INTEGRIDAD DE MENBRANA EN SEMEN DESCONGELADO

8.4.1 Cerenkov scheme

We will assume a step-index profile with a peak refractive index change An^ of 0.11 (at 1.084 |im), which would occur when using a KNOg/benzoic acid melt. Table 1 lists the dependence of the Cerenkov angle a on the effective index N^, along with the required waveguide thickness h

(rijsub) (tijsub) Nf h(jim ) a (d e g ) 2.146 0.302 15.12 2.166 0.462 13.00 2.186 0.598 10.47 2.206 0.789 7.09 2.221 1.020 2.43 2.223 1.061 0

Table 8.1. Dependence of the Cerenkov angle on the effective index.

The Cerenkov angle was calculated from equation (8.2-7), and the waveguide thickness from the following equation

h = 1 tan-1^ N ? - n 2n1/2 n f - N + tan -1 f J N i - I xl/2' n^ — Nf y (8.4-1)

where ng=2.146 (at 1.084 |im)

At the upper limit of the inequality (8.2-5), (3/ k - > n 2Sub, the Cerenkov angle vanishes, and the phase velocity of the nonlinear polarisation wave is equal to that of free wave in the substrate. At the lower limit, p / k —> n^sub, the waveguide mode of the fundamental wave becomes cut off. By selecting the appropriate processing

conditions we can, by adjusting the waveguide width, fine tune the Cerenkov condition. Let us assume that for a planar guide we have an effective index (for the fundamental mode) of 2.225. By applying the effective index method of Chapter 3 we can obtain an effective index for the equivalent channel guide where

N e q = V " s + b e q ( N f - n , ^ ) (8.4-2) bgq, the normalised guide index of the equivalent guide, can be determined from available slab-guide results

We obtain values of for channel widths ranging from 1 to 7 pm, and plot the following graph of the refractive index as a function of the channel width

2.226 _{n(2)-substrate} 2.216 2.206 E e

I

W idth of channel (microns)

Figure 8.3. Plot showing the Cerenkov zone for frequency doubling in proton exchange channels.

Observe that all the guides below 6 pm in width are in the Cerenkov region. However, the naiTowest guides are closer to cut-off, and would be expected to be relatively lossy. Therefore we should aim for channel widths of between 3 and 5 pm coiTesponding to Cerenkov angles of between 3.4 ° and 1.7 ° respectively.

8.4.2 Non-critical phase-matching scheme

The experimental set-up for non-critical phase-matching is shown in figure 8.4. The collimated pump beam (at 600 or 814 nm) is passed through a X/2 plate (to select TM

radiation) and is focussed by a microscope objective onto the waveguide. Because the fundamental beam is generated within the cavity there is a wide tolerance in the spectral linewidth of the pump source, allowing the use of high power gain-guided lasers. The waveguides would be fabricated by Ti-indiffusion, in order to allow both polarisations of the light to be guided. The sample is placed inside a crystal oven, which has an operating temperature of 140-160 °C, and is accurate to ±0.1 °C.

electrode crystal oven A/2 plate 546 nm PUMP 8 mm f.l lens Nd:MgO:LiNbO 3 sample interference filter

Figure 8.4. Proposed experimental set-up for non-critical phase-matching in Nd:MgO:LlNbO 3 (top view).

The ends of the waveguides are coated with dielectric mirrors, ideally having the following characteristic: M M. Reflectatice 1093 nm 1084 nm 99% 0% 99% 0% Transmittance 546/600 nm 80% 80%

Table 8.2. Mirror characteristic for a self-frequency doubled laser.

The fundamental wave at 1093 nm is almost completely trapped by the resonator. The mirrors should be able to disciiminate between radiation at 1093 nm and at 1084 nm, to ensure that only TM polarised light (with E lc ) oscillates within the cavity. In practice such a mirror characteristic would be difficult to achieve due to the wide

region of peak reflectance in a typical dielectric mirror. Alternatively, a dichroic mirror would selectively absorb one plane of polarisation whilst transmitting the orthogonal plane through the medium. In this scheme no attempt is made to oscillate the second- harmonic, although it should be possible to increase the single-end haimonic output if one of the cavity minors is made highly reflecting at the second-hannonic wavelength. (The Nd:MgO:LiNbOg system has little absorption at the second-harmonic wavelength). The waveguide output is then collimated and passed through an interference filter, which allows only the second-harmonic at 546.5 nm through, and is analysed by the spectrometer. The purpose of the electrodes is to fine tune the optical path length, which is critical for optimum phase-matching. With the optical field polarised along the x-axis (figure 8.5) we utilise the diagonal element of the refractive index matrix, resulting in an index change given by

(8.4-3)

Figure 8.5 shows the electrode placement utilising the electric field parallel to the crystal surface

► z

Figure 8.5. Electrode placement utilising the r electro-optic coefficient.

The nfractive index change An caused by applying a voltage to the electrodes is given by [n

An(V) = - n \ V

2 G (8.4-4)

vsvher V is the applied voltage, G is the interelectrode gap, r is the electro-optic coeffcient, and F is the overlap integral

With G=5 |im, V=20 V, and 4.5x 10'^® cm/V we obtain

Anji = X 4.5 X10“'® x , = -0.14 x 10"^

2 5x10”^

This is a small index change, however it will provide some fine adjustment of the phase-matching condition.

References to Chapter 8

[1] G. I. Stegeman, C. T. Seaton," Nonlinear integrated optics," J. Appl. Phys. 58, R57-R78 (1985).

[2] D. Rugar, C. J. Lin, and R. Geiss, "Submicron domains for high density magneto-optic data storage," IEEE Trans. Magn. MAG-23 (5), 2263-2265 (1987)

[3] T. Y. Fan, A. Cordova-Plaza, M. J. F. Digonnet, R. L. Byer, and H. J. Shaw, "Nd:MgO:LiNbOg spectroscopy and laser devices," J. Opt. Soc. Am. B. 3 (1), 140-147 (1986).

[4] O. Svelto, Principles o f lasers, 3rd ed., 40-41 (Plenum, 1989). [5] J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan,

"Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 128 (1962).

[6] A. M. Prokhorov, and Yu. S. Kuz'minov, Physics and Chemistry o f Crystalline Lithium Niobate, (Adan-Hüger Series on Optics and Optoelectronics, 1990).

[7] K. Shinozaki, T. Fukunaga, K. Watanabe, and T. Kamijoh, "Self-quasi-phase- matched second-harmonic generation in the proton-exchanged LiNbOg optical waveguide with periodically domain-inverted regions," Appl. Phys. Lett. 59 (5), 510-512 (1991).

[8] P. K. Tien, R. Ulrich, and R. J. Martin, "Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide," Appl. Phys. Lett. 17, 447-450 (1970).

[9] T. Taniuchi, and K. Yamamoto, "Second harmonic generation using proton- exchanged LiNbOg waveguide," Optoelectronics-Devices and Technologies, 2 (1), 53-58 (1987).

[10] Q. He, M. P. De Micheli, D. B. Ostrowsky, E. Lallier, J. P. Pocholle, M. Papuchon, F. Armani, D. Delacourt, C. Grezes-Besset, and E. Pelletier, "Self­ frequency-doubled high An proton exchange Nd: LiNbOg waveguide laser," Optics Comm. 89, 54-58 (1992).

[11] D. B. Ostrowsky, "Parametric processes in LiNbOg," in H. P. Nolting and R. Ulrich (eds.). Integrated Optics, Proc. Eur. Conf. on Integrated Optics, 1985, (Springer, Berlin, 1985).

[12] G. Arvidsson, and F. Laurell, "Non-linear optical wavelength conversion in TiiLiNbOg waveguides," Thin Solid Films 136, 29-36 (1986).

[13] W. Koechner, Solid-State Laser Engineering, vol. 1, (Springer Series in Optical Sciences, Springer-Verlag, New York, 1976).

[14] J. E. Midwinter, "Lithium niobate: Effects of composition on the refractive indices and optical second-harmonic generation," J. Appl. Phys. 39 (7), 3033- 3038 (1968).

[15] W. Sohler, and H. Suche, "Frequency conversion in TiiLiNbOg optical waveguides," Proc. SPIE, 408, 163-171 (1983).

[16] J. T. Lin, "Non-linear crystals for tunable coherent sources," Optical and Quantum Electron. 22, S283-S313 (1990).

[17] T. Tamir (ed.), Guided-Wave Optoelectronics, (Springer Series in Electronics and Photonics 26, 1988).

CHAPTER 9

C on clu sion s