Gain-length Product Research Articles

Determination of the saturation length and study of its effects in optical gain measurements of organic semiconductors using the variable stripe length method

Three indicators for the determination of the saturation length limiting the validity of the variable stripe length method are presented. Depending on the maximum stripe length being used for the nonlinear fit, the resulting modal gain, its confidence interval, and the spectral full width at half maximum vary and give clear indications on the saturation length. Exemplarily, a blend of organic semiconducting spiro-compounds has been measured to present the importance of this length and demonstrate its determination. Subsequently, the optical modal gain is calculated with consideration of the saturation length. Both the saturation length and modal gain are shown to be dependent on the pump energy but result in a constant gain-length product of 2.2 ± 0.2, independent of the pump energy. Additionally, spectral gain profiles for different pump energies are presented with a maximum net modal gain of (128±4) cm−1 found at (2.98±0.09) mJ/cm2.

Realization of uniform transverse gain in an edge-pumped multislab pulsed amplifier with a gradient profile doping

Gradient doping ensures uniform transverse gain in an edge-pumped multislab pulsed amplifier, and a 1D iterative method is developed to generate the proper doping profile. Our investigations show that uniform gain under short pump duration tp = 0.25 ms can be readily achieved, where the modulation of the gain distribution is lower than 1.05 even if the diagonal transverse gain-length product (DTGLP) increases up to 5. For tp = 1.0 ms, comparable modulation of the gain distribution is achieved for a much lower DTGLP value of 2.3. To extend the DTGLP range for long pump duration, a modified 1D iterative method with an effectively “shortened” lifetime of the active ions is developed. With the modified method, the gain uniformity for both pumping conditions is greatly improved, and specifically, the DTGLP increases from 2.3 to 3.0 for tp = 1.0 ms. In addition, degradation of the gain uniformity resulting from deviations of the doping concentration is discussed. The deviations should be at least lower than 1% and 5% for tp = 1.0 ms and tp = 0.25 ms to maintain the gain uniformity, respectively. Our investigations might provide a useful way to design the amplifier with uniform gain in the beam aperture of a high average power pulsed laser.

Theoretical analysis of uniform longitudinal gain for a double-end-pumped Yb:YAG multi-slab pulsed amplifier

For high average power lasers with double-end-pumped multi-slab (DEPMS) configuration, a non-uniform gain distribution within each slab caused by the step-doped multi-slab will lead to the amplified spontaneous emission (ASE) effect and then reduce the laser performance. As an example, longitudinal gradient doping is used in a DEPMS Yb:YAG pulsed amplifier to create uniform longitudinal gain (ULG) and then the ASE effect is effectively reduced. The ULG is theoretically derived and we show that the energy storage can be increased by 9% with ULG compared with the step-doped DEPMS. We found that the optimal pump efficiency, longitudinal gain-length product and columnar doping density are determined by the launched pump intensity. Numerical simulation also demonstrated that optimization of the amplifier with uniform gain and high pump efficiency can be achieved by placing additional gradient slabs to the original gradient doping slabs. Our investigations might provide an efficient way to carefully optimize a DEPMS pulsed amplifier with higher efficiency.

Demonstration of gain saturation and double-pass amplification of a 69.8 nm laser pumped by capillary discharge.

With a 45-cm-long capillary, we obtained a saturated 69.8 nm laser with a gain coefficient of 0.4 cm-1 and a gain length product of 18. In order to increase the laser energy further, a double-pass amplification of the 69.8 nm laser was first realized with a SiC mirror without a coating. With a half cavity, the effective plasma column length and the effective gain length product can reach 84 cm and 33.7, respectively. The amplitude of a laser pulse for double-pass amplification is 9 times larger than that for single-pass amplification. In addition, the full width at half-maximum (FWHM) pulse width of a laser pulse and FWHM divergence for single-pass amplification are 1.4 ns and 0.5 mrad, respectively, which increase to 2.2 ns and 3.4 mrad for double-pass amplification.

General formula for calculation of amplified spontaneous emission intensity

A general formula is proposed for calculating the intensity of amplified spontaneous emission (ASE) in low, medium and high intensity regimes for both homogeneous and inhomogeneous line broadening. The calculation of ASE intensity is based on the results that are obtained from the numerical solution of the rate equations. The results compared with the corrected Linford formula in low intensities and asymptotic limiting formula for the high gain saturation. An error analysis over the entire region of the gain length product is also given to evaluate the validity of the proposed formula.

Influence of the gain-length product on the pulse duration of highly saturated capillary discharge soft X-ray laser

In this paper, the variation of the pulse duration was investigated for the highly saturated capillary discharge Ne-like Ar 46.9 nm soft X-ray laser. The evolutions of the pulse duration along the axis of capillary were measured for the 3.2- and 4.0-mm-inner-diameter alumina capillaries. Then, the simulations for the evolution of pulse duration were conducted with consideration of the saturation effect of laser amplification, showing good consistency with the experimental results. The analysis was performed on the variation of pulse duration over plasma length, indicating that the variation of the gain-length product caused the evolution of the pulse duration. Meanwhile, the evolutions of pulse durations were measured for different initial Ar pressures for both capillaries, showing the pulse durations were wider near the optimum pressure. Based on the simulations and the experimental results, it is concluded that the variations of the pulse duration of the soft X-ray laser were mainly due to the effect of gain-length product.

Near-diffraction-limited, high peak power, electro-optically Q-switched, diode-side-pumped Nd:YVO4 grazing-incidence oscillator

Actively Q-switched Nd:YVO 4 laser with grazing-incidence bounce geometry, side pumped with 2D laser diode matrix was elaborated. Because of extremely high gain-length product obtained in that configuration, a BBO Pockels cell was applied for Q-switching regime. A near-diffraction-limited beam with parameter M 2 =1.25 was achieved. The generated output pulse energy of 8.5 mJ and 8 ns pulse duration at 50 Hz repetition rate was demonstrated. • We elaborated Q-switched Nd:YVO 4 laser with grazing-incidence bounce geometry. • We achieved near-diffraction-limited output with beam quality parameter M 2 = 1.25. • Pulse energy of 8.5 mJ with 8 ns pulse duration and 50 Hz rate was achieved.

Switching using PT symmetry in plasmonic systems: positive role of the losses

We analyze the operation of 2 × 2 switches composed of two coupled waveguides operating on the basis of parity-time (PT) symmetry: the two waveguides differ through their gain or loss factors and not through the real part of their propagation constant. Plasmonics constitutes a preferred application for such systems, since combination of plasmonics with gain is increasingly mastered. The exact PT-symmetric case (gain and loss of identical absolute value) is considered as well as various unbalanced cases, thanks to their respective switching diagrams. Although perfect signal-conserving cross and bar states are not always possible in the latter cases, they can nevertheless form the basis of very good switches if precise design rules are followed. We draw from the analysis what the optimal configurations are in terms of, e.g., guide gain or gain-length product to operate the switch. Many analytical or semi-analytical results are pointed out. A practical example based on the coupling of a long-range surface-plasmon-polariton and a polymeric waveguide having gain is provided.

Amplified x-ray emission from core-ionized diatomic molecules.

We predict high-gain x-ray lasing in molecular nitrogen by ultrafast core ionization with an x-ray free-electron laser source. To estimate the spectral and temporal output of this molecular x-ray laser, we solve generalized Maxwell-Bloch equations, keeping track of the electronic and nuclear degrees of freedom. The spectrum of the amplified x-ray emission shows a strong dependence on the gain-length product. Whereas the emission at small gain length is similar to the relatively broad x-ray fluorescence band, the spectrum is determined by a single frequency in the linear gain region. The vibrational wave packet dynamics during the x-ray emission process is examined. By preparation of the initial vibrational quantum state, the x-ray emission frequency can be tuned within the fluorescence band. The present scheme is applicable to other homo- and heteronuclear diatomic systems, thereby extending the spectral range of coherent x-ray radiation sources based on amplification on bound transitions.

Saturation gain-length product during short-wavelength plasma lasing

A scaling-law, function of the longitudinal and the transverse aspect ratios of a laser-produced plasma gain-medium, is derived to predict the saturation gain-length product for short-wavelength lasing. Benchmarking with experimental data from the literature shows how critical is the plasma geometry and, henceforth, the focusing of the pump laser pulse.

Diode-pumped Nd:YAG self-adaptive resonator with a high-gain amplifier operating at 100 Hz

A small gain-length product as high as 5.5 is demonstrated in a diode-pumped core-doped ceramic Nd:YAG amplifier. This module allows one to realize a self-adaptive laser resonator operating at 100 Hz and delivering single longitudinal mode, 20 ns and 100 mJ laser pulses.

Gain and Emission Cross Section Analysis of Wavelength-Tunable Si-nc Incorporated Si-Rich ${\rm SiO}_{\rm x}$ Waveguide Amplifier

Multi wavelength strip-loaded waveguide amplifiers fabricated by growing Si-nanocrystal (Si-nc) incorporated Si-rich <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm SiO}_{\rm x}$</tex></formula> with detuning <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm N}_{2}{\rm O}/{\rm SiH}_{4}$</tex></formula> fluence ratio and RF plasma power are demonstrated, which show blue, yellow, and red multicolor amplified-spontaneous-emission (ASE) with gain coefficients of 157, 62, and 85.6 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">${\rm cm}^{-1}$</tex></formula> , and the corresponding products of Si-ncs emission cross section and Si-ncs radiative lifetime are 2.34 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\,\times 10^{-21}$</tex></formula> , 1.78 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\,\times 10^{-21}$</tex></formula> , and 1.28 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\,\times 10^{-21}~{\rm cm}^{2}\cdot{\rm s}$</tex></formula> , respectively, as deduced from the maximum gain-length product. Combining the time-resolved photoluminescence with the maximum gain-length product result, the Si-ncs cross section/carrier lifetime for the blue-, yellow-, and red-ASE <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm SiO}_{\rm x}$</tex></formula> : Si-nc samples are 1.37 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\,\times 10^{-14}$</tex></formula> /0.17, 6.84 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\,\times 10^{-16}$</tex></formula> /2.6, and 0.64 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\,\times 10^{-16}$</tex></formula> /20 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$({\rm cm}^{2}/\mu{\rm s})$</tex> </formula> , respectively. The high-gain blue-ASE sample exhibits a shorter saturation length of 0.25 mm with the highest loss coefficient due to scattering loss by Si-ncs of the highest density. The gain saturation of the strip-loaded <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm SiO}_{\rm x}$</tex></formula> :Si-nc waveguide is discussed.

Demonstration of soft x-ray laser of Ne-like Ar at 698 nm pumped by capillary discharge

The demonstration of a 69.8 nm laser on 3p 3P2 - 3s 1P1 (J=2-1) transition of Ne-like Ar pumped by capillary discharge is reported in this Letter. A main current of 12 kA with rise time of 43 ns was chosen to generate the plasma in a 35 cm long capillary filling with pressure of Ar as low as 11 Pa, resulting in a gain coefficient of 0.34 cm(-1) and gain-length product of 11 at 69.8 nm. Also observed is a weak laser on 3p 3D2 - 3s 3P1 (J=2-1) transition of Ne-like Ar at 72.6 nm in the same condition. In addition, multiwavelength lasing at 46.9, 69.8, and 72.6 nm was simultaneously realized in a capillary discharge plasma column, conditioning the pressure of Ar to 13 Pa.

Amplification properties of vacuum ultraviolet Ar_2* produced by infrared high-intensity laser

We report optical amplification of Ar(2)* at 126 nm, pumped by optical-field-induced ionization (OFI) created by an infrared high-intensity laser. A gain-length product of 0.84 was obtained by using multipass amplification with a vacuum ultraviolet (VUV) cavity. The gain-length product was increased up to 4.3 through the use of single-pass amplification with a VUV reflector and a hollow 5.0 cm-long fiber. Similar small signal gain coefficients of 0.84 and 0.86 cm(-1) were obtained in two different experiments, in which OFI Ar plasma gain media were produced in free space filled with Ar and inside an Ar-filled hollow fiber.

Characteristics of a Ne-like Ar 46.9-nm soft X-ray laser in capillary discharge at a low Ar pressure

A capillary discharge-pumped Ne-like Ar 46.9-nm soft X-ray laser at a low Ar pressure (28–46 Pa) is proven. To our knowledge, this is the first time an XRD laser output in the condition of the low threshold of a main-current pulse spike (20–21 kA) is demonstrated. The Al2O3 ceramic capillary tube is 20 cm in length (Mo electrode is 4 cm in length) and 3 mm in diameter. The maximum laser energy of the precalibrated XRD is 3.5 μJ. The maximum gain coefficient g = 0.46 cm−1, the maximum gain-length product is 8.28, the beam divergence is 5.4 mrad, and the laser pulse width is 1.65 ns. In addition, the results show that the laser plasma column became difficult to Z-pinch with a increasing Ar pressure, its Z-pinching state of a higher Ar pressure fluctuates more intensely than that of a lower pressure by analyzing the scattering of the delay time between the pre-and main-current pulse.

Output power and spectrum of optical parametric generator in the superfluorescent regime

Explicit expressions for the irradiance and signal spectrum of an optical parametric generator were derived. The calculation is in quantitative agreement with measurements of parametric generators with three different lengths of crystals operating in the superfluorescent regime. The measured spectrum was predicted for the entire measured range up to a gain-length product of 16, and the measured signal power was accurately derived up to a gain-length product of 10.

Characteristics of a Ni-like silver x-ray laser pumped by a single profiled laser pulse

We characterized a Ni-like silver soft x-ray laser realized as, what we believe is, a new variant of the grazing incidence pumping (GRIP) scheme. The x-ray laser was pumped by a single profiled laser pulse from a 10 Hz Ti:sapphire laser system. The Ni-like Ag x-ray laser was saturated with a gain coefficient of 76 cm−1 and an effective gain-length product of 28.2. The spatial characteristics of the new version of GRIP x-ray laser are presented including the far- and near-field beam profiles. Computational modeling of the lasing conditions was used to provide some qualitative explanations of the physical processes occurring in the x-ray laser. Additionally, we obtained some preliminary results on the injection seeding technique applied to the Ni-like Ag active medium using the 59th harmonic of the Ti:sapphire laser pulse as the seed. The single-pulse variant of the pumping scheme proved to be a stable and simple configuration of the table-top x-ray lasers also suitable for the injector-amplifier arrangement.

Blue-green small-signal gain and saturation in a luminescent polymer gain medium

The authors study the optical gain and saturation behavior in a blue-green-emitting luminescent polymer gain medium. Based on the results of amplified spontaneous emission measurements, the gain coefficients, the gain-length product, and the corresponding small-signal gain are determined. By the use of the variable stripe length method, large net gain coefficients of up to 106±6cm−1 have been measured under nanosecond photopumping. The large gain has favorable implications for the development of short wavelength lasers and amplifiers. Their study shows that a small-signal gain of 19dB is achievable with a very compact optical amplifier with a 400μm length.

The output of amplified spontaneous emission lasers

The output of amplified spontaneous emission (ASE) lasers such as X-ray lasers operated without mirrors is calculated exactly for Gaussian and Lorentzian small signal gain profiles by a simple Taylor series expansion. The accuracy of the ‘Linford’ formula commonly used as an approximation for the output of ASE lasers is evaluated by comparison to our exact solutions. The Linford formula is accurate to better than 10% for intensities produced by a Gaussian gain profile, but requires multiplication by a correction factor of 1 / π , at gain length product greater than 5 for Lorentzian gain profiles.

Saturated 132?nm high-repetition-rate laser in nickellike cadmium

We report gain-saturated operation of a 13.2 nm table-top laser in Ni-like Cd at a 5 Hz repetition rate. A gain-length product G x L = 17.6 was obtained by heating a precreated plasma with 8 ps duration Ti:sapphire laser pulses with an energy of only 1 J impinging at a grazing angle of 23 degrees. With an average power of approximately 1 muW [corrected] this laser is an attractive coherent source for at-wavelength metrology of extreme UV lithography optics and other applications.