Tailoring the ³F₄ level lifetime in Tm³⁺: Y₃Al₅O₁₂ by Eu³⁺ co-doping for signal processing application

Highlights

• High purity Czochralski Tm³⁺, Eu³ Y₃Al₅O₁₂ single crystals are studied.

• Tailoring of the optical lifetime of ³F₄ level to improve RF signal processing.

• Characterization of energy transfer processes between Tm³⁺ and Eu³⁺ ions.

• Coherent spectroscopy on ceramics and single crystal are studied.

• Numerical simulation demonstrated Tm,Eu:YAG potential for RF signal processing.

Abstract

Tm³⁺: Y₃Al₅O₁₂ (Tm:YAG) crystal is a promising material for high-resolution spectral analysis of broadband radio-frequency (RF) signals, where the absorption spectrum is modified via spectral hole burning. In Tm:YAG, the efficiency of the spectral tailoring is limited by the long-lived metastable level ³F₄, acting as a bottleneck for the optical pumping mechanism. We demonstrate that co-doping Tm:YAG with Eu³⁺ ions can significantly shorten the optical lifetime of ³F₄ state, while that of ³H₄ is essentially conserved. We show with a model that these modified lifetimes allow faster tailoring of the absorption profile. Because of their low cost and easiness of processing, we use Tm³⁺ and Eu³⁺ co-doped Y₃Al₅O₁₂ ceramics to probe the energy transfer efficiency and find the optimal cation co-doping concentration. Furthermore, we show that Eu³⁺ co-doping increases the inhomogeneous broadening on the Tm³⁺ optical transition, hence the spectral analysis bandwidth. Finally, we confirm these results on a single crystal grown by the Czochralski method.

Introduction

Rare earth ion-doped single crystals (REIC) are widely used and investigated for various opto-electronics applications, including lighting, laser, sensing [1,2] or more recently quantum information technologies [3,4]. Currently, there is a growing demand for fast, high resolution and broadband RF spectrum analyzers, and REIC are particularly appropriate to build such devices using optical processing based on spectral hole burning (SHB) [5,6]. The basic principle of such application can be described as following: a laser beam is modulated by the radiofrequency (RF) signal to be analyzed and propagated to a REIC crystal cooled down to a few K; The optical sidebands thus created are spectrally analyzed by reading out the absorption profile pattern modified by SHB in the REIC optical transition [7], or by diffracting the modulated beam on spectral gratings obtained by a hole burning sequence performed in advance [8]. The superior performance of the REIC compared to purely electronic spectrum analyzers stems from their broad (>GHz) inhomogeneous absorption profile in the optical domain, as well as their narrow homogeneous linewidth in the kHz range, which enable both large bandwidth and high spectral resolution [1,5,6].

Several signal processing schemes have been already demonstrated using Tm³⁺ doped Y₃Al₅O₁₂ (Tm:YAG) single crystals [5,6]. The most attractive characteristics of this crystal is the 20 GHz inhomogeneous linewidth $\left({\Gamma }_{inh}\right)$ of its ³H₆ → ³H₄ optical transition, allowing for wideband spectral analysis of optically-carried RF signals. The homogeneous linewidth Γ_h, which is related to optical coherence time $T_2$ $\left({\Gamma }_h=\frac{1}{\pi T_2}\right)$ and determines the absolute resolution of the system, is relatively narrow, thus providing an ultimate resolution of about 8 kHz [9]. Although this material is currently the most used for RF spectrum analyzers, different approaches have been proposed to improve its performance. For example, several groups proposed to introduce a controlled broadening of ${\Gamma }_{inh}$ in order to improve the signal processing bandwidth [[10], [11], [12]]. The broadening of the optical transition is induced by an increase of the disorder in the crystal host with a suitable co-doping cation like Sc³⁺ and Lu³⁺ that can increase ${\Gamma }_{inh}$ without altering $T_2$ or the spectral hole's lifetime.

In this paper, we address another limitation of the use of Tm:YAG for spectrum analyzers. For RF signal processing, efficient SHB is obtained by applying a small magnetic field to the sample in order to use Zeeman ground state levels to store populations [13]. In practice, the spectral hole pattern creation involves optical pumping at 793 nm which allows ions to cycle between the ground state ³H₆ and excited state ³H₄ (Fig. 1). The efficiency of this optical pumping is however limited as most excited ions at ³H₄ state will decay to the long lived metastable ³F₄ level rather than relax to the ground state. Indeed, the ³F₄ optical lifetime is around 10 ms, whereas the ³H₄ optical lifetime is only about 500 μs at room temperature. This induces a detrimental bottlenecking because of the stored population in the undesired lower excited states. Moreover, the population stored in the ³F₄ level induces a significant erasure of the population grating when the pump laser is switched off, requiring a higher pump duty cycle. A reduction of the optical lifetime in the ³F₄ level would reduce the ³F₄ state population and is therefore actively desired.

Under the circumstance, we employed the strategy of introducing rare earth co-dopants to selectively reduce the lifetime of the metastable level ³F₄. Simultaneously, lifetime of the ³H₄ level is expected to be maintained as much as possible, which is necessary to ensure the narrow homogeneous linewidth of the ³H₄↔³H₆ transition. This lifetime engineering has similarities with the one investigated in the context of 1.54 μm laser emission based on the ³H₄ →³F₄ transition of Tm³⁺, where the long lifetime of ³F₄ level prevents efficient population inversion [14,15]. Among the different rare earth ions that could be used as co-dopants, trivalent europium and terbium are the best candidates because they have transitions in close resonance with the ³F₄→³H₆ one of Tm³⁺ and can significantly decrease the optical lifetime of ³F₄ level. Furthermore, neither Eu³⁺ nor Tb³⁺ absorbs around 800 nm, thus would not influence optical pumping process of ³H₆→³H₄ transitions of Tm³⁺. Eu³⁺ is preferred over Tb³⁺ because the latter was found to also significantly decrease the ³H₄ lifetime [16]. The structure of energy levels in Eu³⁺ and Tm³⁺ is schemed in Fig. 1. In Eu³⁺ ions the energy gaps between states ⁷F₀ to ⁷F₆ are small enough for efficient non-radiative relaxation, meanwhile the energy of the latter is close to ³F₄ in Tm³⁺ ions. Therefore, efficient energy transfer is expected from ³F₄ level of Tm³⁺ to ⁷F₆ level of Eu³⁺ (see ‘Process I’ in Fig. 1). Another unfavorable energy transfer is also expected between the ⁷F₀→⁷F₅ transition of Eu³⁺ and the ³H₄→³H₅ transition of Tm³⁺ (‘Process II’ in Fig. 1), shortening also the ³H₄ state lifetime, although such kind of transfer could be relatively weaker as the ⁷F₀→⁷F₅ transition of Eu³⁺ is forbidden by the select rule. The two processes are summarized as:

(⁷F_0, ³F₄) → (⁷F_6, ³H₆) Process I

(⁷F_0, ³H₄) → (⁷F_5, ³H₅) Process II

Previous experiments have established that ceramics can be used as an inexpensive and quick way to evaluate compositions prior to undertaking the time and expense involved in single crystal growth. Narrow inhomogeneous and homogeneous linewidth close to the bulk crystal were also demonstrated [12,17,18]. Thus, in this paper both ceramics and a single crystal of Y₃Al₅O₁₂ co-doped by Eu³⁺ and Tm³⁺ (Tm,Eu:YAG) were investigated. Composition of single crystal was determined according to spectroscopic analysis of ceramic samples of various dopants’ concentrations. Synthesis, chemical and structural analysis of both ceramics and single crystal will be presented. Afterwards, spectroscopic characterizations, including absorption spectra, fluorescence decay lifetime as well as inhomogeneous broadening will be discussed in order to assess the potential of such crystals for RF signal processing application.