Characterization of domain gratings in KTP and RKTP crystals for second harmonic generation.

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Characterization of domain gratings in KTP and RKTP crystals for second harmonic

generation

Anna Hamberg F‐09, ahamberg@kth.se Sandrine Idlas F‐07, idlas@kth.se

Bachelor Thesis

Laser Physics Division, Department of Applied Physics, Royal Institute of Technology Stockholm, Sweden 2012

Supervisors: Carlota Canalias, Andrius Zukauskas

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Abstract

Lasers are used in a vast range of applications ranging from eye surgery to devices for measuring air pollution. Most of these applications require specific wavelengths that cannot be obtained by regular lasers. Therefore it is important to be able to convert the wavelength of the laser to the desired wavelength for a specific application. This is achieved by using nonlinear optical crystals in which an incoming light frequency can be converted into another.

Due to the material’s chromatic dispersion there is a phase mismatch between the incoming and generated light, which prevents a net increase of the generated light’s power. A solution to this problem is the creation of domain gratings in ferroelectric crystals, which compensates for the phase mismatch between the interacting photons. However, the conversion efficiency will depend on the quality of the grating.

In this study, we have characterized and Rb‐doped ferroelectric crystals in terms of their efficiency to convert infrared light to blue light. This conversion efficiency has been correlated to the domain structure and the quality of the grating. We have found that the homogeneity of the grating and the existence of damage on the crystal’s optical surfaces have a strong impact on the conversion efficiency.

Acknowledgements

We would like to thank our supervisors, Carlota Canalias, and Andrius Zukauskas at the dept.

of Applied Physics at KTH for their support and help throughout this project. They have provided us with well‐structured guidance, always available to address our problems in the most pedagogic way.

Cover picture:

Flaw in an RKTP crystal, photographed with an optical microscope with magnification 5x.

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1. Introduction

Different materials respond to the electric field of light in different ways. In the presence of an oscillating electric field, an oscillating polarization can be induced and modify this field. If the polarization is proportional to the field, the material response is said to be linear. For any other type of relationship between those two elements, we are dealing with a non‐linear interaction.

Effects of optical non‐linearity include changing the frequency of light waves. This will be the subject of our study. When passing through the ferroelectric crystals KTP (Potassium Titanyl Phosphate, ) and RKTP (Rubidium doped KTP), the incoming lights frequency is doubled, thus creating a second harmonic wave. For KTP and its isomorphs, the frequency range for which this effect occurs is wide, extending through the whole spectrum of visible light.

A common problem with crystals used as frequency converters is that the power of the generated frequency oscillates along the crystal. This is due to the dispersion relation between the refractive index and the light’s frequency, causing a different phase velocity for different frequencies. This way, a phase mismatch between the incoming light and the generated light is created in the crystal, causing the latter to be converted back into the incoming frequency.

A possible solution is to use the fact that light is an electromagnetic wave. For this reason, it can be influenced by the electric fields produced by the interaction with the crystal’s polarization. Therefore, the phases of the interacting waves can be reset to zero by periodically inverting the polarization of the ferroelectric crystal.

This technique has a variety of applications such as biomedical instrumentation, color printing and laser displays, to name a few. This study is therefore interesting from both a theoretical and a practical point of view.

Our goal will be the characterization of some of the optical properties of KTP and RKTP: we will try to correlate the efficiency of the crystal optical surfaces to the quality of the

ferroelectric domain gratings.

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2. Theoretical background

2.1. Optics

2.1.1. Nonlinear optics

The linear part of the interaction is responsible for phenomena that we are all familiar with, such as rainbows or the bending of light rays coming from a spoon in a glass of water.

Nonlinearity is also responsible for a number of different phenomena. One of these is changing the light’s frequency.

The condition for second order optical nonlinearity in a material is that the material is non‐

centrosymmetric. There exist many crystals that obey this criterion. In this study, we will discuss KTP and its isomorph RKTP.

A material can respond to an external field by creating a polarization modifying the field. The dipoles inside a ferroelectric material oscillate in the direction of the light’s polarization. In the linear case, the response of the material to this excitation is proportional to the field.

However, in the non‐linear case, extra terms add up to the equation:

Here is the nonlinear part of the polarization, and is the linear part.

2.1.2. Second Harmonic Generation

Equation (1) can be seen as a Taylor development: constitutes a first order term (a linear relation between P and E), and is made of higher order terms (square, cubic, etc.).

We will here consider the second order term in equation (1):

Here, is the incoming electric field, and is the electric field generated by the interaction with the material. We can now introduce the non‐linear coefficient d:

1

2

Out of all second order nonlinear processes, we will focus on second harmonic generation.

This implies that two incoming photons ( ) interact with the crystal by combining their energies to form a third photon . Energy conservation gives:

F

SH

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 (3)

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This process is illustrated in Figure 1:

Figure 1– Second Harmonic Generation.

Phase‐matching criteria

Maximum conversion efficiency is achieved when momentum is conserved, in other words when there is no phase mismatch between the incoming wave and the generated wave. This is described by the phase matching criteria, where denotes the second harmonic wave number and denotes the fundamental wave number:

∆ 2 0

When the phase matching criteria is fulfilled, the intensity of the second harmonic wave increases. But after a certain point, the phase mismatch creates a destructive interference, implying that the generated intensity decreases. This happens each time ∆k π.

Quasi‐phase matching using periodically poled crystals

Due to chromatic dispersion in the material, the phase matching criteria is not automatically fulfilled. This causes an accumulation of phase mismatch as light travels through the crystal, creating destructive interference.

Quasi phase matching is a technique where the phase mismatch, ∆ , is adjusted by creating a “grating” with periodically switched polarization directions in the crystal. This can be done in ferroelectric materials, and how well phase matching is achieved will depend on the grating quality. The function of this grating is to keep the phase mismatch at a minimum and especially make sure that ∆ is always smaller than π, thus giving an increase in SH power.

kSH

kF

k

Figure 2 – Ferroelectric domain grating, where different regions have different polarizations.

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In such a grating, the width of a domain with a certain polarization should equal the distance at which the intensity reaches its maximum. The ideal domain width is called coherent length, , where :

Figure 3 – Oscillation in Second Harmonic power throughout the crystal, curve (a): when no quasi‐phase matching is

used, curve (b): with quasi‐phase matching. The arrows symbolize the polarization direction in the material for curve b.

Figure 3 shows two curves; curve (a) is the second harmonic power in a crystal without any grating (the whole crystal has the same polarization). Due to the variations in ∆ the second harmonic power oscillates throughout the crystal. Curve (b) shows the second harmonic power in a crystal with a ferroelectric domain grating (the arrows in the figure mark different polarization directions). ∆ is always kept below , which causes the SH power to increase.

The effect of this sign modulation is clearer when described in the reciprocal lattice. The periodic sign modulation of d can be described as a rectangular function g(x) and expanded in a Fourier series:

Here, is the harmonic of the grating vector, in the same direction as d. G_m is the Fourier coefficient.

Thus, creating a grating is equivalent to creating an extra artificial wave vector compensating the phase mismatch. This gives an extra momentum, corresponding to the wave vector of the periodic crystal. This way, the phase mismatch is reset to zero by the additional wave vectorⁱ:

Lc  k 

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Figure 4 – Quasi Phase Matching

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Duty cycle

The duty cycle D is a quantity that we will define by taking into account the periodic sign modulation in our calculations. As we will see, this should give:

Λ

In particular, in our study, we will set L as the length of the inverted domains, thus defining the duty cycle as the ratio between the widths of the inverted domains to the period of the crystal:

Taking into account the periodic sign modulation in equation (4), the expression for the effective nonlinear coefficient is:

∙ ∙

For a periodic sign modulation, The Fourier coefficient G_m is:

2 sin

Therefore, to get the maximum nonlinear coefficient, we need to maximize G_m, which gives:

2

And most importantly, this defines the Duty cycle D and its optimum:

Λ deff

domain period Λ

Figure 5 – Picture showing a grating of domains with different polarizations in a ferroelectric crystal. Red line showing a domain, pink line showing a period. The black line equals 5µm.

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1 2

At its optimum, when 0.5, we obtain the largest nonlinear coefficient .

Let us now define the order of quasi phase‐matching as the quotient between the fundamental wavelength and the period of the grating. A crystal of order m=3 has thus a domain width 3 times bigger than the coherence length¹, . This means that the polarization would be reversed at every 3 instead of every , letting the second harmonic power decrease twice in every period. Curve d in figure 6 illustrates a 3^rd order quasi phase‐matching:

Figure 6 ‐ SH power with and without phase matching. a: perfectly matched, b: growth and decay without phase matching, c: 1^st order QPM, d: 3^rd order QPMⁱⁱ.

The nonlinear coefficient decreases as the order of quasi‐phase matching increases, as shown in the figure below:

Figure 7 – Nonlinear coefficient plotted against the duty cycleⁱⁱⁱ.

1 We are here introducing the term “order” as to referring to the “order of the grating”. This should not be confused with the “order of nonlinearity” previously used.

deff

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In our study, we will use crystals of order m=1 and m=3. All the crystals were prepared for being of order m=1, but for different wavelengths. Because the characterization laser only reaches certain wavelengths, we are obliged to use certain crystals as order m=3 with another wavelength than they were originally designed for. The nonlinear coefficient has a maximum at D = 0.5 for both 1^st and 3^rd order. However, as can be seen in figure 7, 3^rd order gratings also have a maximum for the nonlinear coefficient at a duty cycle of 0.15 or 0.85.

High efficiencies achieved for these duty cycles are not interesting to us and will not be considered in this study. This is because the crystal would generate low conversion efficiency if used as a 1^st order grating with a different wavelength of the laser. Thus, we will only consider as a good duty cycle for both m=1 and m=3.

Figure 7 also shows that 3^rd order gratings are much more sensitive to small deviations from 0.5 in duty cycle than 1^st order gratings are.

Efficiency

Our criteria to test the quality of the crystals are the crystal’s efficiency for converting light from fundamental to second harmonic waves.

The conversion efficiency is based on measurements of the fundamental wave power, , and the second harmonic power, . The conversion efficiency depends on the order of the crystal, m.

To be able to compare crystals of different lengths and different order with each other, we use the normalized conversion efficiency, which does not account for the grating’s length or the input power:

This refers to a fundamental power of 1 Watt and a crystal length of 1 cm. As it is independent of the actual length of the crystal, it is an excellent way to compare different crystals.

This definition tells us that a crystal is better than another when converting a higher percentage of photons’ frequencies. Conversion efficiencies over _∙^% are considered good.

0.5 D

PF

PSH

_normP_SH m²

P_F²L  2_F²d_eff² k_F m²

n_F²n_SH₀c³











h(B,) %

W cm

 



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2.2. Nonlinear materials for quasi‐phase matching 2.2.1. KTP and its isomorph RKTP

KTP is a good frequency converter because of its wide transparency range. It is easy to fabricate and its thermal phase matching bandwidth is large. Its low coercive field simplifies poling thick crystals. KTP has also a low sensitivity to laser induced damage, a property that is enhanced by Rb‐doping.

2.2.2. Ferroelectricity

KTP and its isomorph RKTP are ferroelectric crystals, which implies that they possess a net spontaneous polarization. An external electric field, if strong enough (coercive field), will change the polarization direction. In KTP, it can be switched between two equilibrium states, oriented 180° from each other. The surface perpendicular to the + end of the polarization vector is called C+, and the surface perpendicular to the minus end of the polarization is called C‐.

2.2.3. Differences between KTP and RKTP crystal structure

KTP and RKTP crystals have the same crystal structure, apart from the fact that RKTP is doped with Rb. There is less than 1% Rb in an RKTP lattice, but its effect on the poling process is highly perceptible. Doping the KTP crystal with Rb lowers the ionic conductivity with up to two orders of magnitude, which facilitates domain inversion and thus getting a higher quality grating.

Figure 8 – Projection of the KTP structure in the 010 direction^iv.

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KTP and RKTP have approximately the same values for d_eff . The highest d_eff that we can obtain in KTP is 1.031 ∙ 10 and occurs when the polarizations of the fundamental and second harmonic light are parallel to the polarization of the crystal. The crystal gratings have been created so that we can make use of the highest d_eff .

2.2.4. Electric field poling of the crystals

Before poling the crystals, the whole crystal has the same spontaneous polarization. The side perpendicular to the minus side of the polarization vector is called C‐. When poling the crystals, a thin layer of photoresist (an insulator that is sensitive to light) is put on top of the C‐ side. Then one puts a photo mask (metal with the shape of the desired grating, patterned on a glass plate) on top of the C‐ side and exposes it to light. In the exposed parts of the photoresist, many of the bonds between molecules will be broken. The crystal is put in a developing solution (chemical etching), which will remove the rest of the exposed parts of the photoresist. After this, one puts on a thin layer of aluminum on the whole patterned side of the crystal.

To do the poling, the C‐ and C+ sides of the crystal are put in contact with a conductive fluid.

Then an electric field, higher than the coercive field, is applied. This will make the areas without any photoresist switch polarization, while the polarization will stay the same for areas covered with the insulator.

Domains tend to nucleate at the edges of the electrode. They start growing downwards from the to the C+ side, and then broaden. Because of the fringing fields at the edges of the electrode, the domain nucleation does not precisely follow the boundaries set by the electrode:

Figure 9 ‐ Fringing fields causing over‐poling. The electrode is marked in black.

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This is an important factor for the quality of the resulting grating that explains why the domains do not follow the boundaries, as seen in the figure below:

Figure 10 ‐ Growth of inverted domains in KTP: (a) Nucleation. (b) Domain propagation. (c) Domain broadening. (d) Merging of inverted domains. The inverted domains are marked in grey, the photoresist in black and the metal in orange.

Two typical problems encountered during periodic poling described above are over‐poled domains and under‐poled domains. We will refer to over‐poled domains when we talk about inverted domains that have broadened too much, or even merged together. Areas with over‐poled domains have a duty cycle 0.5. We will refer to under‐poled domains for inverted domains that have a smaller width than the coherence length and thus a duty cycle

0.5.

This varying response to external electric field can be caused by internal defects in the crystal or the ionic conductivity in the material. The conductivity can be lowered by doping KTP with Rb. Doping does not provoke significant changes in the optical properties. If the magnitude of the electric field is too high or too low, the domains might get over‐poled or under‐poled.

To visualize the domain structure, selective etching is used. The crystal is put in a liquid that only attacks and breaks down a certain orientation of the polarization, for example only the C‐. This creates a relief pattern on the crystal that can be observed in an optical microscope.

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3. Experimental set‐up

The purpose of this study is to characterize KTP and RKTP crystals with respect to how efficient they are at generating second harmonic waves.

The following two figures show the experimental set‐up:

Figure 11 – Experimental setup^v.

A tunable laser (Spectra‐Physics, Model 3900S) generates a beam of the fundamental frequency, , which is directed through the half wave plate that, together with the polarizer, adjusts the power of the light. A lens with 50 mm focal length focuses the beam before the light enters the crystal, where the diameter of the laser‐beam is 30 µm. After passing through the crystal, the beam passes through a frequency filter that only lets the second harmonic frequency, , through. Thus the power‐meter after the filter only registers the second harmonic power. We used a low‐power meter from Coherent to register the second harmonic power. The fundamental power is registered after the lens,

Figure 12 – Our experimental setup

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The fundamental wavelength is tuned manually, adjusted either by using a spectrometer (Ando, “Optical Spectrum Analyzer”, model AQ‐6315A), or by finding which wavelength gives the highest second harmonic power. The crystal is also aligned manually, by finding the highest second harmonic power and by eliminating reflections.

The second harmonic power at different points over the optical surfaces of the crystal is then measured, in order to create a map of the normalized conversion efficiency along the optical surface. The starting point was an edge of the grating, and measurement steps were 200 µm.

Figure 13 – Direction of light propagation and Measurement points for the efficiency map of the optical surfaces. This figure is not in the right scale.

The measurements of the second harmonic power were used to create plots mapping the normalized efficiency at different points of the optical surface. These were correlated with the quality of the grating observed by microscope at the patterned and non‐patterned surfaces. The quality of the grating inside the crystal cannot be directly observed.

When observing the grating we used an optical microscope from Nikon (Eclipse LV100). We observed both the grating and the optical surfaces of the crystals. We used objectives ranging from 5x to 100x magnification.

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4. Measurements

We have measured seven crystals in total. The four crystals that we have used to illustrate our results are listed in table 1. Two of them are high performing crystals for both orders m=1 and m=3, while the remaining two are poor quality crystals. Together they illustrate the most important features influencing the conversion efficiency. Generally, a crystal achieving a normalized efficiency over 1 ^%_∙ is considered as usable.

Table 1 – Information about measured crystals.

Crystal name A

B C D

KTP/ RKTP KTP RKTP RKTP

RKTP

Domain period 3.18µm 3.18µm 9.01µm 9.01µm

Order 1^st 1^st 3^rd 3^rd

Duty cycle patterned surface

0.4 (middle)

0.32 (near edges)

0.3.

0.5 (right side figure 9)

0.4 (left side figure 9)

0.4 (not uniform)

Duty cycle non‐patterned surface

No duty cycle

0.4 (between 0.3 and 0.6)

0.5 (right side figure 9)

0.4 (left side figure 9)

0.4

Highest 0.8 ^%_∙ 1.2 ^%_∙ 1.4 ^%_∙ 0.6 ^%_∙

normalized



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5. Results

Many factors influence the conversion efficiency of a crystal. In this text we will account for the most important of these factors.

5.1. Crystal properties influencing conversion efficiency

5.1.1. Lattice structure

Relation between domain structure and material choice

When looking at domain structure, it has been observed that RKTP achieve gratings with better quality than KTP, meaning that the gratings are more even and homogenous. This can be due to the fact that the lower conductivity of RKTP simplifies perfection in the poling process. Generally, RKTP shows superior effects. This effect is shown in our measurements by the fact that the efficiencies obtained were higher for RKTP than for KTP. Our most efficient crystals were C (maximum conversion efficiency: 1.4 ^% ) and B (maximum conversion efficiency 1.2 ^% ).

5.1.2. Duty cycle

The high sensitivity of the conversion efficiency for 3^rd order gratings to variations in duty cycle has been observed in two of our crystals.

Crystal C has the highest conversion efficiency of all the crystals measured. The grating on this crystal is homogenous, even and almost without defects throughout the whole crystal.

However, we get big differences in the conversion efficiency for different regions. This is caused by the variation in duty cycle between different regions of the crystal.

Figure 14 – Plot of conversion efficiency. Upper side of the plot corresponds to the patterned side of the crystal.

In the grating corresponding to the region in the plot marked with black, the average duty cycle is very close to 0.5. With few exceptions, the duty cycle on both the patterned and on the non‐patterned side in this region varies between [0.48, 0.52]. Compared to other crystals we have measured, this variation is very small. The region marked with pink has an average

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duty cycle of 0.43. On the patterned side the duty cycle varies between [0.42, 0.45]. On the non‐patterned side the variation is between [0.41, 0.43]. In this example the difference in duty cycle between these two regions, ∆ 0.07, caused a difference in the normalized conversion efficiency of ∆ 0.8 ^%_∙ .

Figure 15 ‐ Pictures of the non‐patterned side. First photo characteristic for region marked with black in the plot, with a duty cycle close to 0.5. Second photo characteristic for the region marked with pink, with an average duty cycle of 0.43.

As already mentioned, the conversion efficiency for a 3^rd order grating is very sensitive to variations in duty cycle. Figure 7 (page 9) shows that the absolute value of the nonlinear coefficient for a 3^rd order grating is 0.22 for a duty cycle of 0.5, and 0.15 for a duty cycle of 0.43. This gives us much higher conversion efficiency for a duty cycle of 0.5 than for 0.43.

However, if crystal C had been used as a 1^st order crystal with a different wavelength of the laser, it would have obtained high conversion efficiency throughout the whole crystal. As can be seen in figure 7, the nonlinear coefficient for 1^st order is 0.64 at duty cycle of 0.5, and 0.61 at a duty cycle of 0.43. The difference in conversion efficiency in different regions would thus be small and the whole crystal would have very high conversion efficiency.

Another illustration of the sensitivity to duty cycle variation was observed in crystal D. In this case, the variation from the average duty cycle is very local. The efficiency plot in figure 16 shows that a small variation is the duty cycle has perceptible effects. The area marked with a cross in figure 16 has a lower efficiency than its neighborhood. A measurement of the duty cycle above this area showed us that the surface is more under‐poled there compared to other areas. There, the duty cycle is around 0.36, whereas outside of this area, the average of the whole surface is 0.4, although a bit irregular and at times over‐poled.

Figure 16 – normalized efficiency plot for crystal D

This very local under‐poled area also reveals one of the causes for under‐poling: this area is

20µm 20µm

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the scratch is also more under‐poled than its neighborhood (D=0.29), as was the case for the patterned side. We can see below the change in domain width, in an area close to the scratch:

Figure 17 ‐ Duty cycle variation near a scratch

5.1.3. Homogeneity of grating

Differences in homogeneity of the grating are highly perceptible when it comes to conversion efficiency. This is true for inhomogeneity both in the direction of light propagation and in the polar direction from one surface to the other.

Measurements indicate that it is better to have a duty cycle that is very regular, even if the duty cycle diverges a bit from the ideal value, than having a good duty cycle on average with big variations. A typical case is crystal B, our second best crystal with an efficiency of 1.2 ^%_∙ , although its average duty cycle is as low as 0.3. This can be explained by the fact that the grating is homogeneous. This crystal was used as a 1^st order crystal, and as already explained, 1^st order gratings are not very sensitive to variation in duty cycle.

Another cause for low conversion efficiency is illustrated by crystal D. In parts of this crystal the inverted domains never reached deep into this crystal. The grating only exists on the patterned surface of the crystal. It never reached a depth accessible to light beams, as illustrated in figure 18.

Figure 18 – Thinning domains. The domains do not reach deep into the crystal.

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5.1.4. Defects in the grating

Holes and effective length of the grating

Efficiency increases with the number of grating periods that light goes through. But at the edges of the grating, the poling process often leaves large areas without any inverted domains. This locally changes the effective length of the grating, which can explain why the conversion efficiency plots usually show a gradual efficiency decrease near the edges.

The conversion efficiency plot for D shows a typical example of this:

Figure 19 – Holes near the edge of the grating shorten the effective length of the grating, and decrease the efficiency.

The top area of this graph corresponds to the patterned surface. On this side, in the area corresponding to the left hand side of the plot, the effective length of the grating (the length without the holes) is roughly 1000 µm. This is much smaller than the grating length, which is supposed to be around 9.1 mm. The non‐patterned surface had a lot of domains merged together on the sides. The area corresponding to the right side of the plot, however, suffered a lot less holes. This could explain the higher efficiency in that area.

5.3. Damage on the optical surfaces

Damages on the optical surface and quality of the grating are two separate problems, without any influence on each other. However, damages are influencing the crystals performance. When analyzing data, it is important not to confuse regions of low conversion efficiency due to cracks on the optical surface with regions of low conversion efficiency due to a non‐homogenous grating.

Damages make the laser‐light scatter, preventing a significant proportion of the light beam from entering the crystal at the right angle. This lowers the measured values of the second harmonic power, and thus the conversion efficiency, in the regions corresponding to the damaged optical surfaces. Re‐polishing the crystal can eliminate the defects.

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An example of how damages on the optical surface affect the measured conversion efficiency is shown below.

The lower part of Figure 20 shows the non‐patterned side of the crystal. The area marked with red on the bottom of the plot has considerably lower conversion efficiency than the area marked with green next to it. One of the optical surfaces of this crystal has a big crack along half the length of the optical surface, close to the non‐patterned side, corresponding to the area marked with red in the plot. There is also a small area on the patterned side, marked with pink, which has dramatically lowered conversion efficiency. This area corresponds to a crack in the optical surface close to the patterned side. This is shown in figure 21.

Figure 21 ‐ Pictures showing the damaged parts on the optical surface. The color marks show the correspondence between efficiency conversion plot and damage on optical surface. The small dark line corresponds to 100 um.

When comparing the conversion efficiency plot and the photos of the optical surface, it is obvious that the low conversion efficiencies of certain areas of the plot are caused by the cracks on the optical surface. Hence, the areas with low conversion efficiency in the plot do not tell us anything about the quality of the grating and the domain structure in the crystal.

Figure 20 ‐ Conversion efficiency plot. The upper side corresponds to the patterned surface of the crystal

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5.4. Temperature Dependence

The temperature dependence was measured on crystal B. The fundamental wavelength was 795.6 nm. It was chosen to give the maximum efficiency, 1.2 µW, at 29 . It was then held fixed, while the temperature variation was controlled by a device relying on thermoelectric Peltier effect. The fundamental power entering the crystal was 345 mW.

Figure 22 ‐ Normalized efficiency plotted against temperature.

We can see that the curve is narrow (∆ 2 ) and the temperature bandwidth is well defined, which is a sign of a good quality crystal.

5.5. Possible errors

Factors that might have influenced the quality of our measurements could be:

‐ The crystals have been aligned manually, which can cause some indetermination in our measurements.

‐ The presence of extra light in order to be able to work can cause noise in the measurements, although we used a dim light.

‐ The power of the laser was not very stable and can have changed while we were taking measurements.

‐ The power detector was fluctuating, making it hard to achieve results with high precision.

The last digit in our measurements is highly unreliable.

5.6. Limitations of the method

‐ Our characterization method does not enable us to analyze the inside of the crystal, thus we can only account for the grating at the surfaces of the crystal. This is not always a problem, since it is often possible to infer what problems have happened during the poling

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6. Conclusion

Several factors have an impact on the conversion efficiency of the KTP and RKTP crystals. It is crucial for obtaining high conversion efficiency that the domain grating is homogenous and has got a duty cycle that does not vary much. It is also important, especially for 3^rd order gratings, that the duty cycle does not differ much from 0.5. Areas without any inverted domains in the grating due to under‐poling, and merged domains due to over‐pooling also lower the efficiency. Big areas with no inverted domains at all are most often found at the edge of the grating, lowering the conversion efficiency in these regions. Defects on the optical surfaces can influence the measurements. However this is not a grating defect, and can be solved by re‐polishing the crystals.

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7. Litterature

Shunhua Wang, “Fabrication and characterization of periodically‐poled KTP and Rb‐doped KTP for applications in the visible and UV”, Laser Physics Division, Department of Physics, Royal Institute of Technology, Stockholm, Sweden, 2005

Carlota Canalias, “Domain engineering in KTiOPO4”, Laser Physics and Quantum Optics, Dept. of Physics, Royal Institute of Technology, Stockholm, Sweden, 2005

Rahul Singh, “Source of Correlated Photons pairs using 2D Periodically Poled KTP Crystal”, Dept. of Quantum and Electro Optics, Royal Institute of Technology, Stockholm, Sweden, 2008

i Figure from: Shunhua Wang, “Fabrication and characterization of periodically‐poled KTP and Rb‐doped KTP for applications in the visible and UV”, Laser Physics Division, Department of Physics, Royal Institute of Technology, Stockholm, Sweden, 2005.

ii Figure from: Fredrik Laurell, Optical material 11, 235 (1999)

iii Figure from: Shunhua Wang, “Fabrication and characterization of periodically‐poled KTP and Rb‐doped KTP for applications in the visible and UV”, Laser Physics Division, Department of Physics, Royal Institute of Technology, Stockholm, Sweden, 2005.

iv Z. W. Hu, P. A. Thomas, and P. Q. Huang Phys. Rev. B. 56, 8559 (1997).

v Figure from: Shunhua Wang, “Fabrication and characterization of periodically‐poled KTP and Rb‐doped KTP for applications in the visible and UV”, Laser Physics Division, Department of Physics, Royal Institute of Technology, Stockholm, Sweden, 2005.

Characterization of domain gratings in KTP and RKTP crystals for second harmonic generation.