Littrow Angle Research Articles

Liquid refractometer based on immersion diffractometry

This study presents a laser diffractometric refractometer for measuring the refractive index of liquids. The refractive index is determined by rotating a reflection grating that is immersed in the fluid under test, and measuring the first-order Littrow diffraction angle. The Littrow angle is easily detected form the interferogram formed by the diffracted beam from the grating and the reflected beam from the liquid surface. No special cell for liquids is required. The alignment and measuring processes are simpler than those of other refractometers. The results of a feasibility experiment reveal that the accuracy of the proposed approach is about 0.003 for a refractive index of around 1.3.

Differential wavelength meter for laser tuning

A simple interferometer for matching the wavelengths of tunable lasers is described. Our interferometer uses the angular dispersion of a diffraction grating at the Littrow angle to produce a tilted wavefront with respect to a reference mirror in an opposing arm of a Michelson interferometer. As a first step, the resulting interference pattern is adjusted to produce a null fringe using a reference laser as a wavelength standard. When a tunable laser, such as a laser diode, is used to illuminate the system, the laser is simply tuned to reproduce the null fringe pattern established using the reference laser. When so tuned, the wavelength of the tunable laser is matched to that of the reference laser within about 3 GHz, close enough for optical heterodyning.

Continuously tunable external-cavity diode laser with a double-grating arrangement

A new external-cavity diode laser system based on an extended version of the Littman configuration is investigated. In our laser system the tuning mirror is replaced with a second grating mounted at the Littrow angle. This double-grating design provides a smaller passive bandwidth than the grating-mirror configuration, which is used to compensate for the large angle-of-incidence-dependent losses of the grazing-incidence grating. This results in a broader continuous tuning range with an improved mode stability. Because two laser diodes, emitting at 820 and 775 nm, respectively, are used, the external-cavity laser is continuously tunable without mode hops across 35 nm at 820 nm and 27 nm at 775 nm. Such a laser was used to measure the absorption lines of the oxygen A band around 762 nm. The complete R - and P -rotational branches of the b summation operator(g)(1) (+)(nu(??)=0)?X (3) summation operator(g)(-)(nu (?)=0) transition were recorded in a single-wavelength scan.

Universal grating design for pulse stretching and compression in the 800–1100-nm range

We have developed a holographically produced master metallic grating that achieves >91% diffraction efficiency over the wavelength range 800-1100 nm and a maximum diffraction efficiency at 1053 nm greater than 93% when used with TM polarization near the Littrow angle. The near-uniform diffraction efficiency with laser wavelength makes this design attractive for use in chirped-pulse amplification systems employing Ti:sapphire, Cr:LiSAF, or Nd:glass and permits high-fidelity stretching and compression of extremely short (10-fs) pulses.

Spatial-frequency bandwidth in the photolithographic transfer of submicron gratings

The principle of the photolithographic mask transfer of high-spatial-frequency gratings under the Littrow angle is shown to be so tolerant that a broad spatial-frequency spectrum can be transferred under the same exposure conditions.

Novel x-ray mask distortion measurement technique employing holographic gratings and phase-shifting interferometry

This article presents a new optical metrology technique that has been developed at CXrL to investigate potential distortions induced in x-ray masks during their fabrication, mounting, and x-ray irradiation. The technique employs a Zygo phase-shifting Fizeau interferometer to acquire the in-plane distortion (IPD) and out-of-plane distortion (OPD) present in the masks. The interferometer measures the OPD directly, while IPD measurements are obtained with the aid of holographic gratings that have been printed onto the masks. When positioned at the Littrow angle of the gratings, the interferometer can acquire a retrodiffracted wavefront that contains the IPD information. Subtraction of the pre- and postdistortion interferograms yields the induced distortions. Computer models to simulate x-ray mask distortions have been developed and implemented using ansys, a commercially available finite element analysis software package. Numerical results have shown excellent agreement with interferometric data. The authors believe that these new interferometric techniques and models should prove invaluable as metrologic and predictive tools for the measurement, characterization, and design of x-ray masks in the 0.25 μm regime.

Multiple-Selected-Line Unstable Resonator

A new type of unstable resonator has been developed that permits multiple-selected-line operation. Selected-line operation is obtained with a diffraction grating that is oriented at an angle that is different from the Littrow angle. Secondary feedback mirrors at the appropriate angles provide an independent threeelement cavity for each wavelength selected. The off-Littrow configuration is less efficient than a singleline cavity at the Littrow angle because there are secondary zero-order beams at each wavelength as well as a primary zero-order beam at all selected wavelengths. In the limit of a high gain this loss in efficiency is shown to be significantly reduced. Two types of multiple-selected-line unstable resonators are considered: an edge-coupled design, which produces an annular beam with a 45 degrees output coupling mirror, and a continuously coupled design, which uses the primary zero-order beam as output. Experiments have been carried out with a multiple-selected-line unstable resonator on a cw HF laser. Selected-line operation was obtained on the P(2) (5) and P(1) (6) HF transitions in a continuously coupled design.