Two-Step Excitation and Blue Fluorescence Under Continuous-Wave Pumping in Nd:YLF

T. Y. Fan and R. L. Byer Vol. 3, No. 11/November 1986/J. Opt. Soc. Am. B 1519

Two-step excitation and blue fluorescence under continuous-wave pumping in Nd:YLF

T. Y. Fan and Robert L. Byer Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305

Received April 18, 1986; accepted July 24, 1986 4 4 Near-UV and blue fluorescence from the D3/2 and D5/2 manifolds in Nd:YLF has been observed at room temperature under cw pumping by a Rhodamine 590 dye laser. Excitation to these manifolds is attributed to two-step excitation involving excited-state absorption from the 4F3/2 metastable level. A similar phenomenon has also been observed in Nd:YAG and Nd:glass. The effective excited-state absorption cross section 2 is measured to be (2 1) X 10-20 cm at 587.4nm in the ir polarization, and the peak effective stimulated emission cross section 2 is measured to be 5 X 10-20 cm at 411.7nm, also in the r polarization. Estimated laser threshold at 411.7nm for two-step pumping at 587.4 nm is 70 mW.

INTRODUCTION level lifetimes. In the case of Nd:YAG, the pump wavelength is different from that in this paper, and consequently There are a number of processes besides fluorescence and the energy levels in two-step excitation are also different. one-photon absorption that can occur in rare-earth-ion- and In the case of LaF , ETU is the dominant process, but two- transition-metal-ion-doped solids. Two-step excitation 3 step excitation is noted at temperatures approaching that of and energy transfer are examples of processes that can be liquid helium. Upconverted blue fluorescence has also been important in laser operation. For example, concentration noted in some fluoride crystals.7 In Nd:YLF, two-step exci- quenching in Nd3+-doped laser materials is an energy trans- tation and subsequent blue fluorescence have been used as a fer phenomenon that reduces the lifetime of the 4F / upper 3 2 technique to investigate Nd3+ ion pairs in YLF at low tem- laser level. Energy transfer upconversion (ETU) and two- peratures (<40 K),8 and the blue fluorescence has been ob- step excitation have also been used to create visible sources, served under ruby-laser pulsed pumping by a two-photon both incoherent and coherent, from infrared pump pho- 9 1 process. In this paper, blue and UV fluorescence is investi- tons. ,2 In two-step excitation, a single photon is absorbed gated, and the excitation mechanism is determined. followed by relaxation to an excited metastable energy level. This is followed by absorption of a second photon from the excited state, excited-state absorption (ESA), to an even EXPERIMENTAL APPARATUS higher lying level. This is followed by relaxation, either Nd:YLF is a uniaxial solid-state laser material. Its one- radiative or nonradiative. In ETU, two nearby ions in excit- photon absorption spectra, infrared fluorescence spectra, ed states interact simultaneously, causing one of the pair to and concentration quenching were previously character- be excited to an even higher-lying level and causing the other ized.'( From previously published data, the dopant concen- to relax. Both of these processes are interesting techniques tration was 2 at. % Nd given the measured fluorescence 4 0 for obtaining higher-energy photons from lower-energy lifetime of 440 Asec for F3/2 manifold in our sample.' How- pump photons because of their large effective nonlineari- ever, more recent measurements of concentration indicate ties.' that the r-polarized absorption line at 872.1 nm has an We have recently noted two-step excitation as well as absorption coefficient of 1.2 cm-' for 1 at. % Nd doping." ETU in Nd:LiYF4 (YLF).3 This paper will discuss two-step By this standard, the concentration of our sample is 1.7 at. % excitation that induces near-UV and blue emission under cw Nd. resonant pumping. These processes were discovered while The experimental apparatus used to record the emission Nd:YLF cw resonantly-pumped miniature lasers were being and excitation spectra consisted of an argon-ion-laser- 4 investigated. Two-step excitation and ETU have been pre- pumped cw Rhodamine 590dye laser for excitation, a lens to dominantly studied in rare-earth ions such as Er3+, which focus the pump beam into the sample, a 31034photomulti- have long (>1-msec) metastable level lifetimes, but similar plier tube for detection, a Chromatix CT-103 1-m monochro- processes have also been noted in Nd3+-doped materials. mator with a 1800-line/mm grating for wavelength selectiv- For example, blue and near-UV emission has been observed ity, and a lock-in amplifier for signal extraction. The dye- by two-step excitation in Nd3+-doped compounds such as laser beam was typically chopped at -30 Hz with '30% duty Nd:YAG (Ref. 5) and Nd:LaF 3 (Ref. 6) under pulsed excita- cycle. A calcite polarizer was used to select the polarization tion. However, in pulsed excitation the dynamics of the for the various measurements. The subsequent signal from processes can be quite different from the cw regime because the lock-in amplifier was digitized and stored in a computer. peak pump powers can be higher and pulse times can be The spectral response of the detection system was normal- much shorter than characteristic times such as metastable ized by using a quartz-halogen lamp.12 A Perkin-Elmer 330

spectrophotometer was used for measuring absorption spec- where v is the transition energy in inverse centimeters, n is tra. All measurements were performed at room tempera- the refractive index, Q,\'sare the experimentally determined ture. intensity parameters for the given ion in the given host, and the (fN(aSL)JII U()fN(a'S'L')J') are reduced matrix ele- 6 BLUE AND NEAR-UV FLUORESCENCE ments. Using the reduced matrix elements,' the Oxparam- eters for Nd:YLF,"7 and the assumption that the relative The 4 4 normalized fluorescence spectra for both r(E ||c) and populations of D3/2 and D5/2 are given by a Boltzmann a(E c) polarizations are shown in Fig. 1. There are four distribution, the calculated radiative transition rates and regions in which emission is observed that are near 358 nm, branching ratios to the 4I term are shown in Table 1; emis- 383 nm, 412 nm, and 450 nm, which correspond to transi- sion to other manifolds was ignored since none was observed. 4 tions from D3/2and 4D5/2 manifolds to 4I9/2, 4I11/2, 4I13/2, and While the Judd-Ofelt theory is correct in predicting strong 4I15/2, 9 3 4 4 respectively, based on energy-level positions. "1 The emission from D3/2 and D / , the branching ratios among 4 4 5 2 D3/2 and D5/2 manifolds should be thermally coupled at the 4I term are not accurate. The Judd-Ofelt theory also 4 room temperature. In other words, the relative populations predicts strong emission to F 5/2; however, this emission was are given by 4 a Boltzmann distribution. There is a signifi- not observed. In the case of emission from F3/2, the Judd- cant discrepancy of approximately 40 cm-' between the ob- Ofelt theory is more accurate in predicting branching ratios. served energy-level positions in Refs. 9 and 13 for these two This is most likely because one of the two fundamental manifolds; our data are more consistent with those in Ref. 9. The branching ratio flij from the upper manifold i to a I I I II I I lower manifold j is given by Nd:YLF POLARIZED FLUORESCENCE

7r A,. E f XIP(X)dX fi = A _ P (1) I-. z E Aik E E | >,ikP(X)d X k p k zF where Aik is the transition rate from the upper manifold i to a > lower manifold k, and the sum on k is over all lower mani- ;a 011I~~~0~-- folds. Note that the sum in the denominator is equal to 1-r, _ _ - _ _~~~~~~~0,__ I -J- where Tris the radiative lifetime. The second part of Eq. (1) w a: gives fij in terms of the polarized emission spectra, where IikP(X) is the polarized emission intensity per unit wavelength interval as a function of wavelength Xfrom manifold i to manifold k, and the sum over p is over polarization. The S. 4 4 results for fluorescence from the D3/2 + D5/2 manifolds are shown in Table 1, where emission to states other than the 4 Ij 350 360 -37 380 390 400 manifolds has been ignored since no emission was observed WAVELENGTH (nm) experimentally. Electric dipole transitions were assumed so (a) the axial spectrum is identical to that for the r polarization. In this case the sum over polarization becomes 2I(X) + IP(X). One difficulty with this measurement is that the emission to the ground-state manifold, 4I9/2, can be reab- sorbed, causing the measured branching ratio to that manifold to be too small. To minimize this problem, the sample C', was pumped near its surface. The radiative transition rates Aij, and therefore the branching ratios, can be calculated from the Judd-Ofelt theory.'4 "l5 The radiative transition rate for electric dipole transitions from a state fN(aSL)J) to state fN(IS'LS)J/), 2 2 -J which denote manifolds S+lLj and S+lLj,', is given by w a:

A = [647r4e2] V3 (2J + 1)-'

X , (2a) X=2,4,6 410 420 430 440 450 460 WAVELENGTH (nm) where (b) Fig. 1. Polarized = n(n + 2)2 emission spectrum of Nd:YLF under pumping at 9 (2b) 587.4 nm. (a) Emission from 350 to 405 nm. (b) Emission from 405 to 460 nm. T. Y. Fan and R. L. Byer Vol. 3, No. 11/November 1986/J. Opt. Soc. Am. B 1521

Table 1. Experimentally Determined and Calculated SEQUENTIAL TWO-PHOTON EXCITATION Branching Ratios The blue fluorescence was first observed when a cw Rhoda- Measured Branching Judd-Ofelt Theory mine 590 dye laser operating near 590 nm was used to pump Lower Manifold Ratio Branching Ratio a Nd:YLF laser operating at 1.047 Am. This fluorescence 4I9/2 0.17 0.37 decreased substantially when the Nd:YLF laser was aligned, 411/2 0.24 0.46 demonstrating that the process is dependent on the popula- 4I13/2 0.40 0.15 tion of the 4F3/2 manifold. This indicates that real one- 4IJs/2 0.19 0.02 photon transitions must be occurring, as opposed to virtual transitions as in two-photon absorption where intermediate states are not populated. Figure 2 shows the square root of approximations in the theory is worse for emission from 4D3 / the blue fluorescence intensity versus the pump intensity. 2 and "D5/2 than for emission from 4F3/2. This can be ex- The linear relation shows that this process involves two plained by the following. Electric dipole transitions are not photons. The 4D3/2 + 4D5/2 to 4I13/2emission at 412 nm is allowed for 4f-4f transitions in a free ion because all 4fN monitored as the pump intensity at 587.4 nm is varied. At configurations have the same parity. However, by placing low pump intensities (of the order of 10 W/cm2, correspond- the ion in a site with no inversion symmetry, opposite parity ing to -0.7 on Fig. 2), a square-law dependence of the blue terms are admixed into the 4 fN configuration. These are fluorescence is observed; at higher pump intensities, satura- typically 4fN-15d configurations, which usually have higher tion effects can begin to be observed. energies than the 4N configurations. One of the fundamen- As previously mentioned, blue fluorescence has been ob- tal approximations used in deriving the Judd-Ofelt theory is served in Nd:LaF 3 under pulsed pumping in the same wave- that the energy difference between the initial manifold, length region. This was attributed to both two-step excita- 2 S+lLj, and 4fN-15d configurations and the energy difference tion and ETU, with ETU being the dominant process.6 2 between final manifold, S'+lLj,', and the 4fN-15d configura- ETU in Nd:LaF 3 involves one excited ion in the 4F3/2 mani- 2 tions are equal. That is, E( S+lLj) - E(4fN-15d) and fold interacting with another excited ion in the 4G / + 2G /2 2 5 2 7 E( S'+lLj,') - E(4fN-15d) are taken to be equal, where manifold, which leads to relaxation of the first to the 4I9/2 E( 2S+lLj) and E(2S'+lLj,') are the energies of the initial and ground manifold and simultaneous excitation of the second 2 final states, respectively, of the transition, and E(4fN-15d) is to the 211/2 + 4D1/2 + 4D5/2 + 4D3/2 + L15/2 manifolds. It is the energy of the 4fN-15d configurations. This approxima- unlikely that this ETU contributes significantly to excita- 2 tion is much worse for the 4D - 4Ij transitions than for the tion in Nd:YLF in the cw regime because the 4G5/2 + G7/2 4F3 /2- 4Ij transitions since the former are more energetic. population should be low owing to fast multiphonon relax- The fluorescence lifetime of the 4D3/2 + 4D5/2 manifolds ation from this manifold as opposed to the pulsed pumped was measured by chopping the Rhodamine 590 pump beam regime where these manifolds can have significant popula- and monitoring the fluorescence around 412 nm. The ob- tion. served lifetime was 23 J 2 sec. The radiative quantum Two-step excitation and ETU have different excitation efficiency 1 is given by wavelength and time dependences. We have used excitation spectra to demonstrate that two-step excitation is the 1/Tr predominant effect. The Rhodamine 590 dye-laser wave- 11T+ /Tnr (3a) length was tuned and the induced fluorescence monitored. where The transition rate for ETU assuming dipole-dipole interac- tion is given by + 1 (3b) Tf Tr Tnr

Tf, Tr, and Tnr are the fluorescence, radiative, and nonradiative lifetimes, respectively. From the measured fluorescence lifetime, the multiphonon relaxation rate, and radia- -a 0.8 tive transition rate calculated from the Judd-Ofelt theory, C: can be estimated. 02) The multiphoton relaxation rate is given a, 0.6 by a) . 4_ -= B exp(-KAE), (4) X 0.4 Tnr where B and K are characteristic of the host material. E is 0.2 the energy gap from the initial state to the next lower-lying state. For the 1750-cm-' energy gap from 4D3/2 to the next 2 0.0 W'- lowest level, P / , 3 2 the multiphonon relaxation rate in YLF 0.0 0.2 0.4 0.6 0.8 1.0 (Ref. 18) is 3.2 X 104 sec-1. From Eq. (3b) the radiative Relative pump intensity lifetime is 90 sec compared with the radiative lifetime cal- Fig. 2. 4D / + 4D,5/2 culated from the Judd-Ofelt theory of 50 sec. These corre- 3 2 - 4I13/2 emission as a function of the pump power at 587.4 nm. The peak pump intensity and emission have spond to radiative quantum efficiencies of 30 and 50%, re- been normalized to 1. The line is a least-squares fit to the lowest spectively. five data points. 1522 J. Opt. Soc. Am. B/Vol. 3, No. 11/November 1986 T. Y. Fan and R. L. Byer

as well as the one-photon absorption spectra. To avoid difficulties with normalization, the pump power was kept 4 .7 constant for each data point. Clearly, the excitation spectra E do not followthe square of the one-photon absorption spectra and, in fact, some of the peaks in the one-photon absorp- z tion spectra do not appear in the excitation spectra. This 3, indicates that two-step excitation is the predominant effect. UL Based on the wavelengths of peak excitation and energy- 4 0 level positions, the ESA transition is F3 /2 -D 5 /2. The two- 2z step excitation process and subsequent fluorescence are ° summarized in Fig. 4. I- The ESA cross sections were also measured at the wave- | length of peak excitation in each polarization. The Rhoda- 2 mine 590 dye laser was tuned to the peak of the excitation, and the beam was focused into the sample with known power and Gaussian beam waist. This causes a certain level of 580 590 600 fluorescence in the sample. Then a He-Cd laser at 325 nm WAVELENGTH (nm) was aligned collinearly with the dye-laser beam. The (a) amount of absorbed power at 325 nm in the sample was measured, and the level of fluorescence was noted. This permits a calibration of the measured level of fluorescence to 4 a pump rate into the 4 Dj states. Then the ESA cross section can be derived from the following. The pump rate as a function of effective ESA cross sec- H tion, esa can be calculated by using a simple rate-equation W approach. The ESA excitation rate, Wesa, is given by

0 Wesa(r,z) = cesaN(r, z)I(r, z) (6) 280 hvp 0 where hvp is the pump photon energy, N(r, z) is the excited- a- state population density of 4F3/2, and I(r, z) is the pump 0

Energy (cm 1x 10-)

0 A6 580 590 600 28 WAVELENGTH (nm) (b)

Fig. 3. Polarized excitation spectra for 4D3/2 + 4D5 /2 - 4I13/2emis- sion of Nd:YLF and one-photon absorption spectra. (a) r polariza- 24 tion, (b) a polarization. 20 WETU NN2' (5)

where N1 and N2 are the population densities of the initial excited energy levels involved in the process. This implies 16 that WETUis proportional to the square of the one-photon absorption coefficient as a function of wavelength. This is because the initial populations are excited by one-photon 12 absorptions from a single monochromatic source and there- 3/2 fore both N1 and N2 are proportional to the one-photon absorption coefficient. On the other hand, in two-step exci- 8 tation, two transitions, the one-photon absorption and ESA transition, must occur at the same wavelength for excitation H tt I - - 115/2 | to occur. Consequently, peaks in the one-photon absorption spectrum may not appear in the excitation spectrum if 4 11 4 there is no or little ESA at the same wavelength. The exci- - - -~~~~~~~91/2 tation spectra were obtained by using the same experimental apparatus as that used for the fluorescence spectra, except that the Rhodamine 590 dye-laser wavelength was tuned Fig. 4. Energy levels in two-step excitation and subsequent fluo- 4 4 rescence. The pump photons are denoted by hvp, and emission and the induced fluorescence on the D + D / - 4I13/2 was 3 12 5 2 from D3 /2 and 4D5/2 by the heavy arrows. The dashed arrow indi- monitored. Figure 3 shows the polarized excitation spectra cates nonradiative decay. T. Y. Fan and R. L. Byer Vol. 3, No. 11/November 1986/J. Opt. Soc. Am. B 1523

intensity. The excited-state population N(r, z) in steady the fluorescence spectra. The effective stimulated emission state can be found from the equation cross section, ae, for a uniaxial medium is given by'9 20 dN(r, z) 0 = yI(r, z) N(r, z) 3X2 5 dt hpp T7 eP(X) = - IPc(X)cI (Ila) 87rn CTrIN (7) where p denotes polarization, c is the speed of light, and IN is where y is the one-photon absorption coefficient at the given by pump frequency and -r1 is the fluorescence lifetime of the F3/2 manifold. The assumption of no depletion of the ground IN = E |q(X)dX, (lib) state, N(r, z) <

hv< .(8) in each polarization for transitions hvp Ti to each of the 4Ij manifolds is shown in Table 2. Under these assumptions and with the pump being a Gauss- It is difficult to assess the error in this calculation, but this ian beam with negligiblediffraction in the sample, the pump cross section is generally difficult to measure accurately. beam intensity is given by The largest error term is probably Tr, which was derived from the measured fluorescence lifetime and the multiphonon I(r, z)= 7rwp22 \ -WP2Jexp-z), (9) relaxation rate in YLF. This multiphonon relaxation rate could be in error by up to a factor of 2, which would lead to a where P is the incident pump power and wp is the beam large change in Tr. One way to determine the accuracy of the radius. Substituting Eq. (9) into Eq. (7), solving for N(r, z), cross section is to compare the absorption cross section with and integrating Wesa(r,z) over the volume, the total pump the emission cross section. This can be done for the line at rate, Wtot, is given by 357.4 nm in the ir polarization that appears in both absorption and emission. This transition is between crystal field splittings 2 Z2 at 132 cm-' in 4I9/2 and L, at 28103 cm-' in 4D3/2. wtot 2(h) 2 - [1 exp(-2-yl)], (10) The absorption coefficient is 2.5 cm-' for 1.7 at. % Nd dop- 2 where is the sample length. This is the expression needed ing. This gives an effective cross section of 1.1 X 10-20 cm . The effective cross section to relate the total ESA pump rate to (-esa. By using Eq. (10), is related to the actual cross the pump rate calibration from the He-Cd-laser pump, and section and absorption coefficients by the signal for a given dye-laser incident pump power, the (e = /Ntot = af, (12) ESA cross sections were calculated to be esa = (2 1) X 2 10-20 cm in the r polarization at 587.4 nm and 'Tesa= (9 4) where Nt0 t is the total population of the ground-state mani- 2 X 10-21cm in the a-polarization at 588.9 nm. These wave- fold, ae is the effective cross section, a. is the actual cross lengths are at the peaks of the excitation spectra for their section, and f is the fractional occupation of the crystal field respective polarizations. splitting involved in the transition given by a Boltzmann distribution. In Eq. (12), degeneracy has been ignored because all the Nd3+ crystal field splittings in YLF have a DISCUSSION degeneracy of 2; consequently all degeneracy factors cancel. 4 4 4 It may be possible to use the D / + D / - So the actual absorption cross section at 357.4 nm is 4.8 X 3 2 5 2 Ij transi- 2 tions for laser action. It may even be possible to make a two- 10-20 cm . The effective stimulated emission cross section 2 step-excitation-pumped laser. This type of laser offers is 1.2 X 10-20 cm , so the actual cross section is 2.6 X 10-20 an 2 alternative method to harmonic or sum-frequency gen- cm , based on the Boltzmann distribution calculated from eration for obtaining shorter wavelengths of light. The the energy levels of 4D3/2 and 4D5 /2 . However, as previously potential advantage is that the effective nonlinearity of noted, this emission is back to the ground manifold, so reab- two-step excitation is orders of magnitude larger than that sorption of the emission causes the measured intensity to be for harmonic generation' because real, resonant transitions too low. The maximum estimated error is 25%,based on an are involved as opposed to virtual, nonresonant transitions. Table 2. Peak ETU, which also has high effective Effective Stimulated Emission Cross nonlinearities, was Sections previously used to provide nearly all the pump power for a BaYi.2Yb075Er0 05F8 visible laser at 670 nm under lamp Wavelength Lower Cross Section pumping at 77 K2 . However, the threshold of this laser was (nm) Manifold Polarization (cm2 ) 170J. With resonant pumping, it is easier to take advantage 355.8 4I9/2 a 0.5 X 10-20 of these high nonlinearities because of the high pump densi- 357.4 4j9/2 7r 1.2 X 10-20 ties achievable. Of course, the main disadvantage is that 383.0 4I11/2 a 0.8 X 10-20 this process depends on resonances, so it is less general. The 383.0 4I11/2 r 2.1 X 10-20 laser threshold for a two-step-excitation pumped laser in 411.7 4I13/2 r 5.0 X 10-20 Nd:YLF can be calculated once the stimulated emission 412.9 4I13/2 a 1.6 X 10-20 cross section is known. 447.3 4I15/2 a 1.6 X 10-20 The stimulated emission cross section can be derived from 448.1 4I15/2 r 3.0X 10-20 1524 J. Opt. Soc. Am. B/Vol. 3, No. 11/November 1986 T. Y. Fan and R. L. Byer

I I I III I I I I excitation processes such as that characterized here in Nd :YAG FLUORESCENCE Nd:YLF probably occur to varying degrees in all Nd3 +- doped compounds. For example, we have also observed near-UV and blue emission from Nd-doped LHG-8 phos- phate glass under cw Rhodamine 590 dye-laser pumping and from Nd:YAG under cw Rhodamine 590 dye-laser pumping Z-z at 593.4 nm. The latter emission, which was previously Z noted,22 is shown in Fig. 5 and can be assigned to transitions 2 4 from the upper states P3/2 and D3/2 to the 4I term. While we have not studied the mechanisms in detail, we believe that the excitation in both cases can also be attributed to two-step excitation.

SUMMARY We have characterized near-UV and blue fluorescence in Nd:YLF under cw Rhodamine 590 dye-laser pumping. The 400 450 4 4 4 emission is due to D3 /2 + D5 /2 to Ij transitions, and it WAVELENGTH (nm) appears that excitation to these levels is by a two-step- Fig. 5. Near-UV and blue emission in Nd:YAG pumping at 593.4 excitation process. It would be interesting to compare these nm. This has not been normalized for the spectral response of the cw results with pulse pumping to characterize the differ- detection system. ences between the two regimes, because the results obtained in Nd:LaF 3 in a pulsed regime suggest that the dynamics of absorption coefficient of 2.5 cm-' and a distance of propaga- the process may be quite different. While measurements tion through the material of 0.1 cm. Without taking reab- and calculations indicate that a two-step-excitation pumped sorption into account, the absorption and emission cross laser in Nd3+ doped systems is a possibility, other rare- sections differ by a factor of 1.8. The calculation of the earth- or transition-metal-ion-doped crystals may be more absorption cross section also has a source of error that is the interesting for this type of laser if an appropriate system can concentration of Nd; however, it appears that the estimate of be found because the long metastable lifetimes in some of radiative quantum efficiency and therefore the stimulated the other ions will permit more efficient pumping. emission cross section may be low based on our comparison. Now a threshold for a two-step excitation pumped laser can be estimated. Assuming a Gaussian pump and negligi- ACKNOWLEDGMENTS ble diffraction in the laser medium, the pump power, Pth, required to reach threshold for the typical one-photon ab- The authors would like to thank the U.S. Office of Naval sorption pumping assuming that one absorbed photon yields Research and NASA for funding this research. They would also like to thank H. P. Jenssen for providing the Nd:YLF one excited ion in the upper laser level is given by2l used in this work.

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