Analysis of Ultra-Broadband Amplified Spontaneous
Emissions Generated by
Cr
4+
:YAG Single and
Glass-Clad Crystal Fibers
Kuang-Yao Huang, Kuang-Yu Hsu, and Sheng-Lung Huang, Senior Member, IEEE, Member, OSA
Abstract—Numerical analysis and experimental verification of the ultra-broadband amplified spontaneous emissions (ASEs) gen-erated byCr4+:YAG crystal fibers are presented. Milliwatt ASE was obtained from a double-clad 25- m-core fiber. Results of the experimental ASE power measurements and the composition anal-ysis using electron probe micro-analyzer were used to determine the absorption, emission, and excited-state absorption cross sec-tions of pump and signal of the crystal fibers. The numerical anal-ysis showed that the ASE output power is improved by reducing the fiber core diameter down to several micrometers despite of the in-creased consumption in excited-state absorption of pump. A com-parison of the cross sections between those in literature and this work indicates that the crystal fiber has good crystal and optical qualities using the laser heated pedestal growth method. The large pump absorption of theCr4+:YAG crystal fiber limits its useful length. With such short fiber length, the ASE lights can not acquire enough gain. The ASE efficiency can be further improved by using bi-direction and cladding pump structure to increase the crystal fiber length and incorporating a high ASE reflector at the input end of the crystal fiber. TheCr4+:YAG crystal fiber has a po-tential for applying to ultra-broadband ASE light source in wave-length division multiplexing network.
Index Terms—Amplified spontaneous emission, codrawing laser heated pedestal growth,Cr4+, double-clad, fiber amplifier, YAG.
I. INTRODUCTION
D
UE TO THE FAST growing communication need, the re-quired capacity of the optical fiber network has been more than doubled every year and the technology break through in dry fiber fabrication opens the possibility for fiber bandwidth all the way from 1.3 to 1.6 m. The fast increasing demand of communication capacity results in the emergence of wavelength division multiplexing (WDM) technology, enabling tens or even hundreds of channels with different wavelengths transmitted si-multaneously on an optical fiber [1].In consequence, it necessitates the requirement of broadband spectral characteristics of all the optical components used in the optical network systems.
Manuscript received October 27, 2007; revised January 23, 2008. This work was supported in part by the National Science Council, R. O. C.
K.-Y. Huang is with the Institute of Electro-Optical Engineering, Na-tional Sun Yat-Sen University, Kaohsiung, Taiwan 804, R.O.C. (e-mail: [email protected]).
K.-Y. Hsu and S.-L. Huang are with the Graduate Institute of Photonics and Optoelectronics, National Taiwan University, Taipei, Taiwan 106, R.O.C. (e-mail: [email protected]; [email protected]).
Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JLT.2008.919448
Broadband light source is one of the key components in WDM networks. Rare earth elements doped silicate fibers are the most common optical fiber light sources. They are highly efficient and mature techniques already [2]–[9]. Transition metal doped garnet crystals are attractive gain media because of their ultra-broadband emission spectra. The active electrons of transition metal ions are not completely shelled by the electron cloud. The subtle interplay between the Coulomb fields of the host matrix ions and the electron-phonon coupling permit ultra-broad absorption and emission spectra. Among the transition metals, Chromium ion is most suitable for doping into the garnet crystal due to its chemical stability, broad absorption bands and large energy-level splitting. The optical characteristics of various ion doped hosts are listed in Table I [10]–[12]. The 3-dB emission bandwidth of
is 277 nm that covers the widest wavelength range in the communication bands. As shown in Table I, has the largest product; therefore, has a potential for a broadband light source in the future WDM networks.
In this paper, complete analysis of the broadband ampli-fied spontaneous emissions (ASEs) generated by
crystal fibers are presented. The simulations indicate that the ASE efficiency is impacted by the fiber core diameter and the propagation loss. The analyses were verified by the ASE experiments using a codrawing laser heated pedestal growth (CDLHPG) technique for preparing samples with several core diameters [13], [14]. By reducing the core diameter from 920 to 25 m, the brightness of the generated ASE was increased by a factor of 6.8 10 . The emission cross section that fitted with the experiments was 7 10 cm , it was larger than the average in literature. The results show that the CDLHPG technique is able to fabricate high quality crystal fibers. The simulation results also show that by reducing the core-diameter down to few-micrometer with the 4.5-cm ab-sorption coefficient, tens-milliwatt ASE output can be achieved. A comparison between the parameters of Chromium-doped fiber (CDF) and Erbium-doped fiber (EDF) is given.
II. NUMERICALMODEL
The energy level diagram of the crystal is shown in Fig. 1 [15]–[17]. It is basically a four-level system. The ions at ground state are excited to the state by the pumping light. The ions then relax non-radiatively to the meta-stable state . When the electrons translate from to , photons are generates by stimulated 0733-8724/$25.00 © 2008 IEEE
TABLE I
LIST OF THECr -IONDOPEDHOSTSWITH THE3-dB EMISSIONBANDWIDTH1, PEAKWAVELENGTH, EMISSIONCROSSSECTION ,
FLUORESCENCELIFETIME ,AND1 PRODUCT ATROOMTEMPERATURE
Fig. 1. Energy-level diagram ofCr :YAG.
and spontaneous emissions. The broadband spontaneous emis-sion spectrum covers from 1.2 to 1.6 m as shown in Fig. 2. The definitions of , , , , and , are the
popula-tion densities of , , , , and
, respectively. The ions at not only involve the spontaneous and stimulated emissions to the lower state , also the excited-state absorptions (ESAs) of the ASE and pump to a higher state and . The , , and are assumed to be negligible due to the fast non-radiative relaxation rates. The is relaxed to ground state ; both the and are relaxed to meta-stable state
. The rate equation for the is given by
(1) (2) where is the absorption cross section at pumping frequency , is the stimulated emission cross section at emission frequency , is the pumping intensity, is the total ASE intensity including both the forward and backward ASEs, is the fluorescence lifetime, and is Planck’s constant. The total ion density is equal to the sum of the and
Fig. 2. Cr :YAG spontaneous emission spectrum.
since the population densities in all other energy states are as-sumed to be negligible. From (1) and (2), the steady-state solu-tion of the populasolu-tion density can be expressed as
(3) By assuming uniform light intensity across the fiber cross section for and , the transport equations for the pumping and ASE intensities can be expressed as
(4)
(5) where and are the propagation loss constants of the pump and ASE, respectively, and are the ESA cross section of pump and ASE, respectively, is the emission frequency, is the mode number of ASE [18], and is the divided bandwidth of the emission spectrum [19]–[21]. The positive and negative signs in (5) represent the forward and backward prop-agating ASEs, respectively. The ions within a differential fiber length dz contribute to the generation of the spontaneous emission and also the amplification of the forward and backward ASEs.
The computation results indicate that the core-diameter of fiber is a critical factor to the ASE output power. Reduction of the core-diameter can increase the pumping and signal light intensity to obtain higher ASE output power and reduce the number of guiding mode.
III. SAMPLEPREPARATION ANDASE MEASUREMENTS
A. Sample Preparation
In order to verify the effect of the core-diameter on the ASE output power, fibers with several core-diameters were prepared. The laser heated pedestal growth (LHPG) method was used for the growth of the Cr:YAG crystal fiber [22]. The absorp-tion coefficient of the Cr:YAG source crystal rod was 4.5 cm at 1064-nm wavelength. The doping concentration was 0.25 wt.% in the source rod measured by electron probe micro-analyzer (EPMA). Single crystalline 920- and 100- m diam-eter fibers were sequentially grown in the orientation. However, for the growth of fiber with its diameter less than 30 m, it becomes very difficult. It is limited by the power sta-bility of the laser. The CDLHPG technique provides a so-lution to further reduce the core diameter of the fiber. In this way, the resultant core diameter could be reduced to less than 30 m. First, a 68- m diameter Cr:YAG crystal fiber was ob-tained by a two-step growth from a 500- m diameter source rod. Then it was inserted into a fused-silica capillary tube with 76-and 320- m inner 76-and outer diameters. The 1970 C melting temperature of the YAG is comparable to the 1600 C soften temperature of the fused-silica. The heating of the CDLHPG method caused a strong inter-diffusion between the YAG core and fused-silica capillary, and an inner cladding layer made of the mixture was formed. With properly controlled growth pa-rameters, double-clad crystal fibers were obtained. The core diameter of the double-clad fiber was controlled during growth process by adjusting the laser power and the fiber growth speed.
The composition analysis was done by EPMA. The result showed that the core and outer-clad were almost YAG and , respectively. The compositions of the inner-clad were mixtures of YAG and . We also used high-resolution transmission electron microscopy (HRTEM) and selected area electron diffraction (SAED) to confirm that the core structure of the double-clad fiber remained crystalline [23]. The fluorescence intensity and refractive index profiles on the cross section of the double-clad fiber were measured by a laser scanning optical microscope. As shown in Fig. 3, the fluorescence concentrates mainly within the core region. The refractive indices of the core, inner-clad, and outer-clad are 1.82, 1.66, and 1.46, respectively. The uniformity of the core diameter is very sensitive to the heating power by the laser. The laser power was maintained with 0.5% stability by using a motorized polarizer with a feedback control loop for obtaining a 25- m core double-clad fiber. For fabricating a fiber with core-diameter smaller than 25- m double-clad crystal fiber, a better control of the heating laser power is required.
Fig. 3. Image (top) is the end face of the double-cladCr :YAG crystal fiber. The figure (bottom) shows the refractive index andCr fluorescence profiles.
Fig. 4. ASE powers versus pump powers for the samples with core diameters of 920, 100, and 25m. The dots and the lines represent the measured and the simulated data.
B. ASE Measurements
A 1064-nm Yb-fiber laser with its wavelength at the peak of the absorption spectrum was used to pump the crystal fibers with 920-, 100-, and 25- m core di-ameters. We used the end pumping scheme for the ASE genera-tion. The pump light was launched into the core at one polished end of the crystal fiber. The corresponding fiber lengths were 1.5, 4.7, and 5.5 cm, respectively. Fig. 4 shows the measured and simulated ASE powers as a function of the absorbed pump power. In the experiments, the ASE efficiency of 25- m core fiber with the strongest optical confinement obtained the higher
TABLE II
SUMMARY OF THEABSORPTION, EMISSION,ANDEXCITED-STATE ABSORPTION OFPUMP AND
SIGNALCROSSSECTIONS OFOURCRYSTALFIBER ANDSAMPLESDESCRIBED IN THELITERATURES
efficiency. The roll-off in the 25 m curve is due to the short CDF length. The ASE power can be further improved by both reducing the core diameter and increasing the fiber length.
IV. DISCUSSION
A. Parameter Fitting
The ratio between the absorption and emission cross sections is critical to the ASE efficiency. Table II shows the absorption, pump ESA, emission, and signal ESA cross sections of our fiber and the samples described in literature. The means of the absorption, pump ESA, emission, and signal ESA cross sections of the crystals described in literature
are 30.4 cm , 7.88 cm , 3.1 cm ,
and 2.2 cm , respectively. For our fiber, these pa-rameters derived from curve fitting are 22 cm ,
4.18 cm , 7 cm , 1.4 cm ,
respec-tively. The crystal fiber growth by the LHPG method has large emission cross section compared with the average value in literature while the absorption cross section is slightly lower than the average value. The average pump and signal ESA cross sections of our samples are also lower than the average value. Over all, the fitting result shows that the double-clad crystal fibers have good quality for optical emission.
The numerical aperture of the double-clad 25- m core fiber is around 0.75 from the refractive index measurement in the Fig. 3. The normalized frequency -value of such a fiber is 56 at 1.4- m wavelength. By the curve fitting, the ASE mode numbers were 5, 28, and 120 in the 25-, 100-, and 920- m crystal fibers; though the mode estimation should all exceed 1000 modes depended on -value. It implied that the few modes were generated and guided in the active waveguide.
B. Power Budget of the Pump Laser
The power budget of pump power for the ASE experiment of the 25- m core fiber was calculated by the simulation. Table III shows the simulated power budget of one-watt absorbed pump
Fig. 5. Cr :YAG emission spectra.
power to the propagation losses and ESAs of pump and ASE, quantum defect, nonradiative decay of population, and ASE, re-spectively. From the simulation of fibers with several core-di-ameters, the results indicated that the ASE efficiency rises up with the reduced core diameter, although the pump ESA dissi-pation also increases. The conditions for each case ESA were optimized for the highest ASE output. The absorption coeffi-cient of pump was assumed to be 4.5 cm . The mode number of local spontaneous emission was assumed to be one to sim-plify the uncertain value of mode number. The simulation re-sults were shown in Table III.
When the core diameter was reduced from 25 to 4 m, the ASE output can be improved around from 0 to 18 dBm. For the 4- m core case, the major loss is the pump ESA which is dou-bled that compared to the loss of 25- m core fiber case. Fig. 5 shows the measured emission spectra of bulk crystal and 25- m core fiber, and simulated ASE simulation of 4- m core fiber. The emission bandwidths were 277, 265, and 205 nm, respectively. As the efficiency increase, the ASE spectra width decreases, mostly in the 1.5- m region.
TABLE III
LIST OF THEPOWERBUDGET OFFIBERSWITHSEVERALCOREDIAMETERSWITHONEWATTPUMPPOWER. THESECONDCOLUMN IS THENUMERICALANALYSIS OF THE ASE EXPERIMENTWITH25-m COREFIBER. THETHIRD ANDFOURTHCOLUMNSCALCULATE THEREQUIREMENTS TOOBTAINTENS-MILLIWATTASE OUTPUT
C. Absorption Coefficient
The doping distributions on the cross sections of the crystal fibers were measured by the EPMA. From the measurement re-sults with several growth conditions, it was observed that the Cr ion concentration decreased after each growth. The decrease is due to Cr ions out diffusion and evaporation at the perimeter of the fiber during growth. The average concentration of CaO, acting as charge compensators, only slightly decreased by less than 10%. But the average concentration decreased quickly during the fiber diameter reduction process. The average concentration during the size reduction process of the crystal fiber is shown in Fig. 6. An empirical formula for the av-erage concentration was derived as
when (6)
where is the average concentration of the source rod material, and are the growth speed and pull/push speed ratio, respectively. is the diameter of source rod.
Crystal fiber grown from a source rod with a larger diameter and at a faster speed will have higher Cr concentration because it takes longer time for the Cr ions to diffuse from the molten zone center to the circumference. For the case of the 25- m core fiber, the concentration was reduced from 0.25 wt.% to 0.04 wt.% with two diameter reduction steps. The absorption coefficient reduced significantly from 4.5 cm to 0.7 cm . Although the absorption coefficient is reduced, it is still rather large from the fiber amplifier’s point of view. For constructing an efficient fiber ASE light source, a longer length of CDF is desired so the spontaneous emission captured by the fiber can be sufficiently amplified as it propagates along the gain fiber in either forward or backward direction. However, the pump ab-sorption along the fiber is large due to the relatively large ground state absorption and the ESA of the pump. To replenish the Cr
Fig. 6. AverageCr O concentrations of various fiber diameters.
ions can further reduce the required CDF length for ASE light source. The circumferential surface of the source rod can be de-posited with the thin layer after the first growth step, the Cr ions then diffuses into the 68- m core fiber in the second growth step.
D. Propagation Loss
By using the cut-back method, the propagation losses of the single crystal fiber and double-clad crystal fiber were found to be 0.6 dB/cm and less than 0.2 dB/cm at the wavelength of 1064 nm. The propagation loss of the double-clad crystal fiber is less than that of the single crystal fiber. The major reason is due to the strong inter-diffusion between the fused-silica and YAG during the CDLHPG process for fabricating the double-clad fiber. It has a smooth and clear interface between the core and the inner-clad, so the scattering of the interface defects can be reduced. Also the core diameter and the refractive index dif-ference between core (1.82) and cladding (1.66) were reduced.
TABLE IV
PARAMETERS OF THECDFAND ATYPICALERBIUMDOPEDFIBER, WHERE THE IS THEABSORPTIONCROSSSECTION FOREMISSION
WAVELENGTH. THEv ISASSUMED TO BE THE1400-nm CENTER
EMISSIONWAVELENGTH FORCALCULATINGI
During the fiber growth, the temperature gradient between the interface of the solid and the melt is as high as 1 C/cm; therefore, residual strain exists in the interface between core and inner-clad of the double-clad fiber. To release the residual strain and further reduce the propagation loss of the double-clad fiber, post-growth annealing is suitable.
E. Comparison Between CDF and EDF
The important optical parameters of the CDF and a typical EDF are summarized in Table IV [33]. The active ion concen-tration of a typical EDF is much higher than the CDF’s. This is because the Erbium ions in the silica host are naturally in the de-sired trivalent state. The highest Erbium doping concentration is limited by the interactions between the Erbium ions like up-con-version and concentration quenching. Unlike the EDF case, the Chromium ions in the YAG host are initially in the trivalent state. A charge compensation mechanism is used to turn the oxi-dation state of some of the Chromium ions into the quadrivalent state. The charge compensation efficiency for generating ions out of the ions is typically less than 6%. Most of the Chromium ions still remain in the trivalent state. This charge compensation efficiency is the limiting factor of the con-centration. As described in the previous section, the Chromium ions evaporate out of the melt during the fiber growth process so the concentration of the fiber further decreases.
The pump absorption cross section and the signal stimulated emission cross section of the CDF are several orders of magni-tude larger than those of the EDF. As shown in (4) and (5), the
absorption constant and the gain constant are related to the prod-ucts of the ion concentration and the corresponding cross sections. These products and of the CDF are 35 and 5 times larger than those of the EDF. This implies required CDF length will be shorter, which is favorable with consideration of the significant propagation losses of the CDF. The CDF length could be even shorter by increasing the doping concentra-tion. The product related to the gain constant of the CDF is absolutely large as compared to that of the EDF. However, for the application of fiber ASE light source, the relative magnitude of compared to its own product is more suitable for evaluation of its performance. The product of the CDF is about one third of its product. If including the effect of the ESAs of the pump and ASE, the ratio of the ASE gain con-stant to the pump absorption concon-stant becomes even smaller. As a result, before the ASEs acquire sufficient gain the pump light in CDF already decays below its pump saturation inten-sity and has no ability to achieve population inversion within a short fiber length. Using the EDF as a reference, its product is two times of the product for 980-nm pump. Therefore the ASE can acquire enough gain while it propagates along the gain fiber. The ratio is a useful parameter in evaluating an optical material for a fiber ASE source or ampli-fier. Although the wide emission bandwidth is very attractive, the light amplification ability of the is not so strong as its ratio is only 0.318. For EDF, the ratios are 2 and 2.78 for 980- and 1480-nm pumps, respectively. Measures to further improve the ASE efficiency of CDF are necessary. In order to extent the CDF length that the pump light can deliver its power along and thus improve the ASE powers, the bi-direc-tional pumping scheme is suitable. In addition, since our CDF has a double-cladding structure, cladding pump scheme is useful in relieving the pump absorption while keeping the same gain constant since both the forward and backward ASEs are only propagating in the core. Incorporating a high reflectivity mirror at the input end of the CDF will improve the ASE efficiency be-cause the backward ASE is reflected and can experience more gain as it travels again through the CDF.
The lifetime of the CDF is about three orders of magnitude shorter than that of the EDF. The pump power for EDF can be as low as a few tens of milliwatts but still maintaining a good optical efficiency due to the long lifetime of the Erbium ion. For CDF the much shorter lifetime of the excited ions leads to a faster spontaneous emission rate. As a consequence, a faster pumping rate is required for the CDF for maintaining the excited state population. The saturation intensities described below are useful in evaluating the optical materials as gain media
(7) (8) where and are the saturation intensities of the pump and ASE, is the emission frequency. As shown in Table IV, the pump saturation intensity of the CDF is about two times larger than that of the EDF. The much larger cross-sections of CDF compensate the drawback of its short lifetime. So the much shorter lifetime of the CDF does not cause a serious issue in
achieving population inversion. But when taking into consider-ation that the core diameter of the CDF is much larger than the EDF’s, which can be as small as 3–4 m, the pump power of CDF will be much larger. In our calculation, the pump power for the CDF should be at least in the order of watt level to have a better ASE output power. The low ASE efficiency of the CDF can be ascribed to the relatively small emission cross-section, compared with its own pump absorption cross-section.
V. CONCLUSION
A complete numerical model was established for investi-gating the ASE efficiency of the crystal fibers. The numerical results shows that the ASE efficiency is significantly influenced by the core diameter of the crystal fibers. But it also tormented by the pump ESA with the reduction process of the core diameter. As the simulations, the ASE power could be improved from 0 dBm to 18 dBm for a 4- m core fiber with an absorption coefficient of 4.5 cm in one watt pump. In our experiments, the ASE efficiency of a 25- m core double-clad fiber was demonstrated to have improvements compared with those of the 920- and 100- m core single crystal fibers. By curve fitting of the ASE experiments for the absorption, emission, and ESA of pump and signal cross sections, they were found to be 22 cm , 7 cm , 4.2 cm , and 1.3 cm , respectively. Compared with those in literature, the crystal fibers grown by LHPG method are good in optical performance and crystal quality. The present low ASE efficiency of the CDF is ascribed to the relatively low emission cross-section and the large ground-state and excited-state absorption cross sections of the pump. The ASE efficiency can be further improved by using bi-directional and cladding pump structure to extend the CDF length and increase ASE gain and incorporating a high ASE reflector at the input end of CDF to redirect the backward ASE.
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Kuang-Yao Huang was born in Kaohsiung, Taiwan,
in 1978. He received the B.S. degree in electrical engineering from National Sun Yat-Sen University, Taiwan, R.O.C., in 2001, and the M.S. degree from the Institute of Electro-Optical Engineering, National Sun Yat-Sen University, Taiwan, R.O.C., in 2003, where he is currently pursuing the Ph.D. degree.
His research interests include the developments of ultra-broadband amplified spontaneous emission light source, optical amplifier, and fabrication of the crystal fiber with special attention to growth control.
Kuang-Yu Hsu was born in Hualien, Taiwan,
R.O.C., in 1968. He received the B.S. and M.S. degrees from National Taiwan University, Taiwan, R.O.C., in 1990 and 1994, respectively, both in electrical engineering. He is currently pursuing the Ph.D. degree at the Graduate Institute of Photonics and Optoelectronics, National Taiwan University.
He has worked in the microwave communication system and the fiber-optics industries for years. His research interests include the design, fabrication, and characterization of the erbium-doped and chromium-doped fiber amplifiers, optical switches, and fiber polarizers.
Sheng-Lung Huang (M’98–SM’04) was born in
Taipei, Taiwan, R.O.C., in 1964. He received the B.S. degree from National Taiwan University (NTU), Taiwan, R.O.C., in 1986, and the M.S. and Ph.D. degrees from the University of Maryland, College Park, in 1990 and 1993, respectively, all in electrical engineering.
He is currently a Professor and the Chairman of the Graduate Institute of Photonics and Optoelectronics, NTU. His research interests include laser and non-linear crystal fiber growth, diode laser pumped solid-state lasers, and dielectric thin-film deposition. He worked for the Institute of Electro-Optical Engineering, National Sun Yat-Sen University, before joining NTU.
Dr. Huang is a member of the Optical Society of America and the Photonics Society of Chinese-Americans. He served as Chairman of IEEE/LEOS Taipei Chapter in 2005–2006, and is presently a Topical Editor of Optics Letters.
