Littrow Angle Research Articles

Grating compressor optimization aiming at maximum focal intensity of femtosecond laser pulses

It is shown that the optimal geometry of a Treacy compressor is the full-aperture compressor, in which the beam size at the first diffraction grating is equal to its length. Despite the energy losses and greater size of the focal spot, such a compressor provides considerably higher (by 1.5–2 times) focal intensity than an energy lossless compressor. Decreasing the density of grooves from 1200–1400/mm to about 1000/mm also increases the focal intensity by tens of percent. The constructed theory is generalized to the full-aperture two-grating compressor, which is the best design due to the angle of incidence on the first grating being smaller than the Littrow angle. Two gratings with a length of 138 cm allow obtaining an intensity of 4.09 × 1024W/cm2 and 5.01 × 1024W/cm2 in the focus of F/2 parabola for the projects XCELS and SEL-100PW, reaching the 139 PW and 174 PW power.

Common-mode plasmon sensing scheme as a high-sensitivity compact SPR sensor.

A deep metal grating enables quasi-phase-matched simultaneous excitation of two counterpropagating surface plasmon modes by means of its +1st and -2nd diffraction orders. The resulting angular reflection spectra of the scattered -1st and zeroth orders exhibit three interleaved zeros and maxima in a range centered around the Littrow angle. The spectra differ thoroughly from the usual reflection dip resulting from single-order plasmon coupling that produces strong absorption. The zeroth and -1st orders exhibit two crossing angles enabling high-sensitivity common-mode detection schemes designed to reject variations in source power and environmental noise. The proof of concept and experimental assessment of this new surface plasmon resonance (SPR) sensing scheme are demonstrated by monitoring gases in a pressure-controlled chamber. A limit of detection (LOD) of 2 × 10-7 refractive index unit (RIU) was achieved.

Advantages of out-of-plane pulse compression gratings.

Diffraction gratings for pulse compression generally perform best at the Littrow angle, but reflection gratings require a nonzero deviation angle to separate the incident and diffracted beams, so they cannot be used at the Littrow angle. In this paper, we show both theoretically and experimentally that most practical multilayer dielectric (MLD) and gold reflection grating designs can be used with quite substantial beam-deviation angles-as large as even 30°-by mounting the grating out-of-plane and choosing the optimal polarization. The impact of polarization when mounting out-of-plane is explained and quantified.

All-Fiber Laser Feedback Interferometry for Sequential Sensing of In-Plane and Out-of-Plane Displacements

In this paper, an all-fiber laser feedback interferometer (LFI) with a diffraction grating was developed for sequential measurement of in-plane and out-of-plane displacements without changing the optical arrangement. When the light emitted from an erbium-doped fiber ring laser is incident on a reflection grating at the Littrow angle, the diffracted light will return into the laser cavity along the original path, thus generating laser feedback interference. Experimental results reveal that the all-fiber system could achieve a precision of 40 nm in both in-plane and out-of-plane displacements sensing. Compared with the traditional all-fiber LFI, the proposed sensing system transfers the measuring scale from laser wavelength to grating period, and it has the advantages of good anti-interference performance and reliability.

Study of wavelength-switchable watt-level blue external cavity diode laser for NO2 S-DIAL

A 2.3 W wavelength-switchable blue external cavity diode laser (ECDL) was studied. The laser was built on Littrow configuration and a piezoelectric ceramic transducer (PZT) driver was employed to change the Littrow angle for wavelength tuning. Its emitting wavelength can be switched between 447.46 nm and 448.10 nm which are the required wavelengths for NO2 differential absorption lidar application. The measured spectral linewidth of the proposed ECDL was 0.08 nm. The main peak was at least 35 dB stronger than its adjacent freely running emission peak and background amplified spontaneous emission (ASE). The wavelength switching dynamics were inspected and shows good repeatability at frequencies of 16.7 Hz and 50 Hz.

Simply structured polarization-independent high efficiency multilayer dielectric gratings.

A polarization-independent multilayer dielectric diffraction grating with a low aspect ratio and high diffraction efficiency was designed and fabricated. The diffraction grating designed with a grating density of 1200 lines/mm had an aspect ratio of 0.59, mean polarization-independent diffraction efficiency in the Littrow angle of ±2.5∘, and 1030-1080 nm wavelength range of 97.2%. The designed grating was fabricated using ion assisted deposition and reactive ion etching techniques. The mean polarization-independent diffraction efficiency of the fabricated grating was 96.1%, and its standard deviation was 0.68%. The fabricated diffraction grating was irradiated with a 1064 nm cw laser, with a power density of 30kW/cm2, for 1 min to measure the temperature change before and after the laser application. It was verified that the temperature variation of the diffraction grating without heat treatment was 8.8°C, and the temperature variation after heat treatment at 400°C decreased to 2.3°C.

Ultralow‐threshold wideband‐tunable single‐mode ultraviolet lasing from lanthanide‐doped upconversion nanomaterials

AbstractUltraviolet (UV) lasers with dynamic wavelength‐tunability and high monochromaticity are crucial in a multitude of practical applications yet still remarkable challenges. Here, we show wide wavelength‐tuning of single‐mode UV lasing based on lanthanide‐doped upconversion nanoparticles (UCNPs). The rationally designed Yb3+/Er3+/Tm3+/Gd3+/Ce3+ co‐doped multilayer UCNPs, which exhibits a broad gain spectrum with the full width of half maximum of around 57 nm in the UV regime, are developed. More importantly, by taking advantages of a diffraction grating as the tuning component, stable single‐mode emission can be achieved in the UCNPs‐based external‐cavity‐extended Fabry–Pérot laser at room temperature. Specifically, the lasing threshold is around 137 µJ cm–2, which is two orders of magnitude lower than that in the previously reported articles. Precise wavelength‐tuning from 310 to 363 nm can be realized by adjusting the Littrow angle. This achievement highlights a portable alternative to continuously wideband‐tunable UV lasers and opens up new opportunities for constructing compact solid‐state UV photon sources.

Nonnull interferometric testing of spherical gratings under Littrow conditions with opposite diffraction orders.

Diffracted wavefront measurements are qualitative and comprehensive verifications for the spherical grating that was manufactured to specifications. Direct interferometric testing of the diffracted wavefront is convenient and implemented by tilting the spherical grating at a Littrow angle to obtain autoreflection and then results in a nonnull interferometric testing configuration. The diffracted wavefront of the spherical grating contains not only wavefront errors induced by the manufacturing imperfections but also inherent wavefront contributions from the autoreflection testing setup. The magnitudes of the latter are affected by both the spherical substrate and the groove pattern. Through the analysis of geometric aberrations of spherical gratings, the groove pattern contributions are demonstrated to be contrary for the opposite diffraction orders. A nonnull interferometric testing of spherical gratings is proposed without foreknowledge of the groove pattern, in which the wavefront errors contributed only by the manufacturing imperfections are derived from dual measurements under Littrow conditions with opposite diffraction orders. Simulations are implemented for varied line spacing (VLS) spherical gratings with an F-number slower than 1.5 and groove density varying from 150 to 300 lp/mm, and the residual error less than 0.004λ RMS is obtained. The residual misalignment error after conventionally removing defocus and tilt is further analyzed and discussed. A VLS grating in which the NA is 0.13 and groove density is 200 lp/mm is chosen as an experimental sample, and the diffracted wavefront error with 0.018λ RMS is obtained.

Characteristics of a cascaded grating multi wavelength dye laser

Characteristics of a multi wavelength dye laser in two cascaded grating resonator configurations are presented. DCM dye dissolved in ethanol, was transversely pumped by second harmonic of Nd:YAG laser and four wavelength, independently tunable, collinear dye laser operation was obtained in Cascaded Grazing Incidence Grating cavity (CGIG) and Hybrid CGIG with fourth grating in Littrow angle (HCGIG) configuration. Gain competition effect of all the sub-cavities was fully characterized and wavelength zones of operation were identified for each cavity for sustaining four wavelength operation. Overall efficiency of the oscillator was measured to be around 2% in CGIG and 7% in HCGIG.

Littrow angle based autocollimation method for precision online monitoring three-dimensional angular drifts of chirped-pulse compression-gratings

A simple optical method for online precisely monitoring three-dimensional (3D) angular drifts of chirped-pulse compression-gratings in chirped-pulse amplification (CPA) lasers is proposed. Monitoring objects include all dimensional angular drifts of a grating, especially the grating groove in-plane-rotation. Monitoring contents contain direction and amount. And monitoring results are obtained by detecting the direction and the amount of 2D relative offsets of three focal spots formed by a ternary monitoring beam line. The theoretical model of the proposed method is set up using a matrix ray-tracing method, and a simplified monitoring equation is concluded based on numerical simulations. And the validity of this method is verified by a simple demonstration experiment. Besides, monitoring error and reliability discussion of the method are presented, as well.

High-spectral-resolution characterization of broadband high-efficiency reflection gratings

An optical characterization method with high spectral resolution for broadband, multilayer dielectric gratings working at the -1st reflection order is demonstrated in this paper. The diffraction-efficiency measurement setup for the broadband gratings with high efficiencies mainly consists of a double-light-path system with a monochromator as the illumination source and an automatic rotation stage for incident and diffraction angles adjustment. Two typical practical difficulties, namely (1) the mismatch between the spot size of diffracted light and the limited detector aperture and (2) the shared propagation path between the incident and diffracted light at the Littrow angle, were well solved. A fabricated multilayer dielectric grating was measured on the established measurement setup. Diffraction efficiencies greater than 90% in the wavelength range from 763 to 852 nm were obtained with an average relative deviation less than 1.0%. At the moment, the wavelength resolution is 1 nm and the angle resolution is 0.2 deg. The high-resolution broadband diffraction spectrometry testing method is applicable to characterizing broadband pulse compression gratings in the laser systems.

Perfect blazing with echelle gratings in TE and TM polarization

Perfect blazing with echelle gratings in a high-order Littrow mount exists not only with TM polarization, as can perhaps be assumed, but also with TE and TM polarizations simultaneously. This finding contradicts with a heuristic explanation as to why perfect blazing is not possible simultaneously in TE and TM polarizations given by Loewen and Popov [Diffraction Gratings and Applications (Marcel Dekker, 1997)]. As a matter of fact, in the ideal case of infinite conductivity, light is diffracted in the Littrow order with 100% efficiency for both polarization states. For metal gratings, a small loss occurs. Three conditions are necessary for perfect blazing: (A) the apex angle must be very close to 90°, (B) a specific Littrow order has to be used, and (C) the blaze angle has to be 4° to 6° larger than the Littrow angle. The last property is particularly intriguing because typically the difference between the two angles is smaller than 1.0°.

Design and properties analysis of total internal reflection gratings for pulse compressor at 1053 nm

High-efficiency compression gratings based on total internal reflection (TIR) are promising alternatives of compressor gratings because of their high diffraction efficiency, potential high damage resistant ability, and compact structure. Dependence of the −1 order diffraction efficiencies on grating parameters is analyzed for TE- and TM-polarized incident light of 1053 nm at Littrow angle, which is calculated by using the rigorous coupled-wave analysis. A more intuitional view on the relation is offered through three-dimensional slicing figures instead of two-dimensional ones. The performances of high-efficiency gratings are compared and regarded as criteria for further choices, including spectral bandwidth, angle bandwidth, dispersion, and intensity distribution. For TE- and TM-irradiations, similar spectral bandwidth and angle bandwidth can be achieved by different grating parameters. However, the computer simulation result on the intensity distributions of the two polarized waves shows that such design should be used under the illumination of TE-polarized wave for lower intensity enhancement ratio, which is an important factor related to the gratings’ damage threshold.

Realization of the broad angular spectrum of multilayer dielectric gratings based on the leaky mode resonance

Based on the leaky mode resonance theory,the physical mechanism of producing the broad angular spectrum of Multilayer Dielectric Grating (MDG) in the -1 st order reflection diffraction direction is presented in this paper.It is found that the thin match layer would improve the bandwidth of angular spectrum effectively.A good result of ±11 degree near Littrow angle 37.9 over 90% diffraction efficiency centered at 1040nm is obtained,and the parameters of the result have excellent fabrication tolerance.The Fourier modal method is employed for calculating the diffraction efficiency.

Precise diffraction efficiency measurements of large-area greater-than-99%-efficient dielectric gratings at the Littrow angle

We have developed improved cavity-finesse methods for characterizing the diffraction efficiencies of large gratings at the Littrow angle. These methods include measuring cavity length with optical techniques, using a Michelson interferometer to calibrate piezoelectric transducer nonlinearities and angle-tuning procedures to confirm optimal alignment. We used these methods to characterize two 20 cm scale dielectric gratings. The values taken from across their surfaces collectively had means and standard deviations of micro=99.293% and sigma=0.164% and micro=99.084% and sigma=0.079%. The greatest efficiency observed at a single point on a grating was (99.577+/-0.002)%, which is also the most accurate measurement of the diffraction efficiency in the literature of which we are aware. These results prove that a high diffraction efficiency with low variation is achievable across large apertures for gratings.

Characterization of polarization sensitive, high efficiency dielectric gratings for formation flight interferometry

Reflective diffraction gratings enable novel optical configurations that simplify and improve laser interferometers. We have proposed an all-reflective grating interferometer that can be used in LISA type interferometers for space gravitational wave detection [1]. One configuration requires a highly polarization sensitive grating. We report on characterizations of a grating made atop high reflective dielectric layers. Using a direct measurement method, the diffraction efficiency at the Littrow angle for s-polarization is measured as 97.3% and for p-polarization 4.2%, leading to a s/p polarization diffraction ratio of 23.2. The depolarization from s- to p-polarization is measured to be ∼1.7×10-4, and from p- to s-polarization 1.8×10-4. We derived a transfer matrix based on these measurements. Furthermore, we have developed a more accurate method for diffraction efficiency measurement using a grating cavity. These measurements are encouraging steps taken towards the requirements of an ideal grating interferometer.

高消光比反射式偏振分束硅光栅

A deep binary silicon grating as high-extinction-ratio reflective polarizing beam splitter (PBS) at the wavelength of 1550 nm is presented. The design is based on the phenomenon of total internal reflection (TIR) by using the rigorous coupled wave analysis (RCWA). The extinction ratio of the rectangular PBS grating can reach 2.5\times10^5 with the optimum grating period of 397 nm and groove depth of 1.092 \mum. The efficiencies of TM-polarized wave in the 0th order and TE-polarized wave in the -1st order can both reach unity at the Littrow angle. Holographic recording technology and inductively coupled plasma (ICP) etching could be used to fabricate the silicon PBS grating.

Littrow angle method to remove alignment errors in grating pulse compressors

An alignment method for pulse-compression gratings that obviates the need to place the gratings at normal incidence to remove grating-tip error is proposed. Grating-tip and groove-orientation errors are removed using two alignment wavelengths in a manner analogous to a laser-beam pointing and centering procedure entirely at the respective Littrow angles for the two wavelengths. By choosing wavelengths with Littrow angles close to the use angle of the grating, the residual tip and groove-orientation errors that may be introduced when the grating mount is tilted to its use angle are reduced. This method has greatly facilitated the alignment of the OMEGA Extended Performance (EP) large-aperture pulse compressors, thereby reducing residual pulse-front tilt caused by nonparallel gratings. OMEGA EP is a high-energy, petawatt-class laser at the University of Rochester's Laboratory for Laser Energetics. A numerical simulation of the alignment procedure is presented.

Diffraction property of multi-layer dielectric gratings studied by rigorous coupled-wave analysis

The rigorous coupled-wave analysis technique for describing the diffraction of multi-layer diffraction grating (MDG) is put forward. Formulations for a stable and efficient numerical implementation of diffraction efficiency are presented for MDG for TE polarization and Littrow angle. With the merit function of the -1 order diffraction efficiency higher than 96%, the parameters of MDG are optimized for HfO2 and SiO2 top layers, respectively. Numerical calculation indicates that a larger grating parameter range can be obtained with HfO2 rather than the SiO2 on the top. The manufacture tolerance and the effective incident angle for the optimized structure of MDG are discussed in the end.

Design of high-efficiency diffraction gratings based on total internal reflection for pulse compressor

We present designs of high-efficiency compression grating based on total internal reflection (TIR) for picosecond pulse laser at 1053 nm. The setup is devised by directly etching gratings into the bottom side of a prism so that light can successfully enter (or exit) the compression grating. Dependence of the −1 order diffraction efficiencies on the constructive parameters is analyzed for TE- and TM-polarized incident light at Littrow angle by using Fourier modal method in order to obtain optimal grating structure. The electric field enhancement within the high-efficiency TIR gratings is regarded as another criterion to optimize the structure of the TIR gratings. With the criterion of high diffraction efficiency, low electric field enhancement and sufficient manufacturing latitude, TIR compression gratings with optimized constructive parameters are obtained for TE- and TM-polarized incident light, respectively. The grating for TE-polarized light exhibits diffraction efficiencies higher than 0.95 within 23 nm bandwidth and relatively low square of electric field enhancement ratio of 5.7. Regardless of the internal electric field enhancement, the grating for TM-polarized light provides diffraction efficiencies higher than 0.95 within 42 nm bandwidth. With compact structure, such TIR compression gratings made solely of fused silica should be of great interest for application to chirped pulse amplification (CPA) systems.