Organization of this thesis - 埋入菱形溝槽內之光纖透鏡模組與直立式相位型微光柵

Chapter 1 Introduction

1.4 Organization of this thesis

This thesis includes the following chapters. Chapter 1 introduces the current development of optical micro-pickup-heads and the objectives of this thesis. The fundamental optics of the design principles of this module will be described in Chapter 2. The simulation of microgratings will be presented in Chapter 3. The fabrication of the rhombus-shaped channel and free-space microgratings will be shown in Chapter 4. The measurement of the fiberlens and microgratings will be described in Chapter 5. Finally, a conclusion is presented in Chapter 6.

Chapter 2 Principle

2.1 Introduction

Some components of our proposed micro-pickup-head are presented in this thesis, including an edge-emitting laser source, a fiber-alignment structure, a fiberlens, and a free-space micrograting. We will explain the design principles of these components in this chapter. First, the origin and principles of collimation are presented for estimating the beam-shaping of the fiberlens. Then, gratings suitable for the optical pickup-head are discussed. Finally, it is the conclusion.

2.2 Lateral laser beam-shaping

2.2.1 Collimation of astigmatic beams

The task of the beam-shaping components is to transform a non-symmetrical astigmatic laser beam into a uniform Gaussian beam. This is typically necessary for the collimation of edge-emitting laser diodes. Due to their compact and cheap manufacturability, edge-emitting laser diodes are important optical sources for a large variety of applications. However, the astigmatic characteristics of the emitted radiation will require additional optics for specific applications. Therefore, significant effort is devoted to the transformation of astigmatic and asymmetrical beam into a symmetrical and collimated beam.

The origin of the beam characteristics can be detected in the structure of the

edge-emitting laser diodes. An edge-emitting laser diode consists of a layered stack of semiconductor materials with different doping (p-n junctions). The resonator structure is oriented parallel to the layers and generally has a highly asymmetrical shape. The layer thickness representing the height of the resonator is fractions of one micron, while its width is several microns. This asymmetry of the laser resonator is the reason for an asymmetrical beam shape which upon propagation generates astigmatism due to different divergence angles caused by diffraction.

In the most general case, the shaping of such a beam into asymmetrical and collimated beam requires both amplitude and phase shaping. In order to generate the symmetrical amplitude distribution, anamorphic imaging systems are used to perform the necessary geometrical transformation. Additional microlenses are necessary to compensate for the different divergence angles in x and y [1].

Large angles of diffraction occur in the direction of the small output window (typical values are 30∘<α^⊥< 60∘). The divergence in the perpendicular direction is much smaller due to the larger output window (typicallyα^∥=10∘). Consequently, at a specific distance z0, the beam has a symmetrical intensity distribution. Efficient shaping of the laser beam is possible with a single micro-optical element aligned at z0

to compensate for the different phase distributions [2].

2.2.2 Design principles of the beam-shaping and collimation

In the following, we briefly outline the design process for the beam-shaping and collimated components. For the design, it is sufficient to assume a constant phase distribution at the output window of the diode. The beam profile in each dimension

can be approximated by a Gaussian function with widths σ^x,0 and σ^y,0, respectively.

Since we assume constant phase over the output window of the laser diode, σ^x,0 and σ^y,0 are real quantities:

Eq. 2-1 The propagation of the beam (wavelength λ) along the z-axis can be calculated by a Fresnel transform. However, since the phase distribution is no longer constant over the beam diameter the Gaussian widths are now complex quantities. For the real part of the beam width σ^x (z) and σ^y at a distance z from the diode, they are:

Eq. 2-2 The plane z0 where we wish to position the micro-optical elements is chosen in such a way that the real parts of the Gaussian widths are σ^x (z0) =σ^y (z0). We obtain for z0 :

Eq. 2-3

The phase profile of the beam is represented by the imaginary part of the Gaussian widths resulted from the Fresnel transform:

Eq. 2-4

Φbeam (y, z) is found analogously. The beam-shaping component at z0 is designed to compensate for the phase profile of the beam at this location (Φbeam (x, z0)).

Collimation of the astigmatic beam is possible with an astigmatic microlens. Such a lens is described by two different focal lengths fx, fy in the two axial directions. The phase terms introduced by the lens are written as:

Eq. 2-5

The two tasks of the astigmatic microlens are to compensate for the difference in the beam divergence, and to collimate the beam. It can be easily verified that a constant phase results for an astigmatic lens with the focal lengths:

Eq. 2-6

The microlens described by Eq. 2-6 generates a flat phase profile over the beam diameter in the plane z0. The phase distribution over the beam diameter is rather not important in the optical pickup heads. Therefore, single optical element performing geometrical transformations are sufficient to perform the beam-shaping. From the point of view of design flexibilities, the fiberlens is the most desirable.

2.3 Beam-shaping components of Fiberlenses

Optical fibers have the advantages of low weight and high flexibility while used as light-guiding media, and they are inexpensive. Fibers can overcome the tight tolerance found in high numerical aperture (NA) optical path. Thus, fiber systems are good candidates for high access rate, and to be applied in the next-generation of free-space pickup-head systems.

Microlenses formed on the end of single-mode fibers (SMFs) are widely used as optoelectronic passive elements to facilitate laser-to-fiber coupling in optical communication systems. The objective of the coupling scheme is to (1) maximize the coupling efficiency, and (2) to minimize the optical feedback due to Fresnel reflection from fiber to laser. Several authors have proposed several techniques [3-8] for

producing such end-of-fiber lenses as laser-to-fiber coupling elements shown in Fig. 2-1. These techniques include photolithography [5], chemical etching [6], mechanical polishing [7], and thermal melting [8]. The radius of curvature of these lenses is only a few micrometers. These microlenses are not adequate for use in optical pickup-head systems, because they require relatively complex fabrication processes to ensure small microlens radius of curvature.

(a) tapered core

(b) tapered cladding

microlens

Fig. 2-1 Various conventional small-radius-curvature microlenses on the end of SMF.

(a) tapered core, (b) tapered cladding, and (c) small-radius-curvature microlens

A novel design and fabrication of a microlens on the front end of a single-mode fiber (SMF) was described [9]. Its beam quality and spot size are analyzed in this section.

In our pickup-head system, a SMF with a fiber-front-end microlens is used to guide laser beams from an outside laser diode into the pickup-head, and circularizing the shape of incident beams. The objective of our scheme is to achieve the smallest spot on the three-beamed micro-grating at a reasonable working distance. The distance between the front-end of fiberlens and micro-grating is adjusted until the beam waist of focused spot is just located on the three-beamed micro-grating, because

the beam has a perfect plane wavefront at its beam waist position, while the wavefront of laser beams quickly becomes curved on both sides of the waist.

The distance between the SMF and the microlens is filled with the pure silica rod of the same diameter and same refractive index as the core of the SMF to avoid reflection, as shown in Fig. 2-2. The radius W0 ofmode field is computed by Eq. 2-7 [10]

Where a=4um is the core radius of the step-index fiber, and V is the normalized frequency 2 a n₁² n²₂

V −

= π (n1 and n2 are the refractive indices of the core and

cladding respectively). The mode field diameter 2W0 at wavelength λ = 0.4 µm is about 3.6 µm.

Fig. 2-2 Illustrated schematics of the microlens on the end face of the SMF (refractive index of the silica rod n = 1.47, cladding diameter 2a = 125 µm, mode field diameter 2W0 = 3.6 µm at λ = 0.4 µm) [9].

W1 and r1, beam waist and radius at output plane RPOUT (Plane 1), can be

Where W0 is the mode field radius of an SMF, g is the propagation distance from RPIN

(Plane 0) to RPOUT(Plane 1), and ZR is the Rayleigh range, where the beam diameter has the value √2W0.

After passing through the end face of the silica rod, the radius of the beam size W2

and the curvature r2 at Plane 2 becomes

Where f is the focal length under paraxial approximation given by

( 0,f 0) n

f 1 < >

= −R R

Eq. 2-13

Where R is the radius of the plano convex lens on the fiber front end. Thus, the focused beam waist W and working distance Z can be written as

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).

(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.

2.5 Summary

As discussed above, the design principles of beam-shaping components of fiberlenses are mentioned. The recognition related to gratings is necessary for designing and fabricating gratings suitable for the pickup-head. We adopted symmetric transmission microgratings as the beam-splitter in our proposed optical pickup-head.

The grating designed in this thesis is according to Rigorous Coupled Wave Analysis (RCWA), which is a more accurate solution of Maxwell’s equations [11] [12].

Since the package software, GAOLVER, based on RCWA is already available to the analyses of diffraction, there is no further introduction about RCWA in this thesis. We used the software, GAOLVER, to perform the simulation which will be discussed in detail in chapter 3.

Chapter 3 Simulated Results

3.1 Introduction

In the pickup-head system, the gratings have been widely used as beam-splitters to divide into three beams for tracking error detection. We will discuss the design of microgratings in this chapter. First, the simulation tool, GSOLVER software, will be briefly introduced. Then, we use GSOLVER to calculate the optical performance of our micrograting. The parameters considered in our design, includes the material, period, thickness, and filling factor of the micrograting. Finally, a brief summary about the micrograting will be given.

3.2 Simulation Tool

GSOLVER software is an analytic tool available to diffraction simulation of gratings. It calculates diffracted fields, phases, and diffraction efficiency of plane wave illuminated to arbitrarily complex grating structures, while the illumination may be at any incidence (conical mounts) and any polarization (TE, TM, circular, or elliptical). The grating structure is defined by a piecewise constant approximation, so that it permits the analyses of simple classical grating profiles (blaze, sinusoid, holographic, binary, 3-point plotline, etc), and complicated structures (multi-layers, coatings, interweaving of material, shadows, etc).

GSOLVER employs full 3D rigorous coupled wave algorithm (RCWA), which can be applied to explaining the diffraction phenomenon of gratings. We will not discuss further theory of RCWA here, since the derivations of these equations are too complicated to be introduced here. The references of RCWA theory will be listed in the Appendix 2. Thus, for the pickup head, by calculating the energy distribution of all retained diffraction orders beams, the features of microgratings will be optimized in the following sections.

3.3 Material and dimension of microgratings

To achieve simultaneously high light-efficiency, expected energy distribution and realization of fabrication, the structure of microgratings, including their period, filling factor, and thickness, must be optimized. Thus, these parameters and material of microgratings will be determined in the following sections.

3.3.1 Material of microgratings

While most transmission gratings are used in the visible light spectrum, it is possible to extend their performance into the near UV (250nm) and near IR (2.5um), with choices of appropriate materials. Generally, maximum value of diffraction efficiency depends somewhat on the refractive index of the grating, in that lower index leads to greater efficiency, due to reduced backward diffraction that results from lowered reflectivity. But decreasing the index also calls for increased grating depth, while thick layers tend to have rough surface and even cracks or corrugation.

In the surface-micromachining processes, generally, SiO layers are applied to

the sacrificial layers, and Si3N4 layers are used as the structures or electric insulation.

Contrast to the poly-silicon, Si3N4 has higher transmission efficiency in the blue-laser spectrum. Compared with the photoresist, the thickness of Si3N4 layers can be controlled more accurately by LPCVD than the photoresist by the spinner, since the

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