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 \(\omega_{\text{p}}\) spontaneously splits into two photons, the signal at ω 1 and the idler at ω 2, with \(\omega_{\text{p}} = \omega_{1} + \omega_{2}\). The signal and idler fields are coherently amplified during propagation in the nonlinear medium, 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 frequency-conversion 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 trade-off 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.

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 sum-frequency generation (AdSFG). The downconverted light is mixed with the same strong narrowband pump, adding considerable simplicity to the overall design. We use the 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 \(\omega_{\text{p}}\) is converted into a signal wave and an idler wave, with frequencies ω 1 and ω 2, respectively, satisfying \(\omega_{\text{p}} = \omega_{1} + \omega_{2}\). The pump laser is a Q-switched 1 kHz Nd:YLF laser producing 100 ns pulses at a center wavelength of 1053 nm. The 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 \(\omega_{3} = \omega_{1} + \omega_{\text{p}}\), and \(\omega_{4} = \omega_{2} + \omega_{\text{p}}\), so that \(\omega_{3} + \omega_{4} = 3\omega_{\text{p}}\). A dichroic filter eliminates the long wavelengths above 1000 nm, and the upconverted frequencies at ω 3 and ω 4 are measured using a fiber-coupled spectrometer and liquid N2-cooled detector.

Fig. 1
figure 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 \(\lambda_{p} = 1053 \;{\text{nm}}\), \(\lambda_{1} = 2090 \;{\text{nm}}\), \(\lambda_{2} = 2122 \;{\text{nm}}\), \(\lambda_{3} = 700.2 \;{\text{nm}}\) and \(\lambda_{4} = 703.8 \;{\text{nm}}\)

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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 the pump amplitude to be constant along the propagation \(\left( {A_{\text{p}} (z) \cong A_{\text{p}} (0)} \right)\). Under these conditions, the dynamical nature of the coupled equations can be simplified considerably to the following set of equations:

$$i\frac{{{\text{d}}\tilde{A}_{1} }}{{{\text{d}}z}} = \gamma_{12} \tilde{A}_{2}^{*} e^{{i\Delta k_{\text{SPDC}} z}} + \kappa_{13} \tilde{A}_{3} e^{{ - i\Delta k_{{{\text{SFG}}_{13} }} z}} ,$$
(1a)
$$i\frac{{{\text{d}}\tilde{A}_{2} }}{{{\text{d}}z}} = \gamma_{12} \tilde{A}_{1}^{*} e^{{i\Delta k_{\text{SPDC}} z}} + \kappa_{24} \tilde{A}_{4} e^{{ - i\Delta k_{{{\text{SFG}}_{24} }} z}} ,$$
(1b)
$$i\frac{{{\text{d}}\tilde{A}_{3} }}{{{\text{d}}z}} = \kappa_{13} \tilde{A}_{1} e^{{i\Delta k_{{{\text{SFG}}_{13} }} z}} ,$$
(1c)
$$i\frac{{{\text{d}}\tilde{A}_{4} }}{{{\text{d}}z}} = \kappa_{24} \tilde{A}_{2} e^{{i\Delta k_{{{\text{SFG}}_{24} }} z}} ,$$
(1d)

where we have used the following phase mismatch parameters:

$$\Delta k_{{{\text{SFG}}_{13} }} = k_{1} + k_{p} - k_{3}$$
(2a)
$$\Delta k_{{{\text{SFG}}_{24} }} = k_{2} + k_{p} - k_{4}$$
(2b)
$$\Delta k_{\text{SPDC}} = k_{p} - k_{1} - k_{2}$$
(2c)

where \(k_{i} \left( {i = 1,2,3,4,p} \right)\) is the associated wave number of each wave, and z is the position along the propagation axis. The coupling parameter for the downconversion process (in cgs units) is \(\gamma_{12} = \frac{{4\pi \omega_{1} \omega_{2} }}{{\sqrt {k_{1} k_{2} } c^{2} }}\chi^{(2)} A_{\text{p}}\), whereas the coupling coefficients for the SFG processes are \(\kappa_{ij} = \frac{{4\pi \omega_{i} \omega_{j} }}{{\sqrt {k_{i} k_{j} } c^{2} }}\chi^{(2)} A_{\text{p}}\), where ω i and ω j are the frequencies of the seed and frequency converted waves, respectively, \({\text{c}}\) is the speed of light in vacuum, and \(A_{\text{p}}\) 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 \(\Delta k\) between the seeds (ω 1) or (ω 2) and the pump (\(\omega_{\text{p}}\)) is denoted by \(\Delta k_{{{\text{SFG}}_{13} }}\) and \(\Delta k_{{{\text{SFG}}_{24} }}\), respectively. Both are therefore swept from \(\Delta k_{{{\text{SFG}}_{ij} }} < 0\) to \(\Delta k_{{{\text{SFG}}_{ij} }} > 0\) 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 \(\omega_{\text{p}}\), energy is efficiently converted from frequency \(\omega_{1}\) (or ω 2) to ω 3 (or ω 4) in analogy with adiabatic population transfer in two-level quantum systems. The adiabaticity condition can be written:

$$\frac{{{\text{d}}\Delta k_{{{\text{SFG}}_{ij} }} }}{{{\text{d}}z}} \ll \frac{{\left( {\Delta k_{{{\text{SFG}}_{ij} }}^{2} + \kappa_{ij}^{2} } \right)^{{\frac{3}{2}}} }}{{\kappa_{ij} }}.$$
(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 temperature-controlled segmented SLT crystal with total length of 5 cm. The first segment is a periodic grating with a period of \(\varLambda = 16.3 \;\upmu{\text{m}}\) 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 \(\varLambda = 9.05\text{-}8.8\;\upmu{\text{m}}\). 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 \(\lambda_{\text{p}} = 1053 \;{\text{nm}}\) \(\lambda_{1} = 2090 \;{\text{nm}}\), \(\lambda_{2} = 2122 \;{\text{nm}}\), \(\lambda_{3} = 700.2 \;{\text{nm}}\) and \(\lambda_{4} = 703.8 \;{\text{nm}}\). As seen, during the propagation of the pump in the first segment of the crystal, the seeds (ω 1) and (ω 2) 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 ω 1 are ω 2 are converted efficiently by the presence of the pump to ω 3 and ω 4, respectively, each in a different location along the nonlinear crystal. The simulation accounts for the evolution of the four different waves (the downconverted seeds \(\omega_{1} , \omega_{2}\) and upconverted fields \(\omega_{3} , \omega_{4}\)) 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.

Fig. 2
figure 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

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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.

Fig. 3
figure 3

Broadband 3ω/2 photon pair spectrum as a function of crystal temperature. Robust conversion is observed over a range of several degrees Celsius

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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, 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 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.