Download Broadband photon pair generation at 3ω/2

Appl. Phys. B (2016) 122:25
DOI 10.1007/s00340-015-6304-9
Broadband photon pair generation at 3ω/2
Haim Suchowski1,2 · Barry D. Bruner1 · Yonatan Israel1 · Ayelet Ganany‑Padowicz3 ·
Ady Arie3 · Yaron Silberberg1 Received: 12 July 2015 / Accepted: 7 December 2015
© Springer-Verlag Berlin Heidelberg 2016
Abstract We experimentally demonstrate a method for
creating broad bandwidth photon pairs in the visible spectral region, centered at a frequency that is higher than that
of the initial pump source. Spontaneous down conversion
of a narrowband 1053 nm pulsed Nd:YLF laser is followed
by highly efficient upconversion in adiabatic nonlinear
frequency-conversion process. Photon pairs are generated
from 693 to 708 nm, and the complete conversion process
occurs within a single monolithic 5-cm-long stoichiometric lithium tantalate nonlinear crystal. We have characterized the dependence of this structure with respect to pump
intensity and crystal temperature.
Spontaneous parametric down conversion (SPDC) plays
a key role in nonlinear and quantum optics as it enables
amplification of broadband, tunable light in optical parametric oscillators and the reliable generation of entangled
photon pairs [1, 2]. SPDC originates from the stimulation
of random vacuum fluctuations, induced by a strong pump
in a optical parametric generation (OPG) process [3]. In
this process, the pump photon at ωp spontaneously splits
into two photons, the signal at ω1 and the idler at ω2, with
ωp = ω1 + ω2. The signal and idler fields are coherently
amplified during propagation in the nonlinear medium,
* Haim Suchowski
[email protected]
1
Department of Physics of Complex Systems, Weizmann
Institute of Science, 76100 Rehovot, Israel
2
School of Physics and Astronomy, Tel Aviv University,
69978 Tel Aviv, Israel
3
School of Electrical Engineering, Faculty of Engineering, Tel
Aviv University, 69978 Tel Aviv, Israel
where the amount generated in each color is dependent on
the phase mismatch value of the process and the length of
the nonlinear interaction between the waves [4]. By definition, SPDC is a nonlinear process in which the frequencies of the photon pairs are lower than that of the pump
wave. For this reason, conventional generation of photon pairs in the visible optical regime typically requires
ultraviolet pump frequencies. The use of ultraviolet light
in such schemes is very challenging because of the large
phase mismatch between the waves, resulting in very
poor conversion efficiency. Furthermore, several highly
efficient nonlinear crystals—LiNbO3 and KTiOPO4—are
opaque in the ultraviolet range and therefore cannot be
used.
One way to overcome such difficulties is to perform
SPDC followed by an upconversion process that allows for
frequency conversion of light from near-infrared to visible.
In addition, nonlinear frequency conversion of photon pairs
provides a wavelength flexibility that is important for many
applications, including the realization of practical quantum communication networks [5]. Yet, as the generation of
SPDC spectra typically spans a large bandwidth, the conventional approach of optical upconversion in a nonlinear
device fails due to the narrowband nature of the frequencyconversion process in a perfect phase-matched interaction [1, 6]. Thus, for broadband photon pair generation,
the total nonlinear efficiency of such sequential processes
is commonly quite poor. However, it is possible to tradeoff efficiency for high phase-matching bandwidth by using
carefully designed QPM crystals. But owing to the high
dispersion of most quasi-phase-matched crystals, which
increases significantly in the visible regime, the required
width of the QPM pattern for phase-matching compensation is very small and is currently beyond the limits of most
fabrication methods.
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#### Page 2 of 5
H. Suchowski et al.
Fig. 1 (Color online) Experimental setup for efficient SFG
of downconverted light. a A
strong narrowband pump is
injected into a cascaded nonlinear crystal, which first downconverts the pump into signal
and idler photon pairs, followed
by adiabatic sum-frequency
conversion with the same pump.
b A 5 cm cascaded SLT crystal,
where the first 3 cm is a periodically poled structure and the
latter 2 cm is an adiabatic aperiodic design. c Numerical simulation of the wave mixing in the
nonlinear crystal as described in
Eqs. 1a–1d. The color scheme
shows the generation, amplification and conversion of the
interacting waves. The evolution
of the interacting waves is for
p = 1053 nm, 1 = 2090 nm,
2 = 2122 nm, 3 = 700.2 nm
and 4 = 703.8 nm
The adiabatic nonlinear frequency-conversion scheme
allows conversion of very broadband spectra with very high
efficiency. It is based on an analogy between the dynamics
of a two-level atomic system induced by coherent light, and
the processes of SFG/DFG in the undepleted pump approximation [7, 8]. The use of adiabatic phase-matching techniques to perform efficient population transfer in multilevel
systems has been well established over the years [9–17]. It
was shown in a series of experimental demonstrations that
adiabatic schemes are very attractive in nonlinear optics
because they are robust to small changes in parameters
that affect the phase evolution of the process [10, 11, 14,
15]. In this article, we show highly efficient generation of
a broad photon pair spectrum via the sequential process of
SPDC in the near-infrared, followed by an adiabatic sumfrequency generation (AdSFG). The downconverted light
is mixed with the same strong narrowband pump, adding
considerable simplicity to the overall design. We use the
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adiabatic undepleted SFG scheme as an integral part of a
new frequency-conversion scheme for broadband and efficient photon pair generation, with a central frequency that
is equal to 3/2 of the pump frequency. Thus, we overcome
the frequency limitations of SPDC by producing broadband photon pairs at frequencies higher than that of the
pump, while simultaneously maintaining a high efficiency
of bi-photon production despite the cascaded nonlinear
processes.
The design of our nonlinear crystal is composed of
two segments as portrayed in Fig. 1. The first segment is
a periodically poled stoichiometric lithium tantalate (SLT)
crystal optimized for nearly degenerate down conversion.
In the first segment, the pump wave of frequency ωp is converted into a signal wave and an idler wave, with frequencies ω1 and ω2, respectively, satisfying ωp = ω1 + ω2. The
pump laser is a Q-switched 1 kHz Nd:YLF laser producing 100 ns pulses at a center wavelength of 1053 nm. The
Page 3 of 5 ####
Broadband photon pair generation at 3ω/2
second segment is an aperiodically poled SLT crystal optimized for efficient and broadband adiabatic sum-frequency
conversion [7–9] of the pump and downconverted photons.
Both segments are poled on a single monolithic crystal.
The resulting SFG process produces additional fields at
frequencies ω3 = ω1 + ωp, and ω4 = ω2 + ωp, so that
ω3 + ω4 = 3ωp. A dichroic filter eliminates the long wavelengths above 1000 nm, and the upconverted frequencies at
ω3 and ω4 are measured using a fiber-coupled spectrometer
and liquid N2-cooled detector.
The dynamical evolution of the generated waves in this
configuration is dictated by four nonlinear coupled-mode
equations. By assuming an undepleted pump wave condition, where the intensity of the pump wave is much stronger
than that of the rest of the interacting waves, one can take
to be constant along the propagation
the pump amplitude
Ap (z) ∼
= Ap (0) . Under these conditions, the dynamical
nature of the coupled equations can be simplified considerably to the following set of equations:
i
dÃ1
= γ12 Ã∗2 ei�kSPDC z + κ13 Ã3 e−i�kSFG13 z ,
dz
(1a)
i
dÃ2
= γ12 Ã∗1 ei�kSPDC z + κ24 Ã4 e−i�kSFG24 z ,
dz
(1b)
i
dÃ3
= κ13 Ã1 ei�kSFG13 z ,
dz
(1c)
i
dÃ4
= κ24 Ã2 ei�kSFG24 z ,
dz
(1d)
where we have used the following phase mismatch
parameters:
kSFG13 = k1 + kp − k3
(2a)
kSFG24 = k2 + kp − k4
(2b)
kSPDC = kp − k1 − k2
(2c)
where ki (i = 1, 2, 3, 4, p) is the associated wave number of
each wave, and z is the position along the propagation axis.
The coupling parameter for the downconversion process
4π ω1 ω2 (2)
χ Ap, whereas the coupling
(in cgs units) is γ12 = √
k k c2
1 2
4π ω ω
coefficients for the SFG processes are κij = √ i j2 χ (2) Ap ,
ki kj c
where ωi and ωj are the frequencies of the seed and frequency converted waves, respectively, c is the speed of light
in vacuum, and Ap is the pump amplitude and χ(2) is the
second-order susceptibility of the crystal (assumed here to
be frequency independent).
In order to produce an adiabatic passage of energy from
the downconverted beam to the sum-frequency beam, the
phase mismatch parameter of both of the SFG processes
should vary slowly along the propagation axis, from a
large negative phase mismatch value to a large positive
one (or vice versa). The phase mismatch k between the
seeds (ω1) or (ω2) and the pump (ωp) is denoted by kSFG13
and kSFG24, respectively. Both are therefore swept from
�kSFGij < 0 to �kSFGij > 0 along the propagation axis
through the crystal, by a chirped structure of decreasing period poling length. In the presence of a sufficiently
strong pump field ωp, energy is efficiently converted from
frequency ω1 (or ω2) to ω3 (or ω4) in analogy with adiabatic
population transfer in two-level quantum systems. The adiabaticity condition can be written:
d�kSFGij
≪
dz
2
+ κij2
�kSFG
ij
κij
3
2
.
(3)
In the experimental realization, as shown in Fig. 1a, we
have used a quasi-phase-matching (QPM) technique following the adiabatic design consideration that appears
elsewhere [1, 15]. The sketch of our crystal is illustrated
in Fig. 1b. The pump pulse is focused into a temperaturecontrolled segmented SLT crystal with total length of
5 cm. The first segment is a periodic grating with a period
of Λ = 16.3 µm and is 3 cm in length, which is designed
to downconvert the pump at 30 °C. The second segment
is an adiabatic chirped grating and is 2 cm in length,
with poling periodicity varied linearly across the range
Λ = 9.05-8.8 µm. This segment is designed to efficiently
convert the generated spectrum using the adiabatic SFG
method. For the available pump intensity in the experiment (maximum 50 MW/cm2), at least 80 % conversion
efficiency from IR to visible is expected across the entire
bandwidth. For higher intensities, the efficiency asymptotically approaches 100 %, as supported by a number of earlier experiments using adiabatic frequency conversion [10,
17].
From numerical simulations, in the segment where
downconversion occurs, signal and idler photon pairs are
generated in the range of 1950–2270 nm at 30 °C, while
in the AdSFG segment, a broadband input signal range
of 2030–2170 nm is converted to photon pairs spanning
693–708 nm. The central wavelength of the AdSFG output is 702 nm, corresponding to the 2/3 of the pump wavelength. In Fig. 1c, we show the evolution of the interacting waves, as described in Eqs. 1a–1d, for p = 1053 nm
1 = 2090 nm, 2 = 2122 nm, 3 = 700.2 nm and
4 = 703.8 nm. As seen, during the propagation of the
pump in the first segment of the crystal, the seeds (ω1)
and (ω2) are generated and amplified with an exponential dependence that grows along the propagating axis.
In the second segment of the nonlinear crystal, designed
for adiabatic conversion, the waves of ω1 are ω2 are converted efficiently by the presence of the pump to ω3 and
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#### Page 4 of 5
ω4, respectively, each in a different location along the
nonlinear crystal. The simulation accounts for the evolution of the four different waves (the downconverted seeds
ω1 , ω2 and upconverted fields ω3 , ω4) during the nonlinear
processes that occur during propagation as summarized in
Eqs. 1a–1d and 2a–2c. We assume flattop intensity profiles
for all beams and no other approximations except for that
of the undepleted pump. Though our numerical simulations
solved the full dynamical evolution of Eqs. 1a–1d, we can
see that the main contribution of each segment of the nonlinear crystal is associated with the relevant nonlinear process that was phase matched.
Our experiments consist of two sets of measurements.
First, we measured the output bandwidth as a function of
the intensity of the narrowband strong pump. ND filters
were used to vary the intensities of the pump wave from 25
to 50 MW/cm2. This ensured that the spatial properties of
the pump beam were constantly maintained when the pulse
energy was varied. The experimental results, as shown in
Fig. 2, show the measured spectrum of the broadband 3ω/2
photon pairs, from 693 to 708 nm. The measured spectrum
matches the calculated spectrum, as determined by the integration of Eqs. 1a–1d, for all the measured intensities. The
intensity of the final upconverted spectrum increases exponentially with an increase in pump intensity, as expected
from the numerical predictions. The nonuniform shape of
the spectrum is associated with different asymmetric gain
coefficients of the downconverted light, and the spatial
chirp induced by the QPM design.
In addition, we measured the final, upconverted spectrum for different crystal temperatures, between 26 and
34 °C. As shown in Fig. 3, varying the temperature affects
the intensity of the 3/2 photon pair spectrum. This is
mainly due to the the effect of temperature on the SPDC in
the first segment of the crystal. The temperature affects the
dynamics most significantly via the temperature-dependent
index of refraction of the nonlinear crystal, which in turn
alters the phase mismatch relations between the interacting
waves. Adiabatic conversion on its own is demonstratively
robust to temperature variations. In some cases, the center
frequency of the converted spectrum can shift, but with
negligible effects on the efficiency [18]. Here, the nonadiabatic SPDC segment of the crystal does affect the robustness with respect to temperature; however, the conversion
efficiency remains high (more than 85 % of the maximum
observed signal) within a 3 degree Celsius temperature
range (Fig. 3). This represents a considerable improvement over the necessary temperature stability using type-II
phase-matched nonlinear crystals, which typically operate
efficiently over a much narrower ±0.1–0.2 °C range.
The adiabatic conversion processes demonstrated here
should also be applicable both to quantum and to classical
sources of SPDC photons. With reference to Eqs. 1a–1d,
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H. Suchowski et al.
Fig. 2 Measured broadband 3ω/2 photon pair signal as a function
of pump intensity. As expected, the intensity of the upconverted
photon pair spectrum decreases exponentially with decrease in pump
intensity
Fig. 3 Broadband 3ω/2 photon pair spectrum as a function of crystal
temperature. Robust conversion is observed over a range of several
degrees Celsius
the adiabatic conversion process is sensitive to the bandwidth of the SPDC light, but not to the field amplitude.
Efficient frequency conversion is possible for any field
amplitudes, provided that the amplitude of the pump field
is strong enough to make the process sufficiently adiabatic. Crossing over from the regime of classical to quantum
light requires sufficiently low SPDC flux, where the flux
does not exceed one photon per mode [19]. Though, in the
current experiment, the correlation properties of the upconverted photon pairs were not characterized and the SPDC
efficiency in the first segment of our SLT crystal was not
separately measured, many other groups have demonstrated highly efficient photon pair generation using similar
Broadband photon pair generation at 3ω/2
pulsed pump laser sources [20, 21], so it is expected that
our method can be applied to both classical and quantum
sources of SPDC light.
In conclusion, we have experimentally demonstrated
efficient conversion of broadband photon pairs into the
visible wavelength range with high efficiency despite the
additional nonlinear conversion step. This design can enable the generation of broadband bi-photons at frequencies
that are higher than the input pump frequency. Cascading
of a downconversion process with adiabatic sum-frequency
generation in a single crystal can also be implemented in an
OPO cavity for generating tunable upconverted light [22].
We have measured the dependency of the generated broadband spectra with respect to the pump intensity and the
crystal temperature. The robustness and high efficiency of
adiabatic conversion methods, along with the simplicity of
the monolithic nonlinear crystal design, hold much promise
for opening new avenues in nonlinear optics for extending
the versatility of high flux sources of classical and nonclassical light.
Acknowledgments This work was financially supported by the
Israel Science Foundation through Grants 1310/13, the ERC grant
QUAMI, the ERC Grant MIRAGE 20-15 and the Crown Photonics
Center.
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