**9. Conclusions**

Photocurrents generated by TPA in PDs were studied. The ratios of nonlinear susceptibility tensor elements were deduced from the polarization dependence of self-TPA for Si- and GaAs-PDs. The photocurrent was isotropic for linear polarization in the Si-PD. On the other hand, TPA is anisotropic and the photocurrent depends on the linear polarization direction in GaAs-PD. The photocurrents for elliptically and circularly polarized light can also be ana‐ lyzed by the imaginary parts of the nonlinear susceptibility.

The polarization dependence of cross-TPA was measured for a Si-APD. Three types of cross-TPA that are linear-linear, linear-elliptic, and circular-elliptic polarizations were studied. The measured results agree with theoretical values calculated by using parameters obtained from the polarization dependence of self-TPA. These results demonstrate that both self- and cross-TPA can be well described by analysis based on the nonlinear susceptibility tensor.

Cross-TPA was applied to polarization measurements. The Jones vector elements of anarbi‐ trarily polarized signal light can be determined from the four photocurrents generated by cross-TPA between the signal light and the linearly polarized reference light. The time reso‐ lution is limited only by the pulse width of the reference light pulse. This measurement method can thus be used to detect rapid polarization variation. It was demonstrated that the polarization of a light pulse from a polarization-maintaining optical fiber and a SOA can be measured by this method.

## **Author details**

Toshiaki Kagawa\*

Address all correspondence to: kagawa@elec.shonan-it.ac.jp

Shonan Institute of Technology, Japan

#### **References**

in Fig. 12(a) show the measured amplitudes *a <sup>e</sup> <sup>2</sup>*

24 Photodiodes - From Fundamentals to Applications

**9. Conclusions**

measured by this method.

**Author details**

Toshiaki Kagawa\*

and *a <sup>m</sup> <sup>2</sup>*

amplitudes of the Jones vectors for TE and TM polarization. The open circles and dashed line show the measured output pulse shape. The polarization at the head of the pulse is al‐ most the same as that of the injected light pulse. However, the carrier density modulation in the SOA rotates the polarization because the gains for the polarizations of the TE and TM modes have different carrier density dependences. Figure 12(b) shows the measured phase difference *α*. The phase difference varies dynamically due to self-phase modulation in the

Photocurrents generated by TPA in PDs were studied. The ratios of nonlinear susceptibility tensor elements were deduced from the polarization dependence of self-TPA for Si- and GaAs-PDs. The photocurrent was isotropic for linear polarization in the Si-PD. On the other hand, TPA is anisotropic and the photocurrent depends on the linear polarization direction in GaAs-PD. The photocurrents for elliptically and circularly polarized light can also be ana‐

The polarization dependence of cross-TPA was measured for a Si-APD. Three types of cross-TPA that are linear-linear, linear-elliptic, and circular-elliptic polarizations were studied. The measured results agree with theoretical values calculated by using parameters obtained from the polarization dependence of self-TPA. These results demonstrate that both self- and cross-TPA can be well described by analysis based on the nonlinear susceptibility tensor.

Cross-TPA was applied to polarization measurements. The Jones vector elements of anarbi‐ trarily polarized signal light can be determined from the four photocurrents generated by cross-TPA between the signal light and the linearly polarized reference light. The time reso‐ lution is limited only by the pulse width of the reference light pulse. This measurement method can thus be used to detect rapid polarization variation. It was demonstrated that the polarization of a light pulse from a polarization-maintaining optical fiber and a SOA can be

SOA as a result of the carrier density modulation and spectrum hole burning.

lyzed by the imaginary parts of the nonlinear susceptibility.

Address all correspondence to: kagawa@elec.shonan-it.ac.jp

Shonan Institute of Technology, Japan

, respectively. *a <sup>e</sup>* and *a <sup>m</sup>*are the


[16] Takahashi, Y., Neogi, A., & Kawaguchi, H. (1998). Polarization-Dependent Nonlinear Gain in Semiconductor Lasers. *IEEE J. Quantum Electron.*, 34(9), 1660-1672.

**Chapter 2**

**Physical Design Fundamentals of High-Performance**

Minimal value of dark current in reverse biased *p* −*n* junctions at avalanche breakdown is determined by interband tunneling. For example, tunnel component of dark current be‐ comes dominant in reverse biased *p* −*n* junctions formed in a number semiconductor ma‐ terials with relatively wide gap *Eg* already at room temperature when bias *Vb* is close to avalanche breakdown voltage *VBD* (Sze, 1981), (Tsang, 1981). The above statement is ap‐ plicable, for example, to *p* −*n* junctions formed in semiconductor structures based on ter‐ nary alloy *I n*0.53*Ga*0.47*As* which is one of the most important material for optical communication technology in wavelength range *λ* up to 1.7 μm (Tsang, 1981), (Stillman, 1981), (Filachev et al, 2010), (Kim et al, 1981), (Forrest et al, 1983), (Tarof et al, 1990), (Ito et al, 1981). Significant decreasing of tunnel current can be achieved in avalanche photo‐ diode (APD) formed on multilayer heterostructure (Fig. 1) with built-in *p* −*n* junction when metallurgical boundary of *p* −*n* junction (*x* =0) lies in wide-gap layer of heterostruc‐ ture (Tsang, 1981), (Stillman, 1981), (Filachev et al, 2010), (Kim et al, 1981), (Forrest et al, 1983), (Tarof et al, 1990), (Clark et al, 2007), (Hayat & Ramirez, 2012), (Filachev et al, 2011). Design and specification of heterostructure for creation high performance APD must be such that in operation mode the following two conditions are satisfied. First, space charge region (SCR) penetrates into narrow-gap light absorbing layer (absorber) and second, due to decrease of electric field *E*(*x*) into depth from *x* =0 (Fig. 1), process of avalanche multiplication of charge carriers could only develop in wide-gap layer. This concept is known as APD with separate absorption and multiplication regions (SAM-

> © 2012 Kholodnov and Nikitin; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Kholodnov and Nikitin; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

**Avalanche Heterophotodiodes with Separate**

**Absorption and Multiplication Regions**

Viacheslav Kholodnov and Mikhail Nikitin

http://dx.doi.org/10.5772/50778

**1. Introduction**

Additional information is available at the end of the chapter
