Diffractive optical components

A hemispherical microlens at the front end is used as the focusing element. The length of the pure silica rod d is designed to control the focused beam waist Wi, which is defined as half-width at 1/e² maximum intensity, and position Zi, which is defined as the distance from the beam waist position to the front end of the lens. The relationship of Wi and Zi is a function of propagation distance g = d + R, where R is the radius of the hemispherical lens.

2.4 Diffractive optical components

The beam-splitters must provide good extinction ratio, a broad wavelength range for operation with broadband source, a large angular tolerance and a small size for effective packaging. Conventional beam-splitters are based on the use of the natural birefringence of crystals (Wollaston prisms, for example) or in the use of the polarization selectivity of multilayer dielectric coatings. Diffractive optical elements (DOEs) are attractive because they can solve problems of compactness inherent to the use of MOEMS processes and are adapted to mass production. In some implementations of DOEs, the two orthogonally polarized optical fields of TM and TE are both reflected, while in some cases both are transmitted, and in yet another category, one is reflected and the other transmitted.

The potential of diffractive optics lies in the fact that any phase profile can be fabricated as a DOE, even if refractive implementation is impossible due to constraints in the fabrication process. Most of the microlithographic techniques for pattern transfer are optimized for the fabrication of grating step profiles. The fabrication is possible with the same technological approaches of phase quantization, independent of the functionality. On the other hand, DOEs for any functionality can be implemented optimally, and reduce the number of optical elements required because they perform complex phase transformation that are not possible with refractive optical elements (ROEs). Besides, the DOEs have less aberration than the ROEs. In Fig. 2-3, we summarize some of the frequently used types of DOEs,

(a) The 1*3 beam-splitting gratings, which are general gratings with constant periods, can be used to replace the conventional beam-splitters. Their periods and diffraction angles can be evaluated according to the grating formula:

2dsinθ=mλ

(b) The 1*N beam-splitter gratings with variant periods perform multiple beam -splitting.

Fig. 2-3 Examples of DOEs: (a) 1*3 beam-splitter; (b) 1*N beam-splitter (e.g., Dammann grating), (c) beam deflector, and (d) diffractive lens (e.g., Fresnel lens).

(c) The beam deflectors with multiple steps within a period are used to approximate the reflected blazed gratings.

(d) The diffractive lens such as a Fresnel lens performs focusing.

2.4.1 Transmission gratings

As with any grating, the objective of transmission gratings is to control the division of incident light into the various orders beams. Diffraction efficiency describes the fraction of the incident light that is diffracted into the orders of use at the wavelength band. The efficiency of transmission gratings mainly depends on groove geometry, with the physics of transmission gratings simpler than for reflection gratings because there is no metal surface. Therefore, they operate largely in the scalar domain due to the near absence of polarization effects.

Phase gratings only change the phase of the incident light in the different groove regions, and amplitude gratings are presumed to change the amplitude. It means that phase gratings have variation of the real part of the refractive index of the grating material, while amplitude gratings vary in the imaginary part. The incident beams diffracted through amplitude gratings will be absorbed or reflected partially, so that its light-efficiency is lower than phase grating. Besides, phase gratings are generally adopted because their optical behavior is controlled by the physical phase retardation.

Amplitude gratings, or Ronchi rulings, have a line pattern that is alternately opaque and transmitting and therefore low diffraction efficiency. Their maximum first order efficiency is about 11%, and naturally occurs when the filling factor is 50%. Under this condition, the sum of the zeroth and two first orders is about 47.6%, which implies that the sum of all remaining orders is only 2.4%, because even orders vanish

under ideal conditions and odd orders decrease rapidly with the square of diffraction order values.

Transmission gratings are usually classified as rectangular, sinusoidal, triangular and other groove shapes. At normal incidence the symmetry of rectangular or lamellar gratings leads to equal energy in both plus and minus first orders, while the fraction devoted to the zero order at one wavelength can vary from near 0 to over 90%.

Sinusoidal gratings share the property of symmetry, but not quite the wide control over zero order. Cylindrical sections or parabolic grooves with several segments of different angles are called multiple order transmission gratings or fan-out gratings, and they are generally designed to split 5 to even 20 orders beams with their intensities as equal as possible.

The echelette gratings, which are low-order echelle gratings, have the well known profile for blazed gratings. The blazed angle is defined as the diffraction angle of the wavelength whose efficiency is maximal. Blazed or triangular gratings can serve as efficient and compact beam-dividers for monochromatic light, especially when the angle between the beams is to be small and well-controlled. They are also designed to deliver a particular ratio of first to zero order at a constant wavelength.

Bragg-condition gratings usually deliver exceptionally high first order efficiency in both planes of polarization, and high diffraction angles. Zero order diffraction (ZOD) gratings are used to vary intensity of zeroth order from zero to unity at a specific wavelength, and therefore enable construction of high contrast optical transmission filters such as subtractive color filters. With incident white light illuminating in subtractive color systems, cyan (minus red), magenta (minus green), and yellow (minus blue) can be obtained from the three primary colors.

In summary, symmetric transmission gratings are used as beam splitters for optical pickup heads, where the wavelength of the laser source is constant, since the efficiency of plus and minus first orders must be equal as possible.

2.4.2 Grating anomalies

An ideal grating is one of infinite size with perfectly uniform groove spacing, and uniformly illuminated with collimated light. It is designed to diffract only in the directions dictated by the grating equation. However, in practice the finite size of real gratings will generate small secondary maxima between the diffraction orders.

Therefore, the back face of a grating needs an anti-reflection coating, usually with a resin transparent at the operating wavelengths, to prevent light loss due to reflection, and to avoid multiple scattering effect inside the grating.

Grating anomalies significantly degrade the optical behavior of gratings, as is the case with surface wave and non-linear second-harmonic generation. Besides, spectral purity or the absence of stray light describes the signal to noise, and is strongly related to the uniformity of groove spacing. Moreover, the corrugation and holes in the grating surface, inherent to the fabrication error or probing the grating, should be eliminated with the CMP (Chemical Mechanical Polishing). But the CMP machines are available only to 6 inches wafers in NDL. Therefore, our microgratings necessarily have serious aberration inherent to the fabrication errors.