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Noncritical phase matching fourth harmonic generation properties of KD2PO4 crystals

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Abstract

Noncritical phase matching (NCPM) fourth-harmonic-generation (FHG) experiments were conducted on different deuterium content DKDP crystals by adjusting crystal temperature to generate 266 nm deep UV laser. Specially, near room temperature NCPM is realized in extremely high deuterium content DKDP crystal at 38.6 °C, which is the lowest temperature to the best of our knowledge. NCPM temperature of DKDP crystals in 60-100% deuterium content range and 1050-1070 nm wavelength range are determined by a linear relationship according to the experimental and calculated results. Angular tuning properties are independent with deuterium content in medium and higher deuterium content DKDP crystals. All of these results will provide good references for future FHG applications of 1 μm laser with DKDP crystals.

© 2015 Optical Society of America

1. Introduction

Noncritical Phase Matching (NCPM) is an ideal condition to obtain efficient frequency conversion. For NCPM, the first order parameters of the wave vector mismatching are zero, which leads to broad parameter bandwidths. When the wavelength parameter is considered, the wavelength sensitivity is determined only by the second and higher order wavelength sensitivity parameters and roughly proportional to the inverse square root of the crystal length. So the efficient frequency conversion can be maintained over a broad wavelength range. Likewise, angular NCPM is the condition under which high efficiency harmonic generation can be maintained over a broad angle tuning range.

NCPM can be realized in many nonlinear optical (NLO) crystals, such as LBO [1,2], KTP [3,4], LN [5,6], KN [7,8], and KDP type [9] crystals. Among them, KDP type crystals are prominent candidates which can realize spectral NCPM and angular NCPM over broad wavelength range and temperature range. Wavelength insensitive NCPM second harmonic generation (SHG) can be realized in 1030-1090 nm range by adjusting the deuterium content of DKDP crystal [10]. Typically, 12% deuterium content DKDP crystal can realize wavelength insensitive NCPM SHG of Nd:glass laser (1053 nm), which is very important for Inertial Confinement Fusion (ICF) facilities. It is more attractive to gain deep UV fourth harmonic generation (FHG) by using KDP type crystals. Specially, high efficiency, angular insensitive type-I NCPM FHG had been realized previously [11–22]. Compared with the critical phase matching [23], this configuration has many other advantages beside of broad angular tuning range, such as large effective nonlinear optical coefficient (deff), no beam walk-off and high utilization of the as-grown crystal.

It is more preferable to realize NCPM FHG at room temperature to simplify the temperature requirement. According to the Bredikhin’s prediction [13], angular NCPM FHG in deuterated KDP (DKDP) crystal can be realized by adjusting deuterium content and crystal temperature. However, this prediction is rough and does not agree well with experimental results. For example, at room temperature angular NCPM has achieved extremely high efficiency FHG for 1053 nm in 70% deuterium content DKDP crystal rather than in the predicted 80% deuterium content DKDP crystal [18]. For more commercial 1064 nm Nd:YAG laser, however, the existing results show that the lowest NCPM temperature is beyond 42 °C, even in the absolutely deuterium content DKDP crystal. Besides, large discrepancies can be found from these results due to the deuterium content uncertainty and narrow deuterium content range of DKDP crystal. Considering the inconsistency among theoretical prediction and existing experimental results, a careful experimental study of NCPM FHG properties in DKDP crystals with respect to deuterium content, wavelength, and temperature is very necessary.

Recently, extremely high deuterium content DKDP crystals were grown in our laboratory. Near room temperature NCPM FHG was realized in these crystals. In this work, we present direct experimental verification of the NCPM FHG behavior in DKDP crystals. Predictions are made from approximate calculation within appropriate uncertainty, considering the accuracy of refractive indexes data. Then we compare our calculated results with those of other researchers, and put forward possible explanations for disagreements. All of these are helpful for better understanding of NCPM FHG in DKDP crystals.

2. Calculation

2.1 First-order parameter sensitivity

The intensity of NCPM FHG by a thin crystal slab in the low drive regime can be described as [24]:

IFHGsin2(1/2ΔkL)(1/2ΔkL)2
where L is the thickness of the crystal and Δk is the total phase mismatch. Δk is mainly determined by refractive indexes. While refractive indexes are the functions of external parameters such as wavelength λ and crystal temperature T, for DKDP crystal, refractive indexes are also affected by internal parameter, deuterium content XD. DKDP is a negative uniaxial crystal and Δk has the following form for type I NCPM FHG:
Δk=4πλ1[no(λ1,T,XD)ne(λ2,T,XD)]
For wavelength near λ0, temperature near T0 and deuterium content near XD0, ∆k can be extended to the first order terms with respect to λ, T and XD as follows:
Δk(kXD)λ,T(XDXD0)+(kT)λ,XD(TT0)+(kλ)T,XD(λλ0)βXD(XDXD0)+βT(TT0)+βλ(λλ0)
Theoretically, first-order parameter sensitivitiesβXD,βTandβλcan be calculated from the deuterium content, temperature and wavelength dependent refractive indexes based on the followed equations [25]:

βXD=4πλ1(no1XDne2XD)
βT=4πλ1(no1Tne2T)
βλ=4πλ1(no1λ12ne2λ)

However, all of the existing dependent refractive indexes data [26–30] are debatable and can’t cover UV wavelength range and high temperature range. On the other hand, there are few data suitable for partly deuterium content DKDP crystal except for Zhu’s results [31]. Even so, Zhu’s results are available only at room temperature. These limitations hinder the accurate calculation of PM properties in partly deuterium content DKDP crystal. That is why the predications based on numerical simulation do not agree well with the experimental results. To make the calculation reliable and simple, we make some approximation based on the direct experimental data. Thus the calculated results and the experimental results can be verified with each other.

It is worth noting that the first-order parameter sensitivity can be evaluated and calculated in another way. When λ0 is fixed, for small deuterium content and temperature detuning, the locus of point (T, XD) where Δk = 0 is given by:

βTδT+βXDδXD=0
The deuterium content sensitivity βXD evaluated at the phase-matching temperature TNCPM is essentially a constant for small changes in XD, so the deuterium content sensitivity can be calculated from:
βXD=βT(dTdXD)
Likewise when deuterium content is fixed and for small fundamental wavelength and temperature detuning, the wavelength sensitivity can be calculated from:
βλ=βT(dTdλ)
On the other hand, βXDcan also be determined by the FWHM of the signal versus deuterium content curve generated by Eq. (1):
βXD=5.566ΔXDL
where ΔXD and L are the determined FWHM and crystal length respectively. Similarly, βXDand βλ can also be determined in the same way by equations:

βλ=5.566ΔλL
βT=5.566ΔTL

2.2 Second-order parameter sensitivity

Phase matching condition is also affected by the direction of DKDP crystal. For the small deviation δ(Δθ) from the of exact phase matching angle θpm, Δk can be expanded in a Taylor series:

Δk=(Δk(Δθ))δ(Δθ)+12(2Δk(Δθ)2)δ(Δθ)2+=βθδ(Δθ)+12βθ'δ(Δθ)2+
To the first order term, the angle sensitivity is related to the dependence of the phase-matching temperature on the angle. For small angle deviations, the locus of point (T, Δθ) for Δk = 0 is given by:
βTδT+βθδΔθ=0
The angular sensitivity βθ at the phase-matching angle θpm is essentially a constant for small changes in Δθ, so it can be calculated from:
βθ=βT(dTd(Δθ))
For θNCPM = 90° where the NCPM realizes, the first-order angle sensitivity parameter βθ=(Δk/(Δθ)) will vanish and(dT/d(Δθ))=0. By differentiating both sides of Eq. (15) with respect to Δθ, the following relationship is obtained:
βθ'=(βθ(Δθ))=(βT(Δθ))(T(Δθ))βT(2T(Δθ)2)=βT(2T(Δθ)2)
On the other hand under the NCPM condition, the bandwidth is roughly determined by the second-order angle sensitivity parameter βθ'. Thus βθ' can be calculated by the FWHM of the signal versus Δθ as follows:

Δθ22.26βθ'L

3. Experiment

3.1 Experimental facilities

The fundamental wavelength of 1064 nm was supplied by a PY61 Nd:YAG pico-second laser with a repetition rate of 10 Hz. The SHG was obtained by a 30 mm thick, (41°, 45°)-cut KDP crystal (type-I PM direction). To perform the FHG experiment, a series of different deuterium content, 8 mm-thick DKDP crystals with an aperture of 10 × 10 mm2 were cut at the type-I FHG PM direction (45°, 90°). The transmittance faces of the crystals were fine polished to reduce the back reflection at the crystal surfaces. The DKDP sample was placed in a sealed but two sides transparent copper chamber to control the crystal temperature in an accuracy of 0.05 °C.

3.2 Experimental procedure

To determine the temperature sensitivity of series deuterium content DKDP crystals, the retro-reflection position was found by rotating the crystal around θNCPM = 90°. Then the temperature tuning curve was plotted by monitoring the FHG output at different temperatures. NCPM Temperature (TNCPM) can be determined from the temperature tuning curve. Likewise, the angle tuning curve was plotted by monitoring the FHG output at different angles with the crystal temperature fixed at TNCPM. At the same time, the NCPM properties of DKDP crystals are also affected by the deuterium content. Thus the deuterium content tuning curve was determined by monitoring the FHG signal with different deuterium content DKDP crystals fixed at the retro-reflection position under 40 °C. The FHG conversion efficiency with respect to the 2ω (532 nm) energy was measured with different DKDP crystals at their individual NCPM conditions.

4. Results and discussion

4.1 Temperature tuning

For DKDP crystal, NCPM can be realized by adjusting the crystal temperature to make the FHG PM angle to aim the direction θ = 90°. The TNCPM various with deuterium content as well as fundamental wavelength. Figure 1 shows the temperature tuning curve of different deuterium content DKDP crystals. All curves were fitted by sin2x/x2 to evaluate the TNCPM and the FWHM of the curve. It is obvious that the NCPM temperature increase inversely with the deuterium content. For the highest deuterium content DKDP crystal (99%), NCPM is realized at a temperature of 38.6 °C, close to the room temperature of our laboratory (28 °C). This characteristic reduces the requirement of temperature controlling. At the same time, the near room temperature NCPM is more favorable than the room temperature NCPM which does not use temperature controlling, because high efficiency, stable frequency conversion demands that the NLO crystal temperature is kept within ± 0.1 °C bias from TNCPM. On the other hand, as we have known, 38.6 °C is also the lowest TNCPM ever obtained in DKDP crystal for the FHG of 1064 nm laser.

 figure: Fig. 1

Fig. 1 Temperature tuning curves of different deuterium content DKDP crystals. The black dots are experimental data and the solid red lines are fitted by sin2x/x2.

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The deuterium content dependence of TNCPM was plotted in Fig. 2. An extremely straight line can be fitted to the experimental data, corresponding a linear formula TNCPM(°C) = −2.22XD + 259.1, which describes the relationship between TNCPM and deuterium content. From the fitted straight line, the 70% deuterium content DKDP crystal can be predicted to realize NCPM FHG of 1064 nm at 103.7 °C. It is in good agreement with the S. T. Yang’s result [18], which predict NCPM FHG of 1064 nm at 104.3 °C with 70% deuterium content DKDP. It proves the reliability of the present fitting.

 figure: Fig. 2

Fig. 2 Deuterium content dependent TNCPM. The black dots are fitting data from temperature tuning curves, and the solid red lines are linear fit of the black dots.

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The FWHM and βT for each deuterium content crystal were measured and calculated according to Eq. (12). The results were listed in Table 1. The βT varies a little with the deuterium content. However, this direct method to determine βT by measuring the output intensity as a function of temperature is not accurate enough [32]. Given the little change of βT and the lack of temperature dependent refractive indexes data in partial deuterium content DKDP crystals, it is rational to suppose that βT keeps almost unchanged and is independent with deuterium content.

Tables Icon

Table 1. FWHM of the temperature tuning curve and βT for different deuterium content DKDP crystals.

On the other hand, the deuterium content sensitivity is calculated to be 7.27%−1cm−1 according to Eq. (8) by using the average value of βT, i.e. 3.275 °C−1cm−1. To verify the accuracy of deuterium content sensitivity, experiments were performed to determine the deuterium tuning curve at 40 °C. The results were plotted in Fig. 3. The FWHM of the deuterium tuning curve is 0.9%. Thus the deuterium content sensitivity is estimated to be 7.73%−1cm−1 by Eq. (10) given the crystal length is 8 mm. According to Zhu’s and Kirby’s results, refractive indexes are almost in linear relationship with deuterium content. Thus (no1/XDne2/XD)=2.94×105%1 and βXDis calculated to be 6.9%−1cm−1 according to Eq. (4). Above three results determined by different methods are close to each other, which confirm the accuracy of our result.

 figure: Fig. 3

Fig. 3 Deuterium content tuning curve at 40°C. The black dots are experimental data and the solid red lines are fitted by sin2x/x2.

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According to the G. C. Ghosh’s result [29], the relationship between TNCPM and fundamental wavelength is linear for DKDP crystal. From the report of Yang [18], this relationship can be described as TNCPM(°C) = 7.8λ -8194.84. In a small wavelength range and large deuterium content range, we can make an extrapolation that TNCPM has linear relationships with both fundamental wavelength and deuterium content. According to our results and Yang’s, TNCPM can be described by TNCPM(°C) = 7.8λ-2.22XD + 8040.1, as plotted in Fig. 4. Here we consider the 60-100% deuterium content range and 1050-1070 nm wavelength range, which have the practical meaning. Because tetragonal DKDP crystal has two phase transitions at −60 °C [33] and 157 °C [34] respectively. As shown in Fig. 4, above ranges make DKDP crystal can realize NCPM FHG in its stable temperature range. The red line shows the deuterium content of DKDP crystal, which can realize room temperature NCPM at the corresponding wavelength. These results can provide good references for designing DKDP crystal to fulfill specific usage in the future.

 figure: Fig. 4

Fig. 4 Calculated diagram of NCPM temperature in the 60-100% deuterium content range and 1050-1070 nm wavelength range.

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In all experiments, the wavelength can be determined precisely. The initial crystal temperature is controlled with an accuracy of 0.05 °C. However, the local crystal temperature in the scope of the light spot may be a little higher than the initial temperature due to the light absorption of the crystal. This increases the uncertainty of the temperature accuracy. The influence of temperature inhomogeneous on conversion efficiency will be discussed in part 4.3. The largest uncertainty comes from the deuterium content of the sample. The deuterium content of our sample was estimated indirectly from the deuterium content of the solution. According to the research of G. M. Loiacono [35], the deuterium content of DKDP crystal can be determined by the equation: Keff = 0.68 exp(0. 00382M), where Keff and M are the effective segregation coefficient and the mole% D in the solution respectively. Loiacono reported that the accuracy of this method is ± 0.2%. However, our earlier experiments showed that this equation was only available for highly deuterium content DKDP crystal and traditional low speed growth method. The Keff can be affected by crystal growth conditions such as growth temperature, supersaturation, and hydrodynamics. These effects are especially serious in rapid growth crystals and large size crystals when the deuterium content of solution is in the middle range. All of these factors increase the deuterium content uncertainty as well as inhomogeneous. Our experiments were performed in the highly deuterium content range, and the medium deuterium content range was extrapolated from the highly deuterium content range. A ± 2% error was estimated to produce ± 4.5 °C discrepancy of TNCPM. We compare our results with others’ in Table 2. It shows that in the high deuterium content range, almost all the results agree well with our predictions within the estimated error, which indicates that our results and calculation are convincing. The inconsistency in medium deuterium content DKDP crystals is mainly because of the relatively large error of deuterium content.

Tables Icon

Table 2. A comparison between our calculation and the previously reported experimental results.

4.2 Angle tuning

When the crystal temperature is fixed near TNCPM, the crystal orientation should be adjust around θ = 90° to make Δk = 0 according to the Eq. (2). For DKDP crystal, angle tuning will only change ne(λ/2) which is an even function of Δθ. Thus Tpm is an even function of Δθ. It indicates that when the crystal temperature deviates from TNCPM, symmetrical doublet of 4ω output will appear around θNCPM = 90°, as shown in Fig. 5. When the temperature rises gradually towards TNCPM, the doublet becomes closer to each other. Finally, the doublet will turn into a single wide peak at TNCPM. This phenomenon can be used to determine the optical axis position of the crystal. It is also helpful for deciding the (Tpm, Δθpm) curve.

 figure: Fig. 5

Fig. 5 Angle tuning curves of a 99% deuterium content DKDP crystal under different temperature. The color dots are experimental data.

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Figure 6 shows the relationship of Tpm and Δθ in different deuterium content DKDP crystals. The resultant (Tpm, Δθ) curves can be well fitted to a quadratic equation:

Tpm=A(Δθ)2+B(Δθ)+C
The parameter A represents the one half of the curvature (2T/(Δθ)2) and can be used to calculateβθ' indirectly. (2T/(Δθ)2) and βθ' are calculated from Eq. (16) and listed in Table 3. On the other hand, the βθ' can be determined directly by the angle tuning curve. Figure 7 shows the angle tuning curve of different deuterium content DKDP crystals. All curves are fitted by the function sin2x/x2 to evaluate the FWHM of the curves. Then theβθ' can be calculated from the Eq. (17). These results are also listed in Table 3. It can be seen that the βθ' values obtained from different methods agree with each other basically, which confirm the reliability of our experimental results. All of the βθ' values vary little in different deuterium content DKDP crystals. It is rational to assume that βθ' is independent with deuterium content. It indicates that the properties of medium deuterium content DKDP crystal are more similar to highly deuterium content DKDP crystal rather than KDP.

 figure: Fig. 6

Fig. 6 Relationship of Tpm and Δθ in different deuterium content DKDP crystals. The black dots are experimental data and the solid red lines are fitted by a quadratic equation.

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Tables Icon

Table 3. Comparison of indirectly calculated βθ' and directly calculated βθ'.

 figure: Fig. 7

Fig. 7 Angle tuning curve of different deuterium content DKDP crystals. The black dots are experimental data and the solid color lines are fitted by sin2x/x2.

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4.3 Conversion efficiency

For NCPM there is no beam walk-off, so the conversion efficiency is mainly limited by the linear absorption coefficient α. It is reported that nonlinear absorption coefficient during FHG in DKDP crystal can be neglected [23]. DKDP crystals have low absorption coefficient and high transmittance in the visible range, which will not limit the conversion efficiency. However, the transmittance of different deuterium content DKDP crystals in the UV range differs from each other, which will affect the conversion efficiency obviously. Figure 8 shows the transmittance spectra of different deuterium content DKDP crystals in the UV range. Transimittance at 266 nm and FHG conversion efficiency of different deuterium content DKDP crystals are listed in Table 4. It is obvious that the low transimittance at 266 nm corresponds to the lower conversion efficiency. The decreasing of transimittance in UV range is attributed to the presence of impurity and can be affected by raw material as well as growth conditions [36–38]. The influence of impurity is more serious in rapid growth procedure. It is possible to elevate the UV transimittance and get high quality crystal by using higher purity raw materials and improving growth techniques.

 figure: Fig. 8

Fig. 8 Transimittance of different deuterium content DKDP crystals in 200-300 nm range.

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Tables Icon

Table 4. Transimittance at 266 nm and FHG conversion efficiency of different deuterated DKDP crystals.

On the other hand, high absorption coefficient α will not only decrease the 4ω output directly, but also increase the local temperature of the crystal and causes additional phase mismatch due to the thermo-optical effect. Thus the local temperature around the back surface of crystal will deviated from TNCPM. It is difficult to make the temperature of all parts fixed at TNCPM. If the deuterium content in the back surface is a little higher than the front surface, it is possible to make the whole crystal under NCPM condition and gain better frequency conversion. Kruglik [17] reported that the maximal conversion efficiency is reached when the temperature gradient along z axis varies according to the linear law and exists within the PM temperature curve. If the deuterium gradient along z axis is adjusted according to the relationship TNCPM(°C) = −2.22XD + 259.1, it is possible to make all parts of the crystal work at their exactly NCPM condition, which will gain much higher conversion efficiency. The growth of deuterium gradient DKDP crystals will be discussed in the future.

5. Conclusion

In summary, NCPM FHG of Nd:YAG laser was realized in different deuterium content DKDP crystals to generate 266 nm deep UV laser. Specially, the NCPM temperature in extremely high deuterium content DKDP crystal can drop to 38.6 °C, which is convenient for practical application. TNCPM is modulated by deuterium content and fundamental wavelength. It can be described by the new developed formula TNCPM(°C) = 7.8λ-2.22XD + 8040.1 in 60-100% deuterium content range and 1050-1070nm wavelength range. The second order angular sensitivity βθ' is found to be independent with the deuterium content, Under NCPM FHG condition, conversion efficiency is mainly limited by the linear absorption coefficient and the local temperature inhomogeneous. These limitations can be relieved by improving crystal quality and growing gradient deuterium content crystals.

Acknowledgments

This research is supported by the National Natural Science Foundation of China (Grants No. 51323002, 51402173, and 61178060), the Ministry of Education (Grants No. 625010360) and the NPL, CAEP (Project 2014BB07).

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Figures (8)

Fig. 1
Fig. 1 Temperature tuning curves of different deuterium content DKDP crystals. The black dots are experimental data and the solid red lines are fitted by sin2x/x2.
Fig. 2
Fig. 2 Deuterium content dependent TNCPM. The black dots are fitting data from temperature tuning curves, and the solid red lines are linear fit of the black dots.
Fig. 3
Fig. 3 Deuterium content tuning curve at 40°C. The black dots are experimental data and the solid red lines are fitted by sin2x/x2.
Fig. 4
Fig. 4 Calculated diagram of NCPM temperature in the 60-100% deuterium content range and 1050-1070 nm wavelength range.
Fig. 5
Fig. 5 Angle tuning curves of a 99% deuterium content DKDP crystal under different temperature. The color dots are experimental data.
Fig. 6
Fig. 6 Relationship of Tpm and Δθ in different deuterium content DKDP crystals. The black dots are experimental data and the solid red lines are fitted by a quadratic equation.
Fig. 7
Fig. 7 Angle tuning curve of different deuterium content DKDP crystals. The black dots are experimental data and the solid color lines are fitted by sin2x/x2.
Fig. 8
Fig. 8 Transimittance of different deuterium content DKDP crystals in 200-300 nm range.

Tables (4)

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Table 1 FWHM of the temperature tuning curve and βT for different deuterium content DKDP crystals.

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Table 2 A comparison between our calculation and the previously reported experimental results.

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Table 3 Comparison of indirectly calculated β θ ' and directly calculated β θ ' .

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Table 4 Transimittance at 266 nm and FHG conversion efficiency of different deuterated DKDP crystals.

Equations (18)

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I F H G sin 2 ( 1 / 2 Δ k L ) ( 1 / 2 Δ k L ) 2
Δ k = 4 π λ 1 [ n o ( λ 1 , T , X D ) n e ( λ 2 , T , X D ) ]
Δ k ( k X D ) λ , T ( X D X D 0 ) + ( k T ) λ , X D ( T T 0 ) + ( k λ ) T , X D ( λ λ 0 ) β X D ( X D X D 0 ) + β T ( T T 0 ) + β λ ( λ λ 0 )
β X D = 4 π λ 1 ( n o 1 X D n e 2 X D )
β T = 4 π λ 1 ( n o 1 T n e 2 T )
β λ = 4 π λ 1 ( n o 1 λ 1 2 n e 2 λ )
β T δ T + β X D δ X D = 0
β X D = β T ( d T d X D )
β λ = β T ( d T d λ )
β X D = 5.566 Δ X D L
β λ = 5.566 Δ λ L
β T = 5.566 Δ T L
Δ k = ( Δ k ( Δ θ ) ) δ ( Δ θ ) + 1 2 ( 2 Δ k ( Δ θ ) 2 ) δ ( Δ θ ) 2 + = β θ δ ( Δ θ ) + 1 2 β θ ' δ ( Δ θ ) 2 +
β T δ T + β θ δ Δ θ = 0
β θ = β T ( d T d ( Δ θ ) )
β θ ' = ( β θ ( Δ θ ) ) = ( β T ( Δ θ ) ) ( T ( Δ θ ) ) β T ( 2 T ( Δ θ ) 2 ) = β T ( 2 T ( Δ θ ) 2 )
Δ θ 22.26 β θ ' L
T p m = A ( Δ θ ) 2 + B ( Δ θ ) + C
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