REGIONS

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims priority under 35 U.S.C. §119(e) of United States Provisional Patent Application No. 61/817,084 filed on April 29, 2013, the contents of which are hereby incorporated by reference.

TECHNICAL FIELD

[0002] The present invention relates to the field of grating structures, and particularly to the dependence of second harmonic generation on the position of domain-inverted (or poled) regions in the grating structures.

BACKGROUND

[0003] Apodized chirped structures can be used as wavelength converters with better transfer functions than unapodized structures. However, these structures suffer from ripples that do not exist in theoretical simulations. These ripples cause the output of second harmonic generation power to vary with wavelength. The source of the ripples may be errors in the fabrication or in the engineering of the apodized chirped gratings.

[0004] Therefore, there is a need for a design for a grating structure which is less sensitive to fabrication errors and can help minimize errors in second harmonic broadband intensity responses.

SUMMARY

[0005] There is described herein a grating structure having a specifically located domain- inverted region within each period. Altering the location of the domain-inverted region leads to a frequency shift in a uniform and apodized grating, depending on the symmetry of the function, and influences the profile of second harmonic intensity versus wavelength in chirped gratings.

[0006] According to a broad aspect, there is provided a wavelength converter comprising a substrate having an input and an output and adapted to receive and propagate a fundamental harmonic signal at the input and generate a second harmonic signal at the output, and a grating structure within the substrate, the grating structure having a plurality of segments, each one of the segments composed of a domain-inverted region surrounded by a non-inverted region on each side thereof, the domain-inverted region overlapping with a center position of a segment.

[0007] Throughout the present specification, the expression "positioned centrally within the segment" will be understood to mean positioned within the segment such that at least a portion of the domain-inverted region corresponds with a center of the segment, and a non-inverted region is provided on either side of the domain-inverted region within the segment. Thus the center of the domain-inverted region may be offset from the center of the segment. A domain-inverted region will be referred to as a "poled region" throughout the description, and a non-inverted region will be referred to as an "unpoled region". The unpoled regions may correspond to regions of natural polarization or engineered polarization. The poled regions correspond to regions of reverse polarization compared to the unpoled regions.

BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Further features and advantages of the present invention will become apparent from the following detailed description, taken in combination with the appended drawings, in which:

[0009] Fig. 1 is a schematic of a wavelength converter having a substrate and a channel, in accordance with an embodiment;

[0010] Fig. 2 is a schematic of a grating having poled regions located at a specific position within each segment, in accordance with an embodiment;

[0011] Figs. 3a - 3c are exemplary illustrations of three proposed structures for placing the poled region on the right, in the middle, and on the left of a segment, respectively;

[0012] Fig. 4 is a graph illustrating an effect of moving a poled mark space with a duty cycle of ½ on the wavelength shift from left to right according to figure 3b, in which the central poled region C changes from Λ/4 to 3Λ/4; [0013] Fig. 5 is a graph illustrating relative wavelength shift for the structures of figs 3a-3c in uniform gratings according to inset functions for change of nonlinearity as asymmetric;

[0014] Fig. 6 is a graph illustrating relative wavelength shift for the structures of figs 3a-3c in uniform gratings according to inset functions for change of nonlinearity as symmetric;

[0015] Fig. 7 is a graph illustrating normalized SH intensity response for a 10 mm long chirped APPLN crystal with different structures;

[0016] Fig. 8 is a graph illustrating normalized bandwidth and ripple for the structures of figs. 3a-3c;

[0017] Fig. 9 is a graph illustrating normalized SH intensity versus the FH using a hyperbolic tangent apodized function;

[0018] Fig. 10 is a graph illustrating the influences of different types of errors in the structure of fig. 3b; and

[0019] Fig. 11 is a graph illustrating constant broadening errors in the structures of figs. 3a-3c.

[0020] It will be noted that throughout the appended drawings, like features are identified by like reference numerals.

DETAILED DESCRIPTION

[0021] There is described herein a wavelength converter based on a chirped or uniform and apodized structure having poled regions provided at specific locations. Second Harmonic (SH) intensity responses, resulting from the effective second-order nonlinearity, are dependent on the physical location of the poled regions within each period of the gratings. Altering the location of the poled region from a specific position leads to a frequency shift in a uniform grating depending on the symmetry of the function. In a chirped grating, changing the place of poled region strongly influences the profile of SH intensity versus wavelength. Thus, there is described a proper grating design to obtain an SH response for a desired nonlinearity function. [0022] Figure 1 illustrates one embodiment of the wavelength converter 10. The converter 10 comprises a planar substrate 12 having a channel 14 extending along an axis x from an input to an output. A fundamental harmonic signal enters the channel 14 by the input and propagates along the channel 14 while generating a second harmonic signal at the output. The fundamental harmonic signal is an optical signal. The wavelength of the fundamental harmonic signal may be comprised within the visible spectrum, the infrared spectrum, or the like. The generated second harmonic signal is also an optical signal.

[0023] The substrate 12 comprises a grating structure 18 having one or more segments extending along the channel axis x, which each comprise a poled or domain-inverted region 16 and a non-inverted or unpoled region 20. The width of a segment corresponds to the period of the grating. The width of a poled region to the width of a segment is the duty cycle of the grating. The grating structure 18 may have segments of increasing, fixed, or decreasing widths. Thus, the grating structure 18 may have an increasing, decreasing or constant period, and the grating structure 18 may have an increasing, decreasing, or constant duty cycle. Various combinations of periods and/or duty cycles may be provided by dividing the grating structure 18 into sections, each section having one or more segment, and having differing periods and/or duty cycles per section.

[0024] In one exemplary embodiment, the grating structure 18 is divided into sections, each section having multiple segments and the width of the segments are constant within a given section and progressively increase from one section to another section. In another exemplary embodiment, the grating structure 18 is divided into sections, each section having multiple segments and the width of the segments are constant within a given section as well as from one section to another section. In yet another exemplary embodiment, the grating structure 18 is divided into sections, each section multiple segments and the width of the segments are constant within a given section and progressively decrease from one section to another section.

[0025] In some embodiments a plurality of grating structures 18 are aligned end to end. Each one of the grating structures 18 may be composed of any one of the embodiments described above. For example, a portion having increasing duty cycles may be followed by a portion having constant duty cycles, which may itself be followed by a portion have decreasing duty cycles. Such an embodiment is described in more detail in US Patent No. 8,411 ,353, the contents of which are hereby incorporated by reference.

[0026] The grating structure 18 may be uniform and apodized or chirped and apodized. The grating structure 18 may be continuously chirped or step-chirped.

[0027] An exemplary configuration for the grating structure 18 having poled regions specifically located is shown in Fig. 2. In this embodiment, a poled region 16 is provided substantially centrally between two unpoled regions 20, thus forming a segment 30 or 32. Generally, the poled region 16 may be positioned within the segment such that at least a portion of the poled region corresponds with a center of the segment, and an unpoled region 20 is provided on either side of the poled region within the segment. Thus the poled region 16 overlaps with the center of the segment even though a center of the poled region 16 may be offset from the center of the segment, as illustrated in segment 32.

[0028] As illustrated, the relative widths of poled regions 16 to unpoled regions 20 in a segment 30 or 32 may vary throughout the grating structure 18. The width of the poled region 16 may be greater than the width of the unpoled region 20, the width of the poled region 16 may be less than the width of the unpoled region 20, the width of the poled region 16 may be equal to the width of the unpoled region 20. The width of the poled region 16 may also be greater than, less than, or equal to the combined width of both unpoled regions 20. In addition, the overall width of the segment 30 or 32 may also vary throughout the grating structure 18.

[0029] SH generation conversion efficiency is dependent on the position of the poled region 16 within the segment and having the poled region 16 positioned substantially centrally in the segment allows the engineering of effective second-order nonlinearity in uniform and chirped gratings, as will be demonstrated below.

[0030] The coupled wave equations for SH Generation (SHG) in a crystal can be written for a grating by introducing d(z) as: dA _x _ 2 jcofd{z) -JAkz

A,A ^* e

dz

2 jo) ₂ d(z)

dz (1)

where A and A ₂ are the fields of fundamental harmonic (FH) and second harmonic (SH), and Ak = k _2a} - 2k _a} represents the wave vector mismatch between the SH and FH, c is the speed of light, o _{1 2} and « _{1 2} are the angular frequency and refractive index of FH and SH field, d(z) =d _a (z)f _ap (z) is the nonlinearity function in the length of grating where d _a is the modulation of nonlinearity which can possess only the positive and negative states of a constant nonlinear coefficient in ferroelectrics, and is the desired apodization function.

In order to examine the dependence of the SH intensity on the position of the poled region, one segment of grating is considered which includes just one positive and one negative poled region with the total length of Α = 2π / (k _2a - 2k _{t which is a} | _{S0 the pe} riod for the 1- st order quasi-phase matching.

[0031] For a non-depleted pump, the SH field is calculated by integrating over the length of A in the second equation of Eq.1. The duty cycle in one segment is considered as a parameter in Eq.1 to find the required duty cycle for getting the desired nonlinearity in

2 ^{* "l} d

SHG. Integrating over one segment, putting ^{2 a} A = D and considering the duty n ₂ c

cycle as a variable, the SH electric field can be written as i-C-aA/2 . . . i-C+aA/2 . . . fA . . .

A, I D = \ e-' ^Mz dz - \ e-' ^Akz dz + \ e ^~tNa dz ,

JO JC-aA/2 JC+aA/2

[0032] where C represents the poled region center, which can move from αΛ / 2 to Λ - αΛ / 2 by considering the poled region as a frame, and moving from the right to the left of the segment. The SH intensity in frequency of 2ω is proportional to sin( ra) ² for all allowed values of C and the duty cycle can be obtained by a = arcsin( ) / π , but the phase in the SH electric field varies from -iAkaA/ 2 to iAkaA/2 linearly with changing of C from right to the left and it is eliminated when it is placed in the middle of the segment. To apply the desired apodization function f _ap , the duty cycle should change as α(ζ) , however the position of poled region should also be determined.

[0033] In order to examine how the moving of the mark space frame (poled region) can influence the SH output, three positions are assumed as shown in Figs. 3a, 3b, 3c. They are named segment Scheme I (fig. 3a), Scheme II (fig. 3b) and Scheme III (fig. 3c) and the poled regions are placed in the right (maximum negative phase), center (zero phase) and left (maximum positive phase) of the segment, respectively. Based on Schemes I, II and III incorporating several segments with specific poled positions, the three considered structures are called Structure I, II and III.

[0034] The second harmonic electric field produced by apodized Structure I for the function f _ap can be written as:

1 f ^N~l Λ i

A ₂ / D = ^\∑4 smiAk^L 12)e-' ^AkL( ' ^{+a> /2)} I - -^- sin( J / 2)e- ^m/2 ) (2) where L is twice the coherence length for the phase matched wavelength and a, is the duty cycle. N is the number of segments. For apodized Structure III, the phase in the first term of Eq.2 changes to exp(-/ ^' A(/ ^: + 1 - a _i 12)) . However for Structure II the SH electric field for the apodized device is calculated by: / £> sin( NZ / )e ^lAkNLn ) (3)

[0035] The phase of electric field in Structure II is independent of the duty cycle a, and its amplitude just for the specific frequency of ω which satisfies the phase matching condition (AkL = 0) is the same as other structures.

[0036] In chirped gratings, the n period changes as A _n = Α + (η - Υ)δ where the δ is the length difference for the neighbouring segment. Therefore, the phase of the electric field, similar to the uniform grating for Structure I and III remain dependent and for Structure II it is independent of the duty cycle. The SH electric field in the chirped gratings for Structure I I varies as:

A, / D =— (∑ 4 sin( (J - a _n _ _x (L + n - \)δ) 12) _β -' ^ΜΚ "- ^{ι ι+δ)+ιΙ2)]}

-2 sin(AkNL 1 ₂ ) _e - ^imm+{N - ^{X S} + 4 sm(AkL(l - a ₀ ) l 2) r ^Mi/2 ) (4)

where L is first pitch length. Positive and negative values of δ give increasing and decreasing periods for chirped gratings, respectively.

[0037] The intensity, which includes multiples of each one of the two terms of the electric field, is dependent on the duty-cycle difference for Structure I and II I unlike Structure II . The dependence of SH intensity on duty cycle difference in various structures influences the SHG intensity response. The effect of this dependence in the three proposed structures is considered for uniform gratings with a small number of segments and chirped gratings.

[0038] If in the uniform grating with a period of Λ, the mark space frame moves from the left to the right in all segments, it results in a maximum intensity at different wavelengths. The wavelength shift of SH intensity from the phase matched wavelength ( ) for the period of Λ is shown in terms of a relative wavelength shift in Fig. 4 for different numbers of segments.

[0039] Based on Fig. 4 for a small number of segments, the maximum intensity deviates from the phase matched wavelength ( ) due to a movement of the poled mark space.

However for a large number of segments (>30) it is not affected significantly. Since the duty cycle is constant throughout the crystal, the movement of the poled region just changes the first and last segment in the structures. Therefore, by increasing the number of segments it has almost no impact on SHG intensity. If the duty cycle and consequently the effective nonlinearity changes, depending on the function of the nonlinearity (f _ap ), a shift in the peak intensity can be observed.

[0040] The relative wavelength shifts for the intensity peak vs. segment numbers are shown in Figs. 5 and 6 for the three structures. The nonlinearity changes as the functions shown in the insets of the figures. Fig. 5 shows the wavelength shift of the intensity peak for an applied asymmetric nonlinearity function of 1/4 cycle of a sine function, which changes from zero to a maximum. This shift is reduced by increasing the number of segments and becomes constant for a large number of segments. The maximum intensity shifts to longer wavelengths in Structure I and to shorter wavelengths in Structure III relative to the primary phase matching wavelength { ). The minimum wavelength shift occurs when Structure II is used.

[0041] In Fig.6, the relative wavelength shifts are shown for the ½ cycle sine function, which is symmetric. In this case the wavelength shift disappears with an increasing number of segments. The reason is that the shift produced in the first half of the crystal is compensated in the second half. The responses of the Structures I and III are exactly the same but are different compared to Structure II as a result of a different amplitude value in the electric field (Eq. 2 and Eq. 3). The deviation from a constant value for small numbers of segments (<20 segment in the plot) is due to the jump of the value of the duty cycle and the reduction of precision in the applied apodization function.

[0042] The observed wavelength shifts in Fig. 5 are caused by an accumulation of different electric field phases from every segment. The intensity includes multiples of every pair of terms of the electric fields in the summation shown in Eqs. 2 and 3. In these multiplications, the phase difference of every pair appears in terms of cosines. These phases do not depend on duty cycle in Structure II, unlike Structure I and III in which the duty cycles are variable in the crystal length due to the change of nonlinearity. In Structure II the phase is just a function οίΔ&Λ , therefore there is no phase accumulation reliant on the duty cycle differences in this structure.

[0043] If a symmetric apodization function is applied to a uniform grating, there is no difference in the transfer function of SHG for the location of the mark space. However, for an asymmetric function, the position of mark space can introduce a wavelength shift in the intensity output. In chirped gratings another variable, the pitch length, is a contributing factor, which may lead to a different result. The change of SH intensity by applying an apodizing nonlinearity function in chirped gratings is also considered. [0044] The SH intensity in apodized chirped gratings of different lengths are simulated considering the three previous structures, which represent the movement of the mark space frame. In Fig. 7 the normalized SH intensity versus FH wavelengths centered at 1535 nm is plotted for unapodized and apodized linearly chirped grating (LCG) using the three proposed structures with applied apodized sine functions shown in the inset. The lengths of the first and last pitches are 18.97 μηι and 18.22 μηι respectively, to achieve a bandwidth of 25 nm in an approximately 1 -cm-long poled lithium niobate crystal with 500 segments. The intensity is normalized to the maximum intensity for the unapodized grating. The apodized linearly chirped grating's (LCG's) plot represents the SH intensity for a desired sine function applied mathematically to an unapodized LCG, which results in an almost ripple-free response. The SH intensity responses for Structures I and III differ from that for the mathematically apodized LCG. There is lower (higher) intensity at the edges of the response and higher (lower) in the middle for Structure I (III) in comparison with the SH intensity for the apodized LCG and Structure II.

[0045] Normalized ripples and bandwidths for different grating lengths are plotted in Fig. 8. These plots are normalized to the mathematically apodized LCG. The ripple and bandwidth are almost the same for structure II and the apodized LCG, however, the ripple for Structures I and III increases considerably depending on the grating length. The bandwidth for Structure III is reduced by -20% and increases -10% for Structure I compared to that of the structures with apodized LCGs.

[0046] Figures 7 and 8 demonstrate that positioning the poled region in the center of segments proposed by Structure II provides the best response for the required apodization function. This occurs because the position of the poled region within a period affects the overall SH intensity as both amplitude and phase of SH electric field change differently for the three proposed structures. The amplitude and phase can thus be controlled by the duty cycle, and the position of poled region, respectively. This explanation and result are not only applicable for the sine function and linear duty cycle changes, but also to other apodizing functions. For example, the intensity of the hyperbolic tangent apodized function is plotted in Fig. 9.

[0047] The positioning of poling in the center of segments eliminates the electric field phase dependence on the duty cycle as it is symmetric. Whatever position is chosen, except in Structure II, introduces a phase dependence on the duty cycle, when the effective nonlinearity is a function of position. The structure I and III can convert to each other by switching the direction of laser launch as the poled region changes from the right to the left side. Chirped gratings can be considered as many uniform gratings, each with a short length, with the period varying in each section. The wavelength shifts of the intensity peaks, arising from each uniform period short grating, interfere with each other and lead to a digression from the response of the mathematically applied function. Therefore, analytically and numerically it is concluded that using Structure II for apodization is a good match to the mathematically applied function to engineer the effective nonlinearity, and to achieve a substantially flat response. Furthermore, the simulation of similar structures in the linear multilayer device with a modulated refractive index indicates that their reflection responses are sensitive to the positioning of the layers as well. Middle poled (unpoled) spaces between the n ^th and n ^th +1 period change as (Λ + nA)(\ - ^a " ^{+ n+l} ) - y (1 - a _n+l ) .

[0048] In practice, the fabricated device may deviate from the designed device in the poling process or in the preparation of the mask. The errors degrade the intensity and flatness of the SHG intensity response. Common errors such as broadening of poled regions or displacement of poled regions from the intended positions is considered for Structure II. Fig. 10 shows the effect of different errors. In certain cases, the domain boundary can shift from the ideal position without any change in the size of the periods or duty cycle. For this situation, with a 2-μηι domain shift from the center of every segment in a same side, the normalized SH intensity versus FH wavelength is plotted in Fig. 10 and is called error A. Normalization is kept the same as Fig. 8 for the SH response of unapodized LCG. The size of ripple with error A does not change significantly in Structure II. Furthermore, the width of poled regions may increase in the poling process. This broadening is considered in two cases of linear and random 12% broadening of poled region that can occur in the poling process. For a 12 percent mark space broadening in each segment (Error B) and randomly varying between zero and 12% of the mark space ratio in poled regions (Error C), the ripples increase (0.35% of its average of minimum and maximum ripples) and the intensity shrinks while the shape of the output still follows the response of ideal Structure II. [0049] For comparison with the two other structures, an error of 12 percent broadening in the duty cycle (Error B) is plotted in Fig. 11. This error introduces much larger ripples in Structure III and decreases the ripples in Structure I in comparison to Structure II. However, the error in Structure I shrinks the intensity significantly (around 30%) and the size of ripples increases to 52% of its average of ripples, which is still more than Structure II. Even by considering the errors in fabrication, Structure II still results in a better SHG intensity response compared to the other two structures.

[0050] Thus, the SH response is dependent on the location of the poled region within the pitch, as the amplitude and phase of the SH electric field is controlled by the duty cycles and position of the poled regions, respectively. The simultaneous displacement of the poled regions (as a moving frame) from the center in all segments can lead to a wavelength shift in the intensity peak depending on the applied function and structures. In uniform gratings, the displacement of the poled mark space frame from the center of segments can lead to a wavelength shift for asymmetrical functions but it is insignificant for symmetric ones. In chirped gratings, this movement leads to increased ripples in the SH intensity response as a function of wavelength, especially at the bandwidth edges. For a required nonlinear function, Structure II, based on locating the poled region in the center of segments, has the closest response to a desired theoretical function. Simulations show that other structures diverge from the desired mathematical function. These results show that in periodically poled devices, positioning the poling region appropriately within the pitch can dramatically improve the SH transfer function of the structure, and should lead to better device performance, significantly increasing tolerance to fabrication errors. This result is applicable to periodic linear refractive index or phase modulated structures and their reflection response as well.

[0051] It should be understood that the wavelength converter may be adapted to operate at any adequate optical wavelength. Similarly, it should be understood that the particular values for the bandwidth of the wavelength converter presented above are exemplary only. The aperiodically poled grating may be adapted to provide a greater or smaller bandwidth.

[0052] While the present description refers to a wavelength converter comprising a bulk crystal, the wavelength converter may comprise a waveguide. The grating may be constituted from segments which extend across the whole cross-section of the waveguide or across only a portion thereof. An unfocussed fundamental harmonic beam may be input into the waveguide to generate a second harmonic beam. The waveguide may be provided with reflective facets to create a Fabry-Perot cavity.

[0053] The present invention can be applied to three color generation using a single or reduced set of devices, broad-band frequency conversion (femtosecond), broad variable (waveband) wavelength conversion, ultra-short pulse compression and measurement. The wavelength converter may also encompass ultra-high power (kW) frequency conversion of short pulses in bulk crystals, fibre frequency doubling, engineered crystals with complex response, CW high power frequency without time control and/or reduced temperature control.

[0054] The wavelength converter may be made from at least one material, such as lithium niobate, magnesium oxide doped lithium niobate, titanium indiffused lithium niobate, potassium niobate (KNb0 ₃ ), gallium arsenide (GaAs), potassium titanyle arsenate (KTiOAs04) or KTA, adequate polymer, adequate semiconductor material, adequate ferroelectric material, or the like. Some of these materials, such as GaAs, may need cutting and polishing to make up stacked plates of periodic media. The wavelength converter may also be made from two different materials, i.e. the poled regions are made from a first adequate material and the unpoled regions are made from a second adequate material different from the first material. In some embodiments, the substrate may be made from one material while the grating structure may be made from one or more other materials.

[0055] The embodiments of the invention described above are intended to be exemplary only. The scope of the invention is therefore intended to be limited solely by the scope of the appended claims.