3.1. Branching ratios
The rare-earth ions with electron configuration 4f q show a very characteristic spectroscopy due to the fact that the 4f shell is well shielded from the surround- ings. This is also more or less true for the transthorium ions (5fq). These electronic configurations yield optical properties which cannot be observed for other metal ions. These, in turn, lead to many important applications, for lasers, cathode-ray tubes, luminescent lamps and X-ray imaging.
If we consider the optical spectrum of a rare-earth ion, either in absorption or in emission, we are immediately struck by a large number of sharp lines. Their position seems to be independent of the surroundings. Their intensity ratios vary strongly, indicating certain selection rules, which are reflected by the branching ratio defined as the ratio of a specific radiative transition from a given level divided by the sum of all the radiative transitions from this level. The branching ratio is defined as/3q = Aq/Z A~k (the ratio between the transition probability Aq and the sum over all the probabilities Aik of transitions to lower states, including Aq).
When t w o emitting levels are close enough (the separation being about 200cm -a or less) a thermalization takes place and the branching ratio has the following form
~i gi e x p ( - A E i / k T ) A q
~q = E i Ej gi e x p ( - A E i / k T ) A q " (9)
3.2. Glass lasers and rare-earth-based luminescent solar concentrators
Research on neodymium lasers increased rapidly in the 1970's because of the requirement of large neodymium glass lasers for fusion research. Laser-driven fusion is one approach to a long-term solution of the world's energy supply problems as it is based on the inexhaustible fuel deuterium, which is obtained from water. The unique capability of lasers to produce a very high instantaneous power density over a very small area introduces the possibility of driving thermonuclear fuel to extremely high temperatures and densities at which fusion is expected to occur (Weber, 1976; Reisfeld and JCrgensen, 1977; Brown, 1981).
The demonstration of the scientific feasibility of the initiation of a fusion burn
E X C I T E D S T A T E P H E N O M E N A IN V I T R E O U S M A T E R I A L S 35
with the energy produced from the pellet exceeding the absorbed beam energy can be attempted with laser energies of the order of 0.33 to 0.5 MJ and lifetimes of a few nanoseconds. Such a laser, the NOVA neodymium glass laser, is now operating in the Lawrence Livermore National Laboratory.
Neodymium-doped yttrium aluminum garnet lasers have found extensive appli- cations as range finders and have also become standard laboratory equipment for research in photochemistry and related fields.
High-efficiency laser emission has also been observed from yttrium lithium fluoride doped with Er(III) (Chicklis et al., 1972), Tm(III) (Jenssen et al., 1975), Ho(III) (Karayanis et al., 1976; Barnes et al., 1979), and Nd(III) (Knights et al., 1982).
All glass lasers developed to date have used a rare earth as the active ion and optical pumping for excitation (Stokowski, 1982). Of these, flash-lamp-pumped neodymium glass lasers are the most frequently used and the most widely investigated. The spectroscopic data needed for estimation of the laser charac- teristics are usually obtained from small samples (Reisfeld and J0rgensen, 1977).
The data include absorption, emission, nonradiative relaxation, energy transfer probabilities and laser cross sections. Laser operation predictions can be made from such data without actually demonstrating laser action.
Stimulated emission cross sections of neodymium vary with glass composition.
We have previously shown that the amount of covalency between the glass- forming medium and the neodymium ion increases significantly with the emission cross section (Reisfeld, 1982). This fact is demonstrated by the very high cross section of Nd(III) in chalcogenide glasses. The decision about the type of glass laser to be used for a specific application depends on the emission wavelength, pulse duration, signal output and optical configuration requirements.
Additional work is still needed to establish the relative merits of various glasses for lasers. This work includes investigation of spectral inhomogeneities and their effects on large-signal energy extraction, laser-induced damage threshold as a function of wavelength and pulse duration for a wider range of glass compositions (Weber, 1982).
3.2.1. Luminescent solar concentrators
The world's conventional energy supplies, which are based mainly on readily available fossil fuel sources, are diminishing rapidly. The main approach to the energy crisis - nuclear fusion - is raising a great deal of hope but its practicability has still to be demonstrated. There is no doubt that solar energy, which is clear and nonhazardous, could contribute considerably to a solution of the energy problem if appropriate methods were developed to collect, concentrate, store and convert solar radiation, which is diffuse and intrinsically intermittent (Reisfeld and J0rgensen, 1982). Owing to the original efforts of the National Aeronautics and Space Administration to supply electric current from silicon photovoltaic (PV) cells to space vehicles, such devices are now available at a cost of about $8
36 R. REISFELD and C.K. JORGENSEN
per watt of power. At present, large-scale solar cell arrays are operating in inaccessible locations distant from conventional electricity plants. Previous price estimates (predicting a decrease in cost to $1 to $2 per watt in 1984), which were obtained by making comparisons with the aluminum or electronic computer industries, were slightly optimistic, as the difficulties of preparing inexpensive silicon with a high photoelectric yield cannot easily be removed by increased production. One way of lowering the price of PV electricity is to concentrate the solar radiation, particularly the part that is most efficient in PV e n e r g y conver- sion. It is hoped that this can be achieved with luminescent solar concentrators (LSC) (Reisfeld and JCrgensen, 1982).
The operation of an LSC is based on. the absorption of solar radiation in a collector containing a fluorescent species in which the emission bands have little or no overlap with the absorption bands. The fluorescence emission is trapped by total internal reflection and concentrated at the edges of the collector, which is usually a thin plate (Reisfeld and JCrgensen, 1982). LSCs have the following advantages over conventional solar concentrators: (a) they collect both direct and diffuse light; (b) there is good heat dissipation of nonutilized energy by the large area of the collector plate in contact with air, so that essentially "cold light"
reaches the PV cells; (c) tracking the sun is unnecessary; and (d) the luminescent species can be chosen to allow matching of the concentrated light to the maximum sensitivity of the PV cell.
3.2.2. Requirements for glass lasers and luminescent solar concentrators:
similarities and differences
The requirements for a glass laser are (cf. fig. 2) (a) high absorption of the exciting light,
(b) population inversion of the emitting level, (c) high quantum efficiency of light emission, (d) high cross section of stimulated laser emission, (e) nonradiative quick relaxation of the lower laser level.
The requirements of LSCs are
(a) large absorption in a broad spectral range, (b) high population of the emitting level, (c) high quantum efficiency of light emission, (d) high intensity of emitted light,
(e) Stokes shift between the emitted and absorbed light.
As can be seen, the requirements for both devices are quite similar; however, they are more stringent for lasers than for LSCs. An additional need is that the materials will be stable towards corrosion by light, heat, and humidity.
3.2.3. Basic parameters of a laser
The basic parameters of the solid-state laser operation are the following:
(a) The threshold of laser action is defined as the minimum input power or energy needed to start the laser action.
EXCITED STATE PHENOMENA IN VITREOUS MATERIALS 37 Similarities
L A S E R ( f o u r - l e v e l ) stronc
non - r(
relaxa emittir
popul~
inversi (more state E
cond sine if fea~
high q
between conditions for L S C
(luminescent solar concentrator) absorption of t photons :leally a major
of the visible)
#ive relaxation nitting level
J sion useful
high rum
3rational
~ntinuum levels) rapid r
l oundstate
popula ,nto t i t
is favo ~te broad
small . . . e emission
factor : light because of with a
I/exp {(EI-Eo)/kT } self-absorption Stakes shift if (EI-E O) is several and of repeated favorable for
LSC based on times kT at operating /emission resonant internal total
temperature reflection
similar to 3-level laser
Fig. 2. Comparison between (desirable or indispensable) conditions for four- level lasers and luminescent solar con- centrators (LSC).
(b) The output Fower of the laser, Pout, for a given peak power pumping [for a pulsed laser, Pout is given in joules per pulse, for a continuous operation (CW) in watts].
(c) The spectral distribution of the emitted radiation is defined by a central wavelength A 0 or frequency v o and linewidth dA (or d r ) of the emission.
(d) The spatial distribution of energy in the laser beam, both in position and in direction (the latter is usually specified by a mean angular divergence).
The R laser consists of a resonant cavity, containing the amplifying medium, the excited rare-earth ions incorporated in crystals, glasses, or liquids. The laser medium (tube or rod) is placed between two parallel mirrors, having reflection coefficients R~ and R 2. The mirrors may be placed separately or evaporated directly on the ends of the rod.
Oscillations may be sustained in the laser if the amplification of the radiation through the active material is sufficient to compensate for the fraction of energy lost due to all causes. In other words, in order for a fluorescent material to exhibit laser operation, the round-trip optical gain resulting from the optical pumping,
38 R. REISFELD and C.K. J O R G E N S E N
must exceed round-trip losses within the cavity. In each passage through the laser the intensity of the radiation is increased by a factor e eL by virtue of the amplification in the material, where L is the length between the mirrors and/3 the amplification coefficient, expressed as
/3(v) = k(~o) A N , (10)
where k(v0) is the absorption coefficient at maximum wave number v, and AN is the population inversion.
The threshold of laser oscillation is attained when the peak value /3 of the amplification curve satisfies the equation
/3L > 3,, (11)
w h e r e 7 is the loss factor after single passage. Equation (11) is the simplest formulation of the threshold condition.
Thus, a laser of a given length and mirror reflectivity will operate only if the population inversion is large enough to ensure the amplification per unit length satisfying the equation
Y (12)
fi = A N k ( v ) o > i - ~ .
This equation combines the requirements for the qualities of the resonator design (L and 7) and the amplifying medium which is related to the population inversion AN and the radiative transition probabilities reflected in the absorption coefficient k(v)0.
We shall summarize briefly the parameters for the laser design, which are extensively discussed elsewhere (Lengyel, 1971). The laser medium spontaneous- ly emits light into an extremely large number of oscillator modes. The usual optical resonators (Yariv, 1975) provide appreciable feedback for only a limited number of modes, which are the resonator modes (Kogelnik, 1966). From this concentration of radiation in the small number of modes arises the coherence of laser light.
An important parameter of a resonator mode is its decay time re. This is the time at which the nonequilibrium energy AE decays to 1/e of its initial value, AE--~ e x p ( - t / Q ) . The value of t e is related to the fractional round-trip loss of the mode and the round-trip optical length L of the resonator by
t e-- - - - l n ( 1 - 7 ) , L ¢ (13)
where c is the velocity of light. Usually Y ~ 1 and the equation may be
EXCITED STATE PHENOMENA IN VITREOUS MATERIALS 39 approximated by
t e = L / c y (14)
The decay time and the quality factor Q of the cavity are related by
Q = 27r~,12t e , (15)
where Q is the loss rate of the system and depends on the macroscopic properties of the cavity. Any disturbance that decreases Q increases y and increases AN, the population inversion at which the oscillation begins.
From equations (10) and (11) it is evident that the material parameter for the laser condition at a given population inversion is explicitly contained in the k(uo) which is related to the stimulated cross section of emission. This is true both for 3- and 4-level laser systems.
3.2.4. Rare-earth doped laser glasses
Trivalent rare-earth ions present a unique instance for which a priori calcula- tions can be made from a small number of parameters, which are calculated theoretically and/or derived from simple experiments on small samples. Such predictions are of value in devising materials based on transparent media doped by rare-earth ions. The cross sections and performance of glass lasers can be predicted with quite good accuracy based on such calculations (Reisfeld and JOrgensen, 1977; Reisfeld, 1984a,b).
The main difference between optical spectra of inorganic ions in amorphous materials and crystalline media of comparable composition is the inhomogeneous broadening due to the variety of sites in the former (Riseberg, 1973; Weber, 1981). This is due to the fact that the dopant ions in glasses reside in a variety of environments and experience different perturbing local fields. Thus, instead of identical electronic energy levels, there is a distribution of spectroscopic parame- ters which depend on the host glass composition and result in different and nonradiative transition probabilities. These variations are evident in absorption and fluorescence spectra as inhomogeneously broadened lines when conventional light sources are used. The decay times of fluorescence from excited states of different sites normally exhibit a nonexponential behavior. However, if fast diffusion of excitation energy occurs among 'the different sites, then the decay will become exponential with the fastest time constant available among the sites.
Laser-induced-fluorescence line-narrowing (FLN) enables, in some cases, the excitation of a subset of ions having the same energies. In the absence of accidental coincidence of electronic levels, a tunable pulsed laser can be used for determining the electronic levels and transition probabilities of a selected subset of the total ensemble of sites. The intraconfigurational 4f-4f transitions of rare-earth ions are especially suitable in this type of investigation because of small
40 R. REISFELD and C.K. JORGENSEN
electron-phonon coupling. The degree of selectivity of the FLN technique depends on the ratio of homogeneous to inhomogeneous widths (Weber et al.
1976; Brawer and Weber, 1981a,b), which is of the order of 10 -3 for rare earths at low temperatures. Figure 1 of DurviUe et ai, (1983) provides an example of FLN on Eu(III) in phospho-tungstate glasses at 4 K, the excitation being performed into the 5D 0 level of the different sites. The three-line 5D0----~TF 1 emission is shown as a function of excitation frequency of the 7F0----~SD 0 transition and corresponds to the different sites.
Modelling the atomic arrangement in glass is often done using molecular dynamics. In this technique the position of the ions is calculated by numerical integration of Newton's equations of motion using a model interatomic potential function. This method has been applied so far to SiO2, B203, BeF2, ZnC12, KC1, and multicomponent sodium silicate, sodium borosilicate, and fluoroberyllate glasses (Weber, 1982). While the method is very elegant and promising, its validity is still being tested by comparison with experimentally measured physical properties such as thermodynamic and transport characteristics.
The previously discussed radiative transition probabilities and line strengths are connected to the peak-stimulated emission cross sections of the rare-earth ion in a glass by
8,Tr3e 2 ( n 2 + 2) 2 )tp
O'p - 3hc(2J + 1) n m/~eff S(J, J ' ) , (16)
where n is the refractive index, Ap is the wavelength of the emission peak, and AAe~ e is the effective linewidth of the emission between states of J and J'.
3.3. Luminescence efficiency and competing processes
Luminescence is the emission of light in the ultraviolet, visible, and infrared part of the spectrum as a result of excitation of the system in excess of thermal equilibrium. In condensed matter, luminescence of an excited electronic state is the exception rather than the rule, especially at room temperature and above.
Luminescent emission can be excited by light (photoluminescence), by cathode rays, electric field (electroluminescence), and high temperature (candolumin- escence).
In glass, rare-earth luminescence has in general higher quantum efficiencies than the luminescence of the 3d and 4d ions. This is due to the fact that the 4f orbitals are rather isolated from the surrounding medium. The luminescence quantum efficiency is defined as the number of photons emitted divided by the number of photons absorbed, and in most cases is equal to the ratio of the measured lifetime to the radiative lifetime of a given level.
The processes competing with luminescence are radiative transfer to another ion and nonradiative transfers such as multiphonon relaxation and energy transfer
E X C I T E D S T A T E P H E N O M E N A IN V I T R E O U S M A T E R I A L S 41
between different ions or ions of a similar nature. The last transfer is also named cross-relaxation.
The radiative transfer consists of absorption of the emitted light from a donor molecule or ion by the acceptor species. In order that such transfer takes place, the emission of the donor has to coincide with the absorption of the acceptor. The radiative transfer can be increased considerably by designing a proper geometry.
Such transfers may be important in increasing pumping efficiencies of glass lasers (Reisfeld, 1985a) and luminescent solar concentrators, whereby energy emitted from organic molecules can be absorbed by ions such as Cr(III), Mn(II), or Nd(III), followed by characteristic emission from these ions.