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Enjoy this joke

Boring lectures


One of my favorite teachers at Southeast Missouri State University in Cape Girardeau is known for his droll sense of humor. Explaining his ground rules to one freshman class, he said, "Now I know my lectures can often be dry and boring, so I don't mind if you look at your watches during class. I do, however, object to your pounding them on the desk to make sure they're running!"

Warmly Welcome,

welcome to our class!

review : Chapter 9 Electrooptic modulation of laser beams


1. Please read the following Keywords loudly, and then translate into Chinese.

  • Electrooptic Modulation

  • 电光调制

  • electrooptic coefficient

  • 电光系数

  • electrooptic constant

  • 电光常数

  • electrooptic tensor

  • 电光张量

  • electrooptical birefringence

  • 电光双折射

  • electrooptical anisotropy

  • 电学、光学各向异性现象

  • electrooptic effect

  • 电光效应

  • electrooptic retardation

  • 电光延迟

2.Using table 9-1, determine the lectrooptic tensor of KDP crystal

To be specific we choose the direction of the applied field parallel to the Z axis,

so the index ellipsoid for KDP


Find a new coordinate system:






ellipse formed by the intersection of the plane z=0 and the ellipsoid.

The equation of

this ellipse




The difference of at the output plane z=L between two components is called the retardation .

At point a, the retardation is 0 and the field is linearly polarized along x.

At point e, , the electric field vector is circularly polarized.



.At point I, , and the radiation is again linearly polarized, but this time along the y axis---that is, at 900 to its input direction of polarization.


9.3 electrooptic amplitude modulation



An examination of figure 9-3 reveals that the electrically induced birefringence causes a wave launched at z=0 with its polarization along x to acquire a y polarization, which grows with distance at the expense of the x component until at point i, at which , the polarization becomes parallel to y, if point i corresponds to the output plane of the crystal and if one inserts at this point a polarizer at right angles to the input polarization---that is, one that allows only to pass---then with the field on, the optical beam passes through unattenuated (无衰减的), whereas with the field off ( ), the output beam is blocked off completely by the crossed output polarizer. This control of the optical energy flow serves as the basis of the electrooptic amplitude modulation of light.

Figure 9.4 A typical arrangement of an electrooptic amplitude modulation

It consists of an electrooptic crystal placed between two crossed polarizers.

To be specific,we show how this arrangement is achieved using a KDP crystal. Also included in the optical path is a naturally birefringent crystal that introduces a fixed retardation, so the total retardation is the sum of the retardation due to this crystal and the electrically induced one. The incident field is parallel to x at the input face of the crystal, thus having equal-in-phase components along x′ and y′ that we take as:

Three missions

Upon emerging from the output face z=l , the x′ and y′ components have acquired a relative phase shift (retardation) of radians (弧度)

Using the complex amplitude notation(符号):

The incident intensity is thus becomes









Mission one completed



Which corresponds to an output intensity:



The ratio of the output intensity to the input is thus:



1. Without “quarter wave plate” inserted

Sinusoidal modulation voltage



Linear modulation?

Frequenceis identical?


2. “quarter wave plate” inserted


  • For

The intersity modulation is a linear replica of the modulating voltage

analog modulation

Figure 9.5 Transmission factor of a cross-polarized electrooptic modulator as a funtion of an applied voltage.

The modulator is biased to the point . A small applied sinusoidal voltage modulates the transmitted intensity about the bias point.

digital modulation

digital modulation


留声机, 电唱机

Figure 9.6 An optical communication link using an electrooptic modulator

Exercise one: Page:367 problem 9.3

  • Use the Bessel-function expansion of sin (asin(x)) to express (9.3-7) in terms of the harmonics of the modulation frequency .Plot the ratio of the third harmonic ( ) of the output intensity to the fundamental as a function of . What is the maximum allowed if this ratio is not to exceed 10-2


When , the third harmonic is neglectable

  • If , then J1 (1)=0.44, J3(1)=0.02,

  • So

Linear modulation condition:

Challenge your imagination!

Can it be removed?

Any other alternative?


Exercise two: Consider such an applied alternating current

Please derive the expression for transmission factor.













9.4 phase modulation of light

The incident beam is polarized parallel to one of them, x′ ray. In this case the application of the electric field does not change the state of polarization, but merely changes the output phase by




If the bias field is sinusoidal and is taken as :


then an incident optical field, which at the input (z=0) face of the crystal is given by


will emerge as :


where l is the length of the crystal. Dropping the constant phase factor, which is of no consequence here, we rewrite the last equation as :



is referred to as the phase modulation index. The optical field is thus phase-modulated with a modulation index . If we use the Bessel function identity (贝塞尔函数恒等式)

which form gives the distribution of energy in the sidebands as a function of the modulation index . We note that, for , and .




图6.5 电光相位调制器的基本原理框图

  • 6.3.2 M-Z型调制器

  • M-Z型调制器是由一个Y型分路器、 两个相位调制器和Y型合路器组成的, 其结构如图6.6所示。 相位调制器就是上述的电折射调制器。 输入光信号被Y型分路器分成完全相同的两部分, 两个部分之一受到相位调制, 然后两部分再由Y型合路器耦合起来。 按照信号之间的相位差, 两路信号在Y型合路器的输出产生相消和相长干涉, 就得到了“通”和“断”的信号。

图6.6 M-Z型调制器

9.5 transverse electrooptic modulation

In the example of electrooptic retardation discussed in the two preceding sections, the electric field was applied along the direction of light propagation. This is the so-called longitudinal mode of modulation. A more desirable mode of operation is the transverse one, in which the field is applied normal to the direction of propagation. The reason is that in this case the field electrodes do not interfere with the optical beam, and the retardation, being proportional to the product of the field times the crystal length, can be increased by the use of longer crystals.

where d is the crystal dimension along the direction of the applied field. We note that contains a term that does not depend on the applied voltage.

The figure shows the transverse retardation can be obtained using a KDP crystal with the actual arrangement .The light propagation along y′ and its polarization is in the x′-z plane at 450 from the z axis. The retardation, with a field applied along z:


9.6 high-frequency modulation considerations

In the examples considered in the three preceding sections, we derived expressions for the retardation caused by electric field of low frequencies. In many practical situations the modulation signal is often at very high frequencies and, in order to utilize the wide frequency spectrum available with lasers, may occupy a large band-width. In this section we consider some of the typical experimental situations.

The electrooptic crystal is placed between two electrodes with a modulation field containing frequencies near applied to it. Rs is the internal resistance (内阻) of the modulation source and C represents the parallel-plate capacitance due to the electrooptic crystal.

Figure 9-9 Equivalent circuit of an electrooptic modulation crystal in a parallel-plate configuration

  • If , most of the modulation voltage drop is across and is thus wasted, since it does not contribute to the retardation. This can be remedied by resonating (共振) the crystal capacitance with an inductance L, where

  • A shunting resistance is used so that at the impedance of the parallel RLC circuit is , which is chosen to be larger than so most of the modulation voltage appears across the crystal. The resonant circuit has a finite band-width ---that is, its impedance is high only over a frequency interval

  • (centered on ).

  • 3. The maximum modulation bandwidth must be less then



  • study the contents of transit-time limitations to High-Frequency Eletrooptic Modulation.

  • Show that ,if a phase-modulated optical wave is incident on a square-law detector, the output contains no alternating currents


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