Enhanced emission from a PbSe/CdSe core/shell quantum dot-doped optical fiber

Lei Zhang; Liping Zhao; Youjin Zheng

doi:10.1364/OME.8.003551

1. Introduction

Quantum dot (QD)-doped optical fibers have been intensively studied [1–3], owing to the doping materials’ tunability of the emission wavelength over a wide region by changing their composition and particle size [4–6], and their extensive applications, such as QD-doped optical fiber based photonic sources, lasers [7], amplifiers [8–12], sensors [13,14], solar cells [15–17] and LEDs [18,19]. Many studies have focused on the optical property of PbSe QD-doped optical fibers and have made some achievements in the past few decades. For example, Cheng et al. synthesized sodium-aluminum-borosilicate glass doped with PbSe QDs which can apply to designing novel broadband fiber amplifiers [20]. Watekar et al. reported linear and nonlinear optical properties of the PbSe QD doped germano-silica glass optical fiber [21]. Theoretical calculations of signal gain for PbSe QD-doped fiber amplifiers have been reported by Cheng et al. [22] and Bahrampour et al. [12] in a single-mode condition and an inhomogeneous model, respectively. Zhang et al. [23,24] simulated the optical property of PbSe QD-doped optical fiber and investigated a comprehensive size effect and Auger recombination effect. Also, the corresponding experimental studies can be consulted from scientific literature [25–28]. However, PbSe QD materials still have inevitable drawbacks, such as low stability in air [29], small Stokes shift and short fluorescence lifetime, which restrict the emission intensity, and in turn limit their applications. In recent years, with the development of synthesis technology for core/shell QDs, especially the further maturation of ion-exchange method, study on formation and characterization of core/shell QDs has been highly concerned. Researchers have successfully synthesized PbSe/CdSe core/shell QDs using several different methods and have proved that the stability of PbSe QDs can be dramatically improved by the formation of CdSe shell [30–33]. However, study on the property of PbSe/CdSe core/shell QD-doped optical fiber is rare or even difficult to consult from literature, although core/shell QD materials exhibit excellent optical properties compared with plain PbSe QDs.

In this work, PbSe/CdSe core/shell QDs were used as an optical fiber dopant to study emission properties (intensity and peak position) of QD-doped optical fiber. The output spectral properties were calculated as a function of fiber length, fiber diameter, QD diameter, QD concentration and pump power to analyze the size effect and Auger recombination effect. The obtained emission properties were compared with that of PbSe QD-doped optical fibers.

2. Calculation

The absorption spectra of PbSe/CdSe core/shell QD solution have two absorption peaks [34] which imply that their energy level structure can be approximated as a three-level system as shown in Fig. 1(a). Further, PbSe/CdSe core/shell QDs can best be described as a type-I system in which the wave functions of electrons and holes are all confined in the PbSe core [35]. Based on the analysis above, PbSe/CdSe core/shell QDs have a similar electron transition and exciton recombination process with plain PbSe QDs. PbSe QDs have been modeled as we have demonstrated in precious reports [23,24]. $W_{12}$ and $W_{13}$ in Fig. 1(a) represent the absorption probabilities from ground state to excited state; $A_{21}$ , $W_{21}$ and $A_{21}^{NR}$ represent the spontaneous emission, stimulated emission and non-radiative transition probabilities, respectively; $A_{32}^{NR}$ represents a non-radiative transition probability from the higher energy state to the metastable energy levels.

Fig. 1 (a) The electron transition and exciton recombination process of three-level system for PbSe/CdSe QDs [23]. (b) Structure diagram of QD-doped optical fiber.

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QD-doped optical fiber can be fabricated by filling the synthesized QD solution into the hollow fiber, and its structure is shown in Fig. 1(b). A set of rate equations (Eqs. (1)-(4)) was employed to analyze the population distributions in the three energy levels at one point of the fiber, while power propagation equations (Eqs. (5)-(6)) were derived to describe the propagation of emission and pump power throughout the entire optical fiber.

\frac{d n_{1}}{d t} = - (W_{13} + W_{12}) n_{1} + (W_{21} + A_{21} + A_{21}^{N R}) n_{2}

\frac{d n_{2}}{d t} = W_{12} n_{1} - (W_{21} + A_{21} + A_{21}^{N R}) n_{2} + A_{32}^{N R} n_{3}

\frac{d n_{3}}{d t} = W_{13} n_{1} - A_{32}^{N R} n_{3}

n_{t} = n_{1} + n_{2} + n {}_{3}

\begin{array}{l} \frac{d P_{λ_{s}} (z)}{d z} = σ_{e} (λ_{s}) \int_{0}^{R} i_{s} (r) n_{2} (r, z) [P_{λ_{s}} (z) + m h ν_{s} Δ ν_{s}] 2 π r d r \\ - σ_{a} (λ_{s}) \int_{0}^{R} i_{s} (r) n_{1} (r, z) P_{λ_{s}} (z) 2 π r d r - l_{ν} P_{λ_{s}} (z) \end{array}

\frac{d P_{p} (z)}{d z} = - σ_{a} (λ_{p}) \int_{0}^{R} i_{p} (r) n_{1} (r, z) P_{p} (z) 2 π r d r - l_{ν} P_{p} (z)

where

n_{1}

,

n_{2}

and

n_{3}

are population densities of the corresponding energy levels;

n_{t}

is the sum of the population density of all energy levels;

P

is propagation power;

σ_{a} (λ_{S})

,

σ_{e} (λ_{s})

and

σ_{a} (λ_{P})

are absorption and emission cross sections for emission wavelength, and absorption cross section for the pump wavelength, respectively;

i_{s} (r)

and

i_{P} (r)

are the normalized intensity distribution of transversal model;

l_{ν}

is the excess fiber loss per length;

Δ ν_{s}

is the effective noise band-width, m is the number of modes transmitted in the fiber. The first item on the right side of Eq. (5) is the emission, the second term is the absorption, and the last term is the excess fiber loss. Under steady-state approximation, the emission and pump power at any point in the fiber can be obtained.

Absorption (Abs) and photoluminescence (PL) spectra for QD materials are obtained from literature [35], where the authors used a recently reported Pb for Cd ion-exchange reaction to convert PbSe QDs into PbSe/CdSe core/shell colloidal QDs. The overall size and shape of QDs remain unchanged upon ion-exchange, hence the duration of the ion-exchange reaction defines the thickness of the CdSe shell and the size of the remaining PbSe core. Three samples have been synthesized: sample 1 is 3.7 nm PbSe QDs, sample 2 is 3.7 nm PbSe/CdSe core/shell QDs with a core of 3.2 nm, sample 3 is 4.2 nm PbSe/CdSe core/shell QDs with a core of 2.1 nm. Fig. 2 is Abs spectra, PL spectra, and calculated Stokes shift, fluorescence lifetime and absorption cross section of three samples, which have also been listed in Table 1 for comparison.

Fig. 2 Abs and PL spectra of (a) 3.7 nm PbSe QDs (sample 1), (b) 3.7 nm PbSe/CdSe core/shell QDs with a core size of 3.2 nm (sample 2), and (c) 4.2 nm PbSe/CdSe core/shell QDs with a core size of 2.1 nm (sample 3) [35]. Also shown here are correspondingly calculated Stokes shift (d), fluorescence lifetime (e) and absorption cross section (f) of the three samples.

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Table 1. Optical properties of three samples [35]

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The growth of a CdSe shell by Pb-for-Cd exchange leads to a reduction of the PbSe core size, and markedly makes the Abs spectra blue-shifted. The relationship between PbSe core size of the three samples and the corresponding first exciton absorption peak is consistent with the empirical formula of PbSe QDs reported by Dai et al. [36]. Sample 3 has the largest Stokes shift, which is useful for reducing re-absorption loss of the emission when transmitted in the fiber core. Fig. 2(e) is obtained by exponential fitting according to the experimental data [35] and shows that sample 3 has the longest fluorescence lifetime which is also meaningful for maximizing the output intensity. Fig. 2(f) is absorption cross sections calculated on the basis of core size, where sample 1 has the largest value.

3. Results and discussion

QD-doped optical fiber was fabricated by using a capillary waveguide filled with QD solution (PbSe or PbSe/CdSe QDs dissolved in solvent). When a laser source was coupled into the fiber core using a convex lens, QDs in the fiber would be excited and radiate luminescence, transmitting in the fiber due to the limitation of optical waveguides (Fig. 1(b)). The theoretical calculations are based on this experimental process and the three samples described above. Data on three samples are substituted into Eqs. (1)-(6), the emission property of QD-doped optical fiber can thus be obtained.

3.1 Enhanced emission from the PbSe/CdSe core/shell QD-doped optical fiber

Theoretical calculation in this part is performed with a doping concentration of 4.5 × 10²⁰ /m³, a fiber diameter of 60 µm, a pump power of 100 mW and wavelength of 532 nm. Comparing the performance of QD-doped optical fibers with regard to the dopants (Figs. 3(a), 3(b) and 3(d)), the optimal emission intensity from fibers doped with core/shell QDs is higher than that with plain PbSe QDs, which means that PbSe/CdSe core/shell QDs can be a better candidate of the fiber dopant. Besides, comparing Figs. 3(b)-3(d), we obtain that fibers doped with sample 3 have stronger emission intensity than that with sample 2. Larger Stokes shift of sample 3 leads to less re-absorption loss (absorption emission overlap), which can be further proved by Fig. 3(e) that the red-shift decreases due to the increased Stokes shift. In addition, longer fluorescence lifetime of sample 3 makes the particles at upper energy levels easier to accumulate, thereby increases the probability of stimulated emission, resulting in increased emission intensity. Further, when the fiber length is too long, the pump light will be absorbed completely, so spontaneous emission will no longer be generated, but lost by absorption in the remaining fiber length, resulting in an optimal fiber length. We can observe from Fig. 3(f) that sample 3-doped optical fibers have larger optimal fiber length because of the larger Stokes shift and longer fluorescence lifetime.

Fig. 3 Emission spectra of sample 1 (a), sample 2 (b) and sample 3 (c) doped optical fibers with different fiber lengths. Also shown here are correspondingly calculated optimized emission intensity (d), red-shift of the optimal emission spectrum relative to the PL spectrum (e) and optimal fiber length for emission intensity (f). “1, 2, and 3” labeled on the axis represent optical fibers doped with sample 1, sample 2 and sample 3, respectively.

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3.2 Comprehensive size effect of QD-doped optical fibers

In addition to the composition and size of QDs, fiber size (length and diameter) can also affect spectral property. Therefore, we studied a comprehensive size effect of optical fibers doped with sample 1 and sample 3, respectively and made a comparison between them. The conclusions can be drawn as follows: (1) Peak wavelength of emission shifts to red with increasing fiber length when the diameter is fixed, and with increasing fiber diameter when the length is fixed (Figs. 4(b) and 4(d)); (2) there is an optimal fiber length for emission intensity, which increases as the fiber diameter decreases (Figs. 4(a) and 4(c)); (3) there is a special fiber length, which is about 80 cm for sample 3-doped fiber and 37 cm for sample 1-doped fiber. When larger than the special fiber length, the emission intensity decreases as the fiber diameter increases; conversely, the emission intensity increases as the fiber diameter increases; (4) sample 3-doped optical fiber has stronger size effect compared with the fiber doped with sample 1 because of their longer fluorescence lifetime and bigger Stokes shift. Take 20 µm diameter fibers as an example: the changing rate of emission intensity with fiber length is about 0.7 /cm for sample 3-doped optical fibers and 0.06 /cm for sample 1-doped optical fibers. In order to validate the theoretical model, experimental data [26] has been employed and plotted in Fig. 4(c) in which the emission intensity increases first and then decreases with increasing fiber length, showing an optical fiber length for emission intensity. It is noteworthy that the fiber length in experiment is slightly smaller than that in theory because of the higher doping concentration (7.2 × 10²¹ /m³) in experiment, so we have shifted the fiber length in order to compare with the theoretical calculation. Besides, the larger doping concentration in experiment leads to the premature attenuation of emission intensity, but the changing trend is consistent with the theoretical results.

Fig. 4 Evolution of emission intensity and peak position of spectra with fiber length when fiber diameters are 20, 40, 60, 80, 100 and 120 µm for sample 3 and sample 1 -doped optical fibers. The dots are calculated data and the lines are polynomial fitting lines for comparison. Star symbols represent experimental data [26] performed under a fiber diameter of 100 µm, doping concentration of 7.2 × 10²¹ /m³ and pump wavelength of 532 nm.

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The required number of doping QDs for the strongest emission (at the optimal fiber length) is certain under a fixed excitation power. Because the pump light will be absorbed completely by the excess QDs, and the spontaneous emission will no longer occur. Besides, the doping number is determined by fiber length and fiber diameter in fixed doping concentration. Therefore, when the excitation power and doping concentration are determined, the optimal fiber length decreases with the increasing fiber diameter. Further, when the optical fiber is relatively short, the number of doped QDs increases with the fiber diameter, leading to an enhanced emission; on the other hand, the distribution of the emission power along the radial direction satisfies the zero-order Bessel function and can be organized and written as [14]

P_{s} (λ) = \sum_{j = 1}^{M} P_{s} (r_{j}, λ) = \frac{P_{s} (r_{1})}{{[J_{0} (V_{1})]}^{2}} \sum_{j = 1}^{M} {[J_{0} (V_{j})]}^{2}

where

V_{j}

is the normalized frequency;

M

is the number of guided modes in fiber core and is expressed as

M = \frac{4 R^{2}}{λ^{2}} (n_{c o r e}^{2} - n_{c l a d}^{2})

where

n_{c o r e}^{}

and

n_{c l a d}

are refractive indexes of optical fiber core and cladding;

R

is core radius of the optical fiber. Therefore, larger fiber diameter leads to more guided modes propagating in fiber, which also contributes to the enhancement of emission. But when the optical fiber is longer, the emission intensity decreases with the increasing fiber diameter because of the strong absorption.

Number of doped QDs is another important parameter affecting the emission property, which is determined by doping concentration under fixed fiber length and fiber diameter. Therefore, we studied the spectral property of the two optical fibers doped with sample 1 and sample 3, respectively, for a range of different QD concentrations, with a fiber length of 40 cm and fiber diameter of 40 µm. Figure 5 shows that the peak wavelength of emission shifts to red with increasing QD concentration for both of the fibers. The peak wavelength changes more obviously with the doping concentration for sample 1-doped optical fiber because of the smaller Stokes shift. The emission intensity increases first and then decreases when doping concentration beyond an optimal point at about 5 × 10²⁰ /m³ for sample 1-doped optical fiber, which however, has been increasing in the theoretical concentration range for sample 3-doped optical fiber.

Fig. 5 Evolution of the intensity (a) and peak position (b) of the emission spectra with doping concentration for sample 3 (black square) and sample 1 (red circle)- doped optical fibers.

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So far, we have seen that the effect of QD size and fiber size on emission intensity is more obvious for PbSe/CdSe QD-doped optical fibers. In this way, we can change these size parameters in a small range to achieve a greater degree of improvement in the intensity of fiber emission. Also, these size parameters should be properly controlled to maximize the fiber emission.

3.3 Auger recombination effect of QD-doped optical fibers

Studies have shown that a necessary condition for higher emission intensity is a high excitation energy, which however, can excite one QD to generate multiple excitons, whose existence will lead to light attenuation due to the ultrafast non-radiative Auger recombination. Therefore, we calculated the evolution of emission intensity with the pump power using 40 cm-length and 40 µm-diameter fibers with a doping concentration of 4.5 × 10²⁰ /m³, and the corresponding results are plotted in Fig. 6. The emission intensity increases with pump power and then starts to decline at higher powers (more than 30 mW), indicating an optimal pump power in the region of around 30 mW under the parameters we have chosen for sample 3-doped optical fibers. However, for sample 1-doped optical fibers, the emission intensity increases firstly and then tends to saturate as the pump power increases continuously.

Fig. 6 Evolution of the intensity of emission spectra with pump power for sample 3 (black square) and sample 1 (red circle) -doped optical fibers.

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Non- radiative transition (Auger recombination) lifetime can be written as [37]

τ_{NR} = {(C_{A} n_{eh}^{2})}^{- 1} = {(C_{A} \frac{{〈 N 〉}^{2}}{V^{2}})}^{- 1}

where V is QD volume;

C_{A} = β_{A} {(D / 2)}^{3}

,

β_{A} = {2.69}_{} {ps}^{-1} {nm}^{3}

;

D

is QD diameter;

〈 N 〉 = j_{p} σ_{a}

is the average exciton number created per QD;

j_{p}

is the pump fluence, which is directly proportional to pump power;

σ_{a}

is absorption cross section of the pump. Substituting

〈 N 〉

into Eq. (9), we can get

τ_{NR} = \frac{16 π^{2}}{72 β} \cdot \frac{D^{3}}{σ_{a}^{2}} \cdot \frac{1}{j_{p}^{2}} = k \cdot \frac{1}{j_{p}^{2}}

PbSe/CdSe core/shell QD materials have a larger

k

compared with PbSe QDs, so the non-radiative transition lifetime decreases (corresponding to non-radiative probability increases) at a higher rate with the increase of pump power, which leads to the early attenuation of the fiber emission intensity. But, although Auger recombination effect is more serious for PbSe/CdSe core/shell QD-doped optical fibers, their emission intensity are still enhanced compared with PbSe QD-doped optical fibers due to the large fluorescence lifetime and Stokes shift.

4. Conclusions

In summary, we have studied the emission property of PbSe/CdSe core/shell QD- doped optical fibers theoretically and have compared them with optical fibers doped with PbSe QDs. The comprehensive size effect related to fiber size and QD size, and non-radiative Auger recombination effect related to pump power were investigated. The peak wavelength of emission shifted to red with increasing fiber length, fiber diameter and doping concentration. From the evolution of emission intensity with different parameters we determined that PbSe/CdSe core/shell QDs were a better candidate of the fiber dopant due to the enhancement of fiber output spectral intensity compared with the performance of plain PbSe QDs. Besides, we have observed stronger size effect depending on fiber size and QD size, and more obvious Auger recombination effect depending on pump power. This paper demonstrates a useful method for the emission enhancement of QDs material-based optical fiber.

Funding

National Natural Science Foundation of China (61604065); Youth Science Foundation of Heilongjiang Province (QC2016007); Program for Youth Innovative Talents in Heilongjiang Provincial University (UNPYSCT-2017197); Doctoral Research Fund of Mudanjiang Normal College (MNUB201406).

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Sample	Abs peak (nm)	PL peak (nm)	Stokes shift (nm)	FWHM (nm)
3.7 nm PbSe	1143	1165	22	99
3.7 nm PbSe/CdSe	997	1085	88	192
4.2 nm PbSe/CdSe	838	1130	292	221

Enhanced emission from a PbSe/CdSe core/shell quantum dot-doped optical fiber

Abstract

1. Introduction

2. Calculation

3. Results and discussion

3.1 Enhanced emission from the PbSe/CdSe core/shell QD-doped optical fiber

3.2 Comprehensive size effect of QD-doped optical fibers

3.3 Auger recombination effect of QD-doped optical fibers

4. Conclusions

Funding

References

Cited By

Figures (6)

Tables (1)

Equations (10)

Optical Materials Express