集成光学 第八章-1

Electro-Optic Modulators

?8.1 Basic Operating Characteristics of Switches and

Modulators

?8.2 The Electro-Optic Effect

?8.3 Single-Waveguide Electro-Optic Modulators

?8.4 Dual-Channel Waveguide Electro-optic Modulators ?8.5 Mach-Zehnder Type Electro-Optic Modulators

?8.6 Electro-Optic Modulators Employing Reflection or

Diffraction

?8.7 Comparison of Waveguide Modulators to Bulk

Electro-Optic Modulators

在本章将学到

?单波导电光调制器的工作原理

?双沟道波导电光调制器的工作原理

?波导调制器比“体”调制器更为优越?如何设计波导电光调制器

重点掌握单波导电光调制器和双沟道波导电光调制器的工作原理

?modulator：调制器

?switch：开关

?modulation depth：调制深度?bandwidth：带宽

?insertion loss：插入损耗

?power consumption：功率损耗?isolation：隔离度

?Pockels effect：普克尔效应

?Kerr effect：克尔效应

?indicatrix：指标线；光率体?index ellipsoid：折射率椭球

?centrosymmetric：中心对称的

?single-waveguide electro-optic modulators：单波导电光调制器

?phase modulator：相位调制器

?polarizer：起偏器

?polarization–selective filter(usually called an analyzer)：检偏器

?intensity modulator：强度调制器

?electro-absorption modulator：电致吸收调制器

?Franz-Keldysh effect：弗兰茨－凯第希效应（当一半导体材料中存在强电场时，材料的吸收光谱向长波方向移动）

?direct bandgap material：直接带隙材料

?depletion layer：耗尽层

?Mach-Zehnder interferometer：马赫---泽德干涉仪

?Permittivity：介电常数

This chapter begins the discussion of optical-signal modulation and switching. In many cases, the same device can function as either a modulator or a switch, depending on the strength of the interaction between the optical waves and the controlling electrical signal, as well as on the arrangement of input and output ports. The device is considered to be a modulator if its primary function is to impress information on a light wave by temporarily varying one of its properties. A switch, on the other hand, changes the spatial position of the light, or else turns it off and on.

8.1 Basic Operating Characteristics

of Switches and Modulators

One important characteristic of modulators and switches is the modulation depth, or modulation index, η. In the case of an intensity modulator in which the applied electrical signal acts to decrease of the

transmitted light, ηis given by

00)(I I I -=η(8.1.1)

where I is the transmitted intensity and I 0is the value of I with no electrical signal applied.

8.1.1 Modulation Depth

m I I I )(0-=η(8.1.2)

where I m is the transmitted intensity when maximum signal is applied. The maximum modulation depth, or extinction ratio, is given by

00max )(I I I m -=ηfor

I I m ≤(8.1.3)or by m o m I I I )(max -=ηfor

0I I m ≥(8.1.4)It is also possible to define the modulation depth for phase modulators, as long as the phase change can be functionally related to an equivalent intensity change.

If the applied electrical signal acts to increase the transmitted light intensity, ηis given by

For the case of interference modulators, it can be shown that the modulation depth is given by

)2(sin 2?η?=(8.1.5)

where ??is the phase change.

Modulation depth has been defined for intensity

modulators (and indirectly for phase modulators); however, an analogous figure of merit, the maximum deviation of a frequency modulator, is given by

0max f f f D m -=(8.1.6)

where f 0is the optical carrier frequency, and f m is the shifted optical frequency when the maximum electrical signal is applied.

8.1.2 Bandwidth

Another important characteristic of modulators and switches is the bandwidth, or range of modulation frequencies over which the device can be operated. By convention, that bandwidth of a modulator is usually taken as the difference between the upper and lower frequencies at which the modulation depth falls to 50% of its maximum value. In the case of a switch, frequency response is usually given in terms of the switching speed, or switching time. The switching time T is related to the bandwidth ?f by the expression

=π2(8.1.7)

f

T?

Minimizing switching time is most important when large-scale arrays of switches are used to route optical waves over desired paths. Similarly, modulation bandwidth is a critical factor when information channels are to be multiplexed onto the same optical beam. Thus, the unusually fast switching speed and wide bandwidth of waveguide switches and modulators, which will be discussed later in this chapter, make them particularly useful in large telecommunications system.

8.1.3 Insertion Loss

Insertion loss is another important characteristic of optical switches and modulators that must be known for system design. Insertion loss is generally stated in decibels, and for the case in which the modulating signal acts to decrease in the intensity, it is given by

)log(10

0I I L t i (8.1.8)

where I t is the optical intensity that would be

transmitted by the waveguide if the modulator were absent, and I 0is the intensity transmitted with the modulator in place, but with no applied signal.

For a modulator in which the applied signal acts to increase the transmitted intensity, the insertion loss is given by

)log(10

m t i I I L (8.1.9)

where I m is the transmitted intensity when

maximum signal is applied. Insertion loss is, of course, an optical power loss. However, it ultimately increases the amount of electrical power that must be supplied to the system, since higher power optical sources must be used.

8.1.4 Power Consumption

Electrical power must also be supplied to drive the modulator or switch. In the case of modulators, the required drive power increase with modulation frequency. Hence, a useful figure of merit is the drive power per unit bandwidth, P/?f, usually expressed in milliwatts per megahertz. As is discussed in more detail in Sect.8.7, a key advantage of channel-waveguide modulators is that they have a significantly lower P/?f than that required for bulk modulators.

8.1.5 Isolation

The degree of isolation between various

inputs and outputs of a switch or modulator is a major design consideration. In a modulator, the isolation between input and output is merely the maximum modulation index, as defined previously. However, it is usually expressed in decibels when used to specify isolation. In the case of a switch, the isolation between two ports (either input or output) is given by

21[]10log()isolation dB I I =-(8.1.10)

where I1is the optical intensity in the driving port, and I2is the intensity at the driven port when the switch is in the off state with respect to port 1 and 2. Thus, a switch with a signal leakage, or crosstalk, of 1% with respect to two ports would have 20dB isolation.

8.2 The Electro-Optic Effect

The fundamental phenomenon that accounts for the operation of most electro-optic modulators and switches is the change in index of refraction produced by the application of an electric field. In the most general case, this effect is non-isotropic, and contains both linear (Pockels effect)and nonlinear (Kerr effect)components. In crystalline solids, the change in index produced by the linear electro-optic effect, can be most conveniently characterized by the change in the components of the optical indicatrix matrix.

The equation of the index ellipsoid in the presence of an electric field is

11212121116

25242232222212=??? ??+??? ??+??? ??+??? ??+??? ??+??? ??xy n xz n yz n z n y n x n (8.2.1)

If x ,y , and z are chosen to be parallel to the principal dielectric axes of the crystal, the linear change in the coefficients due to an electric field E is given by

∑==??? ???3121j j ij i E r n (8.2.2)

where i =1,2,3,4,5,6, and where j =1,2,3 are associated with x ,y ,z , respectively.

If (8.2.2) is written in matrix form, the 6x3[r ij] matrix is called the electro-optic tensor. It can be shown that the linear electro-optic effect exists only in crystals that do not possess inversion symmetry. Even in the case of these non-centrosymmetric crystals, for most symmetry classes, only a few elements of the electro-optic tensor are nonzero. Hence, in the design of an electro-optic modulator or switch, both the waveguide material and its orientation with respect to the applied electric field must be chosen carefully. Nevertheless, many materials that can be used to make low loss waveguides, such as GaAs, GaP, LiNbO3, LiTaO3and quartz, also have significantly large Pockels coefficients, for certain orientation. Thus, the linear eletro-optic effect is widely used in integrated optic applications.

The nonlinear (quadratic) Kerr electro-optic coefficient is relatively weak in commonly used waveguide materials. Also, a nonlinear dependence in electric field introduces unwanted modulation crossproducts (distortion) into the modulated signal. Consequently, it is not particularly useful in most integrated optic applications.