**1. Introduction**

282 Holograms – Recording Materials and Applications

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Optical circulators [Ramaswami et al., 2009; Hecht, 2005; Mynbaev & Scheiner, 2000] are important nonreciprocal devices that can direct a light from one port to another in only one direction. They are essential components in the construction of fundamental network modules, such as optical add–drop multiplexers, dispersion-compensation, optical amplifiers, and timedomain reflectometry. Different kinds of design of optical circulator have been proposed [Iwamura et al., 1979; Shirasaki et al., 1981; Yokohama et al., 1986; Koga, 1994; Wang, 1998]. According to the operation principles, optical circulators can be divided into three types, traditional, waveguide, and holographic. The traditional optical circulators mainly apply spatial walk-off polarizers (SWPs) [Nicholls, 2001], Faraday rotators (FRs), and half-wave plates (Hs) to implement its function. The waveguide optical circulators utilize a waveguide Mach–Zehnder interferometer to implement the function of SWPs. The holographic optical circulators apply holographic optical elements to replace traditional SWPs. Accordingly, the spatial walk-off polarizer is a key component in the design of optical circulator that significantly influences the performances and cost of a device.

Traditional spatial walk-off polarizers are essentially birefringent crystals that can split an optical beam into two orthogonally polarized beams. However, birefringent crystals suffer from challenges of highly optical qualities, crystal manufacturing, and hard optical fabrications. The highly optical qualities mean high transparency and optical uniformity for a wide spectrum range, high birefringence, and enough hardness. The main crystal growth thechnologies are Czochralski method and Verneuil process. The hard fabrications include xray orientation, slicing, polishing, coating, cleaning, testing, packaging, and related processes. Therefore, the cost is hard to down. In addition, limited by the finite birefringence, the beam splitting distance is small. Therefore, the device length is hard to shorted.

Compare to the crystal-type SWPs, polarization-selective substrate-mode volume holograms (PSVHs) [Huang, 1994] have a large splitting angle and several superior advantages. A PSVH are phase volume holograms stacked on a glass or plastic substrate and signals transmit in the substrate by total internal reflection. With this planar structure, PSVHs have advantages of easy fabrication, low cost, high efficiency, compactness, easy coupling, and easily to combine with other elements. Due to these merits, PSVHs had been widely applied

Polarization-Selective Substrate-Mode

successfully separated.

volume hologram.

and

material, respectively.

Volume Holograms and Its Application to Optical Circulators 285

into HPBS at a special angle. The output diffraction lights of HPBS are split into *s*- and *p*components which are perpendicular to each other. These two components are then total internal reflected (TIR) at the base of the substrate and are diffracted and coupled out normally by HOS and HOP, respectively. Therefore, the *s*- and *p*-polarized lights are

Fig. 1. Schematic representation of the conventional polarization-selective substrate-mode

diffraction efficiencies of *s*- and *p*-components can be written as

where the modulation parameters for *s*- and *p*-components,

*N*1 is the effective index modulation in which

η

υυ

thickness of the recording material, and *n*1 is the refractive index modulation.

υ

In this structure, HI, HPBS, HOS, and HOP are actually transmission-type phase volume holograms and can be designed according to the coupled-wave theory [Kogelnik, 1969]. For a transmission-type phase volume hologram, as shown in Fig. 2, the relation between the

> 2 , , sin ,

 υ

1

1 2 , (cos cos ) *<sup>s</sup> r r* π*N*

 θ

2 1 cos( ),

1 <sup>1</sup> . *n d <sup>N</sup>* λ

λ

corresponding angles of the reconstruction and the diffraction beams in the recording

 θ θ

θ

1/2

*<sup>s</sup> <sup>p</sup>* = *<sup>s</sup> <sup>p</sup>* (1)

<sup>=</sup> (2)

*ps r r* = − (3)

<sup>=</sup> (4)

is the reconstruction wavelength, *d* is the

θ*r*1 and θ*<sup>r</sup>*2 are

*<sup>p</sup>* , are given as

υ*s* and υ

in several optical systems, such as optical sensing, optical data storage, imaging system, and switching network. In 2003, the PSVHs was firstly proposed to replace crystal-type SWPs in a four-port optical ciculator [Chen et al., 2003]. In the application, these PSVHs are consequently termed as holographic spatial walk-off polarizer (HSWP). Due to the introduction of HSWPs, the fabricated four-port optical circulator has advantages of polarization-independence, compactness, high isolation, low polarization mode dispersion, low cost, and easy fabrication.

However, the feasibility of conventional PSVHs is usually limited by the finite refractive index modulation strength of a recording material. The common solution is to increase the thickness of the recording material, in order to compensate the shortage of the refractive index modulation strength in the phase modulation term. However, under the thickness condition of thick material, the distortion effect of interference fringe is worsened. An ideal holographic recording condition hinges on the thin thickness of a recording material with a high refractive index modulation strength. Actually these cannot be completed in both respects. To overcome the problems, based on the coupled-wave theory and the structure of substrate-mode hologram, a special design of PSVHs was proposed with a relatively large splitting angle near 90° [Chen et al., 2008]. With this design, a low refractive index modulation strength is required, which can be easily achieved with common recording materials. In addition, this design should bear all merits of conventional PSVHs.

As the design of optical communication systems becomes more and more complex, an optical circulator with many input and output ports has become highly desirable. However, the port numbers for presently most commercial optical circulators are limited. In 2004, based on holographic spatial- and polarization-modules (HSPMs), two kinds design of holographic-type multi-port optical circulator were also proposed [Chen et al., 2004; Chen et al., 2004]. The HSPM is consisted of two HSWPs, an half-wave plate (H), and a Faraday rotator (FR). The merits of these designs include polarization-independence, compactness, high isolation, low polarization mode dispersion, and easy fabrication. Furthermore, the number of port can be scaled up easily.

Accordingly, this chapter devotes to introduce the polarization-selective substrate-mode volume hologram in several respects and its novel applications in design of optical circulator. The second section, according to coupled-wave theory, will clearly describe the principle and characteristic of conventional PSVHs; a modified design method of PSVHs will also be described to overcome the shortage in refractive index modulation strength. The third section will introduce the applications of PSVH to optical circulators. The principle and operation characteristic of a four-port optical circulator will be introduced. The following context will introduce the principles and operation characteristic of holographic spatial- and polarization-modules (HSPMs) and their applications to multi-port optical circulators. All the design details will be described and their characteristic will be discussed. Finally, the fourth section is conclusion.
