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1.  Fabrication of Indium Bumps for Hybrid Infrared Focal Plane Array Applications
J. Jiang, S. Tsao, T. O'Sullivan, M. Razeghi, and G.J. Brown
Infrared Physics and Technology, 45 (2)-- March 1, 2004 ...[Visit Journal]
Hybrid infrared focal plane arrays (FPAs) have found many applications. In hybrid IR FPAs, FPA and Si read out integrated circuits (ROICs) are bonded together with indium bumps by flip-chip bonding. Taller and higher uniformity indium bumps are always being pursued in FPA fabrication. In this paper, two indium bump fabrication processes based on evaporation and electroplating techniques are developed. Issues related to each fabrication technique are addressed in detail. The evaporation technique is based on a unique positive lithography process. The electroplating method achieves taller indium bumps with a high aspect ratio by a unique “multi-stack” technique. This technique could potentially benefit the fabrication of multi-color FPAs. Finally, a proposed low-cost indium bump fabrication technique, the “bump transfer”, is given as a future technology for hybrid IR FPA fabrication. [reprint (PDF)]
 
1.  Gain-length scaling in quantum dot/quantum well infrared photodetectors
T. Yamanaka, B. Movaghar, S. Tsao, S. Kuboya, A. Myzaferi and M. Razeghi
Applied Physics Letters, Vol. 95, No. 9-- August 31, 2009 ...[Visit Journal]
The gain in quantum dot/quantum well infrared photodetectors is investigated. The scaling of the gain with device length has been analyzed, and the behavior agrees with the previously proposed model. We conclude that we understand the gain in the low bias region, but in the high field region, discrepancies remain. An extension of the gain model is presented to cover the very high electric field region. The high field data are compared to the extended model and discussed. [reprint (PDF)]
 
1.  Conduction‐ and valence‐band offsets in GaAs/Ga0.51In0.49P single quantum wells grown by metalorganic chemical vapor deposition
D. Biswas; N. Debbar; P. Bhattacharya; M. Razeghi; M. Defour; F. Omnes
Appl. Phys. Lett. 56, 833–835 (1990)-- February 26, 1990 ...[Visit Journal]
We have independently estimated the conduction- and valence-band offsets D.Ec and D.Ev in GaAs/Gao . 51 Ino49 P quantum wells by measuring the capacitance transient resulting from thermal emission of carriers from the respective wens. The heterostructure samples were grown by low-pressure metalorganic chemical vapor deposition. The band offsets are extrapolated from the emission activation energies with appropriate corrections. The estimated values of AEc and AEv are 0.198 and 0.285 eV, respectively. [reprint (PDF)]
 
1.  Engineering future light emitting diodes and photovoltaics with inexpensive materials: Integrating ZnO and Si into GaN-based devices
C. Bayram ; K. T. Shiu ; Y. Zhu ; C. W. Cheng ; D. K. Sadana ; F. H. Teherani ; D. J. Rogers ; V. E. Sandana ; P. Bove ; Y. Zhang ; S. Gautier ; C.-Y. Cho ; E. Cicek ; Z. Vashaei ; R. McClintock ; M. Razeghi
Proc. SPIE 8626, Oxide-based Materials and Devices IV, 86260L (March 18, 2013)-- March 18, 2013 ...[Visit Journal]
Indium Gallium Nitride (InGaN) based PV have the best fit to the solar spectrum of any alloy system and emerging LED lighting based on InGaN technology and has the potential to reduce energy consumption by nearly one half while enabling significant carbon emission reduction. However, getting the maximum benefit from GaN diode -based PV and LEDs will require wide-scale adoption. A key bottleneck for this is the device cost, which is currently dominated by the substrate (i.e. sapphire) and the epitaxy (i.e. GaN). This work investigates two schemes for reducing such costs. First, we investigated the integration of Zinc Oxide (ZnO) in InGaN-based diodes. (Successful growth of GaN on ZnO template layers (on sapphire) was illustrated. These templates can then be used as sacrificial release layers for chemical lift-off. Such an approach provides an alternative to laser lift-off for the transfer of GaN to substrates with a superior cost-performance profile, plus an added advantage of reclaiming the expensive single-crystal sapphire. It was also illustrated that substitution of low temperature n-type ZnO for n-GaN layers can combat indium leakage from InGaN quantum well active layers in inverted p-n junction structures. The ZnO overlayers can also double as transparent contacts with a nanostructured surface which enhances light in/out coupling. Thus ZnO was confirmed to be an effective GaN substitute which offers added flexibility in device design and can be used in order to simultaneously reduce the epitaxial cost and boost the device performance. Second, we investigated the use of GaN templates on patterned Silicon (100) substrates for reduced substrate cost LED applications. Controlled local metal organic chemical vapor deposition epitaxy of cubic phase GaN with on-axis Si(100) substrates was illustrated. Scanning electron microscopy and transmission electron microscopy techniques were used to investigate uniformity and examine the defect structure in the GaN. Our results suggest that groove structures are very promising for controlled local epitaxy of cubic phase GaN. Overall, it is concluded that there are significant opportunities for cost reduction in novel hybrid diodes based on ZnO-InGaN-Si hybridization. [reprint (PDF)]
 
1.  Novel Method for Reclaim/Reuse of Bulk GaN Substrates using Sacrifical ZnO Release Layers
A. Rajan, S. Sundaram, Y. El Gmili, P. L. Voss, K. Pantzas, T. Moudakir, A. Ougazzaden, D. J. Rogers, F. Hosseini Teherani, V. E. Sandana, P. Bove, K. Prior, R. McClintock & M. Razeghi
Proc. SPIE 8987, Oxide-based Materials and Devices V, 898719-- April 2, 2014 ...[Visit Journal]
Free-standing (0002)-oriented GaN substrates (f = 2”) were coated with 200 nm of ZnO and used as templates for the growth of GaN thin films. SEM and AFM revealed that such GaN layers had a relatively homogenous surface morphology with an RMS roughness (5 μm x 5 μm) of less than 4nm. XRD studies revealed strained ZnO growth on the GaN substrate and the reproduction of the substrate rocking curve for the GaN overlayers after only a hundred nm of growth, thus indicating that the GaN films had superior crystallographic quality compared to those grown on sapphire or ZnO/sapphire substrates. Quarter-wafer areas of GaN were removed from the GaN substrate (by selective chemical etching away of the ZnO interlayer). The expensive GaN substrates were then reclaimed/reused (without the need for polishing) for a second cycle of ZnO and GaN growth, which gave similar XRD, SEM, CL and AFM results to the first cycle. [reprint (PDF)]
 
1.  

-- November 30, 1999
 
1.  Thermal Conductivity of InAs/GaSb Type II Superlattice
C. Zhou, B.M. Nguyen, M. Razeghi and M. Grayson
Journal of Electronic Materials, Vol. 41, No. 9, p. 2322-2325-- August 1, 2012 ...[Visit Journal]
The cross-plane thermal conductivity of a type II InAs/GaSb superlattice(T2SL) is measured from 13 K to 300 K using the 3x method. Thermal conductivity is reduced by up to two orders of magnitude relative to the GaSb bulk substrate. The low thermal conductivity of around 1 W/m K to 8 W/m K may serve as an advantage for thermoelectric applications at low temperatures, while presenting a challenge for T2SL interband cascade lasers and highpower photodiodes. We describe a power-law approximation to model nonlinearities in the thermal conductivity, resulting in increased or decreased peak temperature for negative or positive exponents, respectively. [reprint (PDF)]
 
1.  High-quality visible-blind AlGaN p-i-n photodiodes
E. Monroy, M. Hamilton, D. Walker, P. Kung, F.J. Sanchez, and M. Razeghi
Applied Physics Letters 74 (8)-- February 22, 1999 ...[Visit Journal]
We report the fabrication and characterization of AlxGa1−xN p-i-n photodiodes (0 < x < 0.15) grown on sapphire by low-pressure metalorganic chemical vapor deposition. The devices present a visible rejection of six orders of magnitude with a cutoff wavelength that shifts from 365 to 338 nm. Photocurrent decays are exponential for high load resistances, with a time constant that corresponds to the RC product of the system. For low load resistances, the transient response becomes non-exponential, with a decay time longer than the RC constant. This behavior is justified by the strong frequency dependence of the device capacitance. By an admittance analysis, we conclude that speed is not limited by deep levels, but by substitutional Mg capture and emission time. [reprint (PDF)]
 
1.  Type-II ‘M’ Structure Photodiodes: An Alternative Material Design for Mid-Wave to Long Wavelength Infrared Regimes
B-M. Nguyen, M. Razeghi, V. Nathan, and G.J. Brown
SPIE Conference, January 25-29, 2007, San Jose, CA Proceedings – Quantum Sensing and Nanophotonic Devices IV, Vol. 6479, p. 64790S-1-10-- January 29, 2007 ...[Visit Journal]
In this work, an AlSb-containing Type-II InAs/GaSb superlattice, the so-called M-structure, is presented as a candidate for mid and long wavelength infrared detection devices. The effect of inserting an AlSb barrier in the GaSb layer is discussed and predicts many promising properties relevant to practical use. A good agreement between the theoretical calculation based on Empirical Tight Binding Method framework and experimental results is observed, showing the feasibility of the structure and its properties. A band gap engineering method without material stress constraint is proposed. [reprint (PDF)]
 
1.  Background limited performance of long wavelength infrared focal plane arrays fabricated from M-structure InAs-GaSb superlattices
P.Y. Delaunay, B.M. Nguyen, D. Hoffman, E.K. Huang, and M. Razeghi
IEEE Journal of Quantum Electronics, Vol. 45, No. 2, p. 157-162.-- February 1, 2009 ...[Visit Journal]
The recent introduction of a M-structure design improved both the dark current and R0A performances of Type-II InAs-GaSb photodiodes. A focal plane array fabricated with this design was characterized at 81 K. The dark current of individual pixels was measured between 1.1 and 1.6 nA, 7 times lower than previous superlattice FPAs. This led to a higher dynamic range and longer integration times. The quantum efficiency of detectors without antireflective coating was 74%. The noise equivalent temperature difference reached 23 mK, limited only by the performance of the testing system and the read out integrated circuit. Background limited performances were demonstrated at 81 K for a 300 K background. [reprint (PDF)]
 
1.  Gain and recombination dynamics in photodetectors made with quantum nanostructures: The quantum dot in a well and the quantum well
B. Movaghar, S. Tsao, S. Abdollahi Pour, T. Yamanaka, and M. Razeghi
Physical Review B, Vol. 78, No. 11-- September 15, 2008 ...[Visit Journal]
We consider the problem of charge transport and recombination in semiconductor quantum well infrared photodetectors and quantum-dot-in-a-well infrared detectors. The photoexcited carrier relaxation is calculated using rigorous random-walk and diffusion methods, which take into account the finiteness of recombination cross sections, and if necessary the memory of the carrier generation point. In the present application, bias fields are high and it is sufficient to consider the drift limited regime. The photoconductive gain is discussed in a quantum-mechanical language, making it more transparent, especially with regard to understanding the bias and temperature dependence. Comparing experiment and theory, we can estimate the respective recombination times. The method developed here applies equally well to nanopillar structures, provided account is taken of changes in mobility and trapping. Finally, we also derive formulas for the photocurrent time decays, which in a clean system at high bias are sums of two exponentials. [reprint (PDF)]
 
1.  Dark current reduction in microjunction-based compound electron barrier type-II InAs/InAs1-xSbx superlattice-based long-wavelength infrared photodetectors
Romain Chevallier, Abbas Haddadi, Manijeh Razeghi
Proc. SPIE 10540, Quantum Sensing and Nano Electronics and Photonics XV Page. 1054007-1-- January 26, 2018 ...[Visit Journal]
Reduction of dark current density in microjunction-based InAs/InAs1-xSbx type-II superlattice long-wavelength infrared photodetectors was demonstrated. A double electron barrier design was used to suppress both generation-recombination and surface dark currents. The photodetectors exhibited high surface resistivity after passivation with SiO2, which permits the use of small size features without having strong surface leakage current degrading the electrical performance. Fabricating a microjunction structure (25×25 μm² mesas with 10×10 μm² microjunctions) with this photodetector double barrier design results in a dark current density of 6.3×10-6 A/cm² at 77 K. The device has an 8 μm cut-off wavelength at 77 K and exhibits a quantum efficiency of 31% for a 2 μm-thick absorption region, which results in a specific detectivity value of 1.2×1012 cm·Hz1/2/W at 77 K. [reprint (PDF)]
 
1.  Beryllium compensation doping of InAs/GaSb infrared superlattice photodiodes
D. Hoffman, B.M. Nguyen, P.Y. Delaunay, A. Hood, M. Razeghi and J. Pellegrino
Applied Physics Letters, Vol. 91, No. 14, p. 143507-1-- October 1, 2007 ...[Visit Journal]
Capacitance-voltage measurements in conjunction with dark current measurements on InAs/GaSb long wavelength infrared superlattice photodiodes grown by molecular-beam epitaxy on GaSb substrates are reported. By varying the beryllium concentration in the InAs layer of the active region, the residually n-type superlattice is compensated to become slightly p-type. By adjusting the doping, the dominant dark current mechanism can be varied from diffusion to Zener tunneling. Minimization of the dark current leads to an increase of the zero-bias differential resistance from less than 4 to 32 cm2 for a 100% cutoff of 12.05 µm [reprint (PDF)]
 
1.  High Power 0.98 μm GaInAs/GaAs/GaInP Multiple Quantum Well Laser
K. Mobarhan, M. Razeghi, G. Marquebielle and E. Vassilaki
Journal of Applied Physics 72 (9)-- November 1, 1992 ...[Visit Journal]
We report the fabrication of high quality Ga0.8In0.2As/GaAs/Ga0.51In0.49P multiple quantum well laser emitting at 0.98 μm grown by low pressure metalorganic chemical vapor deposition. Continuous wave operation with output power of 500 mW per facet was achieved at room temperature for a broad area laser with 130 μm width and 300 μm cavity length. This is an unusually high value of output power for this wavelength laser in this material system. The differential quantum efficiency exceeded 75% with excellent homogeneity and uniformity. The characteristic temperature, T0 was in the range of 120–130 K. [reprint (PDF)]
 
1.  Spatial Noise and Correctability of Type-II InAs/GaSb Focal Plane Arrays
P.Y. Delaunay and M. Razeghi
IEEE Journal of Quanutm Electronics, April 2010, Vol. 46, No. 4, p. 584-588-- April 1, 2010 ...[Visit Journal]
A long wavelength infrared focal plane array based on Type-II InAs/GaSb superlattices was fabricated and characterized at 80 K. The noise equivalent temperature difference of the array was measured as low as 23 mK (f# = 2), for an integration time of 0.129 ms. The spatial noise of the array was dominated by the nonuniformity of the illumination through the circular aperture. A standard two-point nonuniformity correction improved the inhomogeneity equivalent temperature difference to 16 mK. The correctability just after calibration was 0.6. The long-term stability time was superior to 25 hours. [reprint (PDF)]
 
1.  High Frequency Extended Short-Wavelength Infrared Heterojunction Photodetectors Based on InAs/GaSb/AlSb Type-II Superlattices
Romain Chevallier, Abbas Haddadi, Ryan McClintock, Arash Dehzangi , Victor Lopez-Dominguez, Pedram Khalili Amiri, Manijeh Razeghi
IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 54, NO. 6-- December 1, 2018 ...[Visit Journal]
InAs/GaSb/AlSb type-II superlattice-based photodetectors, with 50% cut-off wavelength of 2.1 µm and a −3 dB cut-off frequency of 4.8 GHz, are demonstrated, for 10 µm diameter circular mesas under 15 V applied reverse bias. A study of the cut-off frequency with applied bias and mesa size was performed to evaluate some of the limiting factors of photodetectors high frequency performance. [reprint (PDF)]
 
1.  High Optical Response in Forward Biased (In,Ga)N-GaN Multiquantum-Well Diodes Under Barrier Illumination
J.L. Pau, R. McClintock, C. Bayram, K. Minder, D. Silversmith and M. Razeghi
IEEE Journal of Quantum Electronics, Vol. 44, No. 4, p. 346-353.-- April 1, 2008 ...[Visit Journal]
The authors report on the current–voltage (I–V) characteristic under forward biases obtained in low leakage, small size p-(In,Ga)N–GaN-n multiquantum well diodes. Under barrier illumination, the devices present a high optical response with capabilities to detect optical powers in the pW range without further amplification. This response is attributed to the screening of the internal electric fields. Recombination times of a few seconds are found to be associated to this mechanism. Moreover, a step-like feature is found in the I– V characteristic before the diode turn-on voltage. Our model proposes tunneling current through the multi-quantum-well structure as responsible of this feature. Fast modulation of the tunneling effect under barrier illumination is used to evaluate the detection of low photon fluxes. [reprint (PDF)]
 
1.  Persistent photoconductivity in Ga0.49In0.51P/GaAs heterojunctions
S. Ben Amor; L. Dmowski; J. C. Portal; N. J. Pulsford; R. J. Nicholas; J. Singleton; M. Razeghi
J. Appl. Phys. 65, 2756–2760 (1989-- November 18, 1988 ...[Visit Journal]
We have studied the persistent photoconductivity (PPC) effect in Ga0.49 Ino. sl P IGaAs heterostructures. Through time- and temperature-dependent Hall effect, we observe very small relaxation rates and the PPC remains observable at room temperature. Optical experiments show an optical energy threshold of 1.15 e V and an infrared quenching of the ppc. Thermal cycling of the samples strongly affects the PPC and the quenching temperature. The center responsible for the observed PPC, therefore, appears related to defects, Most of our observations are qualitatively understood in a large lattice relaxation DX-like center approach. However, the origin of the high quenching temperature remains to be explained. [reprint (PDF)]
 
1.  First observation of the two‐dimensional properties of the electron gas in Ga0.49In0.51P/GaAs heterojunctions grown by low pressure metalorganic chemical vapor deposition
M. Razeghi; P. Maurel; F. Omnés; S. Ben Armor; L. Dmowski; J. C. Portal
M. Razeghi, P. Maurel, F. Omnés, S. Ben Armor, L. Dmowski, J. C. Portal; First observation of the two‐dimensional properties of the electron gas in Ga0.49In0.51P/GaAs heterojunctions grown by low pressure metalorganic chemical vapor deposition. Appl. Phys. Lett. 12 May 1986; 48 (19): 1267–1269-- June 12, 1986 ...[Visit Journal]
We report the first observation of a two‐dimensional electron gas from Shubnikov–de Haas and quantum hall effect experiments in GaInP/GaAs heterostructures grown by low pressure metalorganic chemical vapor deposition. Angular‐dependent Shubnikov–de Haas measurements confirm two dimensionality of the system. Low‐temperature persistent photoconductivity was observed. Critical density at which the second electric subband starts to be populated was determined to be 7.3×1011 cm−2. [reprint (PDF)]
 
1.  Reliability in room-temperature negative differential resistance characteristics of low-aluminum contact AlGaN/GaN double-barrier resonant tunneling diodes
C. Bayram, Z. Vashaei, and M. Razeghi
Applied Physics Letters, Vol. 97, No. 18, p. 181109-1-- November 1, 2010 ...[Visit Journal]
AlGaN/GaN resonant tunneling diodes (RTDs), consisting of 20% (10%) aluminum-content in double-barrier (DB) active layer, were grown by metal-organic chemical vapor deposition on freestanding polar (c-plane) and nonpolar (m-plane) GaN substrates. RTDs were fabricated into 35-μm-diameter devices for electrical characterization. Lower aluminum content in the DB active layer and minimization of dislocations and polarization fields increased the reliability and reproducibility of room-temperature negative differential resistance (NDR). Polar RTDs showed decaying NDR behavior, whereas nonpolar ones did not significantly. Averaging over 50 measurements, nonpolar RTDs demonstrated a NDR of 67 Ω, a current-peak-to-valley ratio of 1.08, and an average oscillator output power of 0.52 mW. [reprint (PDF)]
 
1.  High power asymmetrical InAsSb/InAsSbP/AlAsSb double heterostructure lasers emitting at 3.4 μm
D. Wu, B. Lane, H. Mohseni, J. Diaz and M. Razeghi
Applied Physics Letters 74 (9)-- March 1, 1999 ...[Visit Journal]
Midinfrared lasers with an asymmetrical InPAsSb/InAsSb/AlAsSb double heterostructure are reported. Using the asymmetrical double heterostructure, p- and n-cladding layers are separately optimized; high energy-gap AlAsSb (Eg ≈ 1.5 eV) for the p-type cladding layer to reduce the leakage current, and thus to increase To, and low energy-gap InPAsSb (Eg ≈ 0.5 eV) for the n-cladding layer to have low turn-on voltage. 100-μm-width broad-area lasers with 1000 μm cavity length exhibited peak output powers of 1.88 W in pulse and 350 mW in continuous wave modes per two facets at T=80 K with To of 54 K and turn-on voltage of 0.36 V. Maximum peak output powers up to 6.7 W were obtained from a laser bar of total aperture of 400 μm width and cavity length of 1000 μm, with a differential efficiency of 34% and far-field beam divergence narrower than 40° at 80 K. [reprint (PDF)]
 
1.  Improved performance of quantum cascade lasers through a scalable, manufacturable epitaxial-side-down mounting process
A. Tsekoun, R. Go, M. Pushkarsky, M. Razeghi, and C. Kumar N. Patel
Proceedings of the National Academy of Sciences 103 (13)-- March 26, 2006 ...[Visit Journal]
We report substantially improved performance of high-power quantum cascade lasers (QCLs) by using epitaxial-side-down mounting that provides superior heat dissipation properties. We used aluminum nitride as the heatsink material and gold–tin eutectic solder. We have obtained continuous wave power output of 450 mW at 20°C from mid-IR QCLs. The improved thermal management achieved with epitaxial-side-down mounting combined with a highly manufacturable and scalable assembly process should permit incorporation of mid-IR QCLs in reliable instrumentation.
 
1.  Use of Sacrificial Zinc Oxide Template Layers for Epitaxial Lift-Off of Yttria-Stabilised Zirconia Thin Films
D. J. Rogers, T. Maroutian, V. E. Sandana, P. Lecoeur, F. H. Teherani, P. Bove and M. Razeghi
Proc. of SPIE 11687, 116872C (2021) ...[Visit Journal]
275 nm-thick Yttria-stabilised zirconia (YSZ) layers were grown on 240 nm-thick epitaxial (0002)-oriented ZnO buffer layers on c-sapphire substrates by pulsed laser deposition (PLD). X-ray diffraction (XRD) studies revealed high quality epitaxial growth with the YSZ having a preferential (111) orientation and a root mean square surface roughness of 1.4 nm over an area of 10 um x 10 um. The YSZ top surface was then temporary bonded to an Apiezon W wax carrier and the sample was immersed in 0.1M HCl so as to preferentially etch/dissolve away the ZnO underlayer and release of the YSZ from the sapphire substrate. XRD revealed only the characteristic (111) peak of YSZ after lift-off and thus confirmed both the dissolution of the ZnO and the preservation of the crystallographic integrity of the YSZ on the wax carrier. Optical and Atomic Force Microscopy revealed some buckling, roughening and cracking of the lifted YSZ, however, which was probably due to tensile epitaxial strain release. [reprint (PDF)]
 
1.  Resonant cavity enhanced heterojunction phototransistors based on type-II superlattices
Jiakai Li, Arash Dehzangi, Donghai Wu, Ryan McClintock, Manijeh Razeghi
Infrared Physics & Technology Available online 27 October 2020, 103552 https://doi.org/10.1016/j.infrared.2020.103552-- October 27, 2020 ...[Visit Journal]
Resonant cavity enhanced heterojunction phototransistor based on InAs/GaSb/AlSb type-II superlattice grown by molecular beam epitaxy has been demonstrated. The resonant wavelength was designed to be at near 1.9 μm wavelength range at room temperature. An eleven-pair lattice matched GaSb-AlAsSb quarter-wavelength Bragg reflector was used in the RCE-HPT to enhance the photoresponse. The device showed the wavelength selectivity and a cavity enhancement of the responsivity at 1.9 μm at room temperature. [reprint (PDF)]
 
1.  High power, continuous wave, quantum cascade ring laser
Y. Bai, S. Tsao, N. Bandyopadhyay, S. Slivken, Q.Y. Lu, D. Caffey, M. Pushkarsky, T. Day and M. Razeghi
Applied Physics Letters, Vol. 99, No. 26, p. 261104-1-- December 26, 2011 ...[Visit Journal]
We demonstrate a quantum cascade ring laser with high power room temperature continuous wave operation. A second order distributed feedback grating buried inside the waveguide provides both in-plane feedback and vertical power outcoupling. Total output power reaches 0.51 W at an emission wavelength around 4.85 μm. Single mode operation persists up to 0.4 W. The far field analysis indicates that the device operates in a high order mode. The magnetic and electric components of the ring-shaped lasing beam are in radial and azimuthal directions, respectively. [reprint (PDF)]
 

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