1 Introduction

The field of nanophotonics has seen rapid progress in recent years. Nanophotonics exploits the local interactions between nanometer-scale particles via optical near fields in order to meet the requirements of future optical technologies [1]. An optical near field can also be described as a dressed photon (DP), which is a quasi-particle representing the coupled state of a photon and an electron in a nanometric space [2]. By using the energy transfer between semiconductor quantum dots (QDs) via DPs, novel nanophotonic devices and systems have been realized. Useful features such as compactness and low-energy consumption have been experimentally demonstrated [3–7].

A fundamental issue in implementing practicable nanophotonic devices and systems that consist of coupled QDs is the design and assembly of an appropriate nanometric setup using QDs to induce the intended optical near-field interactions and corresponding optical far-field responses [8]. Although there have been several reports of self-assembled QD systems based on crystal growth [9–12], coupling of heterogeneous QDs is not straightforward due to their physical incompatibilities. Achieving more diverse types of coupling and the corresponding optical properties requires self-assembling methods for coupled-QD devices consisting of heterogeneous QDs. Moreover, in recent work by the authors, self-assembling techniques for implementing nanophotonic devices and systems utilizing optical near-field interactions have been studied with the aim of producing an assembled structure that is the optimal nanometric structure for each application [13–16].

Our proposed method utilizes nanometric local curing of a photo-curable polymer solution via an induced phonon-assisted process caused by optical near-field interactions between heterogeneous QDs in order to fix their separation and to capsulate coupled QDs in individual grains of cured polymer. We present the principle of our novel photo-curing method for coupling heterogeneous QDs and report the photo response characteristics of coupled QDs obtained in an experiment for verifying the proposed idea.

2 Principle of phonon-assisted photo-curing

We have demonstrated that a DP can excite a multi-mode phonon in a nanometric material, and excited phonon states can couple with each other [14, 16–18]. The quasi-particle representing this coupled state has been named a dressed-photon-phonon (DPP). In our proposed photo-curing method, we use the DPP for fixing heterogeneous QDs in a solution of a photo-curable polymer. In order to induce photo-curing in a self-assembled manner, the mixture in the solution, in which the QDs freely float due to Brownian motion, is irradiated with assisting light. Specifically, we used CdSe- and ZnO-QDs dispersed in toluene and ethanol, respectively. These QDs emit visible and ultraviolet (UV) light, respectively. These solutions were mixed with a UV-curable polymer, and the mixture was irradiated with visible assisting light whose photon energy was sufficiently high to excite excitons in the CdSe-QDs but too low to do so in the ZnO-QDs and the photo-curable polymer.

An overview of our proposed method is given here. If the number of QDs, or in the other words, their volume density, is sufficiently high for the QDs to frequently encounter each other, multistep excitation of the ZnO-QDs occurs due to DPP interactions with neighboring CdSe-QDs. Subsequently, the ZnO-QDs spontaneously emit UV light, and the UV-curable polymer in their surroundings is locally cured by absorbing the emitted UV light. As a result, the separation between the CdSe-QDs and ZnO-QDs is fixed, and the cured polymer capsulates the QDs. This completes the phonon-assisted photo-curing. The spatial distribution of the DPP energy generated on the surface of the QDs governs the volume of the capsulated QDs, which is expressed by a Yukawa function [19]. Moreover, the coupled QDs to be capsulated must be composed of heterogeneous QDs, CdSe and ZnO-QDs in this case, because the above sequence is induced only when the CdSe and ZnO-QDs encounter each other. On the other hand, if the density is not sufficiently high in the mixture and they rarely encounter each other, only the CdSe-QDs spontaneously emit visible light by absorbing the assisting light. In this case, no physical or chemical reactions occur subsequently. The electronic transitions related to the phonon-assisted photo-curing are explained in the following:

When a solution containing a mixture of QDA (CdSe-QDs of size a A), QDB (ZnO-QDs of size a B), and a photocurable polymer is irradiated with assisting light, the two types of QDs form a coupled state due to interactions mediated by dressed-photon-phonons (DPPs) when the distance between them, r AB, is equal to a A or a B or less. In general, the state of the nanomaterial related to the DPP-mediated interaction can be described by the direct product of the electron state and the phonon state, \( |E;el\rangle \otimes |E;phonon\rangle \otimes .{\text{ Here}}, \, |E;el\rangle \) and \( |E;phonon\rangle \), respectively, represent the states of an electron and a phonon having energy E. When the distance between the QDs and the polymer molecules, r QP, becomes sufficiently smaller than r AB, in other words, when r QP ≤ r AB, the polymer molecules exist in the DPP field at the surfaces of both QDs. Therefore, the polymer molecules also form a coupled state with both QDs. On the other hand, when r QP > r AB, the polymer molecules exist outside the DPP field. In this case, the polymer molecules do not form a coupled state with both QDs via the DPP-mediated interaction. In these two cases, transition processes Process 1 and Process 2 shown in Figs. 1 and 2 occur. Fixing of the distance between the two QDs via Process 1, and capsulation of the coupled QDs by curing of the polymer molecules in the vicinity via Process 2 proceed in a self-organized manner. These transition processes will be described below.

Fig. 1
figure 1

Process 1 of the phonon-assisted QD-coupling method at the case of r QP ≤ r AB

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Fig. 2
figure 2

Process 2 of the phonon-assisted QD-coupling method at the case of r QP > r AB

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2.1 Process 1

First, the case where r QP ≤ r AB will be described. In this case, it is not just the two QDs but also the polymer molecules that interact via the DPP to form a coupled state. The photocuring process in this case is composed of two steps, as shown in Fig. 1.

2.1.1 Step 1

The initial ground state is the ground state of the coupled QDs and polymer molecule, \( |E_{{{\text{A}} . {\text{g}}}} ,E_{{{\text{B}} . {\text{g}}}} , E_{{{\text{Poly}} . {\text{g}}}} ;el\rangle \otimes |E_{{{\text{A}} . {\text{thermal}}}} ,E_{{{\text{B}} . {\text{thermal}}}} ,E_{{{\text{poly}} . {\text{thermal}}}} ;phonon\rangle \). Here, E poly.g and E poly.thermal represent the intrinsic energy of the electronic ground state of the polymer molecules, and the intrinsic energy taking into account the phonon distribution in the thermal equilibrium state. This coupling is brought about by the DPPs, and the initial coupled state transitions to the intermediate state \( C_{1}^{\prime} \left| E_{\text{A}.\text{ex}}^{\prime} ,E_{\text{B}.\text{g}} ,E_{\text{poly}.\text{g}};el\right\rangle \otimes \left| E_{\text{A}.\text{ex}}^{\prime},E_{\text{B}.\text{thermal}},E_{\text{poly}.\text{thermal}} ;phonon \right\rangle \) \( + C_{2}^{\prime } \left| E_{\text{A}.\text{g}},E_{\text{B}. \text{g}} ,E_{\text{poly}.\text{g}};el\right\rangle \otimes \left| E_{\text{A}. \text{thermal}},E_{\text{B}.\text{ex}}^{\prime},E_{\text{poly}. \text{thermal}};phonon \right\rangle \) \( + C_{3}^{\prime } \left| E_{\text{A}.\text{g}},E_{\text{B}. \text{g}},E_{\text{poly}.\text{g}};el \right\rangle \otimes \left| E_{\text{A}.\text{thermal}},E_{\text{B}.\text{thermal}} ,E_{\text{poly}.\text{ex}}^{\prime};phonon \right\rangle \left( {{\text{where}}\,\left| {C_{1}^{\prime} } \right|^{2} + \left| {C_{2}^{\prime } } \right|^{2} + \left| {C_{3}^{\prime } } \right|^{2} = 1} \right) \) which is a superposition of the individual states in cases where an exciton exists in QDA, QDB, or the polymer molecule. Here, \( E_{{{\text{poly}}.{\text{ex}}^{\prime } }} \) represents the intrinsic energy of the excited state of the phonons in the polymer molecules, which have an energy equal to the photon energy of the assisting light, hv assist. Because this intermediate state is electronic-dipole forbidden, the contribution of the DPPs is indispensable in this transition.

2.1.2 Step 2

In the intermediate state, from the state where an exciton exists in QDA, a photon having a photon energy equal to the transition energy in QDA, E A.trans (= E A.ex − E A.g) is generated by spontaneous emission. Here, the transition energies of the two QDs, E A.trans and E B.trans, have the relationship E A.trans < hv assist < E B.trans (=E B.ex − E B.g). Because the energy E A.trans is smaller than the activation energy of the polymer molecule, E poly.act, in other words, the energy difference between the excited state and the ground state, E poly.ex − E poly.g, this light does not contribute to the photocuring process. Therefore, the case where an exciton exists in QDB or the polymer molecule will be considered below. In other words, in Step 2, the coupling of the two QDs and the polymer in the intermediate state is further excited by the assisting light and they transition to the final state \( C_{2}^{\prime \prime } \left| E_{\text{A}.\text{g}},E_{\text{B}.\text{ex}}^{\prime \prime} ,E_{\text{poly}. \text{g}};el \right\rangle \otimes \left| E_{\text{A}.\text{thermal}},E_{\text{B}.\text{ex}}^{\prime \prime} ,E_{\text{poly}.\text{thermal}} ;phonon \right\rangle \) \( + C_{3}^{\prime \prime } \left| {E_{{{\text{A}}.{\text{g}}}},E_{{{\text{B}} . {\text{g}}}} ,E_{{{\text{poly}} . {\text{ex}}^{\prime \prime } }} ;el} \right\rangle \otimes \left| {E_{{\text{A}}.{\text{thermal}}} ,E_{{{\text{B}} . {\text{thermal}}}} ,E_{{{\text{poly}} . {\text{ex}}^{\prime \prime } }} ;phonon} \right\rangle \) (where \( \left| {C_{1}^{\prime \prime } } \right|^{2} + \left| {C_{2}^{\prime \prime } } \right|^{2} + \left| {C_{3}^{\prime \prime } } \right|^{2} = 1 \)), in which an exciton exists in either the QDB or the polymer molecule. Here, because the energy E poly.ex’’, which represents the intrinsic energy of the exited state in the polymer molecule, is larger than the activation energy E poly.act, the polymer is cured. Because this final state is electronic-dipole allowed, the transition from the intermediate state to the final state can be brought about by propagating light, not just the DPP. This curing fixes the distance between the two QDs.

2.2 Process 2

Next, the case where r QP > r AB will be described. The state in which the two QDs are coupled via the DPP-mediated interaction is represented by \( |E_{\text{A}} ,E_{\text{B}} ;el\rangle \otimes |E_{\text{A}} ,E_{\text{B}} ;phonon\rangle \). Here, E A and E B represent the intrinsic energies of QDA and QDB, respectively. The photocuring process in this case is composed of the following three steps, as shown in Fig. 2.

2.2.1 Step 1

The initial state is the ground state of the coupled QDA and QDB, \( |E_{{{\text{A}}.{\text{g}}}} ,E_{{{\text{B}}.{\text{g}}}} ;el\rangle \otimes |E_{{{\text{A}}.{\text{thermal}}}} ,E_{{{\text{B}}.{\text{thermal}}}} ;phonon\rangle \). Here, E A.g and E B.g are the intrinsic energies of the electronic ground states of QDA and QDB, and E A.thermal and E B.thermal represent the intrinsic energies taking account of the thermal equilibrium distribution. The two QDs are excited by DPPs and transition to the intermediate state \( C_{1} \left| {E_{{{\text{A}} . {\text{ex}}^{\prime } }} ,E_{{{\text{B}} . {\text{g}}}} ;el} \right\rangle \otimes \left| {E_{{{\text{A}} . {\text{ex}}^{\prime } }} ,E_{{{\text{B}} . {\text{thermal}}}} ;phonon} \right\rangle + C_{2} \left| {E_{{{\text{A}} . {\text{g}}}} ,E_{{{\text{B}} . {\text{g}}}} ;el} \right\rangle \otimes \left| {E_{{{\text{A}} . {\text{thermal}}}} ,E_{{{\text{B}} . {\text{ex}}^{\prime } }} ;phonon} \right\rangle \) (where |C 1|2 + |C 2|2 = 1). Here, \( \left| {E_{{{\text{A}} . {\text{ex}}^{\prime } }} ,E_{{{\text{B}} . {\text{g}}}} ;el} \right\rangle \otimes \left| {E_{{{\text{A}} . {\text{ex}}^{\prime } }} ,E_{{{\text{B}} . {\text{thermal}}}} ;phonon} \right\rangle \) is the state where an exciton exists in QDA and \( \left| {E_{{{\text{A}} . {\text{g}}}} ,E_{{{\text{B}} . {\text{g}}}} ;el} \right\rangle \otimes \left| {E_{{{\text{A}} . {\text{thermal}}}} ,E_{{{\text{B}} . {\text{ex}}^{\prime } }} ;phonon} \right\rangle \) is the state where an exciton exists in QDB. The energies E A.ex’ and E B.ex’ represent the intrinsic energies of the excited states of the electron or phonon in QDA and QDB, respectively, which have energies equal to the photon energy of the assisting light, hν assist, as shown in Fig. 2. Because this intermediate state is electronic-dipole forbidden, the contribution of the DPP is essential in this transition.

After the transition described above, the exciton in QDA relaxes from the state \( \left| {E_{{{\text{A}} . {\text{ex}}^{\prime } }} ,E_{{{\text{B}} . {\text{g}}}} ;el} \right\rangle \otimes \left| {E_{{{\text{A}} . {\text{ex}}^{\prime } }} ,E_{{{\text{B}} . {\text{thermal}}}} ;phonon} \right\rangle \) to the lowest excited state \( |E_{{{\text{A}}.{\text{ex}}}} ,E_{{{\text{B}}.{\text{g}}}} ;el\rangle \otimes |E_{{{\text{A}}.{\text{ex}}}} ,E_{{{\text{B}}.{\text{thermal}}}} ;phonon\rangle \) within a short time. Then, light having a photon energy corresponding to the transition energy of QDA, E A.trans, is generated by a spontaneous emission process; however, as with Process 1, this light does not contribute to the photocuring process.

2.2.2 Step 2

Similar to above, because the spontaneous emission from the state in which the exciton exists in QDA does not contribute to the photocuring process, only the transition from the state \( \left| {E_{{{\text{A}} . {\text{g}}}} ,E_{{{\text{B}} . {\text{g}}}} ;el} \right\rangle \otimes \left| {E_{{{\text{A}} . {\text{thermal}}}} ,E_{{{\text{B}} . {\text{ex}}^{\prime } }} ;phonon} \right\rangle \) in which an exciton exists in QDB will be described here. In other words, in Step 2, the two QDs in the intermediate state are excited by the assisting light and transition to the final state \( \left| {E_{{{\text{A}} . {\text{g}}}} ,E_{{{\text{B}} . {\text{ex}}^{\prime \prime } }} ;el} \right\rangle \otimes \left| {E_{{{\text{A}} . {\text{thermal}}}} ,E_{{{\text{B}} . {\text{ex}}^{\prime \prime } }} ;phonon} \right\rangle \). Here, the energy E B.ex′′ (>E B.ex′) represents the intrinsic energy possessed by the excited state in QDB. Because this final state is electronic-dipole allowed, this transition can be induced by propagating light, not just the DPP.

2.2.3 Step 3

After being excited to the final state described above, the exciton in QDB relaxes to the lowest excited state \( |E_{{{\text{A}}.{\text{g}}}} ,E_{{{\text{B}}.{\text{ex}}}} ;el\rangle \otimes |E_{{{\text{A}}.{\text{thermal}}}} ,E_{{{\text{B}}.{\text{ex}}}} ;phonon\rangle \) within a short time. Then, propagating light having a photon energy corresponding to the transition energy E B.trans of QDB is generated by a spontaneous emission process. Because E B.trans is sufficiently larger than the activation energy of the polymer molecules, E poly.act, the polymer molecules absorb the propagating light generated in this way, becoming excited. The generated propagating light is a spherical wavefront, and therefore, the probability of absorption by the polymer molecules in the vicinity of the two QDs is higher than the probability of absorption at a distance. Therefore, the polymer is cured close to the two QDs, and capsulation of the two QDs thus proceeds.

3 Experimental results

Figure 3 shows the energy conditions for an experiment conducted to verify the proposed method. These conditions fulfill the previously described energy conditions for inducing the sequential process of the phonon-assisted photo-curing. We used commercially available CdSe-QDs (Ocean Optics; Evidot) and ZnO-QDs prepared by sol–gel synthesis using photo-induced desorption [15]. The QD solutions were then dispersed in a UV-curable polymer (NORLAND; NOA 65) and irradiated with assisting light emitted from a 120 mW laser diode with a photon energy of 2.71 eV. The total amount of the mixed solution was limited to 50 μL to maintain spatially uniform illumination. This volume contained about 1014 CdSe-QDs and about 1012 ZnO-QDs. Under these experimental conditions, the QDs can be assumed to encounter each other at a sufficiently high frequency to induce the phonon-assisted photo-curing.

Fig. 3
figure 3

Practical energy conditions of the materials used for the experimental verification: two heterogeneous QDs, CdSe-QDs and ZnO-QDs, and a UV-curable polymer (Norland, NOA 65)

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First, we verified the effect of the phonon-assisted process by direct observation of the locally cured polymer material. During irradiation of the assisting light, the polymer material in the mixture continued to be cured in a self-organized manner, as we previously described, and the volume of the cured polymer in which coupled QDs were capsulated increased. Figure 4a shows observed AFM images of a sample on a Si substrate after irradiation with the assisting light for 0–30 min. As shown, a number of spherical grains, which were formed of locally cured polymer capsulating coupled QDs, were observed. As summarized in Fig. 4b, the average diameter of the grains increased as the irradiation time of the assisting light increased, and then saturated, as represented by the solid line. The saturated diameter was determined by both the rate of occurrence of the phonon-assisted process and the energy absorption rate of the polymer material.

Fig. 4
figure 4

a AFM images of the sample dispersed on a Si substrate and irradiated for 30 min. b Growth of the grain structures depended on the irradiation time of the assisting light. The solid line represents theoretically predicted values

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Second, photoluminescence (PL) spectral properties of the coupled QDs capsulated in the photo-cured grains were investigated. By irradiating the grains with 3.82 eV excitation light from a He-Cd laser, whose photon energy was sufficiently high to excite both CdSe and ZnO-QDs, as shown in Fig. 5, the preferred DP energy transfer from ZnO-QDs to CdSe-QDs is expected to occur only in the case where these two are coupled. As a result of this transfer, the decreases and increases in the PL intensities from these QDs are expected to vary in an anti-correlated manner. That is, the PL intensity from the CdSe-QDs increases while that from the ZnO-QDs decreases. We measured the relation between irradiation time of the assisting light used for capsulation and the PL intensities from both QDs. Because the surrounding polymer mostly absorbs the PL light emitted from the excited state of an exciton in the ZnO-QDs, we measured the emission intensities from the defect levels in the ZnO-QDs, which are proportional to that from the excited state.

Fig. 5
figure 5

Preferred optical energy transfer from ZnO-QD to CdSe-QD by irradiation with excitation light. The trade-off of the emission intensity, where the intensity of the CdSe-QDs increases and that of the ZnO-QDs decreases, can be induced only when the QDs are coupled to each other

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Figure 6a shows the obtained emission spectra of the coupled QDs capsulated using various irradiation times of the assisting light. The left- and right-hand spectra, whose peak energies were lower and higher than 2.34 eV, represent PL from the lowest excitation level of the CdSe-QDs and the defect levels in the ZnO-QDs, respectively. The peak energies of the two spectra were 2.21 and 2.61 eV, respectively. As summarized in Fig. 6b, the expected decrease and increase in emission intensities from the CdSe- and ZnO-QDs in an anti-correlated manner were successfully observed. These results indicate that coupled QDs selectively consisted of both CdSe and ZnO-QDs, and that the number of coupled QDs gradually increased during irradiation with the assisting light.

Fig. 6
figure 6

a Emission spectra of several samples formed with various irradiation times of the assisting light. The left and right-hand spectra represent PL from the lowest excited level of the CdSe-QDs and defect levels in the ZnO-QDs, respectively. b The plotted variabilities of the emission intensities from the CdSe and ZnO-QDs

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4 Summary

We have described the principle of a phonon-assisted self-organized photo-curing method for fixing the separation between heterogeneous QDs and capsulating them. The proposed method utilizes a phonon-assisted excitation process between QDs and a photo-curable polymer. We verified the effectiveness of our technique via an experiment using sample solutions containing CdSe-QDs, ZnO-QDs, and a UV-curable polymer. Moreover, we observed the expected characteristic optical responses of the sample, demonstrating the validity of our idea.

Under the conditions used in our experiment, the coupling processes, Processes 1 and 2 described above, contributed to fixing the separation between the QDs and capsulating them, respectively. Further experiments conducted under various conditions will be required to reveal the differences in the characteristics of the coupled QDs fabricated by each process. Moreover, it is expected that further studies will confirm the discussion in our recent research work [6], namely, that the most appropriate combination ratio of multiple heterogeneous QDs for inducing optical near-field interactions is not necessarily one-to-one, but one-to-many.