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We generate correlated photon pairs at 839 nm and 1392 nm from a single-mode photonic crystal fiber pumped in the normal dispersion regime. This compact, bright, tunable, single-mode source of pair-photons will have wide application in quantum communications.
©2005 Optical Society of America
1. Introduction
Key to emerging applications such as quantum cryptography [1] and quantum communications [2] is the availability of convenient and bright single-mode sources of photon pairs. The preferred sources for such experiments until recently have been three wave mixing in χ (2) non-linear birefringent crystals such as beta barium borate [3]. Although these crystals have high non-linearity they are inherently wide band, low brightness (per nanometer, per single mode) sources and suffer from mode matching problems when coupling to optical fibre [4]. Previously we have managed to create a second order χ (2) non-linearity by poling a D-shaped silica fibre and showed broad band pair-photon generation at 1.55 µm [5]. Here the limitation has been in the low magnitude of the induced non-linearity and the source brightness remains low. Recently periodically poled waveguides of lithium niobate have been shown to be extremely bright pair photon sources [6] although the non-circular modes of these surface waveguides still limit the coupling efficiency into optical fibres.
Parametric generation and amplification through modulation instability is well known in optical fibres when pumped close to the zero dispersion wavelength in the anomalous dispersion regime. This has been used to generate photon pairs at wavelengths close to a 1.55 µm wavelength pump [7,8] and very recently preliminary data on pair generation in the anomalous dispersion region of a photonic crystal fibre was published [9]. However in both cases the photon pairs are created close to the pump and the parametric idler wavelengths lie within the first Raman band of the fibre, which contributes a high level of background photons.
We have recently shown that it is possible to generate widely spaced parametric gain peaks by pumping close to the zero dispersion wavelength in the normal dispersion regime [10,11] of photonic crystal fibre (PCF). The generated wavelengths are tuneable using fibre parameters or pump wavelength, and may be adjusted such that the idler wavelength lies on or between high order Raman bands. Significant parametric gain is seen when pumping with Q-switched pulses [10]. By pumping with CW light we create a single-mode fibre based pair-photon source with low background noise. Using PCF allows us to adjust the zero dispersion wavelength to phase-match nonlinear processes pumped by common compact (and low cost) Nd3+ and Yb3+(1040–1080 nm) doped lasers. By further shifting the zero dispersion point to the near infra-red (710 nm say) we could generate photon pairs visible to efficient silicon-based photon counting detectors.
In the experiments reported here phase matching is achieved in a PCF designed to have a zero dispersion wavelength, λ0, close to 1060 nm. We pump this fibre in the normal dispersion regime with nanosecond Q-switched laser pulses of 1047 nm wavelength and generate parametric gain [10,11] at widely spaced wavelengths of 834 nm signal and 1404 nm idler. Switching to CW pumping at the same wavelength the parametric gain is reduced and we are able to see high rates of photon pairs generated at the phase matched wavelengths. We show here that the idler signal lies on the shoulder of the fifth order Raman peak which is still a significant source of background light.
2. Theory
In these experiments we use long pulses, where the propagation can be considered as quasi-CW as well as the true CW case. In this case the major nonlinear process is phasematched four-wave mixing (FWM), generating sidebands spaced at equal frequency intervals from the pump[10–14]. Gain for these processes is provided by the nonlinear refractive index of silica, n2=2×10-20 m2/W. Phase matching and conservation of energy give the equations [12]
or
and
where k i,s,p are the wavevectors (propagation constants) of the idler, signal and pump modes, and ω i,s,p the frequencies, of the idler, signal and pump waves; Pp is the pump power (in the quasi-CW case the peak pump power); and γ is the nonlinear coefficient of the fibre,
where Aeff is the effective area of the fibre mode and λ is the pump wavelength. These phasematching conditions will yield the wavelengths for peak gain in a given fibre, which will depend on the chromatic dispersion of the fibre.
Fig. 1 shows the calculated phase-matching curve (solution of (1) and (2)) for an example PCF with λ 0 close to 1064 nm[9]. There are two clearly different regions: for long pump wavelengths in the anomalous dispersion regime, and for short pump wavelengths in the normal regime. In the anomalous regime the parametric wavelengths are close to the pump wavelength and the wavelengths are strongly power dependent. This is conventionally referred to as modulation instability (MI), and has been previously used for the generation of correlated photon pairs in optical fibre [7,8]. In the normal regime the parametric wavelengths are far from the pump and the wavelengths are only weakly power-dependent. This four-wave mixing (FWM) regime has never been used for generation of photon pairs, and we believe that it offers many advantages in lower background noise and narrower bandwidth. A comparison of FWM and MI parametric generation for pair photons is shown in Fig. 2. It is clear from this that the Raman gain in the idler band of a MI fibre OPO will always be a potential problem, whereas a FWM fibre OPO is able to shift the idler wavelength far from the main Raman gain bands. It should be noted that there is nothing physically different in the nonlinear processes occurring at either side of the dispersion zero. In all cases there is a modulation instability which gives gain for phasematched four-wave mixing. However it is useful to have a different designation for the two regimes as the parametric properties are so different.
Fig. 1. Nonlinear phasematching diagram for the process 2ωp→ωs+ωi, calculated from the measured dispersion curve of a certain PCF for input powers Pp=14 W (blue curve); Pp=140 W (red curve); Pp=1400 W (green curve).
Fig. 2. Calculated frequency offset and bandwidth for pair photons generated by MI (pump offset λ pump-λ 0=1.3 nm) and FWM (λ pump-λ 0=-11.7 nm) for a given PCF at Pp=10 W. The Raman gain shape is also shown (from [11]). Each gain curve is normalized individually.
To estimate the brightness of our source we use the coupled wave equations for parametric gain in a lossless fibre [11, 12]. In the limit of no pump depletion the pump wave produces a constant self-phase shift per unit length and the coupled wave equations can be cast in the form
where As, Ai are signal and idler field amplitudes respectively, z is propagation distance in the fibre, 2γPp is pump self phase shift per unit length. The equations are solved when we cast the field amplitudes in a frame where the pump phase remains constant using to give standard parametric amplifier equations
Phase matching is thus achieved when Δk+2γPp=0 and (1) is satisfied. In the low gain limit, the parametric intensity gain of the system is
Here we operate with no input at either the signal or idler wavelengths. In a semiclassical description spontaneous parametric emission can be thought of as amplification of the vacuum to create G photons per mode. Here we have a single spatial mode but many temporal modes. For a phase matching bandwidth Δν (Hertz) the temporal mode length is of order 1/Δν and thus we have Δν temporal modes per second. The pair photon creation rate is thus
For a pump power of 100 mW at 1 µm wavelength and a fibre core area Aeff ~10 µm2 we calculate G ~1.6×10-4/m2. Assuming a fibre of length z=6 m and a 1 nm phase matching bandwidth, we obtain r ~5.6×106/sec.
3. Experiment
The PCF used in this experiment is illustrated in Fig. 3. It has a hole diameter d=1.16 µm and hole period Λ=2.97 µm with filling fraction d/Λ=0.39. A single mode optical waveguide is formed by filling a central hole. The photonic crystal cladding structure shifts the zero dispersion wavelength of the guided mode to λ 0=1065 nm [10]. The PCF is single-mode at all wavelengths[15] and low loss (<5 dB/km at 1500 nm).
In a preliminary experiment we pumped this fibre using an actively Q-switched Nd:YLF laser. This laser produces 6–30 ns pulses at up to 50 kHz repetition rate with a maximum ~250 mW average power, and wavelength 1047 nm [16]. There was no spectral filtering of the pump light, and the output of the fibre was fed directly to an optical spectrum analyzer (OSA) and the optical parametric gain peaks were observed. The OSA trace for low power pumping (peak power ~200 W) is shown in Fig. 4. The two outlying peaks at 834 nm and 1404 nm are evidence of optical parametric gain. The peaks at 1150 and 1200 nm are both artifacts of the OSA used. The peaks close to the pump are from the spontaneous emission of the pump laser.
Fig. 4. Output spectrum of the PCF when pumped with low-power Q-switched laser pulses at 1047 nm. The OPO wavelengths at 834/1404 nm are clearly visible.
Fig. 5. Optical layout. Laser, 1047nm Nd:YLF laser, 250mW CW; WP, halfwave plate; PBS, polarizing beamsplitter cube; P1, P2, SF11 dispersing prisms; O1, ×20 microscope objectives; PCF, 1.5 m, 3 m or 6 m of modified dispersion PCF; M1, protected silver mirror (R>95%); M2, near IR dielectric mirror (R>98%); F1, 850 nm interference filter, bandwidth 70 nm, T=75%; F2, long wave pass filter, cut-on wavelength 1220 nm; O2, ×10 microscope objectives; SMF, fibre patchcords (SMF28); D Si, Silicon single photon detector; D Ge, cooled Germanium single photon detector.
For the photon counting experiments, in-band light from the pump laser spontaneous emission was removed by prism P1 before the PCF input (Fig. 5). A prism, P2, was also inserted in the collimated output from the PCF. This separated the pump, signal and idler wavelengths. Keeping the laser operating in Q-switched mode at highest power we generated a continuum spectrum in the PCF. It was then possible to align the continuum output at the expected parametric wavelengths onto two separate single mode fibers (SMF). The alignment of the fibres was optimized by maximizing the signal when connected to the OSA. We measured a 5 nm bandwidth coupled into the short wavelength collection fibre and 12 nm in the long wavelength fibre. Once the fibres were properly aligned the laser was switched to operate in continuous wave mode. In this mode we were able to launch up to 100 mW into the PCF. The single mode collection fibres were then connected to fibre coupled photon counting detectors. The longer wavelength light was detected in a Ge avalanche photo-diode (APD: DGe). The APD was operated in Geiger mode, biased beyond breakdown and passively quenched using a series resistor [17]. The shorter wavelength light was directed to an off-the-shelf silicon APD photon counting module (Perkin Elmer SPCM: DSi). Further interference filters (F1, F2) were used in front of the collection fibres to reduce scattered pump and background light. F1 was a 1220 nm long wavelength passing filter while F2 was a 70 nm broad bandpass filter centred on 850 nm. Both filters had quoted transmission >75%. The photon-pulses were counted in a Stanford Research Systems SR-400 photon counter (SPC) and also measured in a time interval analysis system (TIA) using the DSi pulses as start and DGe as stop (delayed by ~12m of coaxial cable).
4. Results
The careful pre-alignment guaranteed that the low power parametric fluorescence was immediately detected and pair photon emission was confirmed from the coincidence peak in the time interval histogram (Fig. 6). A slight shift was seen in the wavelengths of the parametric peaks when we reduced the power from Q-switched pulses (peak power >100 W) to 100 mW CW. This required some careful optimization of the alignment of the collection fibres in order to maximize the pair photon counting rates. The CW parametric peaks were found to be at 839/1392 nm. The change in wavelength corresponds to the effect of the 2γP term in the phasematching equation (1). Two sets of data on 3m and 6m length of the same PCF were taken. For the 3 m fibre up to 1% of start pulses were stopped in the peak. The Si detector counting rate was NSi ~4.5×105/s with a coincidence rate of C ~4500/s. However the 1392 nm idler light is just 20 nm from a high order Raman peak, and high background counts were seen in the Ge channel. Measured count rates were NGe ~4.1×105/s but we estimate that only a small fraction of this count rate came from parametric light. We can make some estimates of the various experimental parameters by referring to the equations for the three count rates:
where r is the rate of pair photon generation in the PCF, ηGe, ηSi are Ge and Si detector efficiencies, ηopt, η′opt are the efficiencies of coupling light from the PCF to detector fibres (including filter and prism losses) and BGe,BSi are lumped background and dark count rates in the detectors. The coincidence rate is made up of pair photon events and accidental coincidences Cb. The probability of seeing a silicon (germanium) count in gate time t is N Sit (N Get) and thus the accidental rate Cb is the product of these probabilities multiplied by the number of gates per second 1/t. We would like to estimate the pair photon emission rate in the fibre but have limited knowledge of the values of ηopt, η′opt and BGe,BSi. The prism arrangement provides spectral filtering, so by adjusting the collection fibre launch slightly we can tune the frequency of collected light away from the photon pairs and see immediately the BSi is small and can be neglected. The accidental coincidence rate Cb can be calculated directly from the results and thus we can calculate
This turns out to be just below 1% in optimized experiments. We can estimate ηopt>0.3 from the assumption that filter transmission ~75%, prism transmission ~80% and typical direct fibre-to-fibre coupling efficiency >50% (including microscope lenses). This implies that our Ge detector efficiency could be as low as 3% which could be due efficiency fall-off at the long (1392 nm) wavelength. Previous measurements of Ge detector efficiency were >10% at 1300 nm [17]. If we make the assumption ηopt=ηopt′ and use the manufacturer’s efficiency for the Si detector (ηSi≈0.5) then we can estimate the rate of pair photon generation. We tabulate the results from the 3m and 6m fibre in the table below.
Table 1. Summary of results
From the results table we see that pair photon rates up to 6.7×106 s-1 are generated. This is in line with the predictions of our simple theory (equation 7). However the background rate in the Ge detector constitutes >90% of the total counts. We ascribe this mainly to background counts from fifth order Raman scattering in the fibre.
The presence of the high order Raman peak was confirmed in a separate experiment where a monochromator (resolution 4.5 nm) was placed in the long wavelength channel. NGe measured as a function of wavelength is shown in Fig. 7. In a coarse wavelength scan the broad fifth order Raman peak can be seen with a barely detectable shoulder due to parametric light. Focusing in on the shoulder we see a narrow peak (bandwidth FWHM~6nm, partially determined by the monochromator resolution) from the spontaneous parametric light. At short wavelengths we see the beginning of the fourth order Raman band, suppressed by the edge of the 1200 nm long pass filter and at long wavelengths we see a hint of the sixth order Raman band suppressed by the falling quantum efficiency of our detector. If we integrate under the peak we can estimate that in a 12 nm collection bandwidth the ratio of background to pair photon signal is ~5:1. This is smaller than we estimate above but we do not include the dark count of the Ge detector which is 60000/sec and afterpulsing which will be significant at this bias [17].
Fig. 7. Germanium detector count rate as a function of wavelength. The low wavelength cut-off is from the 1200 nm pump blocking filter and the long wavelength cut-off is due partly to dropping Raman signal but also due to falling detector efficiency. The red curve shows a finely sampled experiment around the pair photon peak at 1392 nm.
5. Discussion
The pair-photon source as demonstrated has high brightness with a manageable level of background noise photons. However, significant improvement in source brightness and reduction of background to negligible levels can be expected if we pump using a picosecond mode-locked laser. The pair photon signal is proportional to the square of the peak intensity while the Raman scattering grows roughly linearly. For a given average power from the pump source, the pair photon signal will scale as the inverse of the mark to space ratio of the pulses, whereas the Raman signal will be unchanged. This technique was used in the MI parametric photon pair creation demonstrated in [7–9] where picosecond pulses of 1–10 W peak power were used. Using careful filtering methods a coincidence to accidentals ratio up to 13 has recently been reached [8]. Here we report a coincidence rate roughly 5 times the accidental rate in a gate width of ~4 ns for our CW measurements at 0.1 W (table 1) but note that this could be easily improved by shortening our coincidence gate to match the width of the coincidence peak (~1.5 ns) shown in Fig. 6. We can estimate the performance of our source given a picosecond pump source with a mark to space ration of 1:1000 (i.e. 10ps pulses at a 100 MHz repetition rate). Firstly to maintain the pair photon rate at the same level we would need to reduce the CW pump power by a factor of 1000 to 100 µW. The linear Raman signal would reduce by a factor of 1000 and the accidental coincidence rate would be almost entirely due to random overlap of pairs of pairs (four-photon events). As a result this high brightness source in a narrow bandwidth could improve separate source quantum interferometry experiments. From the above we estimate with a 100 MHz repetition rate, 10 ps pulses and 1 mW average power that our source will generate >0.1 photon pairs per pulse per nm bandwidth. Note also the simplicity of the wavelength separation with widely separated FWM wavelengths. The pump spectral cleaning and output spectral separation can all be done with prisms, giving higher transmission than for gratings.
Our measurements indicate a low detection efficiency in the Germanium detector which we ascribe to a fall-off in efficiency at these wavelengths. However, recent results show that the Ge detector efficiency should remain flat and fall off beyond 1400nm [18]. We are presently making an independent measurement of our detector efficiency to isolate this uncertainty. The low detection efficiency measured here could also be due to other causes including losses in the photonic crystal fibre and possible in-band background in the short wavelength channel. Such effects may in future be explainable by use of a full quantum theory of parametric gain including losses and Raman effects [19].
As yet we are not certain of the polarization correlation between signal and idler beams. This is due to scrambling of the polarization in the fibre used. With careful polarization control we can in principle expect to be able to generate entangled pairs using a double pumped configuration as has been used for MI parametric pair experiments [20,21].
6. Conclusion
We have reported the measurement of photon pairs generated by four-wave mixing in a singlemode optical fibre, pumped in the normal dispersion regime. The source is bright, narrowband (<10 nm) and tunable by varying laser wavelength or fibre parameters. The wide separation of the generated pair wavelengths means that a CW pump laser can be used without the Raman scattering swamping the long wavelength signal (previous experiments use pulsed sources to avoid this problem). Higher brightness and negligible Raman effects are to be expected if we pump with a picosecond pulsed source. As the source can in principle be tuned we should be able to select idler wavelengths that fall between the Raman scattering peaks. Entangled pair sources could be constructed from this building block and future multiphoton interference experiments could be expected.
Acknowledgments
WJW is a Royal Society University Research Fellow. The authors would like to thank N.Y. Joly for help with fabricating the fibre. The work is partly funded by UK EPSRC and EU IST-2001-38864 RAMBOQ.
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16. Nd:YLF laser kindly donated by Lightwave Electronics Inc..
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