Littrow Condition Research Articles

Compact Numerical Aperture 0.5 Fiber Optic Spectrometer Design Using Active Image Plane Tilt.

The numerical aperture of the spectrometer is crucial for weak signal detection. The transmission lens-based configuration has more optimization variations, and the grating can work approximately in the Littrow condition; thus, it is easier to acquire high numerical aperture (NA). However, designing a large aperture focusing lens remains challenging, and thus, ultra-high NA spectrometers are still difficult to acquire. In this paper, we propose a method of setting image plane tilt ahead directly when designing the large aperture focusing lens to simplify the high NA spectrometer design. By analyzing the accurate demands of the focusing lens, it can be concluded that a focusing lens with image plane tilt has much weaker demand for achromatism, and other monochromatic aberration can also be reduced, which is helpful to increase the NA. An NA0.5 fiber optic spectrometer design is given to demonstrate the proposed method. The design results show that the NA can achieve 0.5 using four lenses of two materials, and the MTF is higher than 0.5 when the spectral dispersion length is 12.5 mm and the pixel size is 25 μm, and thus, the spectral resolution can achieve 6.5 nm when the spectral sampling ratio is 2:1. The proposed method can provide reference for applications when appropriate materials are limited and high sensitivity is necessary.

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.

Understanding diffraction grating behavior: including conical diffraction and Rayleigh anomalies from transmission gratings

With the wide-spread availability of rigorous electromagnetic (vector) analysis codes for describing the diffraction of electromagnetic waves by specific periodic grating structures, the insight and understanding of nonparaxial parametric diffraction grating behavior afforded by approximate methods (i.e., scalar diffraction theory) is being ignored in the education of most optical engineers today. Elementary diffraction grating behavior is reviewed, the importance of maintaining consistency in the sign convention for the planar diffraction grating equation is emphasized, and the advantages of discussing “conical” diffraction grating behavior in terms of the direction cosines of the incident and diffracted angles are demonstrated. Paraxial grating behavior for coarse gratings (<italic>d</italic> ≫ λ) is then derived and displayed graphically for five elementary grating types: sinusoidal amplitude gratings, square-wave amplitude gratings, sinusoidal phase gratings, square-wave phase gratings, and classical blazed gratings. Paraxial diffraction efficiencies are calculated, tabulated, and compared for these five elementary grating types. Since much of the grating community erroneously believes that scalar diffraction theory is only valid in the paraxial regime, the recently developed linear systems formulation of nonparaxial scalar diffraction theory is briefly reviewed, then used to predict the nonparaxial behavior (for transverse electric polarization) of both the sinusoidal and the square-wave amplitude gratings when the +1 diffracted order is maintained in the Littrow condition. This nonparaxial behavior includes the well-known Rayleigh (Wood’s) anomaly effects that are usually thought to only be predicted by rigorous (vector) electromagnetic theory.

Lossless 0th and −1st order switching by dual-excitation of grating waveguide mode

The reflected 0th and −1st diffraction orders of a waveguide grating can be switched between 0 and 1 diffraction efficiency upon the excitation of a forward- and backward-propagating waveguide mode by means of the +1st and −2nd orders. Such mode-coupling trigger of high isolation switching is found to be in the neighborhood of the −1st order Littrow condition under the condition that no transmitted order can propagate; the condition is here fulfilled without loss penalty by reflecting them under total internal reflection. This requires a waveguide refractive index larger than 3, and resorting to a semiconductor in the near infrared. This non-Fano phenomenon is yet another feature of resonant gratings. The reflective switching effect lends itself to a stable monolithic implementation, and can be used for wavelength control, or for the evanescent wave sensing of measurands in the transmission medium.

Broadband spectrographic method for precision alignment of compression gratings

Previous research on achieving the alignment of compression gratings has mainly focused on the parallelism of the gratings. We propose a promising method to achieve parallelism and especially accurately adjust the grating to its optimum working angle to achieve dispersion compensation. A spectrometer and a precisely adjustable mirror pair are cooperatively used to measure the wavelength of the light diffracted by the grating, satisfying the Littrow condition. Meanwhile, the tiny slit of the spectrometer can decrease the grating-tip and in-plane rotation error during the alignment procedure. Using this technique, the residual phase of the compressed pulse is optimized and the compressed pulse duration is 25.4 fs, which is 1.06 times that of the Fourier-transform-limited compressed pulse.

Wavefront analysis of high-efficiency, large-scale, thin transmission gratings

Large-scale (180 × 60 × 1 mm(3)) transmission gratings with groove densities of 1250 and 1740 lines/mm have been developed, resulting in diffraction efficiencies above 95%. The throughput of a folded pulse compressor with two large-scale transmission gratings was approximately 80% in a 20-fs Ti:sapphire chirped-pulse amplification (CPA) laser. The parabolic bending of the transmission grating due to anti-reflection (AR) coating was minimized to 2.9 λ at 633 nm by improving the evaporation process. By a simple analysis, we explain why this level of bending does not induce a wavefront distortion through the transmission grating near the Littrow condition while the wavefront from a reflection grating is distorted to nearly twice the bending of the grating. The calculation based on the measured bending shows that both the group delay difference relative to the ideally flat grating from 750 to 850 nm and the spatial pulse front distortion over a 60-mm-diameter input beam are negligible, even when the dispersive beam covers ~140 mm on the grating. The spatial pulse front distortion measured after the compressor was less than the measurement limit (1.5 fs) for a 20-mm-diameter beam, where the beam size in the dispersive direction on the grating was 85 mm.

Applications of sub-wavelength grating mirrors in high-power lasers

Abstract A grating waveguide mirror (GWM) results from the combination of a waveguide and a sub-wavelength grating which lead, for given incidence conditions, to polarization and or wavelength filtering. In the present paper, we report on the application of such elements for the selection of the polarization (linear, radial, or azimuthal) as well as the narrowing, stabilizing and tuning of the emission spectrum of high-power lasers. Using a leaky-mode circular GWM, beams with radial and azimuthal polarization with output powers of up to 275 W and 145 W, respectively, could be extracted from a Yb:YAG thin-disk with optical efficiencies of 52.5% and 43%, respectively. In both cases, the GWM was composed of a highly reflective (HR) mirror and a sub-wavelength grating as the end-mirror of the resonator. Using a leaky-mode linear GWM operating under Littrow condition, beams with linear polarization and a narrow spectral bandwidth were obtained from a Yb:YAG thin-disk laser. In multimode operation, an output power of 325 W was achieved at an optical efficiency of 53.5%. In near-fundamental mode operation, 110 W was extracted at an optical efficiency of 36.2%. In this latter case, the spectral bandwidth was measured to be around 25 pm. Moreover, continuous wavelength tuning from 1007 to 1053 nm was demonstrated with our device.

Avoiding temporal distortions in tilted pulses

Tilted femtosecond laser pulses, having an intensity front with an angle to the propagation direction, can be generated by a dispersive element and a lens or mirror for imaging. Here we show that conventional geometries, for example with a grating at Littrow's condition, produce significant temporal distortions over the beam profile. The aberrations are the result of a mismatch between the grating's surface and the object plane of the imaging system. This changes the chirp of the pulses over the beam profile and lengthens the pulses to picoseconds for millimeter-sized beams. The distortions can be avoided by choosing a geometry in which the propagation direction of the tilted pulses is perpendicular to the grating's surface.

Measurement of Surface Plasmon Polariton Enhanced Goos–Hanchen Shift Based on Grating and Liquid Crystal Technologies

We measured the surface plasmon polariton (SPP) enhanced Goos-Hanchen (GH) shift based on liquid crystal (LC) and grating technologies. An optical setup is used to convert the spatial displacement to incidence angle variation to a Littrow mounted diffraction grating. As a consequence, the GH shift information could be obtained from the back-reflected center wavelength that fulfills the Littrow condition. An LC cell is used to adjust the polarization state of the incident light without mechanical movement. About 10- μm GH shift difference between transverse-electric (TE) and transverse-magnetic (TM) mode lights were measured associated with the SPP excitation. The corresponding center wavelength shift of the returned beam is 404 pm. The relationship between energy conversion and GH shift is also investigated.

Miniature pulse compressor of deep-etched gratings

We propose a miniature pulse compressor that can be used to compensate the group velocity dispersion that is produced by a commercial femtosecond laser cavity. The compressor is composed of two identical highly efficient deep-etched transmissive gratings. Compared with prism pairs, highly efficient deep-etched transmissive grating pairs are lightweight and small. With an optimized groove depth and a duty cycle, 98% diffraction efficiency of the -1 transmissive order can be achieved at a wavelength of 800 nm under Littrow conditions. The deep-etched gratings are fabricated in fused silica by inductively coupled plasma etching. With a pair of the fabricated gratings, the input positively chirped 73.9 fs pulses are neatly compressed into the nearly Fourier transform-limited 43.2 fs pulses. The miniature deep-etched grating-based pulse compressor should be of interest for practical applications.

Uncertainty evaluation of the NRC imaging diffractometer

A model equation is developed for a diffractometer operating under the Littrow condition. The effects of grating orientation, grating position, source and detector position and source collimation are included. The model is validated against experimental measurements using the NRC imaging diffractometer. Errors due to the effects of coherence and grating position were found to be important for the small area gratings used in these experiments. An uncertainty budget for the NRC imaging diffractometer is developed and reproducibility measurements are presented.

Integrated wavelength stabilization of in-plane semiconductor lasers by use of a dual-grating reflector

We summarize a novel integrated wavelength-stabilization scheme for broad stripe surface-emitting lasers. The method is based on two gratings fabricated on opposite sides of a device in which the first grating disperses light through the substrate to the opposite side, where the second surface has a feedback grating that operates under total internal reflection and in the Littrow condition to provide feedback into the gain medium. Experimental results have been obtained for both high power and a narrow linewidth, showing a CW slope of 0.85 W/A.

Highly efficient transmission gratings in fused silica for chirped-pulse amplification systems

We report on highly efficient transmission gratings in fused silica with a grating period of 800 nm generated by electron-beam lithography. At a wavelength of 1060 nm, 95% diffraction efficiency is achieved under Littrow conditions. The damage threshold, extremely enhanced compared with conventional gold-coated diffraction gratings, makes these gratings the key elements in high average power (>100 W) femtosecond fiber chirped-pulse amplification systems.

A wavelength encoded rotary displacement sensor

A novel concept for a digital rotary displacement sensor is presented. Broadband light issuing from the encoder input fibre is focused on a 9 bit Gray coded dis. Rays emerging from the disc under Littrow conditions are diffracted back to the input fibre by a grating. The output spectrum is encoded as a function of the disc's angular position. The theoretical prediction of the sensor's performance is developed and compared with experimental results. A prototype with a resolution of 0.7 degrees and a nonoperating range of 360 degrees has been successfully tested.

Advantages of an off-Littrow mounting of an echelle grating

A phenomenon is described in which the size of the exit-slit image of the entrance slit is influenced by the angle at which an echelle grating is used. The phenomenon becomes significant only for large deviations from Littrow conditions. A mathematical treatment and experimental results are presented to show that proper exploitation of the effect results in simultaneous improvements in bandpass, range, and intensity for an echelle spectrometer.

Actual blaze angle of the Bausch &amp; Lomb R4 echelle grating

An innovative procedure is described for measuring blaze angle that is free of systematic effects associated with an alternative approach. The method uses the effect of facet diffraction on the blaze function when an echelle grating is used off-Littrow. The angle measurement in the Littrow condition is wavelength independent and locates the actual direction of the grating facet normal.

Efficiency optimization of rectangular groove gratings for use in the visible and IR regions

Rigorous electromagnetic theory is used to investigate the low order diffraction efficiency behavior of perfectly conducting rectangular groove plane diffraction gratings in the lambda/d domain of 0.25-1.8 of interest to spectrometry. We show how to optimize performance and make comparisons with blazed and holographic gratings. The role of finite conductivity and departure from Littrow conditions is also investigated. Comparison with experiment confirms the accuracy of the theory.

The Cassegrain Echelle Spectrograph at Mt John Observatory

The standard formula for the resolving power R(= λ/Δλ) of an astronomical grating spectrograph is Here L is the linear size of the grating, perpendicular to the direction of the grooves, θB is the blaze angle of the grating, θS is the angular size of the slit, projected back on to the sky, and D is the diameter of the telescope objective. The formula is valid for gratings used in the Littrow condition, when the angle of incidence α, and the angle of diffraction β, are both close to θB.