Magnetic dipole emission of Dy3&#x0002B;:Y2O3 and Tm3&#x0002B;:Y2O3 at near-infrared wavelengths

Christopher M. Dodson; Jonathan A. Kurvits; Dongfang Li; Mingming Jiang; Rashid Zia

doi:10.1364/OME.4.002441

1. Introduction

Optical-frequency magnetic dipole (MD) transitions have garnered interest recently as a way for naturally occurring emitters to interact with the magnetic component of light. As a result of recent theoretical [1–4] and experimental [5–14] studies, the need for MD transitions with emission wavelengths in the NIR has increased. Longer wavelengths ease nanofabrication complexities by allowing for larger structure dimensions as well as lower Ohmic losses. These structures could then be leveraged to enhance the magnetic dipole contribution to overall light emission [15–21]. Thus, to help realize technologically relevant devices, we must identify and characterize strong MD emission lines in the NIR that could serve as resonant sources.

Here, we use energy- and momentum-resolved spectroscopy to directly quantify the electric and magnetic dipole contributions to light emission from transitions in Dy³⁺ and Tm³⁺ doped Y₂O₃. Many of these emission lines have been explored for use in upconversion processes where they can be used as the energy transfer donor or acceptor ion [22–31]. Of the emission lines in these ions, we find that the overlapping ⁴F_9/2 → ⁶F_11/2 and ⁴F_9/2 → ⁶H_9/2 transitions in Dy³⁺ and the ¹G₄ → ³H₅ transition in Tm³⁺ exhibit significant MD contributions and offer the best pathways to optical frequency MD enhancement. This work shows how the NIR emission lines of these lanthanide ions could serve as the basis for investigation of magnetic light-matter interactions with optical metamaterials and nanoantennas.

We can first examine the likelihood of MD mediated emission from an initial state |ψ_i〉. To this end, using the previously measured lifetime of the excited levels and calculated spontaneous emission rates for the MD allowed transitions originating from these levels, we can estimate the likely MD branching ratios. We calculate the branching ratio for all MD mediated transitions using

β_{MD} = τ \sum_{f} A_{MD, f} .

Here f runs over all possible decay levels, |ψ_f〉. A_MD,f is the MD spontaneous emission rate to a specific level, and τ is the excited level lifetime. This offers a glimpse at the overall MD branching ratio, from |ψ_i〉, but it fails to shed light on the respective MD contribution, a_MD, for each individual transition. Relationships between these values can be found in Table 1.

Table 1:. Terminology for branching ratios and emission rates. The subscripts r and nr denote radiative and non-radiative decay, while i and f label the initial and final levels of a particular transition. Note that while we have listed a_MD, the same relationships hold for a_ED with the substitution Γ_MD → Γ_ED in the numerator.

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By using energy-momentum spectroscopy [8], we can experimentally quantify the spectrally resolved electric dipole (ED) and MD emission rates, thereby examining the fractional contribution that a particular dipole transition plays in radiative decay between two levels. We use this technique to measure the energy-momentum spectra for each of the NIR emission lines in Dy³⁺ and Tm³⁺, see Fig. 1. These fits yield the ED and MD emission rates by fitting the measured data to analytical theory of isotropic ED and MD momentum cross-sections at each wavelength. Integrating the spectrally resolved emission rates over all wavelengths in the measurement domain allows us to determine the total percentage of ED and MD emission for the transitions of interest. In the case of spectrally distinct transitions, we obtain the total ED and MD emission. We can convert these extracted emission rates to absolute intrinsic emission rates, a_ED and a_MD, by using the methods presented in [14] and the spontaneous emission rates shown in Tables 2 and 3. In the case of spectrally overlapping transitions, we are restricted to relative emission rates for the particular spectral region.

Fig. 1: Free ion energy level diagrams of Dy³⁺ and Tm³⁺. Note that introduction of ions into Y₂O₃ host slightly shifts the energy levels and transition wavelengths.

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Table 2:. Summary of MD emission in Dy³⁺:Y₂O₃. Here, i and f define the initial and final levels of the transition. τ denotes the excited level lifetime that is used in calculations of β. $A = A^{'} n_{r}^{3}$ , where A′ is the vacuum emission rate presented in [1] and n_r=1.72 is the refractive index for the thin films of Y₂O₃. β_i→f,MD is the fractional contribution of MD emission of all radiative decay from the i to f level and a_MD is the relative percentage of MD emission for the specific transition(s). The spectral regions associated with each transition, or overlapping transitions, are defined by the plot ranges in Fig. 2–3.

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Table 3:. Summary of MD emission in Tm³⁺:Y₂O₃. Here, i and f define the initial and final levels of the transition. τ denotes the excited level lifetime that is used in calculations of β. $A = A^{'} n_{r}^{3}$ , where A′ is the vacuum emission rate presented in [1] and n_r=1.72 is the refractive index for the thin films of Y₂O₃. β_i→f,MD is the fractional contribution of MD emission of all radiative decay from the i to f level and a_MD is the relative percentage of MD emission for the specific transition(s). The spectral regions associated with each transition, or overlapping transitions, are defined by the plot ranges in Fig. 4 and 6.

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2. Experimental details

2.1. Sample fabrication

We fabricated luminescent thin films of Dy³⁺ doped Y₂O₃ and Tm³⁺ doped Y₂O₃ by physical vapor deposition and subsequent annealing. First, undoped yttria buffer layers were deposited onto quartz coverslips by electron beam evaporation (20 nm in thickness for the Dy doped samples and 60 nm for the Tm doped samples). Then, lanthanide doped (5% by weight) yttria layers (20 nm for Dy and 50 nm Tm) were deposited followed by a 10 nm undoped yttria capping layer. The buffer and capping layers were included to improve the crystallinity of the thin films and enhance the resulting emission [14]. Following the depositions, the samples were annealed at 1000°C for 1 hour in a dry O₂ tube furnace in order to activate the emitters. The thickness was determined by measuring the film depositions in situ with a quartz crystal microbalance and then subsequently confirmed via ellipsometry.

2.2. Experimental setup

Dy³⁺ and Tm³⁺ ions were excited using the 476.5 nm and 488 nm lines of an argon ion laser, respectively. The experimental setup is the same as that used in [32] in which a 1.3 NA oil immersion objective (Nikon Plan Fluor 100×) was used both to excite the samples as well as collect the emission. A Bertrand lens imaged the back focal plane of the objective through a Wollaston prism, allowing for simultaneous imaging of two orthogonal polarizations. These images were projected onto the entrance slit of a Schmidt-Czerny-Turner imaging spectrograph (Princeton Instruments IsoPlane SCT-320), dispersed by a grating and then imaged using either a silicon based imaging camera (Princeton Instruments Pixis 1024B) for visible wavelengths (all Dy³⁺ emission lines as well as the 639 and 800 nm emission lines in Tm³⁺) or an InGaAs based imaging detector (Princeton Instruments NIRvana) for the 1200 nm emission in Tm³⁺.

3. Results and discussion

3.1. Dy³⁺:Y₂O₃

Dysprosium emission primarily has been explored in regards to the ⁴F_9/2 → ⁶H_13/2 line around 575 nm. This yellow emission is desirable for applications in solid-state lighting [33, 34], lasers [35–37], and dysprosium-based upconversion processes [25, 29]. However, there are many other emission lines in Dy³⁺ that have received far less attention due to their weaker luminescence. Our previous calculations have suggested that these emission lines could be promising for applications as MD sources for optical antennas and other resonant nanostructures [1].

There are three MD emission lines of interest, the ⁴F_9/2 → ⁶H_11/2 transition as well as the spectrally overlapping ⁴F_9/2 → ⁶F_11/2 and ⁴F_9/2 → ⁶H_9/2 transitions. These levels and transitions are shown in Fig. 1(a), which also includes for completeness, the ⁴F_9/2 → ⁶H_13/2 ED transition and the ⁶H_15/2 → ⁴F_9/2 absorption transition used for excitation. These transitions all originate from the same ⁴F_9/2 excited level, and by using Eq. (1) with the previously measured excited level lifetime of 706 μs [38], we find that MD transitions should account for at least 6.8% of all radiative decay from the ⁴F_9/2 level.

As shown in Table 2, the ⁴F_9/2 → ⁶H_11/2 transition has a branching ratio of 1.08%. If we instead examine the MD contribution to this particular transition, shown in Fig. 2, we see that this transition is predominantly ED. Figure 2c shows two representative cross-sections of the experimental measurements (solid) and theoretical fits (dashed) at 658.5 nm and 668.8 nm, respectively. At each wavelength, fitting the cross-sections yields the respective ED and MD contribution. Performing this fit at each wavelength yields the emission rates shown in Fig. 2e.

Fig. 2: Energy-momentum spectra of ⁴F_9/2 → ⁶H_11/2 transition in Dy³⁺:Y₂O₃. (a) Polarized experimental data and (b) corresponding fits. (c) Representative polarized cross-sections of experimental data (solid) and theoretical fits (dashed) at 658.5 nm and 668.8 nm. Both wavelengths show emission that is 100% ED with 0% MD contribution. Vertical polarization is shown in blue and horizontal polarization is shown in red. (d) Total (black) counts for ED (red) and MD (blue) emission. (e) Intrinsic emission rates for ED (red) and MD (blue) emission. The wavelengths of each cross-section are marked with dashed black lines. The white arrows in (a,b) denote polarization.

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By integrating these rates over the measurement domain, we find that this particular transition has a_ED=91.5% and a_MD=8.5%. The overall branching ratio can then be estimated, β_i→f = β_i→f,MD/a_MD=12.7%, which is significantly higher than previous calculations in various crystal hosts with branching ratios ranging from 2.2% in Y₃Sc₂Ga₃O₁₂ (YSGG) to 7.4% in YAl₃(BO₃)₄ (YAB) [35, 39–42].

In addition to this visible emission line, we also examine additional lines originating from the ⁴F_9/2 level that emit at longer wavelengths. These include the ⁴F_9/2 → ⁶F_11/2 and ⁴F_9/2 → ⁶H_9/2 transitions with overlapping emission around 750 nm. Table 2 suggests that this emission should have a strong MD component, A_MD=59.53 s⁻¹. The MD emission from both transitions should account for at least 4.4% of the overall radiative decay from the ⁴F_9/2 level. Though it is an unlikely decay pathway from the ⁴F_9/2 excited level, the emission from these overlapping transitions exhibit strong MD contributions. Integrating the emission rates in Fig. 3, from 730 to 790 nm, yields a_ED=64.8% and a_MD=35.2%. This large fractional contribution suggests that this transition, while relatively weak, has a significant MD component. The branching ratio for the combined transitions is 12.5% of the total radiative decay from the ⁴F_9/2 level, roughly 4× larger than in other materials [35, 39–42] suggesting the importance of crystal hosts.

Fig. 3: Energy-momentum spectra of 4F_9/2 → ⁶F_11/2 and ⁴F_9/2 → ⁶H_9/2 transitions in Dy³⁺:Y₂O₃. (a) Polarized experimental data and (b) corresponding fits. (c) Representative polarized cross-sections of experimental data (solid) and theoretical fits (dashed) at 756.9 nm, 32.0% ED and 68.0% MD, and 758.2 nm, 24.3% ED and 75.7% MD. Vertical polarization is shown in blue and horizontal polarization is shown in red. (d) Total (black) counts for ED (red) and MD (blue) emission. (e) Intrinsic emission rates for ED (red) and MD (blue) emission. The wavelengths of each cross-section are marked with dashed black lines. The white arrows in (a,b) denote polarization.

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3.2. Tm³⁺:Y₂O₃

From the level structure of Tm³⁺ free ions, shown in Fig. 1(b), we see that there are several low lying transitions of interest. Using the 488 nm line from an argon ion laser, we excite from the ³H₆ ground level to the ¹G₄ excited level. From this level, there are four nonzero MD transitions [1] of which we examine three: the ¹G₄ → ³F₄, ¹G₄ → ³H₄, and ¹G₄ → ³H₅ transitions. In particular, we highlight the ¹G₄ → ³H₄ decay path, because ³H₄ is the excited level for the ED mediated ³H₄ → ³H₆ transition that spectrally overlaps with the ¹G₄ → ³H₅ transition. We exclude the ¹G₄ → ³F₃ transition, because it exhibits emission near 1400 nm. Finally, we examine the MD contribution of the ³H₅ → ³H₆ transition which overlaps with the ¹G₄ → ³H₄ emission near 1200 nm. A summary of these MD transitions, corresponding emission rates, and branching ratios can be found in Table 3. Due to this energy level structure, Tm³⁺ has been used as both the donor and acceptor in multi-ion upconversion processes [22–26, 28, 30, 31].

We first examine the emission from the ¹G₄ → ³F₄ transition by means of energy-momentum spectroscopy. Figure 4 shows the energy-momentum spectra and theoretical fits as well as two representative cross-sections, at 654.1 and 656.3 nm, that correspond to peaks in the emission spectrum. By integrating the extracted intrinsic emission rates in Fig. 4(e), we find that the emission from this specific transition is 18.2% MD (a_MD = 18.2%, a_ED = 81.8%). We can infer then that the branching ratio for the ¹G₄ → ³F₄ transition is β_i→f =20.6%, which is ∼2x greater than previous estimations for this transition [44–46].

Fig. 4: Energy-momentum spectra of ¹G₄ → ³F₄ transition in Tm³⁺:Y₂O₃. (a) Polarized experimental data and (b) corresponding fits. (c) Representative polarized cross-sections of experimental data (solid) and theoretical fits (dashed) at 654.1 nm, 78.2% ED and 21.8% MD, and 656.3 nm, 76.3% ED and 23.7% MD. Vertical polarization is shown in blue and horizontal polarization is shown in red. (d) Total (black) counts for ED (red) and MD (blue) emission. (e) Intrinsic emission rates for ED (red) and MD (blue) emission. The wavelengths of each cross-section are marked with dashed black lines. The white arrows in (a,b) denote polarization.

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Examining the emission at 800 nm from the ¹G₄ → ³H₅ transition, see Fig. 5, we find a_ED=82.0% and a_MD=18.0%, which may seem low for an MD spontaneous emission rate of A=115 s⁻¹. This lower than expected a_MD is likely due to the overlapping ³H₄ → ³H₆ transition [47], which is MD forbidden and is calculated to be the dominant decay path from the ³H₄ level [44, 45]. Given that this transition is only allowed by ED emission, we can estimate a lower bound for the branching ratio. The ¹G₄ → ³H₅ transition accounts for ≥ 0.21% of the total radiative decay from the ¹G₄ excited level. By enhancing the MD emission, while suppressing ED emission, one could further study the ¹G₄ → ³H₅ transition and determine better bounds on the MD emission.

Fig. 5: Energy-momentum spectra of ¹G₄ → ³H₅ and ³H₄ → ³H₆ transitions in Tm³⁺:Y₂O₃. (a) Experimental data and (b) corresponding fits. (c) Vertically (blue) and horizontally (red) polarized cross-sections of experimental data (solid) and theoretical fits (dashed) at 797 nm, 61.2% ED and 38.8% MD, and 811 nm, 74.8% ED and 25.2% MD. (d) Total (black) counts for ED (red) and MD (blue) emission. (e) Intrinsic emission rates for ED (red) and MD (blue) emission. The wavelengths of each cross-section are marked with dashed black lines. The white arrows in (a,b) denote polarization.

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Tm³⁺ ions also exhibit emission at longer wavelengths, such as the ¹G₄ → ³H₄ and ³H₅ → ³H₆ transitions at ∼1150 and ∼1200 nm, respectively. Emission from the ³H₅ → ³H₆ transition has been exploited for upconversion applications using Yb³⁺-Tm³⁺ codoped core-shell nanoparticles [29] and accounts for 99% of the radiative decay from the ³H₅ level [46]. Integrating the emission rates in Fig. 6e, we find that the total emission from the two transitions is a_ED=82.2% and a_MD=17.8%. Though the ³H₅ → ³H₆ transition is calculated to have a large spontaneous emission rate, the MD branching ratio for the ³H₅ transition is a fairly low 2.2% suggesting that other decay pathways are more likely. Representative experimental cross-sections and corresponding theoretical fits for emission at 1208.6 nm and 1271.5 nm, see Fig. 6, show good agreement despite the noise from the experimental measurements.

Fig. 6: Energy-momentum spectra of ¹G₄ → ³H₄ and ³H₅ → ³H₆ transitions in Tm³⁺:Y₂O₃. (a) Experimental data and (b) corresponding fits. (c) Vertically (blue) and horizontally (red) polarized cross-sections of experimental data (solid) and theoretical fits (dashed) at 1208.6 nm, 83.6% ED and 16.4% MD, and 1271.5 nm, 86.3% ED and 13.7% MD. (d) Total (black) counts for ED (red) and MD (blue) emission. (e) Normalized emission rates for ED (red) and MD (blue) emission. The wavelengths of each cross-section are marked with dashed black lines. The white arrows in (a,b) denote polarization.

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4. Conclusion

Magnetic dipole emission lines in the NIR region could have broad applications in resonant nanostructures due primarily to the benefits of operating at longer wavelengths (easier fabrication of structures as well as lower Ohmic losses). We characterized the emission rates for multiple transitions in Dy³⁺ and Tm³⁺ doped Y₂O₃. These lines could play important roles in various applications, including imaging and energy based upconversion processes. While these emission lines were previously calculated to have large spontaneous emission rates, we find that the MD contribution to the overall emission is low. Further, we report that the overlapping ⁴F_9/2 → ⁶F_11/2 and ⁴F_9/2 → ⁶H_9/2 transitions in Dy³⁺, centered at 750 nm, as well as the ¹G₄ → ³H₅ and ³H₄ → ³H₆ transitions in Tm³⁺ show the greatest MD contributions, and thus provide the best pathways for future study. Other transitions in Dy³⁺ and Tm³⁺ were also characterized, but we find that their MD contributions in Y₂O₃ are relatively low. Though several of these emission lines have low MD contributions, they operate in the NIR where resonant structures are easier to fabricate and characterize. By integrating Dy³⁺ and Tm³⁺ with resonant nanostructures, one could enhance and engineer these MD emission lines to better leverage upconversion processes for use in energy harvesting and biological imaging.

Acknowledgments

The authors thank A. Larocque for helpful discussions. This work was supported by the Air Force Office of Scientific Research ( PECASE FA9550-10-1-0026 and MURI FA9550-12-1-0488) and the National Science Foundation ( CAREER EECS-0846466).

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Γ_total,i→f	=	Γ_r,i→f + Γ_nr,i→f

β_i→f	:	The contribution of a particular transition to the total decay of an excited state.

	=	$\frac{Γ_{r, i \to f}}{\sum_{f} Γ_{r, i \to f} + Γ_{n r}}$ ,
	where	$\sum_{f} Γ_{r, i \to f} + Γ_{n r} = \frac{1}{τ}$

a_MD	:	The fractional contribution of MD transitions to a specific radiative transition.
a_MD	=	$\frac{Γ_{MD, i \to f}}{Γ_{ED, i \to f} + Γ_{MD, i \to f}}$

i	f	τ (μs)	λ (nm)	A_MD (s⁻¹)	β_i→f,MD	a_MD
¹G₄ →	³F₄	135 [38]	639	9.72	0.13%	18.2%
	³H₅		800	115.00	1.6%	≥18.0%
	³H₄		1167	28.50	0.38%	17.8%
³H₅ →	³H₆	300 [43]	1200	73.78	2.21%	17.8%

Γ_total,i→f	=	Γ_r,i→f + Γ_nr,i→f

β_i→f	:	The contribution of a particular transition to the total decay of an excited state.

	=	$\frac{Γ_{r, i \to f}}{\sum_{f} Γ_{r, i \to f} + Γ_{n r}}$ ,
	where	$\sum_{f} Γ_{r, i \to f} + Γ_{n r} = \frac{1}{τ}$

a_MD	:	The fractional contribution of MD transitions to a specific radiative transition.
a_MD	=	$\frac{Γ_{MD, i \to f}}{Γ_{ED, i \to f} + Γ_{MD, i \to f}}$

i	f	τ (μs)	λ (nm)	A_MD (s⁻¹)	β_i→f,MD	a_MD
¹G₄ →	³F₄	135 [38]	639	9.72	0.13%	18.2%
	³H₅		800	115.00	1.6%	≥18.0%
	³H₄		1167	28.50	0.38%	17.8%
³H₅ →	³H₆	300 [43]	1200	73.78	2.21%	17.8%

Magnetic dipole emission of Dy³⁺:Y₂O₃ and Tm³⁺:Y₂O₃ at near-infrared wavelengths

Abstract

1. Introduction