Green laser pointers, popular in 2016, have the structure shown in Fig. 10.13. A battery-driven infrared diode laser puts out 808-nm light that pumps aNd:YVO₄ laser crystal (neodymium-doped yttrium vanadate; a relative of Nd: YAG). The 1,064-nm light beam from this Nd:YVO₄ laser is frequency doubled by a KTP crystal, resulting in 532-nm green light. An infrared filter removes all the 880-nm and 1,064-nm light from the output, leaving only the green.

(a) To make the frequency doubling as efficient as possible, the light is focused to as small a beam radius ω̅_o as diffraction allows as it travels through the KTP crystal. Assuming that the crystal length is L ≈ 3 mm, show that

12 μm (about 12 times larger than the 1,064-nm wavelength).

(b) The 1,064-nm beam has an input power W_1o ≈ 100mW as it enters the KTP crystal. Show that its energy flux and its electric field strength are F ≈ 230MW m⁻² and A⁽¹⁾ ≈ 400 kV m⁻¹.

(c) Assuming that phase matching has been carried out successfully (i.e., photon energy and momentum conservation have been enforced), explain why it is reasonable to expect the quantity βd_ijk f⁽¹⁾f_j⁽¹⁾f_k⁽³⁾ k in the coupling constant κ to be roughly 4 pm/V . Then show that the green output beam at the end of the KTP crystal has

corresponding to an output power W₃ ∼ 1.5× 10⁻⁴ W_1o ≈ 0.015 mW. This is far below the output power, 5 mW, of typical green laser pointers. How do you think the output power is boosted by a factor ∼5/0.015 ≈ 300?

(d) The answer is 

(i) To put reflective coatings on the two ends of the KTP crystal so it becomes a Fabry-Perot resonator for the 1.064 μm input field; and also 

(ii) Make the input face (but not the output face) reflective for the 0.532 μm green light. Show that, if the 1.064 μm resonator has a finesse F ≈ 30, then the green-light output power will be increased to ≈5 mW.

(e) Explain why this strategy makes the output power sensitive to the temperature of the KTP crystal. To minimize this sensitivity, the crystal is oriented so that its input and output faces are orthogonal to its (approximate) symmetry axis—the z-axis—for which the thermal expansion coefficient is very small (0.6 × 10⁻⁶/C, by contrast with ≈ 10 × 10⁻⁶/C along other axes. Show that, in this case, a temperature increase or reduction of 6 C from the pointer’s optimal 22 C (room temperature) will reduce the output power from 5mW to much less than 1mW. Astronomers complain that green laser pointers stop working outdoors on coolevenings.

Figure 10.13

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