Abstract:
A high-efficiency multiple-pass nonlinear wavelength converter and amplitude modulator employs a variable dispersion element between adjacent passes of a nonlinear wavelength conversion process in a single nonlinear optical material substrate. When controlled by a voltage via the electro-optic effect, the variable dispersion element dynamically alters the phase matching condition of the multiple-pass nonlinear wavelength conversion process and thus modulates the laser output amplitude. When the phase mismatch between passes is completely compensated by the variable dispersion element, the multiple-pass nonlinear wavelength converter achieves its maximum efficiency.

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention is related to an optical-wave processor for simultaneously performing high-efficiency multiple-pass wavelength conversion and effective amplitude modulation of optical waves in a nonlinear optical material. An electro-optic phase tuner monolithically integrated with a nonlinear crystal section is used for correcting phase mismatch in nonlinear wavelength conversion between successive passes and for modulating the output amplitudes of the mixing waves. BACKGROUND OF THE INVENTION  
         [0002]     Nonlinear wavelength conversion, producing tunable laser wavelengths, is very useful in a wide range of applications. It is always desirable to have high efficiency for nonlinear wavelength conversion. The power conversion efficiency of the nonlinear optical process strongly depends on the length of the crystal, the pump power, and the nonlinear coupling coefficient. To maximize the effective nonlinear coefficient in a nonlinear wavelength conversion process, L. E. Myers et al. has disclosed a kind of quasi-phase-matched nonlinear crystal, called periodically poled lithium niobate, in  Quasi-phase-matched  1.064-μm Pumped Optical Parametric Oscillator in Bulk Periodically Poled LiNbO 3  in Opt. Lett. Vol. 20 pp. 52-54 (1995). When the pump power is low and the nonlinear coefficient is fixed, the length of a nonlinear optical crystal often limits power efficiency in nonlinear wavelength conversion. In the low-efficiency regime, power efficiency in a nonlinear optical waveguide is proportional to the square of the crystal length, whereas that in a bulk nonlinear optical crystal is linearly proportional to the crystal length due to diffraction. In the high-efficiency regime, power gain for parametric amplification can grow exponentially along the crystal length. Most nonlinear optical crystals are expensive and not easy to grow, and therefore typical nonlinear crystals have a size varying from a few millimeters to a few centimeters. Although it is possible to access a longer effective gain length by traversing optical waves several times in a nonlinear optical material via internal or external reflections, the phase matching condition for nonlinear wavelength conversion is often destroyed upon reflection. To increase the gain length in a nonlinear crystal of a finite size, T. H. Jeys disclosed a multiple-pass optical parametric amplifier in Opt. Lett. Vol. 21, pp. 1229-1231 (1996). However, Jeys&#39;s device has no phase correction between passes and is only applicable to broadband optical parametrical generation from vacuum noises. A double-pass second-harmonic generation with mechanical phase correction was disclosed by G. Imeshev et al. in  Phase Correction in Double-pass Quasi-phase-matched Second-harmonic Generation with a Wedged Crystal , Opt. Lett. Vol. 23, pp. 165-167 (1998). However, such a mechanical phase correction is unstable and slow.  
         [0003]     It is therefore attempted by the applicants to deal with the above difficulties encountered in a multiple-pass nonlinear wavelength conversion process. It is known in the field that the much faster and more stable electro-optic effect can alter the refractive index of and the phase of an optical wave in a second-order nonlinear optical material. The present invention employs an electro-optic phase compensator properly integrated to a multiple-pass nonlinear wavelength converter to achieve high-efficiency nonlinear wavelength conversion. On the other hand, signal modulation is often necessary for sensitive detection and information transmission in various laser applications. It is desirable to have a high-efficiency nonlinear frequency converter with a built-in convenient modulator. The present invention has the additional advantage of using the high-speed electro-optic phase compensator to function as a high-speed amplitude modulator to the nonlinear mixing waves.  
       SUMMARY OF THE INVENTION  
       [0004]     It is therefore an object of the present invention to propose an optical processor for simultaneously performing multiple-pass wavelength conversion and amplitude modulation of optical waves by using an electro-optic (EO) method to compensate and control the phase mismatch upon wave reflection in a nonlinear optical material.  
         [0005]     It is an aspect of the present invention to propose an optical processor for simultaneously performing multiple-pass wavelength conversion and amplitude modulation of optical waves in a crystal substrate comprising a phase-matched nonlinear element section and a variable dispersion section.  
         [0006]     Preferably, the crystal substrate, the variable dispersion section, and the phase-matched element section are integrated monolithically in a nonlinear optical material.  
         [0007]     Preferably, the phase-matched nonlinear element section is a quasi-phase-matched (QPM) crystal section.  
         [0008]     Preferably, the QPM crystal section is applicable for second-order nonlinear wavelength-conversion processes of second harmonic generation (SHG), sum frequency generation (SFG), difference frequency generation (DFG), and optical parametric generation (OPG).  
         [0009]     Preferably, the optical path of the variable dispersion section varies in the direction perpendicular to the propagation direction of the mixing waves in order to spatially modulate the phase matching condition of the mixing waves.  
         [0010]     Preferably, the said crystal substrate has a plurality of adequate reflection edges in order to reflect the nonlinear interacting waves along an optical path in the nonlinear crystal at least two times longer than otherwise a single-pass path without the adequate reflecting edges.  
         [0011]     Preferably, the variable dispersion section has a plurality of conducting electrodes.  
         [0012]     Preferably, the conducting electrodes are applied with a suitable DC voltage, and the variable dispersion section functions as an EO phase compensator for the reflected nonlinear mixing waves.  
         [0013]     Preferably, the conducting electrodes are applied with an AC voltage, and the variable dispersion section dynamically alters the nonlinear phase matching condition and functions as an amplitude modulator to the mixing waves via the EO effect.  
         [0014]     It is another aspect of the present invention to propose an optical-wave processor, created to simultaneously perform double-pass wavelength conversion and amplitude modulation of optical waves in a crystal substrate comprising a phase-matched nonlinear element section, a variable dispersion section, and a high reflector.  
         [0015]     Preferably, the phase-matched nonlinear element section is applicable for second-order frequency conversion processes of SHG, SFG, DFG, and OPG.  
         [0016]     Preferably, the phase-matched nonlinear element section is a QPM crystal.  
         [0017]     Preferably, the phase-matched nonlinear element section is a nonlinear optical bulk crystal.  
         [0018]     Preferably, the phase-matched nonlinear element section is a nonlinear optical waveguide.  
         [0019]     Preferably, the high reflector is a high-reflection optical dielectric film coated at the single-pass downstream end of the phase-matched nonlinear element section for reflecting the forward mixing waves back into the phase-matched nonlinear element section to execute a double-pass nonlinear optical process.  
         [0020]     Preferably, the high reflector is a high-reflection optical metal film coated at the single-pass downstream end of the phase-matched nonlinear element section for reflecting the forward mixing waves back into the phase-matched nonlinear element section to execute a double-pass nonlinear optical process.  
         [0021]     Preferably, the variable dispersion section has a plurality of conducting electrodes.  
         [0022]     Preferably, the conducting electrodes are applied with a suitable DC voltage, and the variable dispersion section functions as an EO phase compensator for the reflected nonlinear mixing waves.  
         [0023]     Preferably, the conducting electrodes are applied with an AC voltage, and the variable dispersion section dynamically alters the nonlinear phase matching condition and functions as an amplitude modulator to the mixing waves via the EO effect.  
         [0024]     Preferably, a dichroic beam splitter is set at the output of the phase-matched nonlinear element section for transmitting the pump wave while separating the double-pass output waves from the backward pump wave; for the waveguide configuration, it is also possible to replace the dichroic beam splitter with a directional coupler, which is built in parallel to the phase-matched nonlinear waveguide near the output end of the double-pass process for extracting the energy of the wavelength converted signals in the backward direction.  
         [0025]     Preferably, the directional coupler used in the waveguide configuration has a pair of conducting electrodes functioning as a coupler modulation element for optimizing the coupling efficiency of the directional coupler via the EO effect.  
         [0026]     For a design requiring an electrode directly above an optical waveguide, a low-loss dielectric film with an adequate thickness is fabricated between the optical waveguide and the electrode to avoid optical loss in the electrode.  
         [0027]     It is another aspect of the present invention to propose an optical-wave processor, created to simultaneously perform double-pass wavelength conversion and amplitude modulation of optical waves in a crystal substrate, comprising a U-shaped nonlinear optical waveguide and an electrode-coated variable dispersion section.  
         [0028]     Preferably, the U-shaped nonlinear optical waveguide, consisting of two parallel phase-matched nonlinear waveguides and a curved optical waveguide, is built for guiding mixing waves and performing double-pass nonlinear wavelength conversion.  
         [0029]     Preferably, the phase-matched nonlinear waveguides are applicable for second-order nonlinear wavelength-conversion processes of SHG, SFG, DFG, and OPG.  
         [0030]     Preferably, the phase-matched nonlinear waveguides are QPM waveguides.  
         [0031]     Preferably, the curved optical waveguide is fabricated on the variable dispersion section.  
         [0032]     Preferably, the variable dispersion section has a plurality of conducting electrodes.  
         [0033]     Preferably, the conducting electrodes are applied with a suitable DC voltage, and the variable dispersion section functions as an EO phase compensator for the reflected nonlinear mixing waves.  
         [0034]     Preferably, the conducting electrodes are applied with an AC voltage, and the variable dispersion section dynamically alters the nonlinear phase matching condition and functions as an amplitude modulator to the mixing waves via the EO effect.  
         [0035]     Preferably, a dichroic beam splitter is set at the output end of the U-shaped nonlinear optical waveguide for separating the double-pass output waves from the backward pump wave.  
         [0036]     Preferably, a directional coupler is built near the output end of the U-shaped nonlinear optical waveguide for extracting the energy of the wavelength converted signals in the backward direction.  
         [0037]     Preferably, the directional coupler has a pair of conducting electrodes functioning as a coupler modulation element for optimizing the coupling efficiency of said directional coupler via the EO effect.  
         [0038]     For a design requiring an electrode directly above an optical waveguide, a low-loss dielectric film with an adequate thickness is fabricated between the optical waveguide and the electrode to avoid optical loss in the electrode. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0039]     The Cartesian coordinate system defined in each figure is only for the convenience of description and does not necessarily coincide with the crystallographic principal coordinate system of a nonlinear crystal. The choice of the crystal orientation for implementing the present invention depends on the principle of nonlinear frequency conversions and electro-optic effects, as known in the practice of prior arts.  
         [0040]      FIG. 1  ( a ) is the schematic illustration of a high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator as an embodiment of the optical-wave processor of the present invention.  
         [0041]      FIG. 1  ( b ) is the side view of the embodiment shown in  FIG. 1  ( a ).  
         [0042]      FIG. 2  ( a ) is a graph illustrating the experimentally measured laser output power that varies with a variable dispersion length in the present invention.  
         [0043]      FIG. 2  ( b ) is a graph illustrating the experimentally measured laser output power that varies with an applied voltage in the variable dispersion section of the present invention.  
         [0044]      FIG. 3  ( a ) is the schematic illustration of another high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator as an embodiment of the optical-wave processor of the present invention.  
         [0045]      FIG. 3  ( b ) is the cross-sectional view at A-A shown in  FIG. 3  ( a ).  
         [0046]      FIG. 4  ( a ) is the schematic illustration of another high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator as an embodiment of the optical-wave processor of the present invention.  
         [0047]      FIG. 4  ( b ) is the cross-sectional view at A-A shown in  FIG. 4  ( a ).  
         [0048]      FIG. 5  ( a ) is the schematic illustration of another high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator as an embodiment of the optical-wave processor of the present invention.  
         [0049]      FIG. 5  ( b ) is the cross-sectional view of the A-A hatches shown in  FIG. 3  ( a ).  
         [0050]      FIG. 6  ( a ) is the schematic illustration of another high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator as an embodiment of the optical-wave processor of the present invention.  
         [0051]      FIG. 6  ( b ) is the cross-sectional view at A-A shown in  FIG. 6  ( a ).  
         [0052]      FIG. 7  ( a ) is the schematic illustration of another high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator as an embodiment of the optical-wave processor of the present invention.  
         [0053]      FIG. 7  ( b ) is the cross-sectional view at A-A shown in  FIG. 7  ( a ).  
         [0054]      FIG. 8  ( a ) is the schematic illustration of another high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator as an embodiment of the optical-wave processor of the present invention.  
         [0055]      FIG. 8  ( b ) is the cross-sectional view at A-A shown in  FIG. 8  ( a ).  
         [0056]      FIG. 9  ( a ) is the schematic illustration of another high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator as an embodiment of the optical-wave processor of the present invention.  
         [0057]      FIG. 9  ( b ) is the cross-sectional view at A-A hown in  FIG. 9  ( a ).  
         [0058]      FIG. 10  ( a ) is the schematic illustration of another high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator as an embodiment of the optical-wave processor of the present invention.  
         [0059]      FIG. 10  ( b ) is the cross-sectional view at A-A shown in  FIG. 10  ( a ).  
         [0060]      FIG. 11  ( a ) is the schematic illustration of another high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator as an embodiment of the optical-wave processor of the present invention.  
         [0061]      FIG. 11  ( b ) is the cross-sectional view at A-A shown in  FIG. 11  ( a ).  
         [0062]      FIG. 12  ( a ) is the schematic illustration of another high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator as an embodiment of the optical-wave processor of the present invention.  
         [0063]      FIG. 12  ( b ) is the cross-sectional view at A-A shown in  FIG. 12  ( a ).  
         [0064]      FIG. 13  ( a ) is the schematic illustration of another high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator as an embodiment of the optical-wave processor of the present invention.  
         [0065]      FIG. 13  ( b ) is the cross-sectional view at A-A shown in  FIG. 13  ( a ).  
         [0066]      FIG. 14  ( a ) is the schematic illustration of another high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator as an embodiment of the optical-wave processor of the present invention.  
         [0067]      FIG. 14  ( b ) is the cross-sectional view at A-A shown in  FIG. 14  ( a ). 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0068]     Although this invention is susceptible to embodiments of different forms, some preferred embodiments are described and illustrated in details hereinafter. The present disclosure exemplifies the principle of the invention and is not to be considered a limitation to a broader aspect of the invention to the particular embodiment as described below.  
         [0069]      FIG. 1  ( a ) illustrates the first preferred embodiment of a high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator. The whole optical wave processor is constructed on a monolithic nonlinear crystal substrate  100  comprising a variable dispersion section  200 , a phase-matched nonlinear crystal section  300 , and a crystal substrate section  202 . The nonlinear crystal substrate  100  has four reflection edges  10 ,  11 ,  12 ,  13  to reflect the nonlinear interacting waves along an optical path  21  at least two times longer than otherwise a single-pass path  20  without the reflecting edges. The crystal substrate  202  can be an extension of the phase-matched nonlinear crystal section  300 . The phase-matched nonlinear crystal section  300  can be a QPM crystal section.  
         [0070]     Without losing generality, we illustrate the functional principle of the present invention by using QPM SHG as an example. To apply this technique to other phase-sensitive nonlinear wavelength conversions, one can follow the same concept described in the SHG example. Throughout the description, we label the variables of the fundamental optical wave with the subscript ω and those of the SHG wave with the subscript 2ω, where ω is the angular frequency of the fundamental wave. Assume the length of the phase-matched nonlinear crystal section  300  is l, when the pump wave E ω  enters the crystal substrate  202  and passes through the QPM crystal section, it produces a second harmonic wave E 2ω,1  with an intensity I 2ω,1 . Then, the waves E ω  and E 2ω,1  propagate backward into the QPM crystal section again through two total internal reflections caused by edges  12  and  13  in the variable dispersion section  200 . As shown in  FIG. 1  ( a ), the spatial distance that the interacting waves E ω  and E 2ω,1  travel in the variable dispersion section is l d =2l d1 +l d2 . When traveling through the QPM section in the backward path, the pump wave E ω  again produces another second harmonic wave E 2ω,2  with an intensity I 2ω,2 . All the interacting waves, E ω , E 2ω,1 , and E 2ω,2 , then enter the crystal substrate  202  and finally emit sideway from the crystal substrate  202  by an additional total internal reflection at edge  10 . If a conversion path more than two passes is desired and the optical path  21  is properly chosen, all the interacting waves, E ω , E 2ω,1  and E 2ω,2 , can enter the QPM section again by a total internal reflection at edge  11  after the first round trip.  
         [0071]     In the low-conversion limit, E ω  remains un-depleted and the total second harmonic output intensity produced from the double-pass optical wavelength conversion path  21  can be described by  
                     I     2   ⁢           ⁢   ω       =       I       2   ⁢           ⁢   ω     ,   1       +     I       2   ⁢           ⁢   ω     ,   2       -     2   ⁢         I       2   ⁢           ⁢   ω     ,   1       ⁢     I       2   ⁢           ⁢   ω     ,   2           ⁢           ⁢     cos   ⁡     (       Δ   ⁢           ⁢     k   0     ⁢     l   d       +     2   ⁢           ⁢   Δ   ⁢           ⁢   φ       )                               ⁢       =         (         I       2   ⁢           ⁢   ω     ,   1         -       I       2   ⁢           ⁢   ω     ,   2           )     2     +     4   ⁢         I       2   ⁢           ⁢   ω     ,   1       ⁢     I       2   ⁢           ⁢   ω     ,   2           ⁢           ⁢       sin   2     ⁡     (       Δ   ⁢           ⁢     k   0     ⁢       l   d     /   2       +     Δ   ⁢           ⁢   φ       )             ,                   (   1   )             
 
 where Δk 0 l d =(k 2ω −2k ω )l d =πd d /l c  is the phase mismatch between the pump wave E ω  and the SHG wave E 2ω,1  in the variable dispersion section  200 , k is the wave number, l c  is the so-called coherence length in nonlinear wavelength conversion, and Δφ=φ 2ω −2φ ω  is the phase difference resulting at the TIR edges. Under the assumption of no pump depletion, the intensities of the double-pass second harmonic waves are approximately the same (I 2ω,1=I   2ω,2 ) in the configuration of the preferred embodiment and Eq. (1) can be simplified to 
 
 I   2ω =4 I   2ω,1  sin 2 (Δk 0 l d   /2+Δφ).    (2) 
 
         [0072]     On the other hand, as shown in  FIG. 1  ( a ), the QPM grating vector of the QPM section has a specific angle with respect to the propagation direction of the pump wave; thereby, one can translate the nonlinear crystal substrate  100  in the Y direction shown in  FIG. 1  ( b ) to vary l d  for the purpose of adjusting the phase mismatch and modulating the total intensity of the second harmonic output wave, I 2ω .  
         [0073]     As can be seen from Eq. (1), the total intensity of the second harmonic wave, I 2ω,  is the interference intensity of E 2ω,1  and E 2ω,2  and the amplitude modulation of I2ω can be achieved by varying the relative phase between E 2ω,1  and E 2ω,2 , which is equivalent to varying the relative phase between the pump wave E ω  and the second harmonic wave E 2ω,1  in the variable dispersion section  200 . Notably the relative phase Δk 0 l d  is a function of the refractive indices of the fundamental and the SHG waves. Specifically, the total phase mismatch is given by 
 
ΔΦ≡Δk 0 l d +2Δφ=2π(n 2ω −n ω )l d /λ 2ω +2Δφ,   (3) 
 
 where n is the refractive index and λ is the wavelength. In an electro-optic crystal, the refractive index is a function of the electric field, given by n(E)=n−rn 3 E/2, where E is the applied electric field, n is the refractive index in the absence of the electric field, and r is the Pockels coefficient. Using a periodically poled lithium niobate (PPLN) crystal as an example, the fundamental and SHG waves are polarized along the optic axis, having extraordinary refractive indices n ω,e  and n 2ω,e , respectively. Assume that the preferred embodiment in  FIG. 1  is a Z-cut periodically poled lithium niobate crystal. If a voltage is applied to the variable dispersion section  200 , the total phase mismatch ΔΦ can be recast into the expression  
                 Δ   ⁢           ⁢   ϕ     =       Δ   ⁢           ⁢     ϕ   0       -     π   ⁢           ⁢     V     V   π             ,           (   4   )             
 
 where ΔΦ 0  is the phase mismatch in the absence of the electric field, and V π  is the half-wave voltage given by  
                 V   π     =       d     l   d       ⁢       λ     2   ⁢           ⁢   ω         (         r     33   ,     2   ⁢           ⁢   ω         ⁢     n       2   ⁢           ⁢   ω     ,   e     3       -       r     33   ,   ω       ⁢     n     ω   ,   e     3         )           ,           (   5   )             
 
 where the parameter d is the separation distance of the electrodes. Equation (5) clearly differs from that for a conventional birefringence electro-optic amplitude modulator between two crossed polarizers. A birefringence amplitude modulator replies on the birefringence of an electro-optic material, whereas the present invention replies on dispersion in an electro-optic nonlinear optical material. 
 
         [0074]     Therefore the EO phase control can be implemented by building the first conducting electrode  400  and the second conducting electrode  403  on the +Z and the −Z surfaces of the variable dispersion section  200 , respectively, as shown in  FIG. 1  ( b ), if an electric field is desired in the crystal cutting direction to induce the electro-optic effect. When a DC compensating voltage is applied to the electrodes and maximizes the sinusoidal term in Eq. (2), the nonlinear optical wave processor can be fully phase matched and has the maximum double-pass conversion efficiency. When a suitable AC voltage is applied to the electrodes, the relative phase Δk 0 l d  is varied with time and the total SHG output intensity is therefore modulated in its amplitude.  
         [0075]     For a configuration with more than two optical passes, the first conducting electrode  400  is decomposed into a plurality of conducting electrodes that are constructed in accordance with the optical paths from different passes in the variable dispersion section  200 . Each electrode is used to tune the phase mismatch of the mixing waves in the optical path under which the electrode is fabricated. By applying adequate DC and/or AC voltages to the electrodes, the present invention functions as a high-efficiency multiple-pass wavelength converter and amplitude modulator.  
         [0076]     The preferred embodiment in  FIG. 1  was experimentally demonstrated in a Z-cut PPLN crystal. The fundamental wave is a linearly polarized 1064-nm laser from a diode-pumped Nd:YVO 4  microchip laser producing 4 mW CW power. The thickness of the PPLN crystal was 0.5 mm, the length of the PPLN section  300  was 2 cm, and the dispersion section was coated with electrodes on the ±Z surfaces. The PPLN grating period was Λ=20.25 μm, phase matched to the 3 rd -order SHG of the 1064-nm wave at 60° C. The two PPLN grating vectors in the forward and backward paths form ±2.7 mrad angles with respect to the X axis. Without the ±2.7 mrad angles, the optical path in the dispersion section is the width of the device or 1.5 cm in the experiment. With the ±2.7 mrad angles, the optical path in the dispersion section and therefore the SHG output is variable, if the PPLN crystal is translated sideway relative to a stationary pump laser propagating in the X direction.  FIG. 2  ( a ) shows that the measured SHG output power varied periodically when the PPLN crystal was translated along the Y direction relative to a stationary pump beam propagating in the X direction. The 2.5 mm periodicity in the curve corresponds to the change of 2 coherence lengths or 13.5 μm in the dispersion-section length, as expected from the ±2.7 mrad design angles of the PPLN grating vectors.  FIG. 2  ( b ) shows the SHG output power versus the electrode voltage, from which one can deduce a half-wave voltage of 360 volts or 1.1 V ×t(μm)/l d (cm), where t is the electrode separation in μm and l d  is the electrode length in cm. Therefore in the following preferred embodiments employing nonlinear optical waveguides, the electrode separation can be on the order of the waveguide width or ˜10 μm and the half-wave voltage is only about 10 V.  
         [0077]     Base upon the same principle, the present invention of a high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator can be constructed on an optical waveguide device.  FIG. 3 ( a ) and  FIG. 3 ( b ) schematically illustrate the second preferred embodiment of a high-efficiency double-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator in an optical waveguide. The whole structure is constructed on a monolithic nonlinear crystal substrate  102  comprising a variable dispersion section  204 , and a phase-matched nonlinear crystal section  302 . A nonlinear optical waveguide  500  is built along the X axis on the +Z surface of the nonlinear crystal substrate  102  for guiding optical waves with specific wavelengths and modes in the phase-matched nonlinear crystal section  302  and in the variable dispersion section  204 . In the phase-matched nonlinear crystal section  302 , the nonlinear waveguide has a proper design for performing a desirable nonlinear wavelength conversion. The single pass output end of the nonlinear optical waveguide  500  is coated with a high reflector  600  to reflect the forward guiding waves, including the pump wave and the wavelength converted waves, back into the nonlinear optical waveguide  500  to form a double-pass guiding path. Using SHG as an example, the second-harmonic output intensity, I 2ω  in the backward direction, can be efficiently coupled out by a directional coupler  700  built on the nonlinear crystal substrate  102  with an adequate length and spacing in parallel to the nonlinear optical waveguide  500 .  
         [0078]     According to Eq. (2), the conversion efficiency of the double-pass SHG in the second preferred embodiment is enhanced due to the doubled interaction length. The enhanced conversion efficiency can be as high as four times when the interaction length is doubled, according to the low-efficiency model of nonlinear wavelength conversion. From Eqs. (1-5), a phase compensator and amplitude modulator comprising a plurality of conducting electrodes is fabricated on the variable dispersion section  204  as an electro-optic phase tuner to the phase mismatch between the reflected mixing waves. The modulation electrode comprises a first conducting electrode  404  on a buffered layer on the +Z surface and a second conducting electrode  405  on the −Z surfaces in the variable dispersion section  204 . A voltage supply is used to provide an adequate modulation voltage to the modulation electrodes and introduce a voltage difference across the +Z and the −Z surfaces. The phase mismatch induced between the forward and backward paths is therefore tuned through the EO effect. Thus, the interference intensity from E 2ω,1  and E 2ω,2  can be modulated in amplitude if an AC voltage is used, and high conversion-efficiency phase-matched double-pass nonlinear wavelength conversion can be accomplished if a suitable DC offset voltage is used. In this preferred embodiment, the phase-matched nonlinear crystal section  302  can be a QPM crystal section, and the high reflector  600  can be a high-reflection optical dielectric film or a high-reflection optical metal film directly coated at the single-pass downstream end of the nonlinear optical waveguide  500 . It should be noted that this preferred embodiment is also applicable to a bulk nonlinear crystal, in which the waveguide is removed and mixing waves propagates in the bulk region of the nonlinear crystal.  
         [0079]      FIG. 4  ( a ) and  FIG. 4  ( b ) schematically illustrate the third preferred embodiment of a high-efficiency double-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator. In the preferred embodiment, the functional principles of the nonlinear crystal substrate  104 , the variable dispersion section  204 , the phase-matched nonlinear crystal section  302 , the first conducting electrode  404 , the second conducting electrode  405 , the nonlinear optical waveguide  500 , the high reflector  600 , and the buffered layer  800  are the same as those in the second preferred embodiment. The difference is that the third preferred embodiment employs a dichroic beam splitter  900  as a replacement of the directional coupler  700  in the second preferred embodiment. The dichroic beam splitter is set at the input end of the nonlinear optical waveguide  500  and used for separating the reflected pump wave from the wavelength converted backward propagation waves while transmitting the forward pump wave. In the same spirit, the dichroic beam splitter can be a suitable wavelength-division multiplexer such as a wavelength-dependent fiber circulator.  
         [0080]      FIG. 5  ( a ) and  FIG. 5  ( b ) schematically illustrate the fourth preferred embodiment of a high-efficiency double-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator. In the preferred embodiment, the functional principles of the nonlinear crystal substrate  106 , the variable dispersion section  204 , the phase-matched nonlinear crystal section  302 , the nonlinear optical waveguide  500 , the high reflector  600 , the buffered layer  800 , and the directional coupler  700  are the same as those in the second preferred embodiment. The difference is that the EO phase compensator and amplitude modulator of the fourth preferred embodiment now has three electrodes, the first conducting electrode  406 , the second electrode  408 , and the third electrode  410 . The first conducting electrode  406  and the second electrode  408  sandwiches the third conducting electrode  410  with all three electrodes parallel to each other and above a buffered layer  800  in the variable dispersion section  204 . The third electrode  410  is aligned with the longitudinal direction of the nonlinear optical waveguide  500 . The first and the second conducting electrodes  406 ,  408  are at a voltage potential that is in general different from the one at the third conducting electrode  410 . Therefore, there is an electric-field component normal to the crystal cutting surface in the nonlinear optical waveguide  500  and in the variable dispersion section  204 . Such an electrode arrangement is particularly suitable for inducing an EO effect requiring an electric field along the surface normal direction of the nonlinear crystal, the Z direction in  FIG. 5  ( b ). When the three electrodes are applied with a suitable DC voltage, the preferred embodiment functions as a high-efficiency phase-matched double-pass wavelength converter; when the electrodes are applied with a suitable AC voltage, the preferred embodiment functions as a high-efficiency wavelength converter with a built-in amplitude modulator.  
         [0081]      FIG. 6  ( a ) and  FIG. 6  ( b ) schematically illustrate the fifth preferred embodiment of a high-efficiency double-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator. In the preferred embodiment, the functional principles of the nonlinear crystal substrate  108 , the variable dispersion section  204 , the phase-matched nonlinear crystal section  302 , the first conduction electrode  406 , the second conducting electrode  408 , the third conducting electrode  410 , the nonlinear optical waveguide  500 , the high reflector  600 , and the buffered layer  800  are the same as those in the fourth preferred embodiment. The difference is that the fifth preferred embodiment employs a dichroic beam splitter  900  as a replacement of the directional coupler  700  in the fourth preferred embodiment. The dichroic beam splitter is set at the input end of the nonlinear optical waveguide  500  and used for separating the reflected pump wave from the wavelength-converted backward waves while transmitting the forward pump wave. In the same spirit, the dichroic beam splitter can be replaced by a suitable wavelength-division multiplexer such as a wavelength-dependent fiber circulator.  
         [0082]      FIG. 7  ( a ) and  FIG. 7  ( b ) schematically illustrate the sixth preferred embodiment of a high-efficiency double-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator. In the preferred embodiment, the functional principles of the nonlinear crystal substrate  110 , the variable dispersion section  206 , the phase-matched nonlinear crystal section  304 , the nonlinear optical waveguide  502 , the high reflector  602 , and the directional coupler  702  are the same as those in the second preferred embodiment. The difference is that the sixth preferred embodiment does not build a dielectric buffered layer  800  on the +Z surface of the nonlinear crystal substrate  110 , because the electrodes are not arranged immediately above an optical waveguide and do not introduce optical loss to the optical waves. The phase compensator and amplitude modulator comprises the first conducting electrode  412  and a second conducting electrode  414 . The first conducting electrode  412  and the second electrode  414  are arranged in parallel and along the two sides of the nonlinear optical waveguide  502  on the +Z surface of the nonlinear crystal substrate  110  and in the variable dispersion section  206 . This arrangement is particularly useful for inducing an EO effect requiring an electric field in the Y direction. By applying an adequate voltage to the electrodes, a voltage difference occurs across the two sides of the nonlinear optical waveguide  502  in the variable dispersion section  206 .  
         [0083]      FIG. 8  ( a ) and  FIG. 8  ( b ) schematically illustrate the seventh preferred embodiment of a high-efficiency double-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator. In the preferred embodiment, the functional principles of the nonlinear crystal substrate  112 , the variable dispersion section  206 , the phase-matched nonlinear crystal section  304 , the first conduction electrode  412 , the second conducting electrode  414 , the nonlinear optical waveguide  502 , and the high reflector  602  are the same as those in the sixth preferred embodiment. The difference is that the seventh preferred embodiment employs a dichroic beam splitter  902  as a replacement of the directional coupler  702  in the sixth preferred embodiment. The dichroic beam splitter is set at the input end of the nonlinear optical waveguide  502  and used for separating the reflected pump wave from the wavelength-converted backward waves while transmitting the forward pump wave. In the same spirit, the dichroic beam splitter can be replaced by a suitable wavelength-division multiplexer such as a wavelength-dependent fiber circulator.  
         [0084]      FIG. 9  ( a ) and  FIG. 9  ( b ) schematically illustrate the eighth preferred embodiment of a high-efficiency double-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator. In the preferred embodiment, the functional principles of the nonlinear crystal substrate  114 , the variable dispersion section  206 , the phase-matched nonlinear crystal section  304 , the nonlinear optical waveguide  502 , the high reflector  602 , and the directional coupler  702  are the same as the sixth preferred embodiment. The difference is that the EO phase compensator and amplitude modulator of the eighth preferred embodiment now has three electrodes, the first conducting electrode  416 , the second electrode  418 , and the third electrode  419 . The electrode  419  can be paired with either electrode  418  or  416  at a voltage potential that is in general different from that at the rest electrode. This electrode configuration is particular useful for pulling the electric flux lines towards the waveguide depth direction.  
         [0085]      FIG. 10  ( a ) and  FIG. 10  ( b ) schematically illustrate the ninth preferred embodiment of a high-efficiency double-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator. In the preferred embodiment, the functional principles of the nonlinear crystal substrate  116 , the variable dispersion section  206 , the phase-matched nonlinear crystal section  304 , the first conduction electrode  416 , the second conducting electrode  418 , the third conducting electrode  419 , the nonlinear optical waveguide  504 , and the high reflector  602  are the same as those of the eighth preferred embodiment. The difference is that the ninth preferred embodiment employs a dichroic beam splitter  902  as a replacement of the directional coupler  702  in the eighth preferred embodiment. The dichroic beam splitter is set at the input end of the nonlinear optical waveguide  502  and used for separating the reflected pump wave from the wavelength-converted backward waves while transmitting the forward pump wave. In the same spirit, the dichroic beam splitter can be replaced by a suitable wavelength-division multiplexer such as a wavelength-dependent fiber circulator.  
         [0086]      FIG. 11  ( a ) and  FIG. 11  ( b ) schematically illustrate the tenth preferred embodiment of a high-efficiency double-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator. In the preferred embodiment, the functional principles of the nonlinear crystal substrate  118 , the variable dispersion section  208 , the phase-matched nonlinear crystal section  306 , the first conduction electrode  420 , the second conducting electrode  421 , and the buffered layer  802  are the same as those of the second preferred embodiment. The difference is that the nonlinear optical waveguide  504  in the tenth preferred embodiment is a U-shaped nonlinear optical waveguide for routing back the mixing waves to continue the nonlinear wavelength conversion process in the same nonlinear optical crystal. In the U-shaped waveguide structure, the effective interaction length of the nonlinear wavelength conversion process becomes twice compared to the otherwise single-pass design in the prior art. It is also possible to employ a directional coupler or a dichroic beam splitter to separate the pump wave from the wavelength converted backward waves in the double-pass guiding path.  
         [0087]      FIG. 12  ( a ) and  FIG. 12  ( b ) schematically illustrate the eleventh preferred embodiment of a high-efficiency double-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator. In the preferred embodiment, the functional principles of the nonlinear crystal substrate  120 , the variable dispersion section  208 , the phase-matched nonlinear crystal section  306 , the nonlinear optical waveguide  504  and the buffered layer  800  are the same as those of the tenth preferred embodiment. The difference is that the phase compensator and amplitude modulator now has three electrodes, the first conducting electrode  422 , the second electrode  424 , and the third electrode  426 . The three conducting electrodes, having an adequate spacing with each other, are fabricated on the dielectric buffer layer  802  above the +Z surface of the variable dispersion section  208 . This electrode arrangement has the same purpose as that in the fourth preferred embodiment.  
         [0088]      FIG. 13  ( a ) and  FIG. 13  ( b ) schematically illustrate the twelfth preferred embodiment of a high-efficiency double-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator. In the preferred embodiment, the functional principles of the nonlinear crystal substrate  122 , the variable dispersion section  210 , the phase-matched nonlinear crystal section  308 , and the nonlinear optical waveguide  506  are the same as those of the tenth preferred embodiment. The difference is that the twelfth preferred embodiment does not build a dielectric buffered layer  802  on the +X surface of the nonlinear crystal substrate  122 , because the electrode arrangement does not introduce optical loss to the optical waves. The phase compensator and amplitude modulator consists of the first conducting electrode  428 , the second electrode  430 , and the third electrode  432 . In operation, the voltage on either the electrode- 428  or the electrode- 32  side is the highest and steps down towards the other side. The electrode arrangement is particularly useful for generating an electric-field component tangential to the crystal surface, if required for a certain EO crystal.  
         [0089]      FIG. 14  ( a ) and  FIG. 14  ( b ) schematically illustrate the thirteenth preferred embodiment of a high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator. In the preferred embodiment, the functional principles of the nonlinear crystal substrate  124 , the variable dispersion section  210 , the phase-matched nonlinear crystal section  308 , and the nonlinear optical waveguide  506  are the same as those of the twelfth preferred embodiment. The difference is that the phase compensator and amplitude modulator of the thirteenth preferred embodiment now has 4 electrodes, consisting of the first conducting electrode  434 , the second electrode  436 , the third electrode  438 , and the fourth electrode  439 . The first, the second, and the third conducting electrodes  434 ,  436 ,  438 , are arranged on the +Z surface of the variable dispersion section  210  and in adequate spacing corresponding to the width of the U-shaped nonlinear optical waveguide. The fourth conducting electrode  439  is fabricated on the −Z surface of the variable dispersion section  210 . The voltage on the 3 electrodes,  434 ,  438 ,  436 , steps down from one side to the other along the Y direction, whereas the voltage on the fourth electrode  439  is kept lowest. This electrode arrangement has the effect of pulling down the electric flux toward the waveguide depth direction as described in the eighth preferred embodiment.  
         [0090]     Although the above embodiments are mostly illustrated by using a second-harmonic-generation example, the present invention, a high-efficiency multiple-pass nonlinear wavelength converter with an EO phase compensator and amplitude modulator, is applicable to other phase-sensitive nonlinear wavelength conversion processes such as the SFG, DFG, and OPG.