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Polarization influence of excited state absorption on the performance of Cr4+:YAG laser
Optics Communications 242 (2004) 605–611 www.elsevier.com/locate/optcom
Polarization influence of excited state absorption on the performance of Cr4+:YAG laser V. Kartazaev *, R.R. Alfano Department of Physics, Institute for Ultrafast Spectroscopy and Lasers and New York State Center for Advanced Technology for Ultrafast Photonics Materials and Applications, The City College and Graduate School of the City University of New York, Convent Ave. at 138th Street, New York, NY 10031, USA Received 22 July 2003; received in revised form 1 September 2004; accepted 2 September 2004
Abstract The polarization dependence of the excited-state absorption (ESA) on the gain of the Cr4+:YAG medium is described. Using laser efficiency data, the emission and ESA cross-section for r- and p-polarization at 1450 nm are determined. Due to excitation of the two types of Cr4+ oriented centers in Cr4+:YAG for unpolarized pumping, the effective ESA cross-section rESAu = r1p + r1r = 1.6 · 1019 cm2 is obtained. The effective ESA cross-section for linearly polarized pumping, with direction of the electric vector along the S4 local symmetry axis, is rESAp = r1p = 0.8 · 1019 cm2. 2004 Elsevier B.V. All rights reserved. PACS: 42.55.Rz; 42.55.Xi Keywords: Laser; Solid-state; Excited state absorption
Since the first demonstration of near-infrared (NIR) laser action in Cr4+-doped forsterite [1] and YAG [2], there has been a great deal of interest in the spectroscopic and laser properties of Cr4+ doped other materials [3–5]. Cr4+:YAG laser has many applications in the areas of communica* Corresponding author. Tel.: +1 212 650 5531/5527; fax: +1 212 650 5530. E-mail addresses: [email protected] (V. Kartazaev), [email protected] (R.R. Alfano).
tions, medicine and imaging. It covers an important spectral region of 1310–1600 nm [6–8]. Cr4+:YAG lasers can be pumped by high power cw lasers such as Nd-doped solid-state laser, Ybdoped fiber laser [9] and direct diode-pumping [10–12]. The presence of excited state absorption (ESA) at the lasing wavelengths is one of most serious limiting factor for efficient laser operation. The ESA process limits the laser efficiency of a Cr4+:YAG laser, resulting in only a few percent
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.09.007
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saturated round trip gain [13,14]. No serious attempts have been made in earlier research to assign the ESA to one or more transitions for differently orientated Cr4+ centers in the host. Spectroscopic studies on Cr4+:YAG showed the D2d symmetry point group describes the polarization properties of the Cr4+ center emission [15–17]. Strong polarization dependence in absorption saturation for Cr4+:YAG was observed [15]. The absorption saturation at 1064 nm can be described by two absorption cross-section: r0p for light polarized along the S4 local symmetry axis and r0r for light polarized perpendicular to the S4 local symmetry axis. The estimation of emission- and ESA-cross-section, using efficiency data for a cw Cr4+:YAG laser that is pumped by Nd:YAG laser, was reported [16,18]. In these works, a Brewster-cut Cr4+:YAG crystal was used and the pump light was linearly polarized. However, neither the polarization dependence effects nor the orientation of the S4 local symmetry axis with respect to the electric vector of the pump beam was discussed in these works. When an unpolarized pump beam is used or when the orientation of the S4 local symmetry axis does not coincide with the electric vector of the pump light, then polarization dependence effects are significant and can reduce the efficiency of the laser operation.
In this article, an investigation of the laser performance is undertaken to study the effects of ESA in Cr4+:YAG crystal and its influence on laser performance for a flat–flat Cr4+:YAG laser crystal using both the plane-polarized and unpolarized pump beams at 1112 nm. It is found that ESA and ESA polarization dependence play an important role in the laser operation. A schematic of the experimental setup to characterize the performance of different states of polarization of Cr4+:YAG laser is shown in Fig. 1. An L-fold cavity with 5 cm radius back mirror and 10 cm radius folding mirror having high reflectivity over 1300–1600 nm range was used. Various output couplers (OC) having 1-, 2- and 5-percent transmission at 1450 nm were used. A total length of the cavity was 42 cm. The Cr4+:YAG laser setup in this configuration was longitudinally end pumped by a commercial cw Fiber laser (JDSUFL10a) operating at 1112 nm. A 5-mm diameter by 2 cm long cylindrical flat/flat Cr4+:YAG rod (Bicron) was wrapped with indium foil and tightly clamped between two copper holders attached to a copper heat sink via a thermoelectric cooler. The temperature of the crystal was maintained at 10 C during the experiments. To prevent water vapor condensation on the crystal surfaces the crystal was purged with dry nitrogen gas. The Cr4+:YAG crystal was oriented along crystallographic axis.
Fig. 1. Schematic diagram of the experimental arrangement for measuring the efficiency of the Cr4+:YAG laser and the orientation of the Cr4+ centers in the YAG crystal (a): L – focusing lens; M1 – 10 cm radius folding mirror; M2 – 5 cm radius back mirror; OC – output mirror; P1, P2 – Glan prisms polarizes; D1, D2 – photodiodes. Insert: p and r are the local symmetry axis and the local symmetry plane of the Cr4+ center – p is parallel to the S4 local symmetry axis, r is perpendicular to the S4 local symmetry axis.
V. Kartazaev, R.R. Alfano / Optics Communications 242 (2004) 605–611
Orientation of the crystal was adjusted such that propagation of the pump beam was along the crystallographic axis [1 0 0]. The crystallographic axis [0 1 0] or [0 0 1] was parallel to the vertically oriented electric vector of the pump light (Fig. 1(a)). A Glan prism (P1) was used to obtain either a vertically or horizontally plane polarized pump beam from the fiber laser. The output power from the laser was measured for both polarization components (i.e., one being parallel and the other being perpendicular to the polarized pump beam). A second Glan prism (P2) was used to separate vertical and horizontal polarization of the output laser beam. The separated polarization components of the laser beam were detected by two different photodiodes (D1 and D2). The intensity dependence of state of polarization of Cr4+:YAG laser on the polarization of the pump Fiber laser was measured. The output radiation of Cr4+:YAG laser was polarized when linearly polarized pump beam was used. The plane of polarization of emission depends on the orientation of the Cr:YAG crystal. When the crystal was rotated so that S4 local symmetry axis coincided with the direction of the electric vector of the pump beam, the plane of polarization of the laser beam was the same as the plane of polarization of the pump beam. When the crystal was rotated for a small angle, the plane of polarization of the laser beam also rotated by the same angle. When the angle between S4 local symmetry axis and the direction of the electric vector of the pump light was nearly 45, lasing for both polarization components was observed. Strong fluctuations of output power at these polarization components were observed. Lasing on both polarization components for an unpolarized pump beam was detected and strong fluctuations of output power at these polarization components were observed. Correlations of fluctuations of laser output in two orthogonal polarizations were measured for unpolarized pump. A light chopper chopped the pump beam to see the dynamics of fluctuations after the pump beam was on. A light chopper was introduced into the pump beam and placed before focusing lens. Signals from two photodiodes for two orthogonal
607
Fig. 2. Temporal dependence of laser output at 1450 nm at two orthogonal polarizations for unpolarized pump (V, vertical; H, horizontal) at 1112 nm.
polarizations were simultaneously recorded in two different channels of a digital oscilloscope. Fig. 2 shows the correlation in fluctuations of laser output for two orthogonal polarizations. When the intensity of one polarization component increased, the other polarization component decreased and vice versa. The observed anti-correlation in the power for the two polarizations occurs in the Cr4+:YAG crystal. It is not due to correlated power fluctuations between the two eigen-polarizations of the pump fiber laser. Measurements of the output power of the fiber laser for different polarizations show that there are no correlated power fluctuations. Moreover, the same anti-correlation in the output power of Cr4+:YAG laser for the two polarizations was observed when linearly polarized pump beam was used and lasing for the both polarization components was observed. Laser efficiency data for Cr4+:YAG laser at the free running wavelength (k = 1450 nm) were recorded for three different output couplers of 1-, 2-, and 3-percent for both the unpolarized and polarized pump beams in two orthogonal directions. The output power as a function of absorbed pump power for output coupler of 1-percent is shown in Fig. 3 for unpolarized pump beam (U) and for polarized beam in two orthogonal directions (i.e., vertical (V) and horizontal (H)). Fig. 3
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Fig. 3. Cr4+:YAG laser output power at 1450 nm as a function of absorbed pump power at 1112 nm for output coupler of 1% for unpolarized pump beam (U) and for polarized beam in two orthogonal directions (i.e., vertical (V) and horizontal (H)).
clearly shows that the threshold power (0.4 W) of the polarized pump is less than half of the threshold power (1.5 W) for the unpolarized pump. The slope efficiencies for the polarized and unpolarized pump beams are 18% and 6%, respectively. Using the slope efficiency and threshold power data (measured for different output couplers) the emission and ESA cross-sections were calculated for both the polarized and unpolarized pump beams. It appears that the excited-state absorption crosssection for unpolarized pump is almost twice more than the cross-section for the polarized pump beam. We calculated the absolute magnitudes of both the stimulated emission (SE) re and ESA rESA cross-section following the model reported by Payne et al. [19]. Similar approach was used in works [13,18]. The expressions for the slope efficiency gs and the threshold absorbed pump power Pth are: gs ¼ ðkp =kl Þgp ð1 rESA =re ÞðT =ðT þ LÞÞ;
ð1Þ
and P th ¼
pðx2p þ x2l Þhmp ðT þ LÞ ; 4re ð1 rESA =re Þsgp
ð2Þ
respectively, where kp and kl are the wavelengths of the pump and the lasing beam; T is the transmission of the output coupler; L is the total round trip passive cavity losses; s is the fluores-
cence lifetime of the transition (at room temperature s = 3.5 ls [16]); xp and xl are the waist of the pump and lasing beams, respectively; and gp is the pumping efficiency (which is defined as the fraction of the absorbed pump photons that populate the upper laser level). The pump and laser beam radii have the values of 70 and 60 lm, respectively. The presence of pump ESA could affect the pumping efficiency gp. The ESA crosssection at k = 1064 nm is 1020 cm2 and it is much less then the ground state absorption cross-section at this wavelength [15,17,20]. As ESA at 1064 and 1112 nm belong to the same absorption band that is due to the transitions from the 3B2 level to the 1E level [15], the ESA cross-sections at k = 1064 and 1112 nm are the same order of magnitude. Thus, the pumping efficiency gp is set to unity. In Cr4+:YAG laser the transition from the higher-lying levels (excited first either due to the ESA of pump light or ESA of laser radiation) to 3B2(3s2) could be fast, so that their associated lifetimes are small (typical a few ps) [15]. Even if ESA of pump light takes place it does not affect the population of the 3 B2(3s2) level and only affect the pumping efficiency gp. We obtained upper bound values, using pumping efficiency to be unity, for the ratio of the ESA to emission cross-sections. From the slope efficiency (Eq. (1)) and the threshold power (Eq. (2)), one can see that with the increasing exited state absorption cross-section rESA and total cavity losses L the slope efficiency decreases whereas the threshold power increases. Using laser efficiency data, we calculated an average value of 2% for the round trip cavity loss. The calculated value of the SE and ESA cross-sections, averaged over measured data taken for different output couplers for unpolarized pump light are: reu = (2.2 ± 0.2) · 1019 cm2 and rESAu = (1.6 ± 0.3) · 1019 cm2, and for polarized pump are: rep = (2.0 ± 0.2) · 1019 cm2 and rESAp = (0.8 ± 0.2) · 1019 cm2. The SE crosssection is about the same for the polarizedand unpolarized-pump. The estimation for re is approximately two times higher than the reported value of 0.95 · 1019 cm2 [13] but compares favorably with the results of works
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Table 1 Summary of measured ratio of the ESA cross-section to emission cross-section at k = 1.45l Cr4+:YAG
Polarized pumping
Unpolarized pumping
rESA/re [13] rESA/re [18] rESA/re [This work]
0.31 ± 0.07 0.209–0.312 0.40 ± 0.14
0.73 ± 0.25
[18,20]. The most interesting result of this experiment is that the ESA cross-section rESA for unpolarized pump is two times higher than the one for the polarized pump. We compare our results, for the polarized pump, with the results of works [13,18], where polarized light was used to pump the Cr4+:YAG crystal. Table 1 summarizes our results and compares with those obtained from previous studies. Our estimation of the rESA/re for the polarized pump is 0.40, which is in reasonable agreement with earlier results. To understand the measured ESA cross-section being two times higher for the unpolarised pump light than for the polarized pump light, and the slope efficiency being more than two folds higher and the threshold power being less than half for polarized pump with respect to unpolarized pump, the spectral characteristics of the Cr4+:YAG crystal are taken into consideration. The spectroscopy of Cr4+:YAG leads to D2d symmetry point group, which describes the polarization properties of the Cr4+ center emission [15–17]. YAG is a cubic crystal system. Due to the distortion of tetrahedral site, the symmetry is changed into an elongated cube. The actual site symmetry of the optical centers is less than cubic. The site symmetry for Cr4+ is D2d [15]. The site symmetry of Cr4+ centers differs for crystal axis orientation. There are three classes of sites oriented along the crystallographic axes. In the case of D2d symmetry, the electric dipole transitions between any two electronic states must be subdivided by polarization into two types. The first type is for the electric-field vector of light being parallel the S4 local axis of symmetry, and the second type is for an electric vector being perpendicular to this axis, as shown in Fig. 1. Using polarized light, it is possible to selectively excite these oriented classes of ions. A highly polarized
Fig. 4. Energy level diagram for tetrahedrally coordinated Cr4+ ion in D2d point group symmetry. Solid arrows show absorption and emission transitions: (p) – the electric vector of light is parallel to the S4 local symmetry axis, (r) – it is perpendicular to the S4 axis.
emission was reported [16], when Cr4+:YAG crystal was excited with 1064 nm light propagating along one and polarized along another crystallographic axis. The emission intensity in NIR is much stronger when detected parallel to the excitation polarization than when detected perpendicular to it [16]. The pumping wavelength at k = 1112 nm is closed to the absorption band of Cr4+:YAG that belongs to the 3B1(3A2)–3A2(3T1) transition [15,16]. The transitions are shown on energy level diagram (Fig. 4). Energy position of 3A2(3T1) and 3E(3T2) are very close to each other. The 3 B1(3A2)–3E(3T2) electronic dipole transition is allowed for lower symmetry D2d and the absorption from the 3B1(3A2)–3A2(3T1) transition is considerably stronger than that from the 3B1(3A2)–3E(3T2) transition. These two transitions are allowed for p-polarization (the electric vector of light is parallel to the S4 local symmetry axis) and for r-polarization (electric vector is perpendicular to the S4 axis), respectively. The transitions of 3B2–3B1 are forbidden and become partly allowed by electron–vibronic interaction in emission and absorption [15]. The ratio of emission probabilities Ar/ Ap = 0.15 [12] shows that the emission with electric
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vector parallel to local axis S4 is more probable. The ESA transitions are shown in Fig. 4 from 3 B2 and 3E to 3E. From the dependency of optical transmittance and luminescence of Cr4+:YAG crystals on intensity with excitation at 1064 nm, two ground-state absorption cross-sections for different polarization were determined [15]: r0p = (3.9–5.0) · 1018 cm2 and r0r = (1.5–1.9) · 1019 cm2. Absorption from the metastable exited state 3B2(3T2) is negligible (at least for excitation at 1064 nm). Its absorption cross-section for p- and r-polarization is less than 2 · 1020 cm2 [15]. These results have been confirmed in [14]. Our data with the pump at 1112 nm confirm the results of [15] that the ground-state absorption cross-section for p-polarization is much higher than for r-polarization. For the polarized pump we have excitation of only one class of Cr4+ centers and as consequence lasing with linear polarization that is coincident with polarization of the pump beam. When only one class of Cr4+ centers is excited, the ESA is related with these centers. The ESA cross-section for polarized pump along the S4 axis is rESAp = r1p at the lasing wavelength. For the unpolarized pump both types of Cr4+ oriented centers (along [0 0 1] and [0 1 0] axis) are excited. As a result, absorption of the light at the lasing wavelength with particular polarization is related with both types oriented centers along [0 0 1] and [0 1 0] axes. For unpolarized pump rESAu = r1p + r1r. Using the calculated values of ESA cross-sections for polarized and unpolarized pump beams, we estimate ESA cross-section for p-polarization and for r-polarization. These cross-sections have the same order of magnitude giving r1r = r1p = 0.8 · 1019 cm2. In conclusion, the polarization dependence of the ESA in the Cr4+:YAG gain medium is investigated. The SE cross-section at 1450 nm and ESA cross-section for r and p-polarization at 1450 nm are measured. The SE cross-section is about the same for polarized or for the unpolarized pump and is of the order 2 · 1019 cm2. The effect of ESA is considerably higher when unpolarized pump beam is used. The ESA essentially decreases the slope efficiency and increases the threshold power. Due to excitation
of the two types of Cr4+ oriented centers in Cr4+:YAG crystal for unpolarized pumping, the effective ESA cross-section rESAu = r1p + r1r. In the case of pumping by linear polarized light with direction of the electric vector of the pump light along the S4 local symmetry axis, the effective ESA cross-section rESAp = r1p. As r1p @ r1r, for the unpolarized pump beam the effective ESA cross-section appears to be two times higher than for the polarized pump (rESAu = (1.6 ± 0.3) · 1019 cm2, and rESAp = (0.8 ± 0.2) · 1019 cm2). The observed anti-correlation in the output power for the two polarization is associated with ESA. Due to the ESA the two laser beams with orthogonal polarization are coupled. A detailed analysis of this issue is a subject of further work.
Acknowledgements This work was supported by NASA and organized research at the CCNY.
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Polarization influence of excited state absorption on the performance of Cr4+:YAG laser V. Kartazaev *, R.R. Alfano Department of Physics, Institute for Ultrafast Spectroscopy and Lasers and New York State Center for Advanced Technology for Ultrafast Photonics Materials and Applications, The City College and Graduate School of the City University of New York, Convent Ave. at 138th Street, New York, NY 10031, USA Received 22 July 2003; received in revised form 1 September 2004; accepted 2 September 2004
Abstract The polarization dependence of the excited-state absorption (ESA) on the gain of the Cr4+:YAG medium is described. Using laser efficiency data, the emission and ESA cross-section for r- and p-polarization at 1450 nm are determined. Due to excitation of the two types of Cr4+ oriented centers in Cr4+:YAG for unpolarized pumping, the effective ESA cross-section rESAu = r1p + r1r = 1.6 · 1019 cm2 is obtained. The effective ESA cross-section for linearly polarized pumping, with direction of the electric vector along the S4 local symmetry axis, is rESAp = r1p = 0.8 · 1019 cm2. 2004 Elsevier B.V. All rights reserved. PACS: 42.55.Rz; 42.55.Xi Keywords: Laser; Solid-state; Excited state absorption
Since the first demonstration of near-infrared (NIR) laser action in Cr4+-doped forsterite [1] and YAG [2], there has been a great deal of interest in the spectroscopic and laser properties of Cr4+ doped other materials [3–5]. Cr4+:YAG laser has many applications in the areas of communica* Corresponding author. Tel.: +1 212 650 5531/5527; fax: +1 212 650 5530. E-mail addresses: [email protected] (V. Kartazaev), [email protected] (R.R. Alfano).
tions, medicine and imaging. It covers an important spectral region of 1310–1600 nm [6–8]. Cr4+:YAG lasers can be pumped by high power cw lasers such as Nd-doped solid-state laser, Ybdoped fiber laser [9] and direct diode-pumping [10–12]. The presence of excited state absorption (ESA) at the lasing wavelengths is one of most serious limiting factor for efficient laser operation. The ESA process limits the laser efficiency of a Cr4+:YAG laser, resulting in only a few percent
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.09.007
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saturated round trip gain [13,14]. No serious attempts have been made in earlier research to assign the ESA to one or more transitions for differently orientated Cr4+ centers in the host. Spectroscopic studies on Cr4+:YAG showed the D2d symmetry point group describes the polarization properties of the Cr4+ center emission [15–17]. Strong polarization dependence in absorption saturation for Cr4+:YAG was observed [15]. The absorption saturation at 1064 nm can be described by two absorption cross-section: r0p for light polarized along the S4 local symmetry axis and r0r for light polarized perpendicular to the S4 local symmetry axis. The estimation of emission- and ESA-cross-section, using efficiency data for a cw Cr4+:YAG laser that is pumped by Nd:YAG laser, was reported [16,18]. In these works, a Brewster-cut Cr4+:YAG crystal was used and the pump light was linearly polarized. However, neither the polarization dependence effects nor the orientation of the S4 local symmetry axis with respect to the electric vector of the pump beam was discussed in these works. When an unpolarized pump beam is used or when the orientation of the S4 local symmetry axis does not coincide with the electric vector of the pump light, then polarization dependence effects are significant and can reduce the efficiency of the laser operation.
In this article, an investigation of the laser performance is undertaken to study the effects of ESA in Cr4+:YAG crystal and its influence on laser performance for a flat–flat Cr4+:YAG laser crystal using both the plane-polarized and unpolarized pump beams at 1112 nm. It is found that ESA and ESA polarization dependence play an important role in the laser operation. A schematic of the experimental setup to characterize the performance of different states of polarization of Cr4+:YAG laser is shown in Fig. 1. An L-fold cavity with 5 cm radius back mirror and 10 cm radius folding mirror having high reflectivity over 1300–1600 nm range was used. Various output couplers (OC) having 1-, 2- and 5-percent transmission at 1450 nm were used. A total length of the cavity was 42 cm. The Cr4+:YAG laser setup in this configuration was longitudinally end pumped by a commercial cw Fiber laser (JDSUFL10a) operating at 1112 nm. A 5-mm diameter by 2 cm long cylindrical flat/flat Cr4+:YAG rod (Bicron) was wrapped with indium foil and tightly clamped between two copper holders attached to a copper heat sink via a thermoelectric cooler. The temperature of the crystal was maintained at 10 C during the experiments. To prevent water vapor condensation on the crystal surfaces the crystal was purged with dry nitrogen gas. The Cr4+:YAG crystal was oriented along crystallographic axis.
Fig. 1. Schematic diagram of the experimental arrangement for measuring the efficiency of the Cr4+:YAG laser and the orientation of the Cr4+ centers in the YAG crystal (a): L – focusing lens; M1 – 10 cm radius folding mirror; M2 – 5 cm radius back mirror; OC – output mirror; P1, P2 – Glan prisms polarizes; D1, D2 – photodiodes. Insert: p and r are the local symmetry axis and the local symmetry plane of the Cr4+ center – p is parallel to the S4 local symmetry axis, r is perpendicular to the S4 local symmetry axis.
V. Kartazaev, R.R. Alfano / Optics Communications 242 (2004) 605–611
Orientation of the crystal was adjusted such that propagation of the pump beam was along the crystallographic axis [1 0 0]. The crystallographic axis [0 1 0] or [0 0 1] was parallel to the vertically oriented electric vector of the pump light (Fig. 1(a)). A Glan prism (P1) was used to obtain either a vertically or horizontally plane polarized pump beam from the fiber laser. The output power from the laser was measured for both polarization components (i.e., one being parallel and the other being perpendicular to the polarized pump beam). A second Glan prism (P2) was used to separate vertical and horizontal polarization of the output laser beam. The separated polarization components of the laser beam were detected by two different photodiodes (D1 and D2). The intensity dependence of state of polarization of Cr4+:YAG laser on the polarization of the pump Fiber laser was measured. The output radiation of Cr4+:YAG laser was polarized when linearly polarized pump beam was used. The plane of polarization of emission depends on the orientation of the Cr:YAG crystal. When the crystal was rotated so that S4 local symmetry axis coincided with the direction of the electric vector of the pump beam, the plane of polarization of the laser beam was the same as the plane of polarization of the pump beam. When the crystal was rotated for a small angle, the plane of polarization of the laser beam also rotated by the same angle. When the angle between S4 local symmetry axis and the direction of the electric vector of the pump light was nearly 45, lasing for both polarization components was observed. Strong fluctuations of output power at these polarization components were observed. Lasing on both polarization components for an unpolarized pump beam was detected and strong fluctuations of output power at these polarization components were observed. Correlations of fluctuations of laser output in two orthogonal polarizations were measured for unpolarized pump. A light chopper chopped the pump beam to see the dynamics of fluctuations after the pump beam was on. A light chopper was introduced into the pump beam and placed before focusing lens. Signals from two photodiodes for two orthogonal
607
Fig. 2. Temporal dependence of laser output at 1450 nm at two orthogonal polarizations for unpolarized pump (V, vertical; H, horizontal) at 1112 nm.
polarizations were simultaneously recorded in two different channels of a digital oscilloscope. Fig. 2 shows the correlation in fluctuations of laser output for two orthogonal polarizations. When the intensity of one polarization component increased, the other polarization component decreased and vice versa. The observed anti-correlation in the power for the two polarizations occurs in the Cr4+:YAG crystal. It is not due to correlated power fluctuations between the two eigen-polarizations of the pump fiber laser. Measurements of the output power of the fiber laser for different polarizations show that there are no correlated power fluctuations. Moreover, the same anti-correlation in the output power of Cr4+:YAG laser for the two polarizations was observed when linearly polarized pump beam was used and lasing for the both polarization components was observed. Laser efficiency data for Cr4+:YAG laser at the free running wavelength (k = 1450 nm) were recorded for three different output couplers of 1-, 2-, and 3-percent for both the unpolarized and polarized pump beams in two orthogonal directions. The output power as a function of absorbed pump power for output coupler of 1-percent is shown in Fig. 3 for unpolarized pump beam (U) and for polarized beam in two orthogonal directions (i.e., vertical (V) and horizontal (H)). Fig. 3
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Fig. 3. Cr4+:YAG laser output power at 1450 nm as a function of absorbed pump power at 1112 nm for output coupler of 1% for unpolarized pump beam (U) and for polarized beam in two orthogonal directions (i.e., vertical (V) and horizontal (H)).
clearly shows that the threshold power (0.4 W) of the polarized pump is less than half of the threshold power (1.5 W) for the unpolarized pump. The slope efficiencies for the polarized and unpolarized pump beams are 18% and 6%, respectively. Using the slope efficiency and threshold power data (measured for different output couplers) the emission and ESA cross-sections were calculated for both the polarized and unpolarized pump beams. It appears that the excited-state absorption crosssection for unpolarized pump is almost twice more than the cross-section for the polarized pump beam. We calculated the absolute magnitudes of both the stimulated emission (SE) re and ESA rESA cross-section following the model reported by Payne et al. [19]. Similar approach was used in works [13,18]. The expressions for the slope efficiency gs and the threshold absorbed pump power Pth are: gs ¼ ðkp =kl Þgp ð1 rESA =re ÞðT =ðT þ LÞÞ;
ð1Þ
and P th ¼
pðx2p þ x2l Þhmp ðT þ LÞ ; 4re ð1 rESA =re Þsgp
ð2Þ
respectively, where kp and kl are the wavelengths of the pump and the lasing beam; T is the transmission of the output coupler; L is the total round trip passive cavity losses; s is the fluores-
cence lifetime of the transition (at room temperature s = 3.5 ls [16]); xp and xl are the waist of the pump and lasing beams, respectively; and gp is the pumping efficiency (which is defined as the fraction of the absorbed pump photons that populate the upper laser level). The pump and laser beam radii have the values of 70 and 60 lm, respectively. The presence of pump ESA could affect the pumping efficiency gp. The ESA crosssection at k = 1064 nm is 1020 cm2 and it is much less then the ground state absorption cross-section at this wavelength [15,17,20]. As ESA at 1064 and 1112 nm belong to the same absorption band that is due to the transitions from the 3B2 level to the 1E level [15], the ESA cross-sections at k = 1064 and 1112 nm are the same order of magnitude. Thus, the pumping efficiency gp is set to unity. In Cr4+:YAG laser the transition from the higher-lying levels (excited first either due to the ESA of pump light or ESA of laser radiation) to 3B2(3s2) could be fast, so that their associated lifetimes are small (typical a few ps) [15]. Even if ESA of pump light takes place it does not affect the population of the 3 B2(3s2) level and only affect the pumping efficiency gp. We obtained upper bound values, using pumping efficiency to be unity, for the ratio of the ESA to emission cross-sections. From the slope efficiency (Eq. (1)) and the threshold power (Eq. (2)), one can see that with the increasing exited state absorption cross-section rESA and total cavity losses L the slope efficiency decreases whereas the threshold power increases. Using laser efficiency data, we calculated an average value of 2% for the round trip cavity loss. The calculated value of the SE and ESA cross-sections, averaged over measured data taken for different output couplers for unpolarized pump light are: reu = (2.2 ± 0.2) · 1019 cm2 and rESAu = (1.6 ± 0.3) · 1019 cm2, and for polarized pump are: rep = (2.0 ± 0.2) · 1019 cm2 and rESAp = (0.8 ± 0.2) · 1019 cm2. The SE crosssection is about the same for the polarizedand unpolarized-pump. The estimation for re is approximately two times higher than the reported value of 0.95 · 1019 cm2 [13] but compares favorably with the results of works
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Table 1 Summary of measured ratio of the ESA cross-section to emission cross-section at k = 1.45l Cr4+:YAG
Polarized pumping
Unpolarized pumping
rESA/re [13] rESA/re [18] rESA/re [This work]
0.31 ± 0.07 0.209–0.312 0.40 ± 0.14
0.73 ± 0.25
[18,20]. The most interesting result of this experiment is that the ESA cross-section rESA for unpolarized pump is two times higher than the one for the polarized pump. We compare our results, for the polarized pump, with the results of works [13,18], where polarized light was used to pump the Cr4+:YAG crystal. Table 1 summarizes our results and compares with those obtained from previous studies. Our estimation of the rESA/re for the polarized pump is 0.40, which is in reasonable agreement with earlier results. To understand the measured ESA cross-section being two times higher for the unpolarised pump light than for the polarized pump light, and the slope efficiency being more than two folds higher and the threshold power being less than half for polarized pump with respect to unpolarized pump, the spectral characteristics of the Cr4+:YAG crystal are taken into consideration. The spectroscopy of Cr4+:YAG leads to D2d symmetry point group, which describes the polarization properties of the Cr4+ center emission [15–17]. YAG is a cubic crystal system. Due to the distortion of tetrahedral site, the symmetry is changed into an elongated cube. The actual site symmetry of the optical centers is less than cubic. The site symmetry for Cr4+ is D2d [15]. The site symmetry of Cr4+ centers differs for crystal axis orientation. There are three classes of sites oriented along the crystallographic axes. In the case of D2d symmetry, the electric dipole transitions between any two electronic states must be subdivided by polarization into two types. The first type is for the electric-field vector of light being parallel the S4 local axis of symmetry, and the second type is for an electric vector being perpendicular to this axis, as shown in Fig. 1. Using polarized light, it is possible to selectively excite these oriented classes of ions. A highly polarized
Fig. 4. Energy level diagram for tetrahedrally coordinated Cr4+ ion in D2d point group symmetry. Solid arrows show absorption and emission transitions: (p) – the electric vector of light is parallel to the S4 local symmetry axis, (r) – it is perpendicular to the S4 axis.
emission was reported [16], when Cr4+:YAG crystal was excited with 1064 nm light propagating along one and polarized along another crystallographic axis. The emission intensity in NIR is much stronger when detected parallel to the excitation polarization than when detected perpendicular to it [16]. The pumping wavelength at k = 1112 nm is closed to the absorption band of Cr4+:YAG that belongs to the 3B1(3A2)–3A2(3T1) transition [15,16]. The transitions are shown on energy level diagram (Fig. 4). Energy position of 3A2(3T1) and 3E(3T2) are very close to each other. The 3 B1(3A2)–3E(3T2) electronic dipole transition is allowed for lower symmetry D2d and the absorption from the 3B1(3A2)–3A2(3T1) transition is considerably stronger than that from the 3B1(3A2)–3E(3T2) transition. These two transitions are allowed for p-polarization (the electric vector of light is parallel to the S4 local symmetry axis) and for r-polarization (electric vector is perpendicular to the S4 axis), respectively. The transitions of 3B2–3B1 are forbidden and become partly allowed by electron–vibronic interaction in emission and absorption [15]. The ratio of emission probabilities Ar/ Ap = 0.15 [12] shows that the emission with electric
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vector parallel to local axis S4 is more probable. The ESA transitions are shown in Fig. 4 from 3 B2 and 3E to 3E. From the dependency of optical transmittance and luminescence of Cr4+:YAG crystals on intensity with excitation at 1064 nm, two ground-state absorption cross-sections for different polarization were determined [15]: r0p = (3.9–5.0) · 1018 cm2 and r0r = (1.5–1.9) · 1019 cm2. Absorption from the metastable exited state 3B2(3T2) is negligible (at least for excitation at 1064 nm). Its absorption cross-section for p- and r-polarization is less than 2 · 1020 cm2 [15]. These results have been confirmed in [14]. Our data with the pump at 1112 nm confirm the results of [15] that the ground-state absorption cross-section for p-polarization is much higher than for r-polarization. For the polarized pump we have excitation of only one class of Cr4+ centers and as consequence lasing with linear polarization that is coincident with polarization of the pump beam. When only one class of Cr4+ centers is excited, the ESA is related with these centers. The ESA cross-section for polarized pump along the S4 axis is rESAp = r1p at the lasing wavelength. For the unpolarized pump both types of Cr4+ oriented centers (along [0 0 1] and [0 1 0] axis) are excited. As a result, absorption of the light at the lasing wavelength with particular polarization is related with both types oriented centers along [0 0 1] and [0 1 0] axes. For unpolarized pump rESAu = r1p + r1r. Using the calculated values of ESA cross-sections for polarized and unpolarized pump beams, we estimate ESA cross-section for p-polarization and for r-polarization. These cross-sections have the same order of magnitude giving r1r = r1p = 0.8 · 1019 cm2. In conclusion, the polarization dependence of the ESA in the Cr4+:YAG gain medium is investigated. The SE cross-section at 1450 nm and ESA cross-section for r and p-polarization at 1450 nm are measured. The SE cross-section is about the same for polarized or for the unpolarized pump and is of the order 2 · 1019 cm2. The effect of ESA is considerably higher when unpolarized pump beam is used. The ESA essentially decreases the slope efficiency and increases the threshold power. Due to excitation
of the two types of Cr4+ oriented centers in Cr4+:YAG crystal for unpolarized pumping, the effective ESA cross-section rESAu = r1p + r1r. In the case of pumping by linear polarized light with direction of the electric vector of the pump light along the S4 local symmetry axis, the effective ESA cross-section rESAp = r1p. As r1p @ r1r, for the unpolarized pump beam the effective ESA cross-section appears to be two times higher than for the polarized pump (rESAu = (1.6 ± 0.3) · 1019 cm2, and rESAp = (0.8 ± 0.2) · 1019 cm2). The observed anti-correlation in the output power for the two polarization is associated with ESA. Due to the ESA the two laser beams with orthogonal polarization are coupled. A detailed analysis of this issue is a subject of further work.
Acknowledgements This work was supported by NASA and organized research at the CCNY.
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