Spectral linewidth narrowing and intensity enhancement of the 5G6→5I8 hypersensitive transition in uv-blue up-conversion from Ho3+ activated Al(NO3)3-SiO2 sol-gel glass

doi:10.1364/OME.1.001307

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Spectral linewidth narrowing and intensity enhancement of the ⁵G₆→⁵I₈ hypersensitive transition in uv-blue up-conversion from Ho³⁺ activated Al(NO₃)₃-SiO₂ sol-gel glass

S. Hazarika and Reeta Rajbonshi »View Author Affiliations

Optical Materials Express, Vol. 1, Issue 7, pp. 1307-1318 (2011)
http://dx.doi.org/10.1364/OME.1.001307

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– Abstract
1. Introduction
2. Experimental
3. Theoretical Considerations
4. Results and discussion
5. Conclusion
– References and links

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Abstract

Uv-blue up-conversion at 365, 407 and 436 nm is reported in Ho³⁺ activated Al (NO₃)₃-SiO₂ sol-gel glass under 641nm excitation. Large intensity enhancement and spectral linewidth narrowing is observed for the ⁵G₆→⁵I₈ ﴾436 nm﴿ hypersensitive transition in up-conversion compared to its luminescence and is attributed to amplified spontaneous emission (ASE).The influence of linewidth narrowing on emission properties of the transition is quantitatively analyzed. Using theoretical rate equations in steady state the proposed energy transfer routes for populating higher emitting states in the up-conversion are verified.

1. Introduction

Trivalent Holmium ion (Ho³⁺) has several high lying metastable states capable of emitting in the UV-VIS region. However, investigations on such short wavelength emissions are comparatively less and Ho³⁺ ions are primarily investigated for its mid infra-red (IR) emissions doped in different matrices for use in fibre communication system. The short wavelength emissions in rare-earth activated matrices are successfully described by laser generation multilevel schemes and mechanisms, such as sensibilisation, cascade generation, up-conversion and technologically can be more important because of its better efficiency in storage, transmission of data etc [1

G. Y. Chen, C. H. Yang, B. Aghahadi, H. J. Liang, Y. Liu, L. Li, and Z. G. Zhang, “Ultraviolet-blue upconversion emissions of Ho³⁺ ions,” J. Opt. Soc. Am. B 27(6), 1158–1164 (2010). [CrossRef]

–5

M. Seshadri, Y. C. Ratnakaram, D. Thirupathi Naidu, and K. Venkata Rao, “Investigation of spectroscopic properties (absorption and emission) of Ho³⁺ doped alkali, mixed alkali and calcium phosphate glasses,” Opt. Mater. 32(4), 535–542 (2010). [CrossRef]

In this communication uv-blue up-conversion in Ho³⁺ ions doped sol-gel derived silica glass in presence of Aluminum Nitrate nonahydrate (Al(NO₃)₃,9H₂O) is reported. Further, spectral linewidth and intensity of the hypersensitive ⁵G₆→⁵I₈ transition in up-conversion in comparison to luminescence is studied and its influence on radiative properties are investigated.

2. Experimental

2.1 Sample synthesis

Sample for the study was prepared by sol-gel technique where polymerization of a metal alkoxide –tetraethylorthosilicate (TEOS)) solution in methanol – is catalyzed using doubly distilled water and dilute nitric acid. 0.01M(0.047 g) of Ho₂O₃ and 0.03M(0.14 g) of Al (NO₃)₃, 9H₂O, with molar concentration (M) considered for 12.5 ml of solvent, were dissolved in 10.5 ml mixture of methanol(8.75 ml), distilled water(1.25 ml) and dilute nitric acid(0.5 ml) taken in proportion of 70 (Methanol): 10 (H₂O): 4 (HNO₃) parts by stirring continuously for 10 min in a magnetic stirrer. To this solution, 2ml of TEOS, that amounts to the remaining 16 parts in a mixture of 12.5ml, was added and further stirred for 1h till formation of gel starts. At this juncture the entire mass of gel was poured into plastic mould and left to dry and solidify at temperature of 25-27°C(room temperature). With progress of hydrolysis the gel solidified to form a stiff hard mass (Xerogel / sol-gel glass) in (2-3 days) 48-72 h time. It may be mentioned that dissolution of salts in solvent mixture is subject to salt solubility. Holmium, taken as Ho₂O₃ in this study, partially dissolves in the solvent mixture used for preparation of sol. The undissolved particles in the liquid phase diffused uniformly into the pores of the host network formed by removal of solvent from the gel (via hydrolysis) as glass formation progressed. This is reflected by the colour uniformity observed in the host (sol-gel glass),which the diffused rare–earth dopants impart. The sample was heat treated at 500°C for 5h after it solidified for reduction in hydroxyl content and densification prior to spectroscopic investigation. On densification a pale orange, transparent material of refractive index (n) 1.497, density (d) 1.453 g/cc and thickness (t) 0.2cm was obtained.

XRD and IR analysis of the Al(NO₃)₃-SiO₂ sol-gel glass reported in author’s earlier work [6

S. Hazarika and S. Rai, “Structural, optical and non-linear investigation of Eu³⁺ ions in sol-gel silicate glass,” Opt. Mater. 27(2), 173–179 (2004). [CrossRef]

], indicates of an amorphous structure with Si-O and Si-O-Si bonds forming the glass network and signs of Al³⁺ entering the network as AlO₄ tetrahedra when treated beyond 300°C.

The mol% concentration of the constituents of the prepared sample worked out as 3Al(NO₃)₃ – 96SiO₂ – 1Ho₂O₃. In these calculation the M.W. % of the fraction of Ho₂O₃ and Al (NO₃)₃ in the total weight of the sample was considered.

The salts and reagents used in sample preparation were of spectroscopic grade with 99.9% purity. Holmium, used as oxide was supplied by Aldrich (Germany) and the tetraethylorthosilicate (metal alkoxide) was of Merck (Germany).

2.2 Refractive index, density and spectra

The refractive index (n) of the glass sample was measured with a Abbe refractometer (Almicro, India, AB 24) using sodium source (λ = 589.3 nm) and monobromonapthelene as the contact liquid. The density of the sample was measured in accordance to Archimedes principle with xylene as the immersion liquid.The UV- VIS absorption and up-conversion & luminescence spectra were recorded in commercially available spectrophotometer (Analytic Jena, Specord 200) and Spectrofluorimeter (Perkin Elmer, MPF 44B), respectively. The wavelengths used for excitation of up-conversion and luminescence were the 641 and 385 nm, respectively, of a xenon lamp source (400 W). All measurements and recordings were done at temperature 27-29 ⁰ C.

3. Theoretical Considerations

3.1 Judd-Ofelt intensity parameters and the radiative transition probability

Oscillator strength (f_cal) of predominantly electric –dipole induced 4fⁿ rare-earth transition ψ J → ψ′ J′ can be determined using Judd-Ofelt theory [7

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962). [CrossRef]

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37(3), 511–520 (1962). [CrossRef]

] from the expression

f_{c a l} = \frac{8 π^{2} m c}{3 h \bar{λ} (2 J + 1)} [{(n^{2} + 2)}^{2} / 9 n] \times \sum_{λ = 2, 4, 6} Ω_{λ} {(| 〈 ψ J ‖ U^{λ} ‖ ψ^{'} J^{'} 〉 |)}^{2},

(1)

where Ω_λ, for λ = 2, 4, 6 are the Judd-Ofelt intensity parameters and are calculated from best fit Judd-Ofelt parameters(T_λ, λ = 2,4,6) and refractive index of glass(n) described by [9

F. Auzel, “Material for ionic solid-state lasers,” in Spectroscopy of Solid-State Laser-Type Material, B. D. Bartolo, ed. (Plenum, 1987), pp. 293.

]

Ω_{λ} = \frac{3 h}{8 π^{2} m c} [9 n / {(n^{2} + 2)}^{2}] (2 J + 1) T_{λ} .

(2)

In the above equations m is the mass of the electron,

\bar{λ}

is the mean value of transition, J, the total angular momentum of the initial(ground) state of transition, [(n² + 2)²/ 9n] is the local field correction factor through the refractive index(n) of host,

‖ U^{λ} ‖

is the reduced matrix element of unit tensor operator of rank λ and are independent of host matrix. The other symbols in the equation have their usual standard meanings. To determine Ω_λ from Eq. (2) T_λ, the Judd-Ofelt parameters needs to be evaluated by least square fit analysis of equations formed by correlating experimentally determined oscillator strength (f_exp) from absorption spectra, derived using

f_{\exp} = 4.318 \times 10^{- 9} \int ε (ν) d ν,

(3)

where ε(ν) is the molar absorptivity at wave number ν(cm⁻¹), with its corresponding theoretical expression given by Judd [7

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962). [CrossRef]

] for electric-dipole induced lanthanide transition, ψ J → ψ′ J′

f_{e d} = ν \sum {(| 〈 ψ J ‖ U^{λ} ‖ ψ^{'} J^{'} 〉 |)}^{2} T_{λ} .

(4)

The theoretical oscillator strengths (f_cal) are then calculated using Eq. (1) and values of Ω_λ derived from Eq. (2)._.

The radiative transition probability A(ψ J, ψ′ J′) of a rare-earth transition ψ J → ψ′ J′, using the Judd-Ofelt intensity parameters (Ω_λ, λ = 2, 4, 6) is calculated from

A (ψ J, ψ^{'} J^{'}) = A_{e d} + A_{m d},

(5a)

where A_ed and A_md are electric- and magnetic- dipole induced radiative transition probabilities that are calculated using Eqs. (5b) and (5c), respectively [10

L. B. Shaw, B. Cole, P. A. Thielen, J. S. Sanghera, and I. D. Aggarwal, “Mid-wave IR and long-wave IR laser potential of rare-earth doped chalcogenide glass fiber,” IEEE J. Quantum Electron. 37(9), 1127–1137 (2001). [CrossRef]

]

A_{e d} = \frac{64 π^{4} e^{2} n {(n^{2} + 2)}^{2}}{3 h {\bar{λ}}^{3} (2 J + 1) 9} \sum_{λ = 2, 4, 6} Ω_{λ} {| 〈 ψ J ‖ U^{λ} ‖ ψ^{'} J^{'} 〉 |}^{2}

(5b)

A_{m d} = \frac{64 π^{4} e^{2} n^{3}}{3 h {\bar{λ}}^{3} (2 J + 1) 4 m^{2} c^{2}} {| 〈 ψ J ‖ L + 2 S ‖ ψ^{'} J^{'} 〉 |}^{2}

(5c)

Using A(ψ J, ψ′ J′) peak emission cross-section (

σ_{e m} (λ_{p})

) of radiative transitions are determined with Füchtbauer-Ladenburg equation [11

B. F. Aull and H. P. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. 18(5), 925–930 (1982). [CrossRef]

σ_{e m} (λ_{p}) = \frac{A (ψ J, ψ^{'} J^{'}) λ_{p}^{5} I (λ_{p})}{8 π n^{2} c \int λ_{p} I (λ_{p}) d λ},

(6)

The symbols in Eqs. (5a) and (5c) are same as in Eq. (1). L and S represent orbital and spin angular momentum of the rare-earth ions. In Eq. (6) I(λ_p) is the measured intensity of the transition with peak at λ_p, n the refractive index of host.

4. Results and discussion

4.1 Absorption spectra and pump band oscillator strength

Up-conversion transitions show variations in their emission wavelength with pump band transition oscillator strength and wavelength apart from factors like nature of hosts, power of excitation etc. Uv-violet and uv-blue-green Ho³⁺ up-conversion reported in Y₂O₃ ceramic and fluoro- zirconate (ZBLAN) fibre, respectively, bears evidence to such variations. In the former case, where transitions are in uv-violet, excitation is by the ⁵I₈ →⁵F₄ + ⁵S₂(532 nm) transition while in the later it is ⁵I₈ →⁵F₅(647 nm) transition [12

F. Qin, Y. Zheng, Y. Yu, Z. Cheng, P. S. Tayebi, W. Cao, and Z. Zhang, “Ultraviolet and violet upconversion luminescence in Ho³⁺-doped Y₂O₃ ceramic induced by 532-nm CW laser,” J. Alloy. Comp. 509(4), 1115–1118 (2011). [CrossRef]

,13

M. Kowalska, G. Klocek, R. Piramidowicz, and M. Malinowski, “Ultra-violet emission in Ho: ZBLAN fiber,” J. Alloy. Comp. 380(1-2), 156–158 (2004). [CrossRef]

]. Change in excitation wavelength affects the energy transfer amongst higher emitting levels causing shift in the wavelength range and number of observed transitions in up-conversion. Thus, for an efficient energy transfer in up-conversion choice of a pump band capable of storing large pump energy –the measure of which can be had from the oscillator strength of absorption transition terminating at the level ─ and suitably placed with respect to emitting energy levels is to be made from absorption spectra. In the present case the transition at 641nm in the UV-VIS absorption spectrum of Ho³⁺ doped Al(NO₃)₃-SiO₂ sol-gel glass, assigned to ⁵I₈ →⁵F₅ Ho³⁺absorption transition is responsible for up-conversion excitation in the glass. The UV-VIS absorption spectrum of Ho³⁺ doped Al(NO₃)₃-SiO₂ sol-gel glass with twelve assigned bands is presented in Fig. 1 . The oscillator strength (f_cal) of the ⁵I₈ →⁵F₅ transition used for up-conversion excitation in the present glass is 2.064 × 10⁻⁶ . The excitation transition responsible for the luminescence in the present case is ⁵I₈ →⁵G_{4 .} The calculated Judd-Ofelt intensity parameters, oscillator strength of the absorption bands are tabulated along with their transition frequency in Table 1 . The values of

\bar{λ}

and

{‖ U ‖}^{λ}

used in calculation of f_cal using Eq. (1) are taken from reported works of Carnall et. al. [14

W. T. Carnall, P. R. Fields, and K. Rajnak, “Spectral intensities of the trivalent lanthanides and actinides in solution. II. Pm³⁺, Sm³⁺, Eu³⁺, Gd³⁺, Tb³⁺, Dy³⁺, and Ho³⁺,” J. Chem. Phys. 49(10), 4412–4423 (1968). [CrossRef]

Fig. 1 UV- VIS absorption spectrum of Ho³⁺ in (AlNO₃)₃-SiO₂ sol-gel glass.

Table 1 Absorption Transitions, Transition Frequency, Oscillator Strengths (f_exp and f_cal) and Judd-Ofelt Intensity Parameters (Ω_λ) in Ho³⁺: Al (NO₃)₃-SiO₂ Sol-Gel Glass

Transition	Frequency in cm^-1	f _exp (x10^-6)	f _cal(x10^-6)
⁵I₈→ (³F,³H,³G)₄ +³K₆	29940	N.M*	0.532
⁵I₈ →³L₉	29069	0.548	0.614
⁵I₈ →³H₆ (⁵G, ³H)₅	27777 27027	2.698	1.909
⁵I₈ →⁵G₄	25974	0.292	0.233
⁵I₈ → (⁵G, ³G)₅	24038	1.717	1.722
⁵I₈ →⁵G₆+⁵F₁	22222	5.736	6.139
⁵I₈ →³K₈  ⁵F₂	21637 21141	0.364	1.125
⁵I₈ →⁵F₃	20618	1.034	0.867
⁵I₈ →⁵F₄+ ⁵S₂	18656	2.821	2.905
⁵I₈ →⁵F₅	15600	2.136	2.064
Root mean square deviation (δ_rms )	± 0.420
J-O intensity parameters ( Ω_λ x 10^-20cm².λ= 2,4,6 ):	Ω₂ =1.13 Ω₄=1.58 Ω₆ =1.56

*Not measureable

4.2. Up- conversion and mechanism of energy transfer

The uv-blue up-conversion spectrum of Ho³⁺ in Al (NO₃)₃-SiO₂ sol-gel glass in the range of 350 −500 nm is shown in Fig. 2(a) alongside its luminescence spectrum in Fig. 2(b). Sharp, well defined up-converted emission peaks observed on excitation by 641 nm wavelength are attributed to ³H₆→⁵I₈ (365 nm), (⁵G, ³G)₅→⁵I₈ (407nm), ⁵G₆→⁵I₈(436 nm) 4f-4f radiative transitions of Ho³⁺. Emission peaks (or bands) beyond 450 nm in up-conversion appear diffused in a strong background and hence not considered. In addition to (⁵G, ³G)₅→⁵I₈ (at 411 nm) and ⁵G₆→⁵I₈(at 436 nm) emission peaks, two more peaks (or features) attributed to ³K₈ → ⁵I₈ (463 nm) and ⁵F₃→ ⁵I₈(498 nm) transitions are observed in the luminescence spectrum under 385 nm excitation. Assignments of Ho³⁺ transitions here are verified with those reported in LaF₃ crystal [15

M. J. Weber, B. H. Matsinger, V. L. Donlan, and G. T. Surratt, “Optical transition probabilities for trivalent holmium in LaF₃ and YAlO₃,” J. Chem. Phys. 57(1), 562–567 (1972). [CrossRef]

Fig. 2 (a) Up-conversion (b) Luminescence spectra of Ho³⁺ in (AlNO₃)₃-SiO₂ sol-gel glass excited by(a) 641 nm and(b) 385 nm wavelength obtained with 400 W CW Xenon lamp.

The energy transfer processes involved in this red to uv –blue up-conversion is explained in a multilevel energy scheme presented in Fig. 3 . Sequential absorption of excitation/ pump energy via excited state absorption (ESA) by the ground state manifolds of Ho³⁺ followed by multi-phonon relaxations are considered responsible for populating the upper energy levels ³H₆, (⁵G,³G)_5, ⁵G₆ of the up-converted emissions achieved in Ho³⁺:Al (NO₃)₃-SiO₂ sol-gel glass.

Fig. 3 Energy level scheme of Ho³⁺ and possible up-converted transitions routes of Ho³⁺ in (AlNO₃)₃-SiO₂ sol-gel glass under 641 nm wavelength excitation.

In the first step ESA from ground manifolds ⁵I_4.5,6 excites Ho³⁺ ions to higher energy states ³L_9, ⁵G₄ and (⁵G,³G)₅, respectively, by absorption of a second pump photon, the first of which is absorbed in ground state absorption(GSA) at ⁵I₈ that precedes ESA . A close look into the oscillator strengths of the absorption transitions terminating at these higher energy levels (Table 1) indicates that except for (⁵G,³G)₅ level, the oscillator strength- an indicator of the storage capacity- of the other levels is comparatively small, thereby reducing the possibility of a substantial population build up at these levels necessary for an intense radiative transition. But, successive fast non-radiative decays to closely separated lower levels viz. ³L_9,^{→ 3}H₆^→5G₄^→(⁵G,³G)₅^→5G₆ (separation ~1800 cm ⁻¹) following ESA help to populate ³H₆ and ⁵G₆ levels responsible for radiative transitions at 365 nm and 436 nm, respectively. The (⁵G,³G)₅ state is primarily populated by ESA and contribution by non-radiative relaxation from ⁵G₄ level is negligible as a very small population accumulates via ESA in the level owing to its small absorbance (see absorption spectra).

Population in the ⁵I_{4, 5, 6,} Ho³⁺ ground manifolds, the initial levels of the considered ESA, results from non-radiative de-excitation to lower levels in steps after excitation of Ho³⁺ ions to ⁵F₅ level by ground state absorption (GSA).

The excitation processes by ESA discussed above in the energy level scheme can be represented as: 1. ⁵I₄ (Ho³⁺) + pump photon →³L₉(Ho³⁺). 2. ⁵I₅ (Ho³⁺) + pump photon →⁵G₄. 3.⁵I₆ (Ho³⁺) + pump photon → (⁵G, ³G)_5, (Ho³⁺) . In addition to ESA, energy transfer (ET) mechanism that can co–exist with ESA may also be considered. In ET process an excited ion transfers energy to another excited ion along resonant channels that may be represented in this present case as: 1 ⁵I₄ (Ho³⁺) + ⁵F₅(Ho³⁺) →³L₉ (Ho³⁺) + ⁵I₈(Ho³⁺). 2. ⁵I₅ (Ho³⁺) + ⁵F₅(Ho³⁺)→⁵G₄(Ho³⁺) + ⁵I₈(Ho³⁺). 3. ⁵I₆ (Ho³⁺) + ⁵F₅(Ho³⁺)→(⁵G,³G)₅ (Ho³⁺) + ⁵I₈(Ho³⁺).

The concentration of Ho³⁺ ions (in ions/cm³ = Avagado’s number (N_A) x mol% of RE ions x density of glass / M.W. of the glass) in the Al(NO₃)₃-SiO₂ glass where energy transfer processes in up-conversion are described is 1.89 x 10²² ions/cm³ of the sample.

4.3 Rate equation analysis

Considering only up-conversion via ESA, rate equations required to describe the processes involved in up-conversion mechanism explained in the energy level scheme in Fig. 3 are

\frac{d N_{1}}{d t} = A_{1, 9} N_{9} - W_{1, 5} N_{1} + A_{6, 1} N_{6} + A_{7, 1} N_{7} + A_{2, 1} N_{2}

(7)

\frac{d N_{2}}{d t} = A_{3, 2} N_{3} - W_{2, 7} N_{2} - A_{2, 1} N_{2}

(8)

\frac{d N_{3}}{d t} = A_{4, 3} N_{4} - W_{3, 8} N_{3} - A_{3, 2} N_{3}

(9)

\frac{d N_{4}}{d t} = A_{5, 4} N_{5} - A_{4, 3} N_{4} - W_{4, 10} N_{4}

(10)

\frac{d N_{5}}{d t} = W_{1, 5} N_{1} - A_{5, 4} N_{5}

(11)

\frac{d N_{6}}{d t} = A_{7, 6} N_{7} - A_{6, 1} N_{6}

(12)

\frac{d N_{7}}{d t} = W_{2, 7} N_{2} + A_{8, 7} N_{8} - A_{7, 1} N_{7} - A_{7, 6} A_{7}

(13)

\frac{d N_{8}}{d t} = A_{9, 8} N_{9} + W_{3, 8} N_{3} - A_{8, 7} N_{8}

(14)

\frac{d N_{9}}{d t} = A_{10, 9} N_{10} - A_{9, 1} N_{9} - A_{9, 8} N_{9}

(15)

\frac{d N_{10}}{d t} = W_{4, 10} N_{4} - A_{10, 9} N_{10}

(16)

In the above equations A_i,j = 1/τ_i,j and W_j,i = B_j,i ρ are the transition probabilities of spontaneous (radiative and non- radiative, as well) emission and absorption, respectively, between levels i and j, where i or j = 1, 2 …..10 [16

M. Csele, Fundamentals of Light Sources and Lasers (Wiley-Interscience, 2004), Chaps. 4 and 5.

]. B_j,i, τ_i,j and ρ are Einstein’s B coefficient, spontaneous decay time and pump energy density, respectively. N_{i =} _1…10 represents population of Ho³⁺ ions in levels marked 1…..10 in Fig. 3. In writing these rate equations approximations like consideration of stimulated emissions from levels, possible non- radiative relaxations among closely spaced higher energy levels like… ³K₈,³F_2,3 etc. are neglected.

In steady state conditions, where the time derivatives of populations in levels are set equal to zero, the rate equations are solved simultaneously to derive expressions for emission intensity in terms of state population using [17

N. R. Giri, S. B. Rai, and A. Rai, “Intense green and red upconversion emissions from Ho³⁺ in presence of Yb³⁺ in Li:TeO₂ glass,” Spectrochim. Acta [A] 74(5), 1115–1119 (2009). [CrossRef]

]

I = h ν_{i, j} A_{i, j} N_{i},

(17)

where h is the Plank’s constant and ν_ij the transition frequency between level i and j, for analysis of parameters affecting the intensities.

Thus, for ³H₆→⁵I₈ transition the intensity is written as

I ({}^{3}H_{6} \to {}^{5}I_{8}) = h ν_{9, 1} A_{9, 1} N_{9}

(18)

Appling the steady state condition, i.e.,

\frac{d N}{d t} = 0

Eq. (15) yields

N_{9} = \frac{A_{10, 9} N_{10}}{(A_{9, 1} + A_{9, 8})}

(19)

and Eq. (16), Eq. (10) and Eq. (11) give

N_{10} = \frac{W_{4, 10} N_{4}}{A_{10, 9}} and N_{4} = \frac{A_{5, 4} N_{5}}{(W_{4, 10} + A_{4, 3})} = \frac{W_{1, 5} N_{1}}{(W_{4, 10} + A_{4, 3})} .

(20)

With the expression of N₄

N_{10} = \frac{W_{4, 10} W_{1, 5} N_{1}}{A_{10, 9} (W_{4, 10} + A_{4, 3})} .

(21)

Substituting Eq. (21) in Eq. (19)

N_{9} = \frac{W_{4, 10} W_{1, 5} N_{1}}{(A_{9, 1} + A_{9, 8}) (W_{4, 10} + A_{4, 3})} .

(22)

∴ I ({}^{3}H_{5} \to {}^{5}I_{8}) = \frac{h ν_{9, 1} A_{9, 1} W_{4, 10} W_{1, 5} N_{1}}{(A_{9, 1} + A_{9, 8}) (W_{4, 10} + A_{4, 3})} .

(23)

Replacing N₁ by N_A , the concentration of Ho³⁺ ions and W_j,i by B_j,iρ for j = 4, 1 and i = 10,5 in the numerator

I ({}^{3}H_{6} \to {}^{5}I_{8}) = \frac{h ν_{9, 1} A_{9, 1} B_{4, 10} B_{1, 5} ρ^{2} N_{A}}{(A_{9, 1} + A_{9, 8}) (W_{4, 10} + A_{4, 3})} .

(24)

The expression may be further simplified as τ_4,3 = 1/A_4,3 the fast non radiative decay time from level 4→3 is a small quantity and makes 1/ τ_4,3 numerically much greater than W_4,10, the absorption probability which may, therefore, be ignored [16

M. Csele, Fundamentals of Light Sources and Lasers (Wiley-Interscience, 2004), Chaps. 4 and 5.

], resulting in the intensity expression

I ({}^{3}H_{6} \to {}^{5}I_{8}) = \frac{h ν_{9, 1} A_{9, 1} B_{4, 10} B_{1, 5} ρ^{2} N_{A}}{(A_{9, 1} + A_{9, 8}) A_{4, 3}} .

(25)

Similarly the intensity of the transition ⁵G₆→⁵I₈ is written as

I ({}^{5}G_{6} \to {}^{5}I_{8}) = h ν_{6, 1} A_{6, 1} N_{6} .

(26)

From Eq. (12) under steady state condition,

A_{6, 1} N_{6} = A_{7, 6} N_{7}

(27)

and from Eq. (13)

N_{7} = \frac{W_{2, 7} N_{2}}{(A_{7, 6} + A_{7, 1})}

(28)

As level 7 is primarily populated by ESA from level 2 contribution of fast non-radiative relaxation from level 8 is neglected in derivation of N₇ from Eq. (13). Further from Eq. (8) and Eq. (9)

N_{2} = \frac{A_{3, 2} N_{3}}{(W_{2, 7} + A_{2, 1})} = \frac{A_{3, 2} A_{4, 3} N_{4}}{(W_{2, 7} + A_{2, 1}) ((W_{3, 8} + A_{3, 2})} .

(29)

From Eq. (10) and Eq. (11) under steady state condition

N_{4} = \frac{A_{5, 4} N_{5}}{(W_{4, 10} + A_{4, 3})} = \frac{W_{1, 5} N_{1}}{(W_{4, 10} + A_{4, 3})} .

(30)

Using Eq. (29) and Eq. (30) N₇ in terns of N₁ is

N_{7} = \frac{A_{3, 2} A_{4, 3} W_{2, 7} W_{1, 5} N_{1}}{(A_{7, 6} + A_{7, 1}) (W_{2, 7} + A_{2, 1}) (W_{3, 8} + A_{3, 2}) (W_{4, 10} + A_{4, 3})} .

(31)

\begin{array}{l} ∴ Intensity \\ I ({}^{5}G_{6} \to {}^{5}I_{8}) = \frac{h ν_{6, 1} A_{7, 6} A_{3, 2} A_{4, 3} W_{2, 7} W_{1, 5} N_{1}}{(A_{7, 6} + A_{7, 1}) (W_{2, 7} + A_{2, 1}) (W_{3, 8} + A_{3, 2}) (W_{4, 10} + A_{4, 3})} . \end{array}

(32)

Replacing W_2,7, W_1,5 and N₁ by B_2,,7ρ, B_1,5ρ and N_A, respectively, and ignoring absorption transition probabilities W_2,7, W_3,8 and W_4,10 from the denominator of Eq. (32) for reasons cited earlier a simplified expression for intensity of the transition ⁵G₆→⁵I₈ is written as

I ({}^{5}G_{6} \to {}^{5}I_{8}) = \frac{h ν_{6, 1} A_{7, 6} B_{2, 7} B_{1, 5} ρ^{2} N_{A}}{(A_{7, 6} + A_{7, 1}) A_{2, 1}} .

(33)

The intensity of transition (⁵G,³G)₅→⁵I₈,

I ({({}^{5}G, {}^{3}G)}_{5} \to {}^{5}I_{8}) = h ν_{7, 1} A_{7, 1} N_{7}

(34)

can be written using Eq. (31) as

I ({({}^{5}G, {}^{3}G)}_{5} \to {}^{5}I_{8}) = \frac{h ν_{7, 1} A_{7, 1} A_{3, 2} A_{4, 3} W_{2, 7} W_{1, 5} N_{1}}{(A_{7, 6} + A_{7, 1}) (W_{2, 7} + A_{2, 1}) (W_{3, 8} + A_{3, 2}) (W_{4, 10} + A_{4, 3})}

(35)

Substituting W_2,7 and W_1,5 by B_2,7ρ and B_1,5ρ, N₁ by N_A, respectively, and ignoring W_2,7, W_3,8 and W_4,10from the denominator as done earlier, the intensity expression simplifies to

I ({({}^{5}G, {}^{3}G)}_{5} \to {}^{5}I_{8}) = \frac{h ν_{7, 1} A_{7, 1} B_{2, 7} B_{1, 5} ρ^{2} N_{A}}{(A_{7, 6} + A_{7, 1}) A_{2, 1}} .

(36)

The three up-conversion intensity Eqs. (25), (33) and (36) show quadratic dependence of transition intensity on the pump energy density (ρ). It confirms the involvement of two photon absorption in the emission processes - a characteristic of up-conversion transitions [17

]. The expressions further indicate the transition intensity dependence on the Ho³⁺ ion concentration (N_A) .

4.4 ⁵G₆→⁵I₈ transition: in up-conversion and luminescence

In disordered or amorphous materials linewidths of transitions are inhomogeneous broadened due to the different local environment experienced by all colour centres [4

R. S. Meltzer, “Line broadening mechanisms and their measurement,” in Spectroscopic Properties of Some Rare-Earths in Optical Materials, G. Liu and B. Jacquier, eds. (Tsinghua University Press and Springer Verlag, 2005).

]. These effects are more pronounced in hypersensitive / environment sensitive 4f-4f transitions like the ⁵G₆→⁵I₈ transition in Ho³⁺ [5

] and can have a large influence on spectral properties of transition. Effective linewidths (Δλ_eff) of inhomogeneously broadened transitions as in glass, ceramics etc. are measured as the fullwidth at half maximum(FWHM) intensity .Apart from serving as an excellent probe to characterize disorders in materials, measurement of such linewidths gives an insight into the spectral quality/purity (Q) of transitions. Q = λ_p/ Δλ_eff, λ_p is the peak emission wavelength.

The spectral quality of the hypersensitive Ho^{3+ 5}G₆→⁵I₈ (436 nm-blue) in this silica sol-gel glass in presence Al (NO₃)₃ is found to be larger in the up-conversion compared to luminescence due to narrowing of linewidth (Δλ_eff) in up-conversion. Its is observed that with a ~1nm shift towards blue the ⁵G₆→⁵I₈ transition at 436 nm is 2.13 times narrower and 1.4 times more intense in the up-conversion compared to the luminescence. However, opposite is the case of the non-hypersensitive (⁵G, ³G)₅→⁵I₈ transition. Its linewidth is broader by ~3nm with a λp shift of ~4nm towards the blue in the up-conversion. A plot of spectral quality /purity (Q) vs. λp of transitions in up-conversion and luminescence is presented in Fig. 4(a) . The relative intensity of ⁵G₆→⁵I₈ transition in up-conversion and luminescence is derived by comparing normalized intensity ratio of I(⁵G₆):I((⁵G, ³G)₅) calculated from the up-conversion and luminescence spectra of Ho³⁺ in Fig. 2.

Fig. 4 Variation of (a) spectral quality (b) peak emission cross-section with peak emission wavelength in up-conversion and luminescence of Ho³⁺ transitions in (AlNO₃)₃-SiO₂ sol-gel glas

The enhancement of ⁵G⁶→⁵I⁸ transition intensity in up-conversion over luminescence is a situation of intensity variation with pump energy density (ρ), considering linear and quadratic dependence of intensities on pump energy density (ρ) in luminescence and up-conversion, respectively. Narrowing of transition linewidth and the variation in peak to peak intensity ratio of I(⁵G₆) to I((⁵G, ³G)₅)transitions under the circumstances described, i.e. with increased pump energy density, are spectral signature of amplified spontaneous emission (ASE) [18

O. Svelto, Principles of Lasers (Plenum Publishing Corporation, Springer, 1998), Chap. 12.

,19

M. F. Joubert, B. Jacquier, and R. Moncorgé, “Exciton-exciton annihilation and saturation effect in TbF₃,” Phys. Rev. B 28(7), 3725–3732 (1983). [CrossRef]

A graphical representation of the peak emission cross-section (

σ_{e m} (λ_{p})

), calculated using Eq. (6), with peak emission wavelength(λ_p ) for up-conversion and luminescence transitions is shown in Fig. 4(b). Computed values of peak emission wavelength (λ_P), effective bandwidth(Δλ_eff,) transition probability(A), quality factor(Q) and peak emission cross-section (

σ_{e m} (λ_{p})

) of observed up-conversion and luminescence transitions in Ho³⁺: Al (NO₃)₃-.

SiO₂ sol-gel glass using the equations described in Sec. 3 are tabulated in Table 2 . It may be noted that the radiative transition probability of ³K₈₊⁵F₂→⁵I₈ emission only include contributions of magnetic- dipole induced radiative probability(A_md) in addition to A_ed.

Table 2 Peak Emission Wavelength (λ_P), Effective Bandwidth (Δλ_eff), Radiative Transition Probability (A), Quality Factor (Q) and Peak Emission Cross-Section (σ(λ_P)) of Observed Up-Conversion and Luminescence Transitions in Ho³⁺: Al (NO₃)₃-SiO₂ Sol-Gel Glass

Transition	Peak emission wavelength (λ_P in nm)		Effective Band width (Δλ_eff in nm)		Radiative Transition Probability (A in s^-1)	Spectral Quality(Q) (λ_P /Δλ_eff)		Peak emission cross-section (σ(λ_P)x 10^-21 in cm²)
	(a)	(b)	(a)	(b)		(a)	(b)	(a)	(b)
³H₆→⁵I₈	365		04		4516	45.23		11.53
(⁵G, ³G)₅→⁵I₈	407	411	09	06	2670	54.5	68.5	4.88	7.51
⁵G₆→⁵I₈	436	437	08	17	5884	91.25	25.65	15.73	7.45
³K₈₊⁵F₂→⁵I₈		463		17	2371		27.24		4.18
⁵F₃→⁵I₈		498		11	1351		45.27		4.46

(a) In up-conversion (b) in luminescence

5. Conclusion

The quadratic character of intensities resulting from steady state equation analysis of the up-converted emissions in Ho³⁺: Al(NO₃)₃-SiO₂ sol-gel glass under 641 nm excitation in a multilevel scheme is an indication of two photon involvement in the process and establishes the experimentally observed uv-blue up-conversion emissions in to be ³H₆→⁵I₈ (365 nm), (⁵G, ³G)₅→⁵I₈ (407nm) and ⁵G₆→⁵I₈(436 nm) transitions of Ho³⁺. The hypersensitive ⁵G₆→⁵I₈ transition showed significant narrowing of effective linewidth (Δλ_eff) and intensity enhancement I(λ_p) in up-conversion, which may be attributed to amplified spontaneous emission(ASE) from the ⁵G₆. However, for conclusive evidence variation of intensity and linewitdh of the hypersensitive transition in up-conversion at different excitation power needs to be studied. Comparison drawn from graphical representation of properties like emission cross-section (

σ_{e m} (λ_{p})

) and spectral quality (Q) of transitions in up-conversion with its corresponding luminescence show reverse order variation for ⁵G₆→⁵I₈ hypersensitive and (⁵G, ³G)₅→⁵I₈ non- hypersensitive transition - increase in hypersensitive and decrease in non- hypersensitive transition in up-conversion. These variations are much pronounced for the environment sensitive ⁵G₆→⁵I₈ transition. The radiative properties data of transitions complied in Table 2 are indicative of the glass in study to be a potential optical material for the up-converted ⁵G₆→⁵I₈ hypersensitive transition at 436 nm.

References and links

1.	G. Y. Chen, C. H. Yang, B. Aghahadi, H. J. Liang, Y. Liu, L. Li, and Z. G. Zhang, “Ultraviolet-blue upconversion emissions of Ho³⁺ ions,” J. Opt. Soc. Am. B 27(6), 1158–1164 (2010). [CrossRef]
2.	M. Malinowski, M. Kaczkan, S. Stopinski, R. Piramidowicz, and A. Majchrowski, “Short-wavelength luminescence in Ho³⁺-doped KGd(WO₄)₂ crystals,” J. Lumin. 129(12), 1505–1508 (2009). [CrossRef]
3.	R. S. Quimby, M. G. Drexhage, and M. J. Suscavage, “Efficient frequency up-conversion via energy transfer in fluoride glasses,” Electron. Lett. 23(1), 32–34 (1987). [CrossRef]
4.	R. S. Meltzer, “Line broadening mechanisms and their measurement,” in Spectroscopic Properties of Some Rare-Earths in Optical Materials, G. Liu and B. Jacquier, eds. (Tsinghua University Press and Springer Verlag, 2005).
5.	M. Seshadri, Y. C. Ratnakaram, D. Thirupathi Naidu, and K. Venkata Rao, “Investigation of spectroscopic properties (absorption and emission) of Ho³⁺ doped alkali, mixed alkali and calcium phosphate glasses,” Opt. Mater. 32(4), 535–542 (2010). [CrossRef]
6.	S. Hazarika and S. Rai, “Structural, optical and non-linear investigation of Eu³⁺ ions in sol-gel silicate glass,” Opt. Mater. 27(2), 173–179 (2004). [CrossRef]
7.	B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962). [CrossRef]
8.	G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37(3), 511–520 (1962). [CrossRef]
9.	F. Auzel, “Material for ionic solid-state lasers,” in Spectroscopy of Solid-State Laser-Type Material, B. D. Bartolo, ed. (Plenum, 1987), pp. 293.
10.	L. B. Shaw, B. Cole, P. A. Thielen, J. S. Sanghera, and I. D. Aggarwal, “Mid-wave IR and long-wave IR laser potential of rare-earth doped chalcogenide glass fiber,” IEEE J. Quantum Electron. 37(9), 1127–1137 (2001). [CrossRef]
11.	B. F. Aull and H. P. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. 18(5), 925–930 (1982). [CrossRef]
12.	F. Qin, Y. Zheng, Y. Yu, Z. Cheng, P. S. Tayebi, W. Cao, and Z. Zhang, “Ultraviolet and violet upconversion luminescence in Ho³⁺-doped Y₂O₃ ceramic induced by 532-nm CW laser,” J. Alloy. Comp. 509(4), 1115–1118 (2011). [CrossRef]
13.	M. Kowalska, G. Klocek, R. Piramidowicz, and M. Malinowski, “Ultra-violet emission in Ho: ZBLAN fiber,” J. Alloy. Comp. 380(1-2), 156–158 (2004). [CrossRef]
14.	W. T. Carnall, P. R. Fields, and K. Rajnak, “Spectral intensities of the trivalent lanthanides and actinides in solution. II. Pm³⁺, Sm³⁺, Eu³⁺, Gd³⁺, Tb³⁺, Dy³⁺, and Ho³⁺,” J. Chem. Phys. 49(10), 4412–4423 (1968). [CrossRef]
15.	M. J. Weber, B. H. Matsinger, V. L. Donlan, and G. T. Surratt, “Optical transition probabilities for trivalent holmium in LaF₃ and YAlO₃,” J. Chem. Phys. 57(1), 562–567 (1972). [CrossRef]
16.	M. Csele, Fundamentals of Light Sources and Lasers (Wiley-Interscience, 2004), Chaps. 4 and 5.
17.	N. R. Giri, S. B. Rai, and A. Rai, “Intense green and red upconversion emissions from Ho³⁺ in presence of Yb³⁺ in Li:TeO₂ glass,” Spectrochim. Acta [A] 74(5), 1115–1119 (2009). [CrossRef]
18.	O. Svelto, Principles of Lasers (Plenum Publishing Corporation, Springer, 1998), Chap. 12.
19.	M. F. Joubert, B. Jacquier, and R. Moncorgé, “Exciton-exciton annihilation and saturation effect in TbF₃,” Phys. Rev. B 28(7), 3725–3732 (1983). [CrossRef]

OCIS Codes
(140.3610) Lasers and laser optics : Lasers, ultraviolet
(160.2750) Materials : Glass and other amorphous materials
(300.6540) Spectroscopy : Spectroscopy, ultraviolet
(140.3613) Lasers and laser optics : Lasers, upconversion

ToC Category:
Laser Materials

History
Original Manuscript: August 2, 2011
Revised Manuscript: October 14, 2011
Manuscript Accepted: October 15, 2011
Published: October 21, 2011

Citation
S. Hazarika and Reeta Rajbonshi, "Spectral linewidth narrowing and intensity enhancement of the ⁵G₆→⁵I₈ hypersensitive transition in uv-blue up-conversion from Ho³⁺ activated Al(NO₃)₃-SiO₂ sol-gel glass," Opt. Mater. Express 1, 1307-1318 (2011)
http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-1-7-1307

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References

G. Y. Chen, C. H. Yang, B. Aghahadi, H. J. Liang, Y. Liu, L. Li, and Z. G. Zhang, “Ultraviolet-blue upconversion emissions of Ho3+ ions,” J. Opt. Soc. Am. B27(6), 1158–1164 (2010). [CrossRef]
M. Malinowski, M. Kaczkan, S. Stopinski, R. Piramidowicz, and A. Majchrowski, “Short-wavelength luminescence in Ho3+-doped KGd(WO4)2 crystals,” J. Lumin.129(12), 1505–1508 (2009). [CrossRef]
R. S. Quimby, M. G. Drexhage, and M. J. Suscavage, “Efficient frequency up-conversion via energy transfer in fluoride glasses,” Electron. Lett.23(1), 32–34 (1987). [CrossRef]
R. S. Meltzer, “Line broadening mechanisms and their measurement,” in Spectroscopic Properties of Some Rare-Earths in Optical Materials, G. Liu and B. Jacquier, eds. (Tsinghua University Press and Springer Verlag, 2005).
M. Seshadri, Y. C. Ratnakaram, D. Thirupathi Naidu, and K. Venkata Rao, “Investigation of spectroscopic properties (absorption and emission) of Ho3+ doped alkali, mixed alkali and calcium phosphate glasses,” Opt. Mater.32(4), 535–542 (2010). [CrossRef]
S. Hazarika and S. Rai, “Structural, optical and non-linear investigation of Eu3+ ions in sol-gel silicate glass,” Opt. Mater.27(2), 173–179 (2004). [CrossRef]
B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev.127(3), 750–761 (1962). [CrossRef]
G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys.37(3), 511–520 (1962). [CrossRef]
F. Auzel, “Material for ionic solid-state lasers,” in Spectroscopy of Solid-State Laser-Type Material, B. D. Bartolo, ed. (Plenum, 1987), pp. 293.
L. B. Shaw, B. Cole, P. A. Thielen, J. S. Sanghera, and I. D. Aggarwal, “Mid-wave IR and long-wave IR laser potential of rare-earth doped chalcogenide glass fiber,” IEEE J. Quantum Electron.37(9), 1127–1137 (2001). [CrossRef]
B. F. Aull and H. P. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron.18(5), 925–930 (1982). [CrossRef]
F. Qin, Y. Zheng, Y. Yu, Z. Cheng, P. S. Tayebi, W. Cao, and Z. Zhang, “Ultraviolet and violet upconversion luminescence in Ho3+-doped Y2O3 ceramic induced by 532-nm CW laser,” J. Alloy. Comp.509(4), 1115–1118 (2011). [CrossRef]
M. Kowalska, G. Klocek, R. Piramidowicz, and M. Malinowski, “Ultra-violet emission in Ho: ZBLAN fiber,” J. Alloy. Comp.380(1-2), 156–158 (2004). [CrossRef]
W. T. Carnall, P. R. Fields, and K. Rajnak, “Spectral intensities of the trivalent lanthanides and actinides in solution. II. Pm3+, Sm3+, Eu3+, Gd3+, Tb3+, Dy3+, and Ho3+,” J. Chem. Phys.49(10), 4412–4423 (1968). [CrossRef]
M. J. Weber, B. H. Matsinger, V. L. Donlan, and G. T. Surratt, “Optical transition probabilities for trivalent holmium in LaF3 and YAlO3,” J. Chem. Phys.57(1), 562–567 (1972). [CrossRef]
M. Csele, Fundamentals of Light Sources and Lasers (Wiley-Interscience, 2004), Chaps. 4 and 5.
N. R. Giri, S. B. Rai, and A. Rai, “Intense green and red upconversion emissions from Ho3+ in presence of Yb3+ in Li:TeO2 glass,” Spectrochim. Acta [A]74(5), 1115–1119 (2009). [CrossRef]
O. Svelto, Principles of Lasers (Plenum Publishing Corporation, Springer, 1998), Chap. 12.
M. F. Joubert, B. Jacquier, and R. Moncorgé, “Exciton-exciton annihilation and saturation effect in TbF3,” Phys. Rev. B28(7), 3725–3732 (1983). [CrossRef]

Aggarwal, I. D.
Aghahadi, B.
Aull, B. F.
Cao, W.
Carnall, W. T.
Chen, G. Y.
Cheng, Z.
Cole, B.
Donlan, V. L.
Drexhage, M. G.
Fields, P. R.
Giri, N. R.
Hazarika, S.
Jacquier, B.
Jenssen, H. P.
Joubert, M. F.
Judd, B. R.
Kaczkan, M.
Klocek, G.
Kowalska, M.
Li, L.
Liang, H. J.
Liu, Y.
Majchrowski, A.
Malinowski, M.
Matsinger, B. H.
Moncorgé, R.
Ofelt, G. S.
Piramidowicz, R.
Qin, F.
Quimby, R. S.
Rai, A.
Rai, S.
Rai, S. B.
Rajnak, K.
Ratnakaram, Y. C.
Sanghera, J. S.
Seshadri, M.
Shaw, L. B.
Stopinski, S.
Surratt, G. T.
Suscavage, M. J.
Tayebi, P. S.
Thielen, P. A.
Thirupathi Naidu, D.
Venkata Rao, K.
Weber, M. J.
Yang, C. H.
Yu, Y.
Zhang, Z.
Zhang, Z. G.
Zheng, Y.

Electron. Lett.

R. S. Quimby, M. G. Drexhage, and M. J. Suscavage, “Efficient frequency up-conversion via energy transfer in fluoride glasses,” Electron. Lett.23(1), 32–34 (1987). [CrossRef]

IEEE J. Quantum Electron.

L. B. Shaw, B. Cole, P. A. Thielen, J. S. Sanghera, and I. D. Aggarwal, “Mid-wave IR and long-wave IR laser potential of rare-earth doped chalcogenide glass fiber,” IEEE J. Quantum Electron.37(9), 1127–1137 (2001). [CrossRef]
B. F. Aull and H. P. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron.18(5), 925–930 (1982). [CrossRef]

J. Alloy. Comp.

F. Qin, Y. Zheng, Y. Yu, Z. Cheng, P. S. Tayebi, W. Cao, and Z. Zhang, “Ultraviolet and violet upconversion luminescence in Ho3+-doped Y2O3 ceramic induced by 532-nm CW laser,” J. Alloy. Comp.509(4), 1115–1118 (2011). [CrossRef]
M. Kowalska, G. Klocek, R. Piramidowicz, and M. Malinowski, “Ultra-violet emission in Ho: ZBLAN fiber,” J. Alloy. Comp.380(1-2), 156–158 (2004). [CrossRef]

J. Chem. Phys.

W. T. Carnall, P. R. Fields, and K. Rajnak, “Spectral intensities of the trivalent lanthanides and actinides in solution. II. Pm3+, Sm3+, Eu3+, Gd3+, Tb3+, Dy3+, and Ho3+,” J. Chem. Phys.49(10), 4412–4423 (1968). [CrossRef]
M. J. Weber, B. H. Matsinger, V. L. Donlan, and G. T. Surratt, “Optical transition probabilities for trivalent holmium in LaF3 and YAlO3,” J. Chem. Phys.57(1), 562–567 (1972). [CrossRef]
G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys.37(3), 511–520 (1962). [CrossRef]

J. Lumin.

M. Malinowski, M. Kaczkan, S. Stopinski, R. Piramidowicz, and A. Majchrowski, “Short-wavelength luminescence in Ho3+-doped KGd(WO4)2 crystals,” J. Lumin.129(12), 1505–1508 (2009). [CrossRef]

J. Opt. Soc. Am. B

G. Y. Chen, C. H. Yang, B. Aghahadi, H. J. Liang, Y. Liu, L. Li, and Z. G. Zhang, “Ultraviolet-blue upconversion emissions of Ho3+ ions,” J. Opt. Soc. Am. B27(6), 1158–1164 (2010). [CrossRef]

Opt. Mater.

M. Seshadri, Y. C. Ratnakaram, D. Thirupathi Naidu, and K. Venkata Rao, “Investigation of spectroscopic properties (absorption and emission) of Ho3+ doped alkali, mixed alkali and calcium phosphate glasses,” Opt. Mater.32(4), 535–542 (2010). [CrossRef]
S. Hazarika and S. Rai, “Structural, optical and non-linear investigation of Eu3+ ions in sol-gel silicate glass,” Opt. Mater.27(2), 173–179 (2004). [CrossRef]

Phys. Rev.

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev.127(3), 750–761 (1962). [CrossRef]

Phys. Rev. B

M. F. Joubert, B. Jacquier, and R. Moncorgé, “Exciton-exciton annihilation and saturation effect in TbF3,” Phys. Rev. B28(7), 3725–3732 (1983). [CrossRef]

Spectrochim. Acta [A]

N. R. Giri, S. B. Rai, and A. Rai, “Intense green and red upconversion emissions from Ho3+ in presence of Yb3+ in Li:TeO2 glass,” Spectrochim. Acta [A]74(5), 1115–1119 (2009). [CrossRef]

Other

O. Svelto, Principles of Lasers (Plenum Publishing Corporation, Springer, 1998), Chap. 12.
M. Csele, Fundamentals of Light Sources and Lasers (Wiley-Interscience, 2004), Chaps. 4 and 5.
F. Auzel, “Material for ionic solid-state lasers,” in Spectroscopy of Solid-State Laser-Type Material, B. D. Bartolo, ed. (Plenum, 1987), pp. 293.
R. S. Meltzer, “Line broadening mechanisms and their measurement,” in Spectroscopic Properties of Some Rare-Earths in Optical Materials, G. Liu and B. Jacquier, eds. (Tsinghua University Press and Springer Verlag, 2005).

2011, Qin, J. Alloy. Comp.
2010, Seshadri, Opt. Mater.
2010, Chen, J. Opt. Soc. Am. B
2009, Malinowski, J. Lumin.
2009, Giri, Spectrochim. Acta [A]
2004, Kowalska, J. Alloy. Comp.
2004, Hazarika, Opt. Mater.
2001, Shaw, IEEE J. Quantum Electron.
1987, Quimby, Electron. Lett.
1983, Joubert, Phys. Rev. B
1982, Aull, IEEE J. Quantum Electron.
1972, Weber, J. Chem. Phys.
1968, Carnall, J. Chem. Phys.
1962, Judd, Phys. Rev.
1962, Ofelt, J. Chem. Phys.

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