett. 33(25), 2155–2156 (1997).
[CrossRef]

1993 (1)

1982 (1)

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields 26(8), 1817–1839 (1982).
[CrossRef]

1957 (1)

K. Shimoda, H. Takahashi, and C. H. Townes, “Fluctuations in amplification of quanta with application to maser amplifiers,” J. Phys. Soc. Jpn. 12, 686–700 (1957).
[CrossRef]

1949 (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. Inst. Radio Eng. 37(1), 10–21 (1949).
[CrossRef]

Abram, I.

Andrekson, P. A.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of the noise figure of a cascaded non-degenerate phase-sensitive parametric amplifier,” Opt. Express 18(14), 14820–14835 (2010).
[CrossRef] [PubMed]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Asobe, M.

T. Umeki, O. Tadanaga, A. Takada, and M. Asobe, “Phase sensitive degenerate parametric amplification using directly-bonded PPLN ridge waveguides,” Opt. Express 19(7), 6326–6332 (2011).
[CrossRef] [PubMed]

T. Umeki, O. Tadanaga, and M. Asobe, “Highly efficient wavelength converter using direct-bonded PPZnLN ridge waveguide,” IEEE J. Quantum Electron. 46(8), 1206–1213 (2010).
[CrossRef]

M. Asobe, T. Umeki, O. Tadanaga, K. Yoshino, E. Yamazaki, and A. Takada, “Low crosstalk and variable wavelength conversion using multiple QPM LiNbO3 waveguide module,” Electron. Lett. 45(10), 519–520 (2009).
[CrossRef]

Blessing, D. J.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

Bogris, A.

Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of the noise figure of a cascaded non-degenerate phase-sensitive parametric amplifier,” Opt. Express 18(14), 14820–14835 (2010).
[CrossRef] [PubMed]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Caves, C. M.

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields 26(8), 1817–1839 (1982).
[CrossRef]

Chen, X.

Crowley, A. M.

Dasgupta, S.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Demeritt, J. A.

Ellis, A. D.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Gallo, K.

Goto, H.

Grangier, P.

Gray, S.

Grüner-Nielsen, L.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Herstrøm, S.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Imajuku, W.

W. Imajuku and A. Takada, “Noise figure of phase-sensitive parametric amplifier using a Mach-Zehnder interferometer with lossy Kerr media and noisy pump,” IEEE J. Quantum Electron. 39(6), 799–812 (2003).
[CrossRef]

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3-dB noise figure in a high-gain phase-sensitive fiber amplifier,” Electron. Lett. 35(22), 1954–1955 (1999).
[CrossRef]

W. Imajuku and A. Takada, “In-line phase-sensitive amplifier with optical-PLL controlled internal pump light source,” Electron. Lett. 33(25), 2155–2156 (1997).
[CrossRef]

Jakobsen, D.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Kakande, J.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

K. J. Lee, F. Parmigiani, S. Liu, J. Kakande, P. Petropoulos, K. Gallo, and D. Richardson, “Phase sensitive amplification based on quadratic cascading in a periodically poled lithium niobate waveguide,” Opt. Express 17(22), 20393–20400 (2009).
[CrossRef] [PubMed]

Karlsson, M.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of the noise figure of a cascaded non-degenerate phase-sensitive parametric amplifier,” Opt. Express 18(14), 14820–14835 (2010).
[CrossRef] [PubMed]

Kasai, K.

Lee, K. J.

Levenson, J. A.

Li, M.-J.

Liu, A.

Liu, S.

Lundström, C.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of the noise figure of a cascaded non-degenerate phase-sensitive parametric amplifier,” Opt. Express 18(14), 14820–14835 (2010).
[CrossRef] [PubMed]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Mazroa, D.

McKinstrie, C. J.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of the noise figure of a cascaded non-degenerate phase-sensitive parametric amplifier,” Opt. Express 18(14), 14820–14835 (2010).
[CrossRef] [PubMed]

Nakazawa, M.

O’Gorman, J.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Parmigiani, F.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

K. J. Lee, F. Parmigiani, S. Liu, J. Kakande, P. Petropoulos, K. Gallo, and D. Richardson, “Phase sensitive amplification based on quadratic cascading in a periodically poled lithium niobate waveguide,” Opt. Express 17(22), 20393–20400 (2009).
[CrossRef] [PubMed]

Petropoulos, P.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

K. J. Lee, F. Parmigiani, S. Liu, J. Kakande, P. Petropoulos, K. Gallo, and D. Richardson, “Phase sensitive amplification based on quadratic cascading in a periodically poled lithium niobate waveguide,” Opt. Express 17(22), 20393–20400 (2009).
[CrossRef] [PubMed]

Phelan, R.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Puttnam, B. J.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

B. J. Puttnam, D. Mazroa, S. Shinada, and N. Wada, “Phase-squeezing properties of non-degenerate PSAs using PPLN waveguides,” Opt. Express 19(26), B131–B139 (2011).
[CrossRef] [PubMed]

Richardson, D.

Richardson, D. J.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Rivera, T.

Ruffin, A. B.

Shannon, C. E.

C. E. Shannon, “Communication in the presence of noise,” Proc. Inst. Radio Eng. 37(1), 10–21 (1949).
[CrossRef]

Shimoda, K.

K. Shimoda, H. Takahashi, and C. H. Townes, “Fluctuations in amplification of quanta with application to maser amplifiers,” J. Phys. Soc. Jpn. 12, 686–700 (1957).
[CrossRef]

Shinada, S.

Sjödin, M.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Slavík, R.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Sygletos, S.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Syvridis, D.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Tadanaga, O.

T. Umeki, O. Tadanaga, A. Takada, and M. Asobe, “Phase sensitive degenerate parametric amplification using directly-bonded PPLN ridge waveguides,” Opt. Express 19(7), 6326–6332 (2011).
[CrossRef] [PubMed]

T. Umeki, O. Tadanaga, and M. Asobe, “Highly efficient wavelength converter using direct-bonded PPZnLN ridge waveguide,” IEEE J. Quantum Electron. 46(8), 1206–1213 (2010).
[CrossRef]

M. Asobe, T. Umeki, O. Tadanaga, K. Yoshino, E. Yamazaki, and A. Takada, “Low crosstalk and variable wavelength conversion using multiple QPM LiNbO3 waveguide module,” Electron. Lett. 45(10), 519–520 (2009).
[CrossRef]

Takada, A.

T. Umeki, O. Tadanaga, A. Takada, and M. Asobe, “Phase sensitive degenerate parametric amplification using directly-bonded PPLN ridge waveguides,” Opt. Express 19(7), 6326–6332 (2011).
[CrossRef] [PubMed]

M. Asobe, T. Umeki, O. Tadanaga, K. Yoshino, E. Yamazaki, and A. Takada, “Low crosstalk and variable wavelength conversion using multiple QPM LiNbO3 waveguide module,” Electron. Lett. 45(10), 519–520 (2009).
[CrossRef]

W. Imajuku and A. Takada, “Noise figure of phase-sensitive parametric amplifier using a Mach-Zehnder interferometer with lossy Kerr media and noisy pump,” IEEE J. Quantum Electron. 39(6), 799–812 (2003).
[CrossRef]

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3-dB noise figure in a high-gain phase-sensitive fiber amplifier,” Electron. Lett. 35(22), 1954–1955 (1999).
[CrossRef]

W. Imajuku and A. Takada, “In-line phase-sensitive amplifier with optical-PLL controlled internal pump light source,” Electron. Lett. 33(25), 2155–2156 (1997).
[CrossRef]

Takahashi, H.

K. Shimoda, H. Takahashi, and C. H. Townes, “Fluctuations in amplification of quanta with application to maser amplifiers,” J. Phys. Soc. Jpn. 12, 686–700 (1957).
[CrossRef]

Tipsuwannakul, E.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

Toda, H.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

Tong, Z.

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of the noise figure of a cascaded non-degenerate phase-sensitive parametric amplifier,” Opt. Express 18(14), 14820–14835 (2010).
[CrossRef] [PubMed]

Townes, C. H.

K. Shimoda, H. Takahashi, and C. H. Townes, “Fluctuations in amplification of quanta with application to maser amplifiers,” J. Phys. Soc. Jpn. 12, 686–700 (1957).
[CrossRef]

Umeki, T.

T. Umeki, O. Tadanaga, A. Takada, and M. Asobe, “Phase sensitive degenerate parametric amplification using directly-bonded PPLN ridge waveguides,” Opt. Express 19(7), 6326–6332 (2011).
[CrossRef] [PubMed]

T. Umeki, O. Tadanaga, and M. Asobe, “Highly efficient wavelength converter using direct-bonded PPZnLN ridge waveguide,” IEEE J. Quantum Electron. 46(8), 1206–1213 (2010).
[CrossRef]

M. Asobe, T. Umeki, O. Tadanaga, K. Yoshino, E. Yamazaki, and A. Takada, “Low crosstalk and variable wavelength conversion using multiple QPM LiNbO3 waveguide module,” Electron. Lett. 45(10), 519–520 (2009).
[CrossRef]

Vasilyev, M.

Wada, N.

Walton, D. T.

Wang, J.

Weerasuriya, R.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Yamabayashi, Y.

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3-dB noise figure in a high-gain phase-sensitive fiber amplifier,” Electron. Lett. 35(22), 1954–1955 (1999).
[CrossRef]

Yamazaki, E.

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[CrossRef]

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[CrossRef]

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Electron. Lett. (3)

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[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Optical spectra of the EDFA and the PSA.

Fig. 3
Fig. 3

ASE power of the EDFA and the PSA.

Fig. 4
Fig. 4

Electrical noise spectra of the EDFA and the cascaded PSA and EDFA.

Fig. 5
Fig. 5

Average noise power density of the EDFA and the cascaded PSA and EDFA.

Fig. 6
Fig. 6

Bit error rate performance.

Equations (9)

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PSA: n out =G n in + 1 4 { ( G1 )+( 1 G 1 ) },
PIA: n out =G n in +(G1) n sp m,
PSA: P ASE = 1 4 η out (G1)( 1+D(αL) ) e αL hνΔν,
EDFA: P ASE =2 η out (G1) n sp hνΔν,
D(αL)= 1 ( αL ) 2 ( e αL 1αL 1 2 ( αL ) 2 ),
G ext = η in G e αL η out ,
PSA: NF= 1 η in G e αL η out + 1+D( αL ) η in G1 G = 1 G ext + P ASE 1 4 G ext hνΔν ,
EDFA: NF= 1 η in G η out + 2 n sp η in G1 G = 1 G ext + P ASE G ext hνΔν ,
F PSA+PIA = F PSA + F PIA 1 G 1 ,

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