Abstract

We report a novel type of active fiber – tapered double clad fiber suitable for pumping by low brightness sources with large beam parameter product of 50÷300 mm×mrad. Ytterbium double clad all-silica fiber (core/1st clad/2nd clad diameters 27/834/890 µm, NAcore=0.11, NAclad=0.21), tapered down by a factor 4.8 for a length of 10.5 m was drawn from a preform fabricated by plasma chemical technologies. At a moderate Yb-ion concentration and 1:31 core/cladding ratio, the tapered double clad fiber demonstrates 0.9 dB/m pump absorption at 976 nm and excellent lasing slope efficiency. An ytterbium fiber laser with 84 W of output power and 92% slope efficiency, a 74 W superfluorescent source with 85% slope efficiency and amplifiers operating both in CW and pulsed regimes have been realized. All devices demonstrated robust single mode operation with a beam quality factor of M2=1.07.

©2008 Optical Society of America

1. Introduction

Fiber laser technology has attracted significant interest during the last decade. The breakthrough in ytterbium fiber laser power scaling looks especially remarkable. Kilowatt-level fiber lasers and amplified laser systems have been demonstrated recently [1, 2].

A double clad amplifying fiber is a key component of a fiber laser. This fiber usually contains a core doped with rare earth elements and the cladding, where pump radiation propagates. Small-signal cladding pump absorption can be estimated from the expression [3]:

αDCfiber=αcore·AcoreAclad

where αcore is core absorption, Acore, Aclad are core and cladding areas, correspondingly.

It can be seen from this equation that the pump absorption increases with the core absorption αcore, i.e. with doping level and/or with the core/clad ratio. These two options available for improvement of the efficiency of pump absorption are, however, restricted.

Particularly, the photodarkening effect [4-6] and background loss [7] set the upper level of rare ions concentration. The acceptable level of in-core absorption limited by the photodarkening effect is about 600-800 dB/m at 976 nm. But even when photodarkening effect is low, a high concentration of dopants may lead to a notable background loss of up to 50-200 dB/km caused by partial glass crystallization in the presence of rare earth ions [7]. The high level of background loss would obviously result in poor efficiency of the fiber lasers and amplifiers. This is one reason why the typical slope efficiency observed experimentally from ytterbium double clad fiber lasers and amplifiers is below 70-80% [2, 8-10], though the theoretical limit is over 90%.

Another method of pump absorption enhancement is scaling of the core/clad ratio. This can be achieved in two ways. First, an increase of the core diameter with simultaneous reduction in the numerical aperture (e.g., down to 0.05 in [2]) allows the V-parameter to be kept relatively small, e.g. V=5.7 in [2] and V=7.4 in [8]. With appropriate bending of the fiber, a nearly diffracted-limited beam quality could be maintained even with enlarged core diameter, e.g. M2=1.4÷1.6, as shown in [2, 8]. Another way to increase the core/clad ratio is to use a photonic crystal fiber (PCF) with a large outer fiber size [9, 10]. However, such devices can not, however, be anymore regarded as truly fiber systems since PCF now represents an unbendable rod-like gain medium with a diameter of a few millimeters. The quality of the fundamental mode regime and the corresponding value of M2 that can be achieved using this approach are still to be reported [10]. It should be noted that the analysis made using Eq. (1) is incomplete since it does not take into account saturation of pump absorption. Indeed, the pump radiation in a cladding propagates in a highly multimode regime. Effectively, it is possible to sort out all these modes into two groups – “well absorbed” and “weakly absorbed” modes. The modes of the first type have an axially symmetrical field distribution with a maximum of intensity at the doped core in the center of a fiber, and are well absorbed, thus contributing efficiently to gain. The other group includes the modes that have poor overlap with the doped core and, therefore, do not contribute notably to pump absorption. These modes could, however, carry a significant fraction of pump power.

In terms of ray optics, there are meridian rays which propagate along the fiber crossing an optical axis of the fiber and skew rays, which are also guided, but propagate in spiral trajectories without core crossing and, as result, without significant absorption. Schematically pump absorption occurs according to the following scenario. The “meridian” modes are absorbed very quickly during the propagation through the initial meters of fiber, while the residual unabsorbed pump corresponding to the “skew” modes propagates practically without significant absorption. Consequently, the first meters of a fiber have significantly higher absorption since the modal content of the pump in double clad fiber is varies strongly along the fiber.

The decrease in pump absorption with propagation distance could be prevented by using a fiber with broken axial symmetry. Among numerous shapes of proposed fiber cross-section, the most popular are truncated or D-shaped, double truncated or double D-shaped, core-offset, octagonal and helical fibers [3, 11-18]. Generally, this method, however, does not eliminate the saturation of pump absorption; instead, the saturation length just becomes slightly longer [12]. An essential problem with non-symmetrical fiber is practical handling. Indeed, the splice of non-symmetrical and conventional circular fibers usually exhibits optical losses for both pump and signal.

An alternative solution for enhancing the pump absorption is introducing the non-regularity in the mode propagation by external mechanical perturbations. Granular matter embedded chaotically in the cladding would cause a non-regular periodical bending of the fiber and lead to a chaotic mode coupling [19]. This mode coupling would direct power from “weakly absorbed” modes to “well absorbed” modes. This technique could be effectively applied only to thin fibers, typically up to 125 µm of outer diameter because the mode coupling coefficient is inversely proportional to the sixth power of the fiber outer diameter [20]. The embedding of “truncated regions” or “filaments” directly into the cladding enhances the scattering of pump light propagated in the cladding [21]. Obviously, this causes efficient mode mixing; however, it would also inevitably lead to a certain loss of pump.

Marcuse has shown that the bending could induce an efficient mode coupling to the waveguide [22]. Based on this observation, non-regular properties could simply be achieved by coiling fibers with special shapes, e.g. kidney, figure-eight, etc. that apply different radii of bending to different fiber locations. As it was shown in [23], bending of one-meter-long piece of Er-Yb fiber could increase absorption by 10.7 dB: from 2.7 dB for straight fiber to 13.4 dB after figure-eight bending. Unfortunately, since the absorption depends strongly on the specific shape of a fiber, this technique has poor reproducibility. Apparently, this approach can be applied only to relatively thin fiber, typically with a diameter less than 400 µm.

Thus, considering that the pump absorption can be essentially increased by using various mode mixing methods, Eq. (1) should be modified by introducing a mode scrambling factor S:

αDCfiber=αcore·AcoreAclad·S

The value of the factor S depends on the exact mechanism of mode mixing applied for a given fiber and could describe the observed increase in pump absorption [23]. The factor S is a ratio of pump absorption in an arbitrary, e.g. longitudinally or transversally non-uniform DCF relative to absorption in a circular, symmetrical and uniform double clad fiber with the same in-core absorption and core/clad area ratio. The value of S factor, therefore, shows an increase in the pump absorption induced by the enhancement of the mode mixing owing to the broken transversal symmetry or longitudinal scrambling in a fiber.

In this work we propose and demonstrate a tapered double clad fiber (T-DCF) that offers a significantly enhanced capability for pump absorption. The proposed fiber design allows for efficient launching of pump light, could have high immunity to photodarkening, and superior slope efficiency. Such fiber has a number of obvious advantages as compared to regular fibers:

  • Efficient intrinsic mode scrambling mechanism for cladding modes. Significant pump absorption in a fiber is due to large value of mode scrambling factor S rather than to a high dopants concentration or a large core/clad ratio. Therefore, using an active tapered fiber allows remarkable properties to be achieved - a high pump absorption in combination with low dopants concentration featuring low background loss. A low doping level would also result in substantial suppression of the photodarkening effect and background losses would allow for efficiency approaching the ultimate value of 90% attainable for ytterbium fiber;
  • Large clad diameters, perhaps up to 2 mm, make T-DCF suitable for using pump sources with poor beam parameter product (BPP) (50- 300 mm×mrad) and would allow for essential increase in output power;
  • Fundamental mode operation could be preserved for large core diameter (tens of microns).

2. Properties of tapered double clad fibers with active core

Tapered active double clad fiber can offer attractive features as compared to ordinary, axially uniform, fibers. The most important properties are a high rate of cladding pump absorption, non-reciprocity of spectral response and high slope efficiency (or pump conversion efficiency). In this section we will discuss the special features of light propagation caused by tapered geometry.

2.1. Pump absorption in T-DCF

As it was mentioned above, the saturation of the pump absorption caused by preferable absorption of certain modes is a main disadvantage of axially regular double clad fibers. The intrinsic reason of this property is the identical characteristics of the regular DCF waveguide over the entire length. T-DCF as an essentially non-regular waveguide has a distinguishing difference owing to the gradual change in the mode content along the fiber. Strictly speaking, the modes in T-DCF should be identified for every given cross-section independently and it is unconstructive to introduce the modes for entire T-DCF.

Following to Marcuse [24], the T-DCF can be approximately modeled with a sequence of uniform multimode fibers with different diameters, as it is shown in Fig. 1. Each of these “partial fibers” guides the specific set of modes. The excitation of all guided modes then occurs in the consecutive fiber by illumination from the preceding fiber with larger diameter thus recovering the quasi-equilibrium mode distribution broken by the mode-dependent absorption [24].

 figure: Fig. 1.

Fig. 1. T-DCF: the optical equivalent scheme

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The different overlap of modes with fiber core allows to distinguish well and weakly absorbed modes in each partial uniform fiber in this step-like taper structure. The fraction of the pump power initially concentrated in the “well absorbed” modes will be rapidly depleted; therefore, the mode content gradually evolves in a partial fiber due to different mode absorption in favor of weakly absorbed modes. This schematic presentation of the tapered structure simulates the mechanism when the “quasi-equilibrium” mode content lost by the selective mode absorption in the uniform part of the guide is recovered at the step-like transition by excitation all guided modes thus ensuring the efficient mechanism for mode mixing. Similarly, the mode content modified by different mode absorption during the light propagation in T-DCF is continuously recovered and thus the population of “well absorbed” modes is maintained.

Ytterbium doped T-DCF was made by drawing on a tower with special pulling regime. The total length was 10.5 m and cladding diameter was dependent on the length as shown in Fig. 2. The preform fabricated by plasma chemical deposition technology [25] has been polished at one side with a 1:0.88 ratio. The preform was then coated by fluorosilicate glass with a low refractive index. Core/clad diameter ratio was 1:31 and numerical apertures of core and cladding were 0.114 and 0.21, respectively. The cross section of fiber is shown in the Fig. 2 as an inset. The core and cladding diameters of the wide part of the tapered fiber were 27 and 834 µm, respectively; the dimension of the truncated part was 732 µm. The core and cladding diameters of the narrow part were 5.8 and 177 µm. The length-dependent outer diameter and corresponding normalized frequency V with a maximum value of V=9.1 is shown in Fig. 2. The taper ratio is 1:4.8. The shape of the fluorosilicate glass cladding was slightly non-uniform and varied within a 35-54 µm range, as seen from Fig. 2, inset.

 figure: Fig. 2.

Fig. 2. T-DCF clad diameter and normalized frequency as function of fiber length.

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The small-signal in-core pump absorption is 280 dB/m at 976 nm. The measured pump absorption in T-DCF was 9.6 dB or 0.9 dB/m. The background loss of T-DCF found from measurement was 10 dB/km at 1µm.

Double clad pump absorption of uniform (non-tapered) fiber with 1:31 core/clad ratio and core absorption of 280 dB/m was found from Eq. (1) to be 0.29 dB/m. The experimentally measured pump absorption of longitudinally uniform fiber pulled from the same preform as the taper has demonstrated an even lower value of 0.22 dB/m at 976 nm. By contrast, the pump absorption of the double clad T-DCF was 0.9 dB/m. In other words, the pump absorption increases compared with ordinary double clad fiber due to a higher value of the mode scrambling factor S [Eq. (2)] which rises from 1 for uniform fiber to 4.1 for T-DCF. The higher level of double clad pump absorption can be explained by efficient cladding mode mixing occurring in the T-DCF.

2.2. Non-reciprocity of T-DCF

The non-reciprocal spectral response is an interesting property of a T-DCF. Indeed, the taper has demonstrated essentially different spectral characteristics for different directions of light propagation. Generally speaking, the taper spectral selectivity is a known effect which has been observed earlier [26, 27], though it was not studied in detail.

The T-DCF spectral selectivity has been studied experimentally. The spectral response of the tapered fiber has been measured with an optical spectrum analyzer and light from the broadband source launched into the fiber core.

The results of experiment displayed in Fig. 3 show the spectral transmission for light propagation from wide-core end towards narrow-core end (black line) and for the opposite direction (red line).

The physical mechanism behind this phenomenon is the multimode character of light propagation in a wide section of the taper, whereas the narrow part of it is a single-mode waveguide. Due to modal interference in the wide multimode part of the taper and subsequent spatial filtering in the single-mode part, the intermodal phase delays are converted into a light intensity modulation. This effect has been studied earlier for multimode fiber as a technique for differential phase modulation [28]. Obviously, the intensity of this intermodal interference pattern has strong wavelength dependence.

 figure: Fig. 3.

Fig. 3. Transmission characteristic of T-DCF: from wide end towards narrow end (black line) and in the opposite direction (red line).

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Spectral selectivity can be observed only for light propagating towards a narrow single-mode section of the taper and when the multimode radiation has been excited in the wide section of taper. Conversely, when light propagates from the narrow to the wide section of the T-DCF, the spatial filtering owing to the interference pattern and, consequently, the spectral selectivity will not be developed. Spectral selectivity will obviously be suppressed when only the fundamental mode has been launched into the multimode end of taper.

As expected from the above consideration, T-DCF displays a strong spectral selectivity with a contrast up to 10 dB for the propagation direction from the wide end towards the narrow end, as seen from Fig. 3 (black line). The specific shape of the spectral dependence is determined by the spectrum of the guided modes excited in the fiber core at the wide end of a taper. In the opposite direction for light propagating from the narrow towards the wide end there is no signature of any spectral selectivity, as can be seen from Fig. 3 (red line).

Another distinctive feature of an active tapered fiber is a difference in the numerical apertures for light propagating in different directions. We assume that the light with large angle divergence, e.g. amplified spontaneous emission (ASE), propagates in a taper, as schematically illustrated in Fig. 4.

 figure: Fig. 4.

Fig. 4. Ray traces in a cladding of T-DCF.

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The numerical apertures for ASE propagating from the fiber position with the local diameter d towards the narrow end and wide end, respectively, without vignetting are different and can be expressed in the form [29]:

NAright=d2d·NAcoreθn2coreNAcore2·(d2d)2and
NAleft=d1d·NAcore+θn2coreNAcore2·(d1d)2,

where d1, d2 are core diameters at the wide and narrow ends of taper, respectively, NAcore=n2coren2clad1 , θ is the angle of the core taper, equal approximately to d1d22L , L is the length of the taper.

The angle θ is small, about 1 µrad and, therefore, the ratio of numerical apertures can be found from Eqs. (3) and (4):

NArightNAleft=d2d1

This expression shows that for any local cross-section of the taper, the ASE power emitted towards the wide end is higher than the power guided to the opposite direction by a factor d21/d22.

2.3. Pumping of T-DCF

The rays propagating in an axially uniform cylindrical optical fiber undergo multiple total internal reflections and maintain the certain angle of propagation with respect to the fiber axis. In contrast, the ray trajectory of light traveling in the T-DCF gradually changes its angle relative to the optical axis of the fiber after each reflection [29, 30]. Eventually, when the propagation angle of the pump radiation exceeds the critical angle of total internal reflection, the light could not be confined within the pump cladding, i.e. it radiated away from the fiber by the so-called vignetting process.

Thus, the two basic mechanisms of pump depletion in T-DCF are vignetting and absorption in the active core. The contribution of each mechanism can be estimated using the numerical aperture for pump radiation guided by the cladding. The numerical aperture of the cladding NAclad for the light propagating from large to small end of the taper without vignetting can be found from the expression [29]:

NAclad=D2D1·NAΩn2clad1NA2·(D2D1)2,

where D1, D2 are cladding diameters for wide and small ends of the taper, respectively, NA=n2clad1n2clad2 , Ω – angle of a taper cone, approximately equals D1D22L to L–length of the taper.

The estimation for the numerical aperture of the cladding for the light propagating towards the small-diameter taper end obtained from this expression is then NAclad=0.044.

The fraction of the pump power lost due to a vignetting in T-DCF has been experimentally estimated using the laser setup shown in Fig. 5(b). The lens with a high numerical aperture of NA=0.15 (≫NAclad=0.044) was used for pump launching. The pump conversion efficiency of the laser of 82% found from the measurement was close to the theoretical limit of 92% determined by the quantum defect, i.e. by λpumpsignal ratio. This feature gives evidence that the pump loss due to vignetting could be neglected and the actual loss of pump power is mainly due to ytterbium ions absorption.

Additionally, the launching scheme with fully filled numerical aperture (NA=0.21) had been studied to illustrate this effect. The slope efficiency of the laser was found to drop down to 30% providing direct evidence of high pump loss due to vignetting when the angle aperture is entirely filled. Therefore, the pump light should be launched into a taper by filling only the fraction of the angle aperture to avoid early vignetting before significant depleting of the pump occurred.

3. Experimental demonstration of T-DCF applications

3.1. Ytterbium doped tapered fiber laser and superluminescent source

Several optical sources based on T-DCF have been constructed during the course of this study – the lasers and a high power superfluorescent source.

The fiber lasers with T-DCF are shown in Figs. 5(a) and 5(b). The emission of a multimode-fiber coupled pump diode laser was used as a pump source with a core/clad ratio and numerical aperture of the multimode fiber of 200/220 µm and NA=0.22, respectively. 135 W at 976 nm from the multimode fiber output of the pump diode laser were launched into a wide part of taper via lenses and dichroic filter resulting in a total coupling efficiency of 85%.

 figure: Fig. 5.

Fig. 5. Schematics of optical sources with T-DCF.

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Three different laser configurations have been investigated experimentally. First, a cavity was formed by 4% Fresnel reflections from both taper ends, as shown in Fig. 5(a). The second cavity uses Fresnel reflections from the wide-core end of the taper and high reflecting (HR) broadband mirror as the other cavity reflector, see Fig. 5(b). The third laser cavity tested contains a fiber Bragg grating (FBG) spliced with the narrow-core side of the taper, see Fig. 5(b), inset.

The of output power as a function of absorbed pump power for the R1,2=4%;4% cavity is shown in Fig. 6. The laser generates dominantly throughout a wide-core output 1 indicated in Fig. 5(a) with a ratio of powers radiated through output 1 and output 2 of approximately 1:25.

The slope efficiency for output 1 in this laser is 91.8%, and the slope efficiency for the total power (output 1 plus output 2) is 93.2%, both with respect to the absorbed pump power.

 figure: Fig. 6.

Fig. 6. Output characteristics of T-DCF laser with R1,2=4%;4%. (a) Output power versus absorbed pump power; Inset : emission spectra for output 1 (black line) and output 2 (red line). (b): beam profile (dots) and Gaussian fit (red line) for output 1. M2=1.07.

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Highest pump conversion efficiency achieved for both outputs is 79.3%. It can be seen from Fig. 6 (inset), that the spectra of emission coming from wide and narrow ends of a tapered laser are essentially different.

The output power versus absorbed pump power for the laser with a broadband high reflective mirror [Fig. 5 (b)] is shown in Fig. 7(a) with a spectrum plotted in Fig. 7(b).

 figure: Fig. 7.

Fig. 7. Output characteristics of T-DCF laser with broadband HR mirror: (a) output power versus absorbed pump power (b) spectrum of output radiation.

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The slope efficiency of this laser with respect to the absorbed pump power is 88%. Pump conversion efficiency is 82% for available pump power.

The dependence of output power as a function of absorbed pump power for the laser cavity with FBG as a reflector is shown in Fig. 8(a). Three FBGs operating with center wavelengths of 1063 nm, 1080 nm and 1083 nm have been investigated experimentally.

 figure: Fig. 8.

Fig. 8. Output characteristics of T-DCF laser with FBG : (a) output power versus absorbed pump power (b) spectrum of output radiation.

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The typical output radiation spectrum for the laser with FBG is presented in Fig. 8(b). The slope efficiency of the laser with λ=1083 nm was 64%. All configurations of tapered fiber laser demonstrate robust single transverse mode operation with M2=1.07, as seen from Fig. 6(b). The beam quality factor M2 has been measured using calibrated BeamScope-P7, DataRay Inc. The measurements did not reveal measurable difference in beam factor M2 for both outputs.

A high power superluminescent source based on T-DCF has also been studied experimentally. The setup of the source is shown in Fig. 5(c). The radiation coming from the wide-core side of the taper was coupled back into the core by a lens and broadband mirror, as seen from Fig. 5(c). The narrow end of tapered fiber was angle cleaved with 8 degrees.

 figure: Fig. 9.

Fig. 9. Output characteristics of T-DCF superluminescent source: (a) output power versus absorbed pump power (b) spectrum of output radiation.

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The dependence of the output power of the superluminescent source on absorbed pump power is shown in Fig. 9(a). Superluminescent source generates broadband radiation with a FWHM of 5.5 nm and a central wavelength at 1079 nm [Fig. 9(b)]. The threshold-free dependence of the output power versus absorbed pump power reveals that the slope efficiency of 85% is equal to the pump conversion efficiency.

3.2. Ytterbium doped tapered fiber amplifier

Efficient operation of a T-DCF amplifier has been achieved experimentally, as described below. The scheme of the experimental setup is shown in the Fig. 10. The seed signal was launched into a single-mode narrow-core taper end via an optical isolator and 1:99 tap coupler. We have examined the performance of tapered amplifier for two types of seed signals - pulsed and continuous-wave narrowband.

 figure: Fig. 10.

Fig. 10. Amplifier with T-DCF: experimental set up

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A mode locked picosecond fiber laser with τpulse=4 ps, freprate=100 MHz, Pave=50 mW and λ=1063 nm has been used as a seed source. The spectrum and autocorrelation function of the seed signal are shown in Fig. 11(a), inset and Fig. 11(b) with black lines, respectively.

 figure: Fig. 11.

Fig. 11. Output characteristics of T-DCF pulsed amplifier : (a) average output power versus launched pump power (circles); inset : seed source spectrum (black line) and amplified signal spectrum (red line). (b) autocorrelation function of seed signal (black line) and amplified signal (red line).

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The dependence of the average output power versus launched pump power is shown in Fig. 11(a). We obtained 10.7 W of average output power for a 50-mW seed signal corresponding to a 23.3 dB gain. Slope efficiency was 71.5% with respect to the launched pump power. The spectrum and autocorrelation function of the amplified signal are displayed in Fig. 11(a) inset and Fig. 11(b) with red color, respectively.

The performance of T-DCF for amplification of a CW signal with linewidth less then 100 kHz at FWHM has been studied. This amplification regime is usually affected severely by a stimulated Brillouin scattering (SBS). In experiments we have used a DFB fiber laser with 30 mW of output power as a seed source. The back scattered emission was recorded through a 1% coupler port as shown in Fig. 10.

The dependence of the output power signal as a function of launched pump power is shown in Fig. 12(a). The amplifier has demonstrated 80% slope efficiency with respect to launched pump power and 25.4 dB gain. The spectra of input and amplified signals are shown in Fig. 12(a) inset.

 figure: Fig. 12.

Fig. 12. Output characteristics of T-DCF amplifier with CW seed signal: a. output power versus launched pump power (black circles); inset: seed source spectrum (black line) and amplified signal spectrum (red line). b. back reflected light power as a function of output power.

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The level of backscattered power has been detected as a function of output power and plotted in Fig. 12(b). As we can see, less than 0.3% of output power is scattered back, providing clear evidence of strong SBS suppression. The output beam has a Gaussian shape with M2=1.07.

4. Discussion

The tapered double-clad gain fiber proposed and demonstrated here represents a novel design of optical amplifier (laser) with unique feature offering a diffraction-limited large-area mode and efficient pump absorption. The wide end of tapered fiber cone allows to couple efficiently the pump radiation from the sources with large beam parameter product, BPP, and to expand the mode field of the radiation guided by the core. The narrow section of the taper acts as a spatial mode filter for higher-order modes resulting in a diffraction-limited quality of the output beam. A significant increase in the pump absorption due to efficient mode scrambling in a fiber taper allows the use a moderate concentration of the dopants in the core thus reducing the background loss to the level below 10 dB/km and preventing the photodarkening effect. The pump-to-signal conversion of 82% and the slope efficiency of 93.2% observed in the experiments have been obtained owing to low cavity losses achievable with tapered gain fiber.

Apparently, the T-DCF using is most prominent for pumping by high power pump sources with poor BPP. The requirement of just partially filling numerical aperture imposes certain limitations on the BPP of the pump source. Although theoretically, the pump source with BPP of 80 mm×mrad can be used for T-DCF with 830 µm cladding diameter and NA=0.21, the above mentioned aperture limitation dictates the use of pump sources with BPP below 60 mm×mrad. Technically, it is possible to fabricate the T-DCF with clad diameter increased up to 2-mm and raise the aperture to NA=0.37 using the fluorosilicate glass coating or to NA=0.5 with polymer coating. Taking into account the requirement for partial, possibly below 70%, filling of the numerical aperture, for a taper with a 2-mm clad diameter and NA=0.37, pump sources with BPP 250 mm×mrad can be used. When the fiber aperture is increased to NA=0.5, the pump could have a beam parameter of 350 mm×mrad.

There is another practical advantage of the taper. For large outer diameters, the longitudinally uniform PCF cannot be bended because of the large effective diameter-to-length ratio. Instead, T-DCF with comparable length has significantly lower diameter-to-length ratio, i.e. the fraction of wide part in the taper could be short and, consequently, the tapered fiber can be easily bended even for diameters of 2 mm.

The non-reciprocal pump absorption and modal evolution in a tapered fiber provide a mechanism for preferable lasing in the direction towards the wide end of the taper. Indeed, the ratio of powers emitted through output 1 and output 2 in a laser with 4%-reflective cavity mirrors, shown in Fig. 5(a), is adequately described by the factor d21/d22 for the T-DCF mentioned in the previous section. The difference in the lasing spectra measured from output 1 and 2, seen in Fig. 6 at the inset, indicates the spectral non-reciprocity of the taper. Different dynamics of mode evolution in a taper for counter-propagating beams discussed above provide an effective “non-reciprocal” filtering effect that result in dissimilar spectra emerging from opposite ends of the taper.

The spectral spiking behavior in a laser with a HR broadband mirror, shown in Fig. 7(b), occurs in the laser because of the spectral selectivity of the taper. ASE is spectrally modulated during the propagation from the wide end towards the narrow end, as shown in Fig. 3 (black line), in agreement with the interferometric mode filtering mechanism discussed above. Simultaneously, the emission appears to be spatially single-mode at the narrow end of the laser cavity. After reflection from the HR mirror, as shown in Fig. 5(b), the single-mode light propagates back towards a wide section of taper and as a result, the output spectrum of the laser consists of discrete lines with a total spectral bandwidth of 20 nm.

Spectral selectivity of T-DCF, however, may limit the laser efficiency when using a fiber Bragg grating as a cavity reflector. The spectral response of the cavity affected strongly by the spectrum of excited modes in the wide part of the T-DCF core is irregular and rather complicated, as seen from Fig. 3. Therefore, insertion in the cavity of the FBG as a wavelength filter would be unavoidably accompanied with additional losses. Using FBGs with different reflectivities and center wavelengths, we have observed that the slope efficiency never exceeded 50-70%, as seen from Fig. 8.

The non-reciprocal spectral response of the taper affects the performance of high power superluminescent source, Figs. 5(c) and 9. During the first pass towards the wide taper end, ASE does not acquire any spectral modulation, as has been argued above. After reflection from the broadband mirror, the ASE propagates in a fundamental mode and is coupled back to the wide end of a taper. The spectral modulation due to differential modal phase modulation disappears since the laser operates at the fundamental mode during consecutive passes through the T-DCF. The design of a CW high power broadband single spatial mode optical source with output at the level of hundreds of watts is actively discussed in the literature [31]. Typically such optical sources are cumbersome devices based on the ASE seed source with good beam quality and power amplifier [31]. Using T-DCF pumped by a diode stack bar, a highly efficient and high power single-transverse-mode broadband source can be realized with rather straightforward technology. The preliminary results reported here demonstrate generation of 74-W fundamental mode broadband radiation (FWHM 5.5 nm) with excellent pump conversion efficiency of 85%. The output power is scalable and was limited only by available pump power.

Active tapered fiber is particularly attractive for use in high power amplifiers. The large core diameter of T-DCF offers an advanced capability for energy storage with reduced nonlinear distortion. An amplifier with gradually increased core diameter already has been investigated earlier, the so-called “flared amplifier” with three consecutive sections of fibers with different core diameters [32]. Using a T-DCF allows realization of a similar amplifier in a more practical way and avoids mode conversion and losses at the fiber splices.

A T-DCF based pulsed amplifier has been studied providing 23.3 dB gain for the input signal from the mode-locked seed source with a pulse duration of τpulse=4 ps and a repetition rate of frep=100 MHz. For an average output power of about 10 W, the amplified pulse shape remains practically undisturbed though the spectrum of the pulse acquires significant broadening due to self-phase modulation shown in Fig. 11(a), (inset). Apparently, the parameters of the T-DCF amplifier were not optimized for ultra short pulse seed signal. Namely, the length of T-DCF is too long, while the core diameter of the single-mode section is too small. Nevertheless, due to the good beam quality of the amplified signal, corresponding to M2=1.07 for 27 µm core diameter with V=9.1, an essential improvement in the performance of the T-DCF amplifiers for high power ultra short pulse applications can be expected.

Amplification of highly coherent radiation is another important application where T-DCF could have a clear advantage. Efficient high power coherent beam combining requires laser beams with extremely long coherent lengths and with spectral bandwidths below 50 kHz (FWHM). The saturation power of such amplifiers should be on the order of hundreds of watts or even kilowatts. The main obstacle for power scaling with this technique is stimulated Brillouin scattering (SBS) which imposes a limitation on the output power of the single-frequency radiation [33]. Power scaling in such systems assumes an essential increase in the threshold of SBS [34, 35]. One proposed solution exploits the acoustic properties of fiber core when the temperature gradient is gradually varied along the fiber owing to the longitudinal change in the pump absorption [34]. Obviously, this approach requires an extraordinarily high pump power that ensures sufficient longitudinal temperature gradient in the fiber. Alternatively, the fiber could be heated with an external furnace, which is, however, unlikely to be the practical solution to the problem [36]. In contrast to the abovementioned techniques using an artificially induced longitudinal variation in the guide properties, the T-DCF amplifier has a natural immunity to SBS due to in-built axial non-uniformity. The increase in the SBS threshold in passive fiber with variable core diameter has been demonstrated earlier [37] and the tapered amplifier would clearly benefit from similar effect when using with narrow band seed signal. Use of an optically pumped T-DCF amplifier may, however, be accompanied by certain broadening of the Brillouin gain spectrum due to heating [34]. A 25.4 dB high gain amplifier reported here, producing over 10 W of output power for 30-mW seed signal, reveals no signature of SBS, as shown in Figs. 12(a), 12(b). The slope efficiency of the amplifier was 80% for a Gaussian beam shape with M2=1.07 and only 0.3% of output power was scattered back.

It is important to note that although the single-mode section of the amplifier has a core diameter of only 5.8 µm, the SBS signal has not been measurable. A further optimization of the T-DCF design should also allow for an essential increase in the saturation power of these amplifiers.

5. Conclusion

A double clad tapered fiber as a gain medium for high power lasers, superluminescent sources and amplifiers has been proposed and demonstrated in this study for the first time. A large clad diameter of tapered fiber allows optical pumping with low brightness sources available commercially with powers up to 6 kW [38]. The specific features of the tapered fiber, e.g. non-reciprocal spectral response and non-reciprocity of the numerical aperture, have been systematically studied. It was demonstrated that an efficient intrinsic mode scrambling mechanism ensures enhanced pump absorption in a tapered fiber with a relatively low doping level. The tapered fiber with modest doping level applicable due to enhanced pump absorption is expected to have a strongly suppressed photodarkening effect and reduced background losses. All these features result in the high efficiency of lasers and amplifiers demonstrated in this study.

A T-DCF based laser producing 84 W with a slope efficiency of 93% and pump conversion efficiency of 82%, a 74 W superluminescent source with pump conversion efficiency of 85% and an amplifier for both pulsed and CW high coherent radiation with slope efficiency of 80% have been demonstrated. The output power of the devices is scalable and was limited here by the pump power available for these experiments. The output beam has a diffraction-limited property with a typical quality parameter of M2=1.07.

We believe that double clad tapered fiber technology using low brightness pump sources represents an exciting opportunity for essential power scaling with excellent pump conversion efficiency and superior output beam quality.

References and Links

1. www.ipgphotonics.com

2. Y. Jeong, J. K. Sahu, D. N. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power,” Opt. Express 12, 6088–6092 (2004). [CrossRef]   [PubMed]  

3. D. Young and C. Roychoudhuri, “Results and comparison of a cladding pumped fiber simulation using a decagon-shaped fiber,” Opt. Express 11, 830–837 (2003). [CrossRef]   [PubMed]  

4. J. J. Koponen, M. J. Soderlund, H. J. Hoffman, and S. K. Tammela, “Measuring photodarkening from single-mode ytterbium doped silica fibers,” Opt. Express 14, 11539–11544 (2006). [CrossRef]   [PubMed]  

5. B. Morasse, S. Chatigny, E. Gagnon, C. Hovington, J-P. Martin, and J-P. de Sandro, “Low photodarkening single cladding ytterbium fiber amplifier,” Proc. SPIE 6453, 64530H-1-64530H-9 (2007). [CrossRef]  

6. S. Yoo, C. Basu, A. J. Boyland, C. Sones, J. Nilsson, J. K. Sahu, and D. Payne, “Photodarkening in Yb-doped aluminosilicate fibers induced by 488nm irradiation,” Opt. Lett. 32, 1626–1628 (2007). [CrossRef]   [PubMed]  

7. J. Kirchhof, S. Unger, V. Reichel, and A. Schwuchow, “Background loss and devitrification in Nd-doped fiber laser glass,” Optical Fiber Conference Technical Digest, 60–61 (1996).

8. P. Koplow, D. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. 25, 442–444 (2000). [CrossRef]  

9. J. Limpert, N. Deguil-Robin, I. Manek-Honninger, F. Salin, F. Roser, A. Liem, T. Schreiber, S. Nolte, H. Zellmer, A. Tunnermann, J. Broeng, A. Petersson, and C. Jacobsen, “High-power rod-type photonic crystal fiber laser,” Opt. Express 13, 1055–1058 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-4-1055 [CrossRef]   [PubMed]  

10. J. Limpert, O. Schmidt, J. Rothhardt, F. Roser, T. Schreiber, A. Tunnermann, S. Ermeneux, P. Yvernault, and F. Salin, “Extended single-mode photonic crystal fiber lasers,” Opt. Express 14, 2715–2720 (2006). [CrossRef]   [PubMed]  

11. A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Optics Commun. 132, 511–518 (1996). [CrossRef]  

12. P. Leproux, S. Fevrier, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6, 324–339 (2001). [CrossRef]  

13. V. Doya, O. Legrand, and F. Mortessagne, “Optimized absorption in a chaotic double-clad fiber amplifier,” Opt. Lett. 26, 872–874 (2001). [CrossRef]  

14. D. Kouznetsov, J. Moloney, and E. Wright, “Efficiency of pump absorption in double-clad fiber amplifiers. I. Fiber with circular symmetry,” J. Opt. Soc. Am. B 18, 743–749 (2001). [CrossRef]  

15. D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. II. Broken circular symmetry,” J. Opt. Soc. Am. B 19, 1259–1263 (2002). [CrossRef]  

16. D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. III. Calculation of modes,” J. Opt. Soc. Am. B 19, 1304–1309 (2002). [CrossRef]  

17. H. Po, “Ring core fiber,” PCT patent WO 02/079829 A1.

18. H. Po, “Optical fiber,” PCT patent WO 03/010578 A1.

19. A. Carter, K. Tankala, and N. Jacobson, “Cladding-pumped optical fiber,” US patent 6.625.363 B2

20. M. Fermann, “Single-mode excitation of multimode fibers with ultrashort pulses,” Opt. Lett. 23, 52–54 (1998). [CrossRef]  

21. A. Carter, K. Tankala, and M. Seifert, “Double-clad optical fiber for lasers and amplifiers,” US patent 6.687.445 B2.

22. D. Marcuse, “Coupled power equations for lossy fibers,” Appl. Opt. 17, 3232–3237 (1978). [CrossRef]   [PubMed]  

23. J. Nilsson, S.-U. Alam, J. A. Alvarez-Chavez, P. W. Turner, W. A. Clarkson, and A. B. Grudinin, “High-power and tunable operation of erbium-ytterbium co-doped cladding-pumped fiber lasers,” IEEE J. Quantum Electron. 39, 987–994 (2003). [CrossRef]  

24. D. Marcuse, Light Transmission Optics, (Van Nostrand Reinhold Company, New York, 1972), Chap. 9.

25. E. M. Dianov, K. M. Golant, V. I. Karpov, R. R. Khrapko, A. S. Kurkov, V. N. Protopopov, S. L. Semenov, and A. G. Shebuniaev, “Application of reduced-pressure plasma CVD technology to the fabrication of Er-doped optical fibers,” Opt. Mater. 3, 181–185 (1994). [CrossRef]  

26. A. C. Boucouvalas and G. Georgiou, “External refractive-index response of tapered coaxial couplers,” Opt. Lett. 11, 257–259, (1986). [CrossRef]   [PubMed]  

27. K. Kieu and M. Mansuripur, “Tuning of fiber lasers by use of a single-mode biconic fiber taper,” Opt. Lett. 31, 2435–2437 (2006). [CrossRef]   [PubMed]  

28. S. A. Kingsley and D. E. N. Davies, “Multimode optical-fibre phase modulators and discriminators: I-Theory,” Electron. Lett. 14, 322–324 (1978). [CrossRef]  

29. V. B. Veinberg and D. K. Sattarov, Waveguide Optics, (Mashinostroenie, Leningrad, 1977), Chap.5 (in Russian).

30. N. S. Kapany and J. J. Burke, Optical Waveguides, (Academic Press, New York, 1972).

31. P. Wang and W. A. Clarkson, “High-power, single mode, linearly polarized, ytterbium-doped fiber superfluorescent source,” Opt. Lett. 32, 2605–2607 (2007). [CrossRef]   [PubMed]  

32. O. G. Okhotnikov and J. M. Sousa, “Flared single-transverse-mode fiber amplifier,” Electron. Lett. 35, 1011–1013, (1999). [CrossRef]  

33. A. Liem, J. Limpert, H. Zellmer, and A. Tunnermann, “100-W single-frequency master-oscillator fiber power amplifier,” Opt. Lett. 28, 1537–1539, (2003). [CrossRef]   [PubMed]  

34. Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500W,” IEEE J. Sel. Top. Quantum Electron. 13, 546–551 (2007). [CrossRef]  

35. V. I. Kovalev and R. G. Harrison, “Suppression of stimulated Brillouin scattering in high-power single-frequency fiber amplifiers,” Opt. Lett. 31, 161–163 (2006). [CrossRef]   [PubMed]  

36. J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen, “Increase of the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” J. Lightwave Technol. 19, 1691–1697 (2001). [CrossRef]  

37. K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fiber by changing the core radius,” Electron. Lett. 31, 668–669 (1995). [CrossRef]  

38. http://www.laserline.de/

References

  • View by:
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  • |

  1. www.ipgphotonics.com
  2. Y. Jeong, J. K. Sahu, D. N. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power,” Opt. Express 12, 6088–6092 (2004).
    [Crossref] [PubMed]
  3. D. Young and C. Roychoudhuri, “Results and comparison of a cladding pumped fiber simulation using a decagon-shaped fiber,” Opt. Express 11, 830–837 (2003).
    [Crossref] [PubMed]
  4. J. J. Koponen, M. J. Soderlund, H. J. Hoffman, and S. K. Tammela, “Measuring photodarkening from single-mode ytterbium doped silica fibers,” Opt. Express 14, 11539–11544 (2006).
    [Crossref] [PubMed]
  5. B. Morasse, S. Chatigny, E. Gagnon, C. Hovington, J-P. Martin, and J-P. de Sandro, “Low photodarkening single cladding ytterbium fiber amplifier,” Proc. SPIE 6453, 64530H-1-64530H-9 (2007).
    [Crossref]
  6. S. Yoo, C. Basu, A. J. Boyland, C. Sones, J. Nilsson, J. K. Sahu, and D. Payne, “Photodarkening in Yb-doped aluminosilicate fibers induced by 488nm irradiation,” Opt. Lett. 32, 1626–1628 (2007).
    [Crossref] [PubMed]
  7. J. Kirchhof, S. Unger, V. Reichel, and A. Schwuchow, “Background loss and devitrification in Nd-doped fiber laser glass,” Optical Fiber Conference Technical Digest, 60–61 (1996).
  8. P. Koplow, D. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. 25, 442–444 (2000).
    [Crossref]
  9. J. Limpert, N. Deguil-Robin, I. Manek-Honninger, F. Salin, F. Roser, A. Liem, T. Schreiber, S. Nolte, H. Zellmer, A. Tunnermann, J. Broeng, A. Petersson, and C. Jacobsen, “High-power rod-type photonic crystal fiber laser,” Opt. Express 13, 1055–1058 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-4-1055
    [Crossref] [PubMed]
  10. J. Limpert, O. Schmidt, J. Rothhardt, F. Roser, T. Schreiber, A. Tunnermann, S. Ermeneux, P. Yvernault, and F. Salin, “Extended single-mode photonic crystal fiber lasers,” Opt. Express 14, 2715–2720 (2006).
    [Crossref] [PubMed]
  11. A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Optics Commun. 132, 511–518 (1996).
    [Crossref]
  12. P. Leproux, S. Fevrier, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6, 324–339 (2001).
    [Crossref]
  13. V. Doya, O. Legrand, and F. Mortessagne, “Optimized absorption in a chaotic double-clad fiber amplifier,” Opt. Lett. 26, 872–874 (2001).
    [Crossref]
  14. D. Kouznetsov, J. Moloney, and E. Wright, “Efficiency of pump absorption in double-clad fiber amplifiers. I. Fiber with circular symmetry,” J. Opt. Soc. Am. B 18, 743–749 (2001).
    [Crossref]
  15. D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. II. Broken circular symmetry,” J. Opt. Soc. Am. B 19, 1259–1263 (2002).
    [Crossref]
  16. D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. III. Calculation of modes,” J. Opt. Soc. Am. B 19, 1304–1309 (2002).
    [Crossref]
  17. H. Po, “Ring core fiber,” PCT patent WO 02/079829 A1.
  18. H. Po, “Optical fiber,” PCT patent WO 03/010578 A1.
  19. A. Carter, K. Tankala, and N. Jacobson, “Cladding-pumped optical fiber,” US patent 6.625.363 B2
  20. M. Fermann, “Single-mode excitation of multimode fibers with ultrashort pulses,” Opt. Lett. 23, 52–54 (1998).
    [Crossref]
  21. A. Carter, K. Tankala, and M. Seifert, “Double-clad optical fiber for lasers and amplifiers,” US patent 6.687.445 B2.
  22. D. Marcuse, “Coupled power equations for lossy fibers,” Appl. Opt. 17, 3232–3237 (1978).
    [Crossref] [PubMed]
  23. J. Nilsson, S.-U. Alam, J. A. Alvarez-Chavez, P. W. Turner, W. A. Clarkson, and A. B. Grudinin, “High-power and tunable operation of erbium-ytterbium co-doped cladding-pumped fiber lasers,” IEEE J. Quantum Electron. 39, 987–994 (2003).
    [Crossref]
  24. D. Marcuse, Light Transmission Optics, (Van Nostrand Reinhold Company, New York, 1972), Chap. 9.
  25. E. M. Dianov, K. M. Golant, V. I. Karpov, R. R. Khrapko, A. S. Kurkov, V. N. Protopopov, S. L. Semenov, and A. G. Shebuniaev, “Application of reduced-pressure plasma CVD technology to the fabrication of Er-doped optical fibers,” Opt. Mater. 3, 181–185 (1994).
    [Crossref]
  26. A. C. Boucouvalas and G. Georgiou, “External refractive-index response of tapered coaxial couplers,” Opt. Lett. 11, 257–259, (1986).
    [Crossref] [PubMed]
  27. K. Kieu and M. Mansuripur, “Tuning of fiber lasers by use of a single-mode biconic fiber taper,” Opt. Lett. 31, 2435–2437 (2006).
    [Crossref] [PubMed]
  28. S. A. Kingsley and D. E. N. Davies, “Multimode optical-fibre phase modulators and discriminators: I-Theory,” Electron. Lett. 14, 322–324 (1978).
    [Crossref]
  29. V. B. Veinberg and D. K. Sattarov, Waveguide Optics, (Mashinostroenie, Leningrad, 1977), Chap.5 (in Russian).
  30. N. S. Kapany and J. J. Burke, Optical Waveguides, (Academic Press, New York, 1972).
  31. P. Wang and W. A. Clarkson, “High-power, single mode, linearly polarized, ytterbium-doped fiber superfluorescent source,” Opt. Lett. 32, 2605–2607 (2007).
    [Crossref] [PubMed]
  32. O. G. Okhotnikov and J. M. Sousa, “Flared single-transverse-mode fiber amplifier,” Electron. Lett. 35, 1011–1013, (1999).
    [Crossref]
  33. A. Liem, J. Limpert, H. Zellmer, and A. Tunnermann, “100-W single-frequency master-oscillator fiber power amplifier,” Opt. Lett. 28, 1537–1539, (2003).
    [Crossref] [PubMed]
  34. Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500W,” IEEE J. Sel. Top. Quantum Electron. 13, 546–551 (2007).
    [Crossref]
  35. V. I. Kovalev and R. G. Harrison, “Suppression of stimulated Brillouin scattering in high-power single-frequency fiber amplifiers,” Opt. Lett. 31, 161–163 (2006).
    [Crossref] [PubMed]
  36. J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen, “Increase of the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” J. Lightwave Technol. 19, 1691–1697 (2001).
    [Crossref]
  37. K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fiber by changing the core radius,” Electron. Lett. 31, 668–669 (1995).
    [Crossref]
  38. http://www.laserline.de/

2007 (3)

2006 (4)

2005 (1)

2004 (1)

2003 (3)

2002 (2)

2001 (4)

2000 (1)

1999 (1)

O. G. Okhotnikov and J. M. Sousa, “Flared single-transverse-mode fiber amplifier,” Electron. Lett. 35, 1011–1013, (1999).
[Crossref]

1998 (1)

1996 (1)

A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Optics Commun. 132, 511–518 (1996).
[Crossref]

1995 (1)

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fiber by changing the core radius,” Electron. Lett. 31, 668–669 (1995).
[Crossref]

1994 (1)

E. M. Dianov, K. M. Golant, V. I. Karpov, R. R. Khrapko, A. S. Kurkov, V. N. Protopopov, S. L. Semenov, and A. G. Shebuniaev, “Application of reduced-pressure plasma CVD technology to the fabrication of Er-doped optical fibers,” Opt. Mater. 3, 181–185 (1994).
[Crossref]

1986 (1)

1978 (2)

D. Marcuse, “Coupled power equations for lossy fibers,” Appl. Opt. 17, 3232–3237 (1978).
[Crossref] [PubMed]

S. A. Kingsley and D. E. N. Davies, “Multimode optical-fibre phase modulators and discriminators: I-Theory,” Electron. Lett. 14, 322–324 (1978).
[Crossref]

Alam, S.-U.

J. Nilsson, S.-U. Alam, J. A. Alvarez-Chavez, P. W. Turner, W. A. Clarkson, and A. B. Grudinin, “High-power and tunable operation of erbium-ytterbium co-doped cladding-pumped fiber lasers,” IEEE J. Quantum Electron. 39, 987–994 (2003).
[Crossref]

Alvarez-Chavez, J. A.

J. Nilsson, S.-U. Alam, J. A. Alvarez-Chavez, P. W. Turner, W. A. Clarkson, and A. B. Grudinin, “High-power and tunable operation of erbium-ytterbium co-doped cladding-pumped fiber lasers,” IEEE J. Quantum Electron. 39, 987–994 (2003).
[Crossref]

Andrekson, P. A.

Basu, C.

Boucouvalas, A. C.

Boyland, A. J.

Broeng, J.

Burke, J. J.

N. S. Kapany and J. J. Burke, Optical Waveguides, (Academic Press, New York, 1972).

Carter, A.

A. Carter, K. Tankala, and N. Jacobson, “Cladding-pumped optical fiber,” US patent 6.625.363 B2

A. Carter, K. Tankala, and M. Seifert, “Double-clad optical fiber for lasers and amplifiers,” US patent 6.687.445 B2.

Chatigny, S.

B. Morasse, S. Chatigny, E. Gagnon, C. Hovington, J-P. Martin, and J-P. de Sandro, “Low photodarkening single cladding ytterbium fiber amplifier,” Proc. SPIE 6453, 64530H-1-64530H-9 (2007).
[Crossref]

Clarkson, W. A.

P. Wang and W. A. Clarkson, “High-power, single mode, linearly polarized, ytterbium-doped fiber superfluorescent source,” Opt. Lett. 32, 2605–2607 (2007).
[Crossref] [PubMed]

J. Nilsson, S.-U. Alam, J. A. Alvarez-Chavez, P. W. Turner, W. A. Clarkson, and A. B. Grudinin, “High-power and tunable operation of erbium-ytterbium co-doped cladding-pumped fiber lasers,” IEEE J. Quantum Electron. 39, 987–994 (2003).
[Crossref]

Davies, D. E. N.

S. A. Kingsley and D. E. N. Davies, “Multimode optical-fibre phase modulators and discriminators: I-Theory,” Electron. Lett. 14, 322–324 (1978).
[Crossref]

de Sandro, J-P.

B. Morasse, S. Chatigny, E. Gagnon, C. Hovington, J-P. Martin, and J-P. de Sandro, “Low photodarkening single cladding ytterbium fiber amplifier,” Proc. SPIE 6453, 64530H-1-64530H-9 (2007).
[Crossref]

Deguil-Robin, N.

Dianov, E. M.

E. M. Dianov, K. M. Golant, V. I. Karpov, R. R. Khrapko, A. S. Kurkov, V. N. Protopopov, S. L. Semenov, and A. G. Shebuniaev, “Application of reduced-pressure plasma CVD technology to the fabrication of Er-doped optical fibers,” Opt. Mater. 3, 181–185 (1994).
[Crossref]

Doya, V.

P. Leproux, S. Fevrier, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6, 324–339 (2001).
[Crossref]

V. Doya, O. Legrand, and F. Mortessagne, “Optimized absorption in a chaotic double-clad fiber amplifier,” Opt. Lett. 26, 872–874 (2001).
[Crossref]

Dross, F.

Ermeneux, S.

Fermann, M.

Fevrier, S.

P. Leproux, S. Fevrier, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6, 324–339 (2001).
[Crossref]

Gagnon, E.

B. Morasse, S. Chatigny, E. Gagnon, C. Hovington, J-P. Martin, and J-P. de Sandro, “Low photodarkening single cladding ytterbium fiber amplifier,” Proc. SPIE 6453, 64530H-1-64530H-9 (2007).
[Crossref]

Georgiou, G.

Golant, K. M.

E. M. Dianov, K. M. Golant, V. I. Karpov, R. R. Khrapko, A. S. Kurkov, V. N. Protopopov, S. L. Semenov, and A. G. Shebuniaev, “Application of reduced-pressure plasma CVD technology to the fabrication of Er-doped optical fibers,” Opt. Mater. 3, 181–185 (1994).
[Crossref]

Goldberg, L.

Grudinin, A. B.

J. Nilsson, S.-U. Alam, J. A. Alvarez-Chavez, P. W. Turner, W. A. Clarkson, and A. B. Grudinin, “High-power and tunable operation of erbium-ytterbium co-doped cladding-pumped fiber lasers,” IEEE J. Quantum Electron. 39, 987–994 (2003).
[Crossref]

Hansryd, J.

Harrison, R. G.

Hickey, L.

Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500W,” IEEE J. Sel. Top. Quantum Electron. 13, 546–551 (2007).
[Crossref]

Hoffman, H. J.

Horley, R.

Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500W,” IEEE J. Sel. Top. Quantum Electron. 13, 546–551 (2007).
[Crossref]

Hovington, C.

B. Morasse, S. Chatigny, E. Gagnon, C. Hovington, J-P. Martin, and J-P. de Sandro, “Low photodarkening single cladding ytterbium fiber amplifier,” Proc. SPIE 6453, 64530H-1-64530H-9 (2007).
[Crossref]

Jacobsen, C.

Jacobson, N.

A. Carter, K. Tankala, and N. Jacobson, “Cladding-pumped optical fiber,” US patent 6.625.363 B2

Jeong, Y.

Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500W,” IEEE J. Sel. Top. Quantum Electron. 13, 546–551 (2007).
[Crossref]

Y. Jeong, J. K. Sahu, D. N. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power,” Opt. Express 12, 6088–6092 (2004).
[Crossref] [PubMed]

Kapany, N. S.

N. S. Kapany and J. J. Burke, Optical Waveguides, (Academic Press, New York, 1972).

Karpov, V. I.

E. M. Dianov, K. M. Golant, V. I. Karpov, R. R. Khrapko, A. S. Kurkov, V. N. Protopopov, S. L. Semenov, and A. G. Shebuniaev, “Application of reduced-pressure plasma CVD technology to the fabrication of Er-doped optical fibers,” Opt. Mater. 3, 181–185 (1994).
[Crossref]

Khrapko, R. R.

E. M. Dianov, K. M. Golant, V. I. Karpov, R. R. Khrapko, A. S. Kurkov, V. N. Protopopov, S. L. Semenov, and A. G. Shebuniaev, “Application of reduced-pressure plasma CVD technology to the fabrication of Er-doped optical fibers,” Opt. Mater. 3, 181–185 (1994).
[Crossref]

Kieu, K.

Kingsley, S. A.

S. A. Kingsley and D. E. N. Davies, “Multimode optical-fibre phase modulators and discriminators: I-Theory,” Electron. Lett. 14, 322–324 (1978).
[Crossref]

Kirchhof, J.

J. Kirchhof, S. Unger, V. Reichel, and A. Schwuchow, “Background loss and devitrification in Nd-doped fiber laser glass,” Optical Fiber Conference Technical Digest, 60–61 (1996).

Kliner, D.

Knudsen, S. N.

Koplow, P.

Koponen, J. J.

Kouznetsov, D.

Kovalev, V. I.

Kurkov, A. S.

E. M. Dianov, K. M. Golant, V. I. Karpov, R. R. Khrapko, A. S. Kurkov, V. N. Protopopov, S. L. Semenov, and A. G. Shebuniaev, “Application of reduced-pressure plasma CVD technology to the fabrication of Er-doped optical fibers,” Opt. Mater. 3, 181–185 (1994).
[Crossref]

Legrand, O.

Leproux, P.

P. Leproux, S. Fevrier, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6, 324–339 (2001).
[Crossref]

Liem, A.

Limpert, J.

Liu, A.

A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Optics Commun. 132, 511–518 (1996).
[Crossref]

Manek-Honninger, I.

Mansuripur, M.

Marcuse, D.

D. Marcuse, “Coupled power equations for lossy fibers,” Appl. Opt. 17, 3232–3237 (1978).
[Crossref] [PubMed]

D. Marcuse, Light Transmission Optics, (Van Nostrand Reinhold Company, New York, 1972), Chap. 9.

Martin, J-P.

B. Morasse, S. Chatigny, E. Gagnon, C. Hovington, J-P. Martin, and J-P. de Sandro, “Low photodarkening single cladding ytterbium fiber amplifier,” Proc. SPIE 6453, 64530H-1-64530H-9 (2007).
[Crossref]

Moloney, J.

Morasse, B.

B. Morasse, S. Chatigny, E. Gagnon, C. Hovington, J-P. Martin, and J-P. de Sandro, “Low photodarkening single cladding ytterbium fiber amplifier,” Proc. SPIE 6453, 64530H-1-64530H-9 (2007).
[Crossref]

Mortessagne, F.

Nilsson, J.

S. Yoo, C. Basu, A. J. Boyland, C. Sones, J. Nilsson, J. K. Sahu, and D. Payne, “Photodarkening in Yb-doped aluminosilicate fibers induced by 488nm irradiation,” Opt. Lett. 32, 1626–1628 (2007).
[Crossref] [PubMed]

Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500W,” IEEE J. Sel. Top. Quantum Electron. 13, 546–551 (2007).
[Crossref]

Y. Jeong, J. K. Sahu, D. N. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power,” Opt. Express 12, 6088–6092 (2004).
[Crossref] [PubMed]

J. Nilsson, S.-U. Alam, J. A. Alvarez-Chavez, P. W. Turner, W. A. Clarkson, and A. B. Grudinin, “High-power and tunable operation of erbium-ytterbium co-doped cladding-pumped fiber lasers,” IEEE J. Quantum Electron. 39, 987–994 (2003).
[Crossref]

Nolte, S.

Ohashi, M.

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fiber by changing the core radius,” Electron. Lett. 31, 668–669 (1995).
[Crossref]

Okhotnikov, O. G.

O. G. Okhotnikov and J. M. Sousa, “Flared single-transverse-mode fiber amplifier,” Electron. Lett. 35, 1011–1013, (1999).
[Crossref]

Pagnoux, D.

P. Leproux, S. Fevrier, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6, 324–339 (2001).
[Crossref]

Payne, D.

Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500W,” IEEE J. Sel. Top. Quantum Electron. 13, 546–551 (2007).
[Crossref]

S. Yoo, C. Basu, A. J. Boyland, C. Sones, J. Nilsson, J. K. Sahu, and D. Payne, “Photodarkening in Yb-doped aluminosilicate fibers induced by 488nm irradiation,” Opt. Lett. 32, 1626–1628 (2007).
[Crossref] [PubMed]

Payne, D. N.

Petersson, A.

Po, H.

H. Po, “Ring core fiber,” PCT patent WO 02/079829 A1.

H. Po, “Optical fiber,” PCT patent WO 03/010578 A1.

Protopopov, V. N.

E. M. Dianov, K. M. Golant, V. I. Karpov, R. R. Khrapko, A. S. Kurkov, V. N. Protopopov, S. L. Semenov, and A. G. Shebuniaev, “Application of reduced-pressure plasma CVD technology to the fabrication of Er-doped optical fibers,” Opt. Mater. 3, 181–185 (1994).
[Crossref]

Reichel, V.

J. Kirchhof, S. Unger, V. Reichel, and A. Schwuchow, “Background loss and devitrification in Nd-doped fiber laser glass,” Optical Fiber Conference Technical Digest, 60–61 (1996).

Roser, F.

Rothhardt, J.

Roy, P.

P. Leproux, S. Fevrier, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6, 324–339 (2001).
[Crossref]

Roychoudhuri, C.

Sahu, J.

Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500W,” IEEE J. Sel. Top. Quantum Electron. 13, 546–551 (2007).
[Crossref]

Sahu, J. K.

Salin, F.

Sattarov, D. K.

V. B. Veinberg and D. K. Sattarov, Waveguide Optics, (Mashinostroenie, Leningrad, 1977), Chap.5 (in Russian).

Schmidt, O.

Schreiber, T.

Schwuchow, A.

J. Kirchhof, S. Unger, V. Reichel, and A. Schwuchow, “Background loss and devitrification in Nd-doped fiber laser glass,” Optical Fiber Conference Technical Digest, 60–61 (1996).

Seifert, M.

A. Carter, K. Tankala, and M. Seifert, “Double-clad optical fiber for lasers and amplifiers,” US patent 6.687.445 B2.

Semenov, S. L.

E. M. Dianov, K. M. Golant, V. I. Karpov, R. R. Khrapko, A. S. Kurkov, V. N. Protopopov, S. L. Semenov, and A. G. Shebuniaev, “Application of reduced-pressure plasma CVD technology to the fabrication of Er-doped optical fibers,” Opt. Mater. 3, 181–185 (1994).
[Crossref]

Shebuniaev, A. G.

E. M. Dianov, K. M. Golant, V. I. Karpov, R. R. Khrapko, A. S. Kurkov, V. N. Protopopov, S. L. Semenov, and A. G. Shebuniaev, “Application of reduced-pressure plasma CVD technology to the fabrication of Er-doped optical fibers,” Opt. Mater. 3, 181–185 (1994).
[Crossref]

Shiraki, K.

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fiber by changing the core radius,” Electron. Lett. 31, 668–669 (1995).
[Crossref]

Soderlund, M. J.

Sones, C.

Sousa, J. M.

O. G. Okhotnikov and J. M. Sousa, “Flared single-transverse-mode fiber amplifier,” Electron. Lett. 35, 1011–1013, (1999).
[Crossref]

Tammela, S. K.

Tankala, K.

A. Carter, K. Tankala, and M. Seifert, “Double-clad optical fiber for lasers and amplifiers,” US patent 6.687.445 B2.

A. Carter, K. Tankala, and N. Jacobson, “Cladding-pumped optical fiber,” US patent 6.625.363 B2

Tateda, M.

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fiber by changing the core radius,” Electron. Lett. 31, 668–669 (1995).
[Crossref]

Tunnermann, A.

Turner, P.

Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500W,” IEEE J. Sel. Top. Quantum Electron. 13, 546–551 (2007).
[Crossref]

Turner, P. W.

J. Nilsson, S.-U. Alam, J. A. Alvarez-Chavez, P. W. Turner, W. A. Clarkson, and A. B. Grudinin, “High-power and tunable operation of erbium-ytterbium co-doped cladding-pumped fiber lasers,” IEEE J. Quantum Electron. 39, 987–994 (2003).
[Crossref]

Ueda, K.

A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Optics Commun. 132, 511–518 (1996).
[Crossref]

Unger, S.

J. Kirchhof, S. Unger, V. Reichel, and A. Schwuchow, “Background loss and devitrification in Nd-doped fiber laser glass,” Optical Fiber Conference Technical Digest, 60–61 (1996).

Veinberg, V. B.

V. B. Veinberg and D. K. Sattarov, Waveguide Optics, (Mashinostroenie, Leningrad, 1977), Chap.5 (in Russian).

Wang, P.

Westlund, M.

Wright, E.

Yoo, S.

Young, D.

Yvernault, P.

Zellmer, H.

Appl. Opt. (1)

Electron. Lett. (3)

S. A. Kingsley and D. E. N. Davies, “Multimode optical-fibre phase modulators and discriminators: I-Theory,” Electron. Lett. 14, 322–324 (1978).
[Crossref]

O. G. Okhotnikov and J. M. Sousa, “Flared single-transverse-mode fiber amplifier,” Electron. Lett. 35, 1011–1013, (1999).
[Crossref]

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fiber by changing the core radius,” Electron. Lett. 31, 668–669 (1995).
[Crossref]

IEEE J. Quantum Electron. (1)

J. Nilsson, S.-U. Alam, J. A. Alvarez-Chavez, P. W. Turner, W. A. Clarkson, and A. B. Grudinin, “High-power and tunable operation of erbium-ytterbium co-doped cladding-pumped fiber lasers,” IEEE J. Quantum Electron. 39, 987–994 (2003).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. Jeong, J. Nilsson, J. Sahu, D. Payne, R. Horley, L. Hickey, and P. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500W,” IEEE J. Sel. Top. Quantum Electron. 13, 546–551 (2007).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (3)

Opt. Express (5)

Opt. Fiber Technol. (1)

P. Leproux, S. Fevrier, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6, 324–339 (2001).
[Crossref]

Opt. Lett. (9)

V. Doya, O. Legrand, and F. Mortessagne, “Optimized absorption in a chaotic double-clad fiber amplifier,” Opt. Lett. 26, 872–874 (2001).
[Crossref]

S. Yoo, C. Basu, A. J. Boyland, C. Sones, J. Nilsson, J. K. Sahu, and D. Payne, “Photodarkening in Yb-doped aluminosilicate fibers induced by 488nm irradiation,” Opt. Lett. 32, 1626–1628 (2007).
[Crossref] [PubMed]

P. Koplow, D. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. 25, 442–444 (2000).
[Crossref]

V. I. Kovalev and R. G. Harrison, “Suppression of stimulated Brillouin scattering in high-power single-frequency fiber amplifiers,” Opt. Lett. 31, 161–163 (2006).
[Crossref] [PubMed]

A. Liem, J. Limpert, H. Zellmer, and A. Tunnermann, “100-W single-frequency master-oscillator fiber power amplifier,” Opt. Lett. 28, 1537–1539, (2003).
[Crossref] [PubMed]

P. Wang and W. A. Clarkson, “High-power, single mode, linearly polarized, ytterbium-doped fiber superfluorescent source,” Opt. Lett. 32, 2605–2607 (2007).
[Crossref] [PubMed]

M. Fermann, “Single-mode excitation of multimode fibers with ultrashort pulses,” Opt. Lett. 23, 52–54 (1998).
[Crossref]

A. C. Boucouvalas and G. Georgiou, “External refractive-index response of tapered coaxial couplers,” Opt. Lett. 11, 257–259, (1986).
[Crossref] [PubMed]

K. Kieu and M. Mansuripur, “Tuning of fiber lasers by use of a single-mode biconic fiber taper,” Opt. Lett. 31, 2435–2437 (2006).
[Crossref] [PubMed]

Opt. Mater. (1)

E. M. Dianov, K. M. Golant, V. I. Karpov, R. R. Khrapko, A. S. Kurkov, V. N. Protopopov, S. L. Semenov, and A. G. Shebuniaev, “Application of reduced-pressure plasma CVD technology to the fabrication of Er-doped optical fibers,” Opt. Mater. 3, 181–185 (1994).
[Crossref]

Optics Commun. (1)

A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Optics Commun. 132, 511–518 (1996).
[Crossref]

Other (11)

H. Po, “Ring core fiber,” PCT patent WO 02/079829 A1.

H. Po, “Optical fiber,” PCT patent WO 03/010578 A1.

A. Carter, K. Tankala, and N. Jacobson, “Cladding-pumped optical fiber,” US patent 6.625.363 B2

www.ipgphotonics.com

J. Kirchhof, S. Unger, V. Reichel, and A. Schwuchow, “Background loss and devitrification in Nd-doped fiber laser glass,” Optical Fiber Conference Technical Digest, 60–61 (1996).

B. Morasse, S. Chatigny, E. Gagnon, C. Hovington, J-P. Martin, and J-P. de Sandro, “Low photodarkening single cladding ytterbium fiber amplifier,” Proc. SPIE 6453, 64530H-1-64530H-9 (2007).
[Crossref]

http://www.laserline.de/

V. B. Veinberg and D. K. Sattarov, Waveguide Optics, (Mashinostroenie, Leningrad, 1977), Chap.5 (in Russian).

N. S. Kapany and J. J. Burke, Optical Waveguides, (Academic Press, New York, 1972).

A. Carter, K. Tankala, and M. Seifert, “Double-clad optical fiber for lasers and amplifiers,” US patent 6.687.445 B2.

D. Marcuse, Light Transmission Optics, (Van Nostrand Reinhold Company, New York, 1972), Chap. 9.

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Figures (12)

Fig. 1.
Fig. 1. T-DCF: the optical equivalent scheme
Fig. 2.
Fig. 2. T-DCF clad diameter and normalized frequency as function of fiber length.
Fig. 3.
Fig. 3. Transmission characteristic of T-DCF: from wide end towards narrow end (black line) and in the opposite direction (red line).
Fig. 4.
Fig. 4. Ray traces in a cladding of T-DCF.
Fig. 5.
Fig. 5. Schematics of optical sources with T-DCF.
Fig. 6.
Fig. 6. Output characteristics of T-DCF laser with R1,2=4%;4%. (a) Output power versus absorbed pump power; Inset : emission spectra for output 1 (black line) and output 2 (red line). (b): beam profile (dots) and Gaussian fit (red line) for output 1. M2=1.07.
Fig. 7.
Fig. 7. Output characteristics of T-DCF laser with broadband HR mirror: (a) output power versus absorbed pump power (b) spectrum of output radiation.
Fig. 8.
Fig. 8. Output characteristics of T-DCF laser with FBG : (a) output power versus absorbed pump power (b) spectrum of output radiation.
Fig. 9.
Fig. 9. Output characteristics of T-DCF superluminescent source: (a) output power versus absorbed pump power (b) spectrum of output radiation.
Fig. 10.
Fig. 10. Amplifier with T-DCF: experimental set up
Fig. 11.
Fig. 11. Output characteristics of T-DCF pulsed amplifier : (a) average output power versus launched pump power (circles); inset : seed source spectrum (black line) and amplified signal spectrum (red line). (b) autocorrelation function of seed signal (black line) and amplified signal (red line).
Fig. 12.
Fig. 12. Output characteristics of T-DCF amplifier with CW seed signal: a. output power versus launched pump power (black circles); inset: seed source spectrum (black line) and amplified signal spectrum (red line). b. back reflected light power as a function of output power.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

α DCfiber = α core · A core A clad
α DCfiber = α core · A core A clad · S
NA right = d 2 d · NA core θ n 2 core NA core 2 · ( d 2 d ) 2 and
NA left = d 1 d · NA core + θ n 2 core NA core 2 · ( d 1 d ) 2 ,
NA right NA left = d 2 d 1
NA clad = D 2 D 1 · NA Ω n 2 clad 1 NA 2 · ( D 2 D 1 ) 2 ,

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