Amplified Spontaneous Emission - IEEE Xplore

IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 35, NO. 1, JANUARY 1999

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Amplified Spontaneous Emission— Application to Nd : YAG Lasers Norman P. Barnes and Brian M. Walsh

Abstract— Amplified spontaneous emission can seriously degrade the Q-switched performance of a strong four-level transition such as the 1.064 m Nd : YAG transition or can even prevent oscillation on a weaker quasi-four-level transition such as the 0.946-m Nd : YAG transition. To characterize, and thus be able to mitigate, amplified spontaneous emission, a closedform model is developed. By employing a closed-form solution, the differential equations describing both the evolution and decay of the upper laser manifold population density can be solved exactly. An advantage of this model is the separation of the spectral and spatial portions of amplified spontaneous emission. Gain measurements, as a function of time and pump energy, are compared with the model and good agreement is found. With these principles in mind, a flashlamp-pumped Nd : YAG laser was designed to operate at 0.946 m. At room temperature, a threshold of 12 J and a slope efficiency of 0.009 was achieved. Index Terms—Amplified spontaneous emission, Nd:YAG, solidstate lasers.

I. INTRODUCTION

A

MPLIFIED spontaneous emission depletes the population density of the upper laser manifold, which degrades the efficiency of a -switched laser operating on a strong transition and can prevent oscillation on a weaker quasi-fourlevel transition. Amplified spontaneous emission can manifest itself as a sublinear dependence of the laser output energy with pump energy and a faster than exponential decay of the population density of the upper laser manifold. Nd : YAG makes a good subject for this investigation since it has a to transition at 1.064 strong transition, the m, and a quasi-four-level transition, the to transition at 0.946 m. Modeling, gain measurements, and laser performance on both transitions are reported. A distinction between amplified spontaneous emission and parasitic lasing can be made. With amplified spontaneous emission, the emission of radiation occurs in all directions and at all frequencies allowed by the fluorescent spectrum. While some directions and frequencies are heavily favored because of higher gain, there is no mode structure. On the other hand, with parasitic lasing, modes are formed. That is, for a particular trajectory and frequency, some of the amplified radiation is returned coherently to the point of origin. While only certain directions and frequencies can form modes, the density of these modes is often so high that it appears to be a Manuscript received February 23, 1998; revised September 9, 1998. This work was supported by NASA under Grant NAG-1–98J. N. P. Barnes is with the NASA Langley Research Center, Hampton, VA 23681 USA. B. M. Walsh is with Boston College, Chestnut Hill, MA 02167 USA. Publisher Item Identifier S 0018-9197(99)00198-0.

continuous distribution. Another distinction between amplified spontaneous emission and parasitic lasing can be observed when plotting -switched energy versus pump energy. If amplified spontaneous emission is limiting performance, the laser output energy versus pump energy curve will become sublinear. If parasitic lasing is limiting performance, the laser output energy versus pump energy will clamp at the level of parasitic lasing threshold. Very little, if any, increase in switched laser output energy is realized by increasing the pump energy beyond the threshold for parasitic lasing. Amplified spontaneous emission is fundamentally different from superradiance. Superradiance is an effect described even before the advent of lasers [1]. If the density of excited state atoms is large enough, cooperative effects can occur in the emission process, leading to emission rates that are quadratic in the number of excited state atoms [2]. On the other hand, there are no cooperative effects involved with amplified spontaneous emission. In the latter case, a spontaneously emitted photon traveling through the gain medium is amplified before it escapes from the gain medium. Emission and amplification are sequential events. While there has been some confusion regarding the terminology, superradiance and amplified spontaneous emission are fundamentally different. To add to the confusion, amplified spontaneous emission has been referred to by other terms such as fluorescent amplification. In this paper, the effect will be referred to as amplified spontaneous emission in keeping with what appears to be a developing trend in the standard notation [2], [3]. Amplified spontaneous emission has been modeled for a few select situations, one being the case where the laser material has spherical geometry or disk geometry [4]. An integration over spatial and angular coordinates was performed for a sphere. To perform the integration over wavelengths as well, a series approximation was used retaining only the first few terms. Effects resulting from diffuse parasitic modes have also been recognized [5]. In this approach, the reflections at the boundary of the gain medium were diffuse rather than specular. Again, a power series approach was taken, retaining only the first two terms, and an average over all directions was performed. Using this particular approach, the radiant intensity can sometimes become negative on the boundary. Improvements in laser performance were demonstrated by attenuating the radiation that propagates in the pump cavity, which couples the flashlamp to the laser rod [6]. Effects of various diffuse finishes on the laser rod performance were empirically investigated [7]. Effects of various absorptive claddings on the laser disk performance and parasitic

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modes were analyzed [8]. Effects of amplified spontaneous emission on long cylindrical laser geometries with essentially nonreflective walls were analyzed and applied to low-pressure Xe lasers [9]. A simple expression relating the gain and the solid angle subtended by the end of the cylindrical laser medium was obtained. However, the approximations, if any, which were used to obtain this expression were not explained. This analysis was applied to an Nd : YAG laser where a gain of 18 dB was obtained [10]. Other surface treatments to suppress amplified spontaneous emission and parasitic oscillation were empirically investigated for laser rods [11]. Parasitic oscillation and stored energy density were analyzed for active mirror and disk configurations [12]. High gain, 62 dB, was achieved in a single Nd : YAG slab laser by utilizing an external optical system to achieve four passes through the laser medium [13]. Four passes were achieved by angular multiplexing the laser beam in a laser slab with wedged ends. An analytical approach to predicting the effects of amplified spontaneous emission was developed, which relies on numerical integration over the length of the laser material and the frequency [14]. In this analysis, a nonsaturable absorber was included. Finally, the analysis and characterization was performed for slab lasers [15]. In the slab configuration, amplified spontaneous emission becomes significant at a gain coefficient and length product of 2.25; parasitic oscillation becomes significant at a gain coefficient and length product of 3.69. Amplified spontaneous emission is modeled here by separating the spectral and spatial portions of the problem, which allows for a considerable simplification. In essence, the separation of the spectral and spatial portions of the problem is associated with the assumption that the possible trajectories of the spontaneously emitted photons are nearly independent of the wavelength. Such an assumption is not strictly valid since the refractive index, and thus the total internal reflection angle, depends on the wavelength. However, the dependence is relatively weak, so the assumption is a good one and allows a closed-form approximation for the amplified spontaneous emission for reasonable gains to be derived. With the approximation, the differential equations describing both evolution and decay of the upper laser manifold are solved exactly. Modeling, spectroscopy, laser measurements, and a discussion of the salient effects appear in the following sections. Modeling, described in Section II, includes a description of the physics associated with amplified spontaneous emission and the separation of the problem into spectral and spatial portions. The spectral portion can be integrated directly, while the spatial portion can be described by a single characteristic parameter: the average path length traveled by a spontaneously emitted photon. This parameter can be determined by measuring the decay of the gain. With this approach, both the evolution of the upper laser manifold during the pump duration and the decay can be described for a variety of practical situations. Spectroscopy needed to characterize the spectral portion of the problem is described in Section III. Spectroscopic parameters needed for characterization are the line-to-line branching ratios and the effective stimulated emission cross sections. Both quantities have been measured for Nd : YAG, as well as for several other Nd : garnet lasers.


Decay of the upper laser level population density and laser gain measurements are described in Section IV. Because most manifold terminate of the transitions originating on the F on unpopulated lower levels and because the pump cavity is flooded, radiation trapping is neglected. Decay of the upper laser level as a function of time can be readily measured by observing the fluorescence of the laser material. Decay characteristics as a function of pump energy are shown to depend on the particular spectral band sampled. Gain measurements are taken as a function of pump energy using a low-power CW Nd : YAG probe laser. Gain decay measurements are compared with the fluorescent decay characteristics taken in two different spectral bands. Using these results, the average path length is evaluated. Results of the decay and gain measurements are discussed in Section V. Laser performance can be optimized by taking into account the effects of amplified spontaneous emission. Laser performance was evaluated on both the 1.064 and 0.946 m wavelengths, as discussed in Section VI. A summary of the effects of amplified spontaneous emission and its effect on both strong transitions and weaker quasi-four-level laser transitions appears in Section VII. II. MODEL Amplified spontaneous emission causes the population density of the upper laser manifold to decay faster than exponentially. Without amplified spontaneous emission, the differential equation governing the population density of the upper laser is given by manifold

where is the lifetime of the upper laser manifold and is the pumping rate per unit volume. If amplified spontaneous emission is not negligible and the pump pulse has terminated, each spontaneously emitted photon is amplified by a factor of , where is the effective emission cross section at the frequency of the emitted photon and is the path length of the spontaneously emitted photon in the laser material. For practical solid-state lasers, the spontaneously emitted photon could be at any of a variety of frequencies, at any position within the laser material and traveling in any direction. To take into account all of these possibilities, an average over all possibilities can be performed. In this case, neglecting pumping, the population density of the upper laser manifold can be described as

where describes the aggregate lineshape function of the can be described by upper laser manifold. In general,

where is the number of transitions from the upper laser is manifold, is branching ratio of the th line, and

BARNES AND WALSH: AMPLIFIED SPONTANEOUS EMISSION—APPLICATION TO Nd : YAG LASERS

a lineshape function, probably Lorentzian, with linewidth and line center . Normalization factors are included such that

and

To perform the integration, the exponential term is expanded in a power series. Suppose that only the first two terms are retained. In this case

With the aid of a reasonable assumption, this expression can be simplified. To simplify the problem, it is assumed that the path length and the direction of propagation are independent of frequency. Because of total internal reflection, this assumption is not strictly true since the refractive index depends on the frequency. However, this dependence is relatively weak. For example, the refractive index at 0.946 and 1.064 m is 1.8204 and 1.8179, respectively. Thus, the difference in the critical angle is only 0.05 . With this approximation, only the effective and the lineshape function emission cross section depend on the frequency. If the population density of the is also independent of position, the upper laser manifold evaluation of the first terms in the expansion is straightforward. A uniform population density is a reasonable assumption in diffusely reflecting cavities with optically thin laser rods, as was used for the experiments. Using similar reasoning, the integration over frequency for the second term is

In these expressions, is the peak emission cross section of is the average effective emission cross the transition and section. Note that, for higher powers of the expansion, the . integration over frequency is over a function of As becomes larger, the integral of this term becomes smaller, abetting the convergence of the expansion. After performing the integration over frequency, the second term becomes

practice, it is more convenient to measure this parameter. However, reasonable values for this parameter can still be estimated. Using the first two terms in the expansion and the concept of an averaged spontaneously emitted photon path length, the upper laser manifold population density becomes

An advantage of this approach is that the resulting differential equation can be solved exactly. After the pumping has termiterm vanishes and the resulting equation can be nated, the rearranged to yield

Integrating this expression and applying a boundary condition , the that the initial upper laser level population density is solution to the differential equation becomes

Thus, the nominal exponential decay becomes more complex and faster than a simple exponential when amplified spontaneous emission is not negligible. Using the above equation, the average path length for a spontaneously emitted photon can be determined by measuring the decay of the upper laser manifold population density versus time. Resulting data can be curve fit using nonlinear curve fitting techniques to determine the parameters. Three and the product parameters characterize the decay: . However, because the average effective emission of cross section can be evaluated using spectroscopic data, the can be determined. Evaluation of the average path length parameter is physically appealing since it can be related to the dimensions of the laser material. For gain measurements, the above equation can be recast into a different but similar form. Multiplying by the effective and the gain length for emission cross section of interest the laser material, the small-signal gain coefficient and length is found to be product

where where is the average path length for the spontaneously emitted photon and is defined by the integral. In principle, the integral defining the average path length could be calculated. However, the value would depend on the geometry of the situation including quantities difficult to characterize such as the surface finish on the laser rod. In

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is the initial small-signal gain coefficient and

is the amplified spontaneous emission parameter. Thus, a measurement of the decay of the small-signal gain coefficient and length product also yields a measurement of the average if both and can be determined from path length spectroscopic data.

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Given the average path length, the effect that amplified spontaneous emission has on laser performance can be assessed by examining the evolution of the upper laser manifold population density under pumping. If the pumping rate term is reintroduced into the differential equation for the population density of the upper laser manifold, the differential equation becomes

Separating the variables yields

Defining

and integrating and applying the boundary condition that the initial population density of the upper laser manifold is zero yields

In this expression, is the length of the pump pulse. Note that for low levels of excitation, where the effects of amplified spontaneous emission are small,

In the latter expression, is the familiar storage efficiency for a square pump pulse with no amplified spontaneous emission effects. As the pumping level increases, the effective storage efficiency decreases. Because of the reduction of the storage efficiency, a quasifour-level laser may have difficulty in achieving threshold. In a quasi-four-level laser, there is a nonnegligible population . The small-signal gain density in the lower laser manifold coefficient and length product in this case is

where is the emission cross section of the transition while and are the thermal occupation factors, or Boltzmann factors, for the lower and upper laser levels, respectively. It can be assumed that the majority of the active atoms are either in the upper or lower laser manifold. Because of the fast relaxation of the pump bands to the upper laser manifold manifolds, this is a good and the fast relaxation of the approximation. With this approximation, the equation can be rearranged to yield

where is the concentration of active atoms, is defined , and is the number density of possible active atom as sites. Thus, for low levels of pumping, the gain coefficient and length product can be negative, indicating loss rather than gain. Optical transparency, that is, neither gain nor loss, occurs


when the upper laser manifold population density is

This value of the upper laser manifold population density can be used to determine the requisite pumping rate. In turn, the pumping rate can be utilized to calculate the storage efficiency and thus determine the relative efficiency of the transition. In actuality, merely achieving optical transparency will not guarantee that the transition will lase since the losses in the resonator must be overcome. Consequently, a value of twice the upper laser manifold population density at optical transparency may be a better estimate. Proper laser design can optimize the performance of the Nd : YAG laser on the 0.946- m transition. Because of the effects of amplified spontaneous emission, the product of the population density in the upper laser level and the length of the laser material is limited. Since the 1.064- m transition has essentially no population in the lower laser level, a high gain can be achieved either by having a high population density in or a long length . Since flashlamps the upper laser level tend to be long cylinders, the laser rods for 1.064- m operation tend to be long cylinders also. A cylindrical laser rod matched the geometry of the flashlamp and produced high gain but a relatively low population density in the upper laser manifold. For 1.064- m operation with no population in the lower laser level, it makes little difference if the population density is high or the length is long. However, for 0.946- m operation, this relatively low population density may not exceed optical transparency. To achieve high gain at 0.946 m, a better strategy is to have a short laser rod and a high population density in the upper laser level. With this approach, optical transparency can be easily exceeded without serious amplified spontaneous emission effects. While this geometry is not well suited to flashlamp pumping, it is very well suited to diode pumped lasers in an end-pumped configuration. III. SPECTROSCOPY Emission spectra taken with Nd : YAG and other Nd : garnet samples yield the needed peak emission cross sections and branching ratios. Samples were typically 10-mm cubes and had a Nd concentration of 0.01. A CW laser diode emitting at 0.785 m, as shown in Fig. 1, was used to excite the Nd atoms. Radiation from the laser diode was focused to a small spot near the top surface of the crystal by a 50-mm focal length lens. A mirror, above the sample and inclined at 45 , directed the fluorescence toward a 1.25-m Ebert monochromator. A collecting lens imaged the fluorescent stripe onto the slits of the monochromator. A 600-g/mm grating blazed at 1 m and a liquid-nitrogen-cooled Ge detector recorded the fluorescence to , , and manifolds in from the to a single data set. Fluorescence from the manifold, known to be less than 0.01 of the total [16], [17], was neglected. A chopper in front of the slits and a lock-in amplifier provided a good signal-to-noise ratio (SNR). A step-and-stare program recorded the data and stepped the monochromator. Fluorescent data was corrected for the response of the system before being analyzed. A tungsten lamp was used as a gray


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TABLE I SELECTED SPECTRAL DATA FOR THE 0.946AND 1.064-m TRANSITIONS OF Nd : YAG

Fig. 1. Spectroscopic experimental arrangement which images excitation volume onto monochromator slits.

Fig. 2. Nd : YAG fluorescence spectrum.

body source to calibrate the response of the optics, monochromator, and detector system. A Hg lamp was used to check the wavelength calibration of the monochromator. A typical effective emission cross-section spectrum is shown in Fig. 2. Corrected fluorescence data was curve fit to 36 Lorentzian lineshape functions to determine the required spectroscopic parameters. All levels in Nd : YAG are doubly degenerate. There are two levels in the upper laser manifold, the manifold, as well as five, six, and seven levels in the lower , , and manifolds, laser manifolds, the respectively. Using all possible combinations yields a total of 36 transito the , , and manifolds. tions from the Results of the curve fitting produced the peak fluorescence and the linewidth of each transition. By integrating under the fluorescence curve and measuring the lifetime, the peak fluorescence can be converted to peak emission cross section. Branching ratios can be computed by comparing the area under a single fluorescence curve with the total area under the fluorescence spectrum. Typical results for these calculations for the lines of interest appear in Table I. An effective emission cross section for the 1.064- m transitions is actually the sum of the contributions from two transitions. Its value is in the mid range of several published values for the emission cross section, adding credence to the measurement technique. Effective emission cross section of the 0.946- m transition is about a factor of eight times smaller than that of the 1.064- m transition. A low effective emission cross section for this transition complicates

the problem of efficient laser operation. Finally, the average effective emission cross section is computed to be larger than the effective emission cross section for the 0.946- m transition, pointing up the difficulty in making an efficient laser when operating on this transition. To improve chances for success, the laser can be cooled. Cooling has several beneficial effects. Primarily, cooling decreases the population of the lower laser level because the thermal occupation factor, or Boltzmann factor, of the lower laser level becomes smaller. On the other hand, because the 0.946- m transition originates on the lower of the two levels, the thermal occupation factor of this upper laser level increases. In addition, because the 1.064- m transition levels, the thermal originates on the upper of the two occupation factor of the upper laser level of this transition decreases with temperature. IV. LASER MEASUREMENTS Laser gain measurements were performed using a CW probe laser. Probe laser output power was on the order of 20 mW and consisted of a single frequency at 1.064 m A flashlamppumped 5 38 mm Nd : YAG laser rod was probed for gain. A 5 6 mm undoped YAG rod was bonded onto each end of the laser rod, for an overall length of 50 mm, so that the entire active length of the laser rod could be pumped. By having undoped ends on the laser rod, absorption by the thermally populated lower laser level in lightly pumped regions of the laser rod was minimized. A 4-mm bore Xe flashlamp driven by a current pulse with a 120- s pulse length pumped the laser. A chopper in the probe beam allowed a measurement of the dark current, the CW level and the gain peak in a single trace. Gain as a function of time was measured by intercepting a small fraction of the amplified beam with a large-area Si photodiode. Output from the photodiode was displayed on an oscilloscope from which the peak gain and the decay could be determined. Typically, the oscilloscope trace was recorded on a magnetic disk for later numerical processing. Processing includes subtracting off the dark current, averaging and dividing by the CW level, truncating irrelevant points, and curve fitting the remainder. Fluorescence could be measured by using the same Si photodiode. Bandpass filters in front of the detector could isolate radiation from either the 1.064- m or the 0.946- m transition. By triggering the oscilloscope to record information before the flashlamp was initiated, a background level could be recorded for every oscilloscope trace. As with the gain

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Fig. 3.

Gain coefficient length product versus electrical energy.

Fig. 5. Gain coefficient and length product versus 0.946-m fluorescence.

Fig. 4.

Peak fluorescence at 0.946 and 1.064 m versus pump energy.

Fig. 6. Relative population density of the upper laser manifold versus time for pump energy of 5.4 J.

measurements, the data was recorded on a magnetic disk for later numerical processing. Processing includes subtracting off the background level, truncating the points before and after the fluorescent pulse, and curve fitting the remainder of the data to the appropriate curve. Peak gain as a function of pump energy shows a definite sublinear dependence. Gain coefficient length product at 1.064 m as a function of the electrical energy delivered to the flashlamp is plotted in Fig. 3. At very low pump energies, the gain coefficient length product is nearly linear with the pump energy, as expected. A linear approximation starts to diverge from the observed values above a gain coefficient length product of 1.0. The model developed here works well to gain coefficient length products of 2.5. Above that, neglect of higher order terms becomes significant. For gain coefficient length products above 2.5, the model overestimates the observed gain coefficient length product. As the gain coefficient length product approaches 3.0, increased pump energy produces diminishing increases in this product. It may be noted that up to the highest pump energies no evidence of gain clamping is observed, which indicates that the parasitic threshold has not been reached. Peak fluorescence at 0.946 and 1.064 m, as a function of pump energy, show a marked difference in behavior. A graph

of peak fluorescence versus pump energy appears in Fig. 4 for both a 0.946 and 1.064 m bandpass filter. While the 0.946- m peak fluorescence shows a nearly linear dependence on the pump energy, the 1.064- m peak fluorescence shows a nearly exponential dependence. Because of the size of the emission cross sections, the 1.064- m radiation enjoys significant amplification before it reaches the end of the laser rod, while the 0.946- m radiation does not. Additional supporting evidence is the correlation between the fluorescence at 0.946 m and the gain coefficient length product at 1.064 m. At various pump energies, measurements of both the gain coefficient length product as well as the fluorescence at 0.946 m are available. Plotting these measurements pairwise produces Fig. 5. A direct relationship between these two quantities is expected and is observed. Thus, while the gain coefficient length product and the 0.946- m fluorescence are directly related, the 1.064- m fluorescence increases faster than the 0.946- m fluorescence. From this, it is natural to conclude that the 1.064- m radiation is being amplified. A sample of the recorded decay curves of the population density of the upper laser manifold and/or the gain versus time are shown in Figs. 6–8 for a low pump energy, a medium pump energy, and a high pump energy, respectively. Included


Fig. 7. Relative population density of the upper laser manifold versus time for pump energy of 10.7 J.

Fig. 8. Relative population density of the upper laser manifold versus time for a pump energy of 21.6 J.

in the figures are the results of the curve fitting procedure. At low pump energy, the fit between the model and the data is quite good. As the pump energy increases, there is some deviation, most noticeable for small time intervals beyond the termination of the pump pulse. Using the results of the curve fitting procedure, the product of the average effective emission cross section and the average length can be determined. Results of the curve fitting procedure can then be plotted versus the pump energy. V. DISCUSSION A plot of the amplified spontaneous emission parameter versus the pump energy, shown in Fig. 9, is sensibly constant. Since neither the stimulated emission cross sections nor the average pathlength is expected to depend on the pump energy, a constant plot is expected. Because the flashlamp pulse does not terminate quickly, the first two points do not follow the expected behavior. However, after that, the average effective stimulated emission cross section times the average length quickly settles down to a constant value. At very high pump energies, there is some increase in the product, however it

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Fig. 9. Amplified spontaneous emission parameter versus electrical energy 38 mm Nd : YAG laser rod. for a 5.0

2

appears that a value for the amplified spontaneous emission parameter of 0.25 is reasonable. At low pump energies, the fitted parameter is somewhat larger than it is believed to be, probably because of the persistence of the flashlamp radiation. Although the current pulse driving the flashlamp was terminated quickly, in a time interval on the order of a few microseconds the flashlamp radiation did not terminate as quickly. As is typical for flashlamps, the radiation remained for a time constant on the order of 15 s. Although only data past the peak were used in the curve fitting procedures, the tail on the flashlamp radiation added some pumping after the peak. While this contribution is negligible at high pump energies, at low pump energies it makes a greater fractional contribution. Consequently, it is believed that the parameter will be somewhat overestimated at low energies. Changing the experimental method to minimize this effect was not done in order to avoid introducing any possible arbitrariness. At high pump energies, the fitted parameter is somewhat higher than it is at intermediate energies probably because of the high level of excitation. In the approximation used to this point, only terms through the second order in the expansion are used. Using higher order terms will provide for more amplified spontaneous emission, especially at short time intervals beyond the peak. This time interval is where the largest differences are indeed observed. Then, if higher order terms were used, smaller values of the average effective stimulated emission cross section and average path length would suffice. However, higher order terms were not employed to keep the expressions for gain relatively simple. Taken together, it appears that the mid pump energy values for the product are probably the most nearly accurate. Knowing the product, the average effective stimulated emission cross section can be used to determine the average length. Using the measured peak emission cross sections and branching ratios, the average path length is 63 mm. It may seem that the average path length would be approximately equal or somewhat smaller than the active laser rod length. However, because of total internal reflection, the average path

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length can be longer. In the plane containing the axis of the laser rod, total internal reflection can increase the path length where and are the refractive indices of to YAG and water, respectively. In addition, spiral trajectories around the periphery of the laser rod can result in even longer path lengths. Thus, an average path length of 63 mm in a 38-mm-long laser rod appears to be reasonable. VI. LASER PERFORMANCE Laser performance on both the 0.946- and 1.064- m transitions was evaluated using the short laser rod in a diffusely reflecting cavity. A 5.0-mm diameter Nd:YAG laser rod with a fine grind finish on the barrel was used. As before, a 4.0mm bore Xe flashlamp driven with a nearly square current pulse was used for pumping. The pulse length of the flashlamp current was 120 s; however, the light lasted somewhat longer. Both the flashlamp and the laser rod were cooled by flooding the cavity with water having a temperature of 15 C. Operation of 0.946 or 1.064 m could be selected by the proper coatings on the highly reflective mirror. A linear resonator consisting of a flat output mirror and a 2.0-m radius of curvature highly reflecting mirror was used. Separation of the mirrors was approximately 0.8 m with the laser rod residing in the middle of the resonator. For 1.064- m operation, the curved mirror was simply made highly reflective at this wavelength. For 0.946- m operation, the curved mirror was made highly reflective at this wavelength and highly transmissive at 1.064 m. Typical reflectivity at the latter wavelength was less than 0.01. With this mirror and the less than unity reflectivity of the output mirror, operation of 1.064 m could be effectively thwarted. Laser operation was characterized at both 1.064 and 0.946 m. Normal mode laser output energy was recorded as a function of electrical energy for a variety of laser output mirrors. Results of these measurements for each output mirror reflectivity were then fit to a simple linear relationship to determine the threshold and slope efficiency, which were then plotted as a function of the negative of the logarithm of the laser output mirror reflectively. Results are shown in Figs. 10 and 11. Curve fits for the threshold are for a simple linear equation while the curve fit for the slope efficiency was to an . expression of the form Performance at 0.946 m can begin to approach the level of performance at 1.064 m. At the lowest 0.946- m output mirror reflectivity, 0.82, the slope efficiency is 0.0090. On the other hand, at the lowest 1.064- m output mirror reflectivity, 0.71, the slope efficiency is 0.030. Thresholds of the two transitions can also be compared. It can be noted that a significant fraction of the threshold at 0.946 m is attributed to the thermal population of the lower laser level. If the miscellaneous losses at 1.064 and 0.946 m are comparable, the electrical energy needed to overcome the thermal population in the lower laser level accounts for most of the difference between the ordinate intercepts, that is 7 J. However, the method of mitigating this difference is clear; use very short laser rods to minimize amplified spontaneous emission and allow a high population inversion to swamp the effects of the thermal population of the lower laser level. Finally, the ratio

Fig. 10.

Threshold versus the negative logarithm of the mirror reflectivity.

Fig. 11. tivity.

Slope efficiency versus the negative logarithm of the mirror reflec-

of the slopes of the curves for threshold versus the logarithm of the mirror reflectivity should be the inverse of the ratio for the emission cross sections. In fact, this is nearly the case. The ratio of the slopes is 6.7 while the ratio of the emission cross sections is 7.9. Results of this approach can be compared with other results of 0.946- m Nd : YAG operation described in the literature [18]. There, the laser rod was cooled substantially to improve performance. Approximately the best performance was obtained at 248 K. At this temperature, a threshold of 62 J and a slope efficiency of 0.0014 was obtained, as shown in Table II. Using the design described here, a substantial increase in performance was achieved near room temperature ( 290 K). At this temperature, a threshold of 12 J and a slope efficiency of 0.0090 was obtained. Also shown in Table II is the comparative performance achieved at 1.064 m. VII. SUMMARY Amplified spontaneous emission was modeled since it contributes heavily to the performance limitations of the 0.946- m transition. A significant advantage was gained by separating the spectral and path length averaging. Spectroscopic data can


TABLE II COMPARISON OF LASER PERFORMANCE AT 0.946 AND 1.064 m. 248 K RESULTS ARE FROM THE LITERATURE [18]. 290 K RESULTS ARE REPORTED HERE

be used to evaluate the spectral portion, while measurements of the decay of the gain can be used to evaluate the average path length. These results can then be used to predict the evolution or rise of the gain or population inversion. Spectroscopic measurements of the fluorescence from the manifold to the , , and manifolds were taken to evaluate the spectral portion of the problem. Experimental data were normalized for the response of the system and the resulting spectral information was analyzed to obtain the branching ratio, linewidth, and peak effective emission cross section for each transition. Using the data, the average effective emission cross section was calculated. Decay of the gain as a function of time was used to evaluate the average path length. Gain was measured using a singlefrequency CW Nd : YAG laser. Results of the gain decay measurements fit the model well and yielded a reasonable value for the average path length. It was also shown that the gain and the fluorescence measurements at some particular wavelengths could be well correlated. Parameters evaluated by observing the decay of the gain could then be used to predict the evolution or rise of the gain. Model predictions and experimental results both show the diminishing returns obtained by pumping above the level where gain coefficient and length product exceeds 3.0. A Nd : YAG laser was assembled and operated at both 1.064 and 0.946 m for comparative purposes. Using the insights gained from the modeling, the laser rod was kept relatively short, 38 mm, and undoped ends were bonded onto the laser rod to minimize absorption by the lower laser level. When operated at 0.946 m, a threshold of 12 J and a slope efficiency of 0.009 was achieved at 290 K. When compared to other 0.946- m Nd : YAG performance, the threshold is about one-fifth as large while the slope efficiency is about a factor of seven times larger. Conversely, when operated at 1.064 m, a threshold of 2.7 J and a slope efficiency of 0.030 was achieved. ACKNOWLEDGMENT The authors would like to acknowledge Dr. H. Meisner of Onyx Optical for providing the bonded laser rods and K. George of Quality Thin Films for the special highly reflecting mirrors. REFERENCES [1] R. N. Dieke, “Coherence in spontaneous radiation processes,” Phys. Rev., vol. 93, pp. 99–110, 1954. [2] A. E. Sigman, Lasers. Mill Valley, CA: University Sci., 1986. [3] W. Koechner, Solid State Laser Engineering, 4th ed. Berlin, Germany: Springer-Verlag, 1996. [4] J. B. Trenholme, “Fluorescence amplification and parasitic oscillation limitations in disc lasers,” Naval Research Labs., Washington, DC 20375, Naval Research Lab. Memo. Rep. 2480, 1972.

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[5] A. N. Chester, “Gain thresholds for diffuse parasitic laser models,“ Appl. Opt., vol. 12, pp. 2139–2146, 1972. [6] N. P. Barnes, V. J. Corcoran, I. A. Crable, L. L. Harper, R. W. Williams, and J. W. Wragg, “Solid state laser technology,” IEEE J. Quantum Electron, vol. QE-10, pp. 195–201, 1974. [7] K. V. Galoyan and K. V. Kahchatryan, “Influence of the surface treatment of a cylindrical yttrium aluminum garnet crystal on laser energy characteristics,” Sov. J. Quantum Electron., vol. 4, pp. 260–261, 1974. [8] J. A. Glaze, S. Guch, and J. B. Trenholme, “Parasitic suppression in large aperture Nd : Glass disk lasers amplifiers,” Appl. Opt., vol. 13, pp. 2808–2811, 1974. [9] G. J. Linford, E. R. Peressini, W. R. Sooy, and M. L. Spaeth, “Very long lasers,” Appl. Opt., vol. 13, pp. 379–390, 1974. [10] G. J. Linford and L. W. Hill, “Nd : YAG long lasers,” Appl. Opt., vol. 13, pp. 1387–1394, 1974. [11] P. Lubudde, W. Seka, and H. P. Weber, “Gain increase in laser amplifiers by suppression of parasitic oscillations,” Appl. Phys. Lett., vol. 29, pp. 732–734, 1976. [12] D. C. Brown, S. D. Jacobs, and N. Nee, “Parasitic oscillation, absorption, stored energy density, and heat density in active mirror and disk amplifiers,” Appl. Opt., vol. 17, pp. 211–224, 1978. [13] T. J. Kane, W. J. Kozlowsky, and R. L. Byer, “62-dB gain, multiple pass, slab geometry, Nd : YAG amplifier,” Opt. Lett., vol. 11, pp. 216–218, 1986. [14] D. D. Lowenthal and J. M. Eggleston, “ASE effects in small aspect ratio laser oscillator and amplifiers with nonsaturable absorption,” IEEE. J. Quantum Electron., vol. QE-22, pp. 1165–1173, 1986. [15] G. F. Albrecht, J. M. Eggleston, and J. J. Ewing, “Design and characterization of a high average power slab YAG laser,” IEEE J. Quantum Electron., vol. QE-22, pp. 2099–2106, 1986. [16] T. Kushida, H. M. Marcos, and J. E. Geusic, “Laser transition cross section and fluorescent branching ratio for Nd3+ in yttrium aluminum garnet,” Phys. Rev., vol. 167, pp. 289–291, 1968. [17] R. K. Watts, “Branching ratios for YA`G : Nd3+ ,” J. Opt. Soc. Amer., vol. 61, pp. 123–124, 1971. [18] S. Dimov, E. Pelik, and H. Walther, “A flashlamp pumped 946 nm Nd : YAG laser,” Appl. Phys. B, vol. 53, pp. 6–10, 1991.

Norman P. Barnes received the B.S. degree in engineering physics, the M.S. degree in physics, and the Ph.D. degree in electrical engineering from Ohio State University, Columbus. Positions at Texas Instruments Incorporated, Dallas, TX, and Martin Marietta, Orlando, FL, have provided industrial experience in solid-state lasers including diode-pumped lasers, nonlinear optics, modulators, mode locking, and detection systems. While at Los Alamos National Laboratory, his work focused on solid-state lasers and nonlinear optical systems for isotope separation, in particular 2.0-m lasers such as Ho : Tm : Er : YLF, and parametric oscillators and mixers for the far infrared. At NASA Langley Research Laboratories, Hampton, VA, he performs research on solid-state lasers and nonlinear optical systems for remote sensing of the atmosphere, in particular, diode-pumped 2.0-m lasers such as Ho : Tm : YLF, Ho : Tm : LuAG, Ho : Tm : LuLF, and Tm : LuAG; ZnGeP2 and AgGaSe2 parametric oscillators and amplifiers in the midinfrared; and Ti : Al2 O3 and Cr : LiSrAlF6 narrow spectral bandwidth lasers in the near infrared.

Brian M. Walsh was born in Cambridge, MA, on October 21, 1962. He received the B.A. degree in physics from Boston University, Boston, MA, in 1987 and the Ph.D. degree in physics from Boston College, Chestnut Hill, MA, in 1995. His doctoral dissertation involved a study of the spectroscopy and excitation dynamics in Tm:Ho:YLF. He performed doctoral research at NASA Langley Research Center, Hampton, VA, where he is currently involved in post-doctoral research. The areas of research he is currently involved in include the spectroscopy of new solid-state laser materials, 2.0-m Tm:Ho laser systems, and 0.94-m Nd-doped lasers for remote sensing of water vapor.