import numpy as np  
from scipy.special import jv, yv # ベッセル関数
from scipy.special import jn_zeros, jnp_zeros, jnjnp_zeros, jnyn_zeros # ベッセル関数の零点
from scipy import optimize
import matplotlib.pyplot as plt
import pandas as pd

import scienceplots
#Warning : As of version 2.0.0, you need to add import scienceplots before setting the style (plt.style.use('science')).
plt.style.use(['science', 'notebook'])
# rcPramsを使ってTeXのフォントをデフォルトにする
#plt.rcParams['font.family'] = 'Times New Roman' # font familyの設定
plt.rcParams['font.family'] = 'serif' # font familyの設定
plt.rcParams['mathtext.fontset'] = 'cm' # math fontの設定
#plt.rcParams["font.size"] = 9
plt.rcParams['figure.figsize'] = [6, 5]

def uvector2(aa):
    norm = np.linalg.norm(aa, axis=1, keepdims=True)
    with np.errstate(divide="ignore", invalid="ignore"):
        uv = np.where(norm==0, np.zeros(aa.shape[1]), aa / norm)
    return norm, uv

def circular_waveguide_xi2(imode,m, n): # 特性方程式の根
    if imode == 1: # TE
        xi = jnp_zeros(m,n)
    elif imode == -1: # TM
        xi = jn_zeros(m,n)
    return xi[n-1]

def beta_alpha(sk, kc): # 位相定数，減衰定数
    beta, wl_g, alpha = 0.0, 0.0, 0.0
    kz2 = sk**2-kc**2
    beta = np.where(sk>kc, np.sqrt(kz2), 0.0)
    alpha = np.where(sk<=kc, np.sqrt(-kz2), 0.0)
    return beta, alpha

# imode = 1 (TE), -1 (TM)
# ic = 1(sin-mode), 2(cos-mode)
def circular_waveguide_mode(rho,phi, a,imode,m,n_xi,xi,ic): # 円形導波管のモード関数
    xia = xi/a
    if m==0:
        em = 1.0
        if imode==1:# TE
            ic = 2
        elif imode==-1:# TM
            ic = 1
    else:
        em = 2.0
    if imode==1:# TE
        besjmx = jv(m,xi)
        amn = np.sqrt(em/np.pi/(xi*xi-m*m)) / np.abs(besjmx)
    elif imode==-1:# TM
        besjmx = jv(m+1,xi)
        amn = np.sqrt(em/np.pi) /xi /np.abs(besjmx)
    phim = m*phi
    sp = np.sin(phim)
    cp = np.cos(phim)
    x = xia * rho
    besjmm = np.where(np.abs(rho)>a, 0.0, jv(m-1,x))
    besjmp = np.where(np.abs(rho)>a, 0.0, jv(m+1,x))
    bmn = amn*xi/2.0/a
    e_rho = (besjmm + imode*besjmp) * bmn
    e_phi = (-besjmm + imode*besjmp) * bmn
    if ic==1:
        e_rho = e_rho * cp
        e_phi = e_phi * sp
    elif ic==2:
        e_rho = e_rho * sp
        e_phi = -e_phi * cp
    h_rho = -e_phi
    h_phi = e_rho
    return e_rho, e_phi

def rhophi_xy(e_rho,e_phi, phi):
    sp = np.sin(phi)
    cp = np.cos(phi)
    e_x = e_rho*cp - e_phi*sp
    e_y = e_rho*sp + e_phi*cp
    return e_x, e_y

def rhophi_xy_eh(e_rho,e_phi, phi): # 
    sp = np.sin(phi)
    cp = np.cos(phi)
    e_x = e_rho*cp - e_phi*sp
    e_y = e_rho*sp + e_phi*cp
    h_x = -e_y
    h_y = e_x
    return e_x, e_y, h_x, h_y

def two_one_dim(aa):
    co_h = aa[::-1,n_phi//2]
    co_h = np.append(co_h, aa[:,0])
    co_e = aa[::-1,n_phi*3//4]
    co_e = np.append(co_e, aa[:,n_phi//4])
    co_45 = aa[::-1,n_phi*5//8]
    co_45 = np.append(co_45, aa[:,n_phi//8])
    with np.errstate(divide="ignore", invalid="ignore"):
        co_e_db = 20.0*np.log10(np.abs(co_e))
        co_h_db = 20.0*np.log10(np.abs(co_h))   
        co_45_db = 20.0*np.log10(np.abs(co_45))
    return co_e, co_h, co_45, co_e_db, co_h_db, co_45_db

n = 5
chi_TE = jnp_zeros(1,n) # TE-mode
chi_TE

array([ 1.84118378,  5.33144277,  8.53631637, 11.7060049 , 14.86358863])

chi_TM = jn_zeros(1,n) # TM-mode
chi_TM

array([ 3.83170597,  7.01558667, 10.17346814, 13.32369194, 16.47063005])

n2 = n*2
chi = np.empty(n2)
chi[0::2] = chi_TE[:]
chi[1::2] = chi_TM[:]
chi

array([ 1.84118378,  3.83170597,  5.33144277,  7.01558667,  8.53631637,
       10.17346814, 11.7060049 , 13.32369194, 14.86358863, 16.47063005])

mm = np.ones(n2, dtype=np.int8) # モードの次数 m
i = np.arange(n, dtype=np.int8)
nn = np.empty(n2, dtype=np.int8) # モードの次数 n
nn[0::2] = i[:]+1
nn[1::2] = i[:]+1
mode = np.empty(n2, dtype=object)
mode[0::2] = 'TE'
mode[1::2] = 'TM'
imode = np.empty(n2, dtype=np.int8)
imode[mode=='TE'] = 1
imode[mode=='TM'] = -1
mm, nn, mode, imode

(array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int8),
 array([1, 1, 2, 2, 3, 3, 4, 4, 5, 5], dtype=int8),
 array(['TE', 'TM', 'TE', 'TM', 'TE', 'TM', 'TE', 'TM', 'TE', 'TM'],
       dtype=object),
 array([ 1, -1,  1, -1,  1, -1,  1, -1,  1, -1], dtype=int8))

D = 23.4 # X-bandで用いられる円形導波管の直径
a = D/2 # 円形の半径 [mm]

k_c = chi/a # 遮断波数
k_c

array([0.15736614, 0.32749624, 0.45567887, 0.59962279, 0.72959969,
       0.86952719, 1.00051324, 1.13877709, 1.27039219, 1.40774616])

wl_c = 2*np.pi/k_c # 遮断波長
wl_c

array([39.92717557, 19.1855191 , 13.78862556, 10.47856317,  8.61182563,
        7.2259791 ,  6.27996218,  5.51748483,  4.94586267,  4.46329423])

CCC = 299.79
f_c = CCC/wl_c # 遮断周波数
f_c

array([ 7.50841991, 15.62584772, 21.74183342, 28.6098385 , 34.81143404,
       41.48780338, 47.73754862, 54.33454   , 60.61429932, 67.16787746])

print("a =",a,'[mm]')
print(f"{'No.':>7s}",f"{'mode':>7s}",f"{'chi':>10s}",f"{'k_c':>10s}",f"{'wl_c[mm]':>10s}",f"{'f_c[GHz]':>10s}")
for i in range(0,n2):
        print(f'{i+1:6d} {mode[i]:2s} {mm[i]:2d} {nn[i]:2d} {chi[i]:10.6f} {k_c[i]:10.6f} {wl_c[i]:10.6f} {f_c[i]:10.6f}')

a = 11.7 [mm]
    No.    mode        chi        k_c   wl_c[mm]   f_c[GHz]
     1 TE  1  1   1.841184   0.157366  39.927176   7.508420
     2 TM  1  1   3.831706   0.327496  19.185519  15.625848
     3 TE  1  2   5.331443   0.455679  13.788626  21.741833
     4 TM  1  2   7.015587   0.599623  10.478563  28.609838
     5 TE  1  3   8.536316   0.729600   8.611826  34.811434
     6 TM  1  3  10.173468   0.869527   7.225979  41.487803
     7 TE  1  4  11.706005   1.000513   6.279962  47.737549
     8 TM  1  4  13.323692   1.138777   5.517485  54.334540
     9 TE  1  5  14.863589   1.270392   4.945863  60.614299
    10 TM  1  5  16.470630   1.407746   4.463294  67.167877

data = {
    "No.": list(range(1, n2+1)),
    "mode": mode,
    "m": mm,
    "n": nn,
    "chi": chi,
    "k_c": k_c,
    "wL_c[mm]": wl_c,
    "f_c[GHz]": f_c
}

df = pd.DataFrame(data)
print(df)

   No. mode  m  n        chi       k_c   wL_c[mm]   f_c[GHz]
0    1   TE  1  1   1.841184  0.157366  39.927176   7.508420
1    2   TM  1  1   3.831706  0.327496  19.185519  15.625848
2    3   TE  1  2   5.331443  0.455679  13.788626  21.741833
3    4   TM  1  2   7.015587  0.599623  10.478563  28.609838
4    5   TE  1  3   8.536316  0.729600   8.611826  34.811434
5    6   TM  1  3  10.173468  0.869527   7.225979  41.487803
6    7   TE  1  4  11.706005  1.000513   6.279962  47.737549
7    8   TM  1  4  13.323692  1.138777   5.517485  54.334540
8    9   TE  1  5  14.863589  1.270392   4.945863  60.614299
9   10   TM  1  5  16.470630  1.407746   4.463294  67.167877

display(df)

f_stop = 50.0
nf = 31
fff = np.empty((n2,nf))
omega = np.empty((n2,nf))
beta_f = np.empty((n2,nf))
alpha_f = np.empty((n2,nf))
beta_f_norm = np.empty((n2,nf))
for i in range(n2):
    if f_stop <= f_c[i]:
        continue
    ff = np.array([f_c[i]+(f_stop-f_c[i])*(j/(nf-1))**4 for j in range(nf)])# リスト内包表記
    fff[i,:] = ff
    omega[i,:] = 2*np.pi*ff
    wwl = CCC/ff # 自由空間波長[mm]
    ssk = 2*np.pi/wwl # 自由空間波数
    tmp = ssk**2-k_c[i]**2
    beta_f[i,:] = np.sqrt(ssk**2-k_c[i]**2)
    beta_f_norm[i,:] = beta_f[i,:]/ssk
k_0 = np.linspace(0.0,1.0,101)
omega_0 = k_0*CCC

fig = plt.figure(figsize=(8, 6))
plt.text( 0.35, 10, f"$a=${a:.1f} mm", fontsize=16)
plt.grid(color = "gray", linestyle="--")
plt.minorticks_on() # 補助目盛りをつける
plt.xlabel(r"$\beta$") # x軸のラベル設定
plt.ylabel(r"$\omega$") # y軸のラベル設定
plt.xlim(0, 0.7) # y軸範囲の設定
plt.ylim(0, 200.0) # y軸範囲の設定
for i in range(4):
    plt.plot(beta_f[i,:], omega[i,:], label=rf"{mode[i]}$_{{{mm[i]}{nn[i]}}}$")
plt.plot(k_0, omega_0, '--', label='light')
plt.legend(ncol=1, loc='lower right', fancybox=False, frameon=True)
fig.savefig('p3_tlt_s13_1.pdf')
plt.show()

fig = plt.figure(figsize=(8, 6))
plt.text( 31.0, 0.9, f"$a=${a:.1f} mm", fontsize=16)
plt.grid(color = "gray", linestyle="--")
plt.minorticks_on() # #補助目盛りをつける
plt.xlabel(r"$f$ [GHz]") # x軸のラベル設定
plt.ylabel(r"$\beta/k_0$") # y軸のラベル設定
plt.xlim(5, 40.0) # y軸範囲の設定
plt.ylim(0, 1.0) # y軸範囲の設定
for i in range(5):
    plt.plot(fff[i,:], beta_f_norm[i,:], label=rf"{mode[i]}$_{{{mm[i]}{nn[i]}}}$")
plt.legend(ncol=1, loc='upper left', fancybox=False, frameon=True)
fig.savefig('p3_tlt_s13_2.pdf')
plt.show()

imode, m, n = 1, 1, 1
if imode==1:
    s_mode = 'TE_'+ str(m) +'_' + str(n)
    t_mode = 'TE '+ str(m) +',' + str(n)
else:
    s_mode = 'TM_'+ str(m) +'_' + str(n)
    t_mode = 'TM '+ str(m) +',' + str(n)
xi = circular_waveguide_xi2(imode, m, n)
s_mode, t_mode, xi

('TE_1_1', 'TE 1,1', 1.8411837813406595)

qq = 180.0/np.pi
rho_min, rho_max, n_rho = 0.001, 1.0, 61
phi_min, phi_max, n_phi = 0.0, 2.0*np.pi, 361
rho = np.linspace(rho_min, rho_max, n_rho)
phi = np.linspace(phi_min, phi_max, n_phi)
pphi, rrho = np.meshgrid(phi,rho, indexing='xy') # xy座標の並び (デフォルト)
#ic = 1# x-pol.
ic = 2# y-pol.
a = 1.0
e_rho, e_phi = circular_waveguide_mode(rrho,pphi, a,imode,m,n,xi,ic)
e_x, e_y, h_x, h_y = rhophi_xy_eh(e_rho,e_phi, pphi)
emax = np.array([e_x.max(), e_y.max(), e_rho.max(), e_phi.max()])
emaxx = emax.max()
e_x = e_x/emaxx
e_y = e_y/emaxx
e_rho = e_rho/emaxx
e_phi = e_phi/emaxx
e_x.max(), e_y.max(),a

(0.316027914617135, 1.0, 1.0)

Diverging_cmaps = ['PiYG', 'PRGn', 'BrBG', 'PuOr', 'RdGy', 'RdBu', 'RdYlBu',\
                   'RdYlGn', 'Spectral', 'coolwarm', 'bwr', 'seismic'] # 0-11

fig = plt.figure(figsize=(12, 8)) # グラフ領域の作成
v = np.linspace(-1.0, 1.0, 101)
mycolor1 = Diverging_cmaps[1]# *0（緑，ピンク），1（緑，紫）
mycolor2 = Diverging_cmaps[5]# *3（紫，茶）5, 8,10,11（赤，青）
irho, iphi = 1, 1
#irho, iphi = 0, 0
if irho == 1:
    ax = plt.subplot(2,2,1, polar=True)
    ax.set_rgrids([0.2, 0.4, 0.6, 0.8, 1], angle=325., fontname="Arial", fontsize=9)
    ax = plt.contour(pphi, rrho, e_rho, colors='gray', linewidths=0.4)# 等高線表示
    ax.clabel(fmt='%1.1f', inline=1, fontsize=9)# 等高線の値を表示
    ax = plt.contourf(pphi, rrho, e_rho, levels=v, cmap=mycolor1)
    ax = plt.colorbar(pad=0.1, shrink=1.0, orientation="vertical")
    ax.set_label(r"Relative amplitude $e_\rho$", fontname="Arial", fontsize=9)

if iphi == 1:
    ax = plt.subplot(2,2,2, polar=True)
    ax.set_rgrids([0.2, 0.4, 0.6, 0.8, 1], angle=325., fontname="Arial", fontsize=9)
    ax = plt.contour(pphi, rrho, e_phi, colors='gray', linewidths=0.4)# 等高線表示
    ax.clabel(fmt='%1.1f', inline=1, fontsize=9)# 等高線の値を表示
    ax = plt.contourf(pphi, rrho, e_phi, levels=v, cmap=mycolor1)
    ax = plt.colorbar(pad=0.1, shrink=1.0, orientation="vertical")
    ax.set_label(r"Relative amplitude $e_\phi$", fontname="Arial", fontsize=9)

if irho == 0 and iphi ==0:
    ax = plt.subplot(1,2,1, polar=True)
else:
    ax = plt.subplot(2,2,3, polar=True)
ax.set_rgrids([0.2, 0.4, 0.6, 0.8, 1], angle=325., fontname="Arial", fontsize=9)
ax = plt.contour(pphi, rrho, e_x, colors='gray', linewidths=0.4)# 等高線表示
ax.clabel(fmt='%1.1f', inline=1, fontsize=9)# 等高線の値を表示
ax = plt.contourf(pphi, rrho, e_x, levels=v, cmap=mycolor2)
if irho == 0 and iphi ==0:
    ax = plt.colorbar(pad=0.1, shrink=1.0, orientation="horizontal") 
else:
    ax = plt.colorbar(pad=0.1, shrink=1.0, orientation="vertical")
ax.set_label(r"Relative amplitude $e_x$", fontname="Arial", fontsize=9)

if irho == 0 and iphi ==0:
    ax = plt.subplot(1,2,2, polar=True)
else:
    ax = plt.subplot(2,2,4, polar=True)
ax.set_rgrids([0.2, 0.4, 0.6, 0.8, 1], angle=325., fontname="Arial", fontsize=9)
ax = plt.contour(pphi, rrho, e_y, colors='gray', linewidths=0.4)# 等高線表示
ax.clabel(fmt='%1.1f', inline=1, fontsize=9)# 等高線の値を表示
ax = plt.contourf(pphi, rrho, e_y, levels=v, cmap=mycolor2)
if irho == 0 and iphi ==0:
    ax = plt.colorbar(pad=0.1, shrink=1.0, orientation="horizontal") 
else:
    ax = plt.colorbar(pad=0.1, shrink=1.0, orientation="vertical")
ax.set_label(r"Relative amplitude $e_y$", fontname="Arial", fontsize=9)

plt.tight_layout()
fig.savefig('p3_tlt_s13_3_'+s_mode+'.pdf')
plt.show()

fig, ax = plt.subplots(1,2,figsize=(12, 4)) # グラフ領域の作成
for axi in ax:   # 直交 Axes を削除
    axi.remove()
v = np.linspace(-1.0, 1.0, 101)
mycolor1 = Diverging_cmaps[1]# *0（緑，ピンク），1（緑，紫）
mycolor2 = Diverging_cmaps[5]# *3（紫，茶）5, 8,10,11（赤，青）
ax[0] = plt.subplot(1,2,1, polar=True)
CS1 = ax[0].contour(pphi, rrho, h_x, colors='gray', linewidths=0.4)# 等高線表示
ax[0].clabel(CS1, fmt='%1.1f', inline=1, fontsize=9)# 等高線の値を表示
CS2 = ax[0].contourf(pphi, rrho, h_x, levels=v, cmap=mycolor2)
#ax = fig.colorbar(CS2, ax=ax[0], pad=0.1, shrink=1.0, orientation="horizontal") 
cbar = fig.colorbar(CS2, ax=ax[0], pad=0.1, shrink=1.0, orientation="vertical")
cbar.set_label(r"Relative amplitude $h_x$", fontname="Arial", fontsize=12)
ax[1] = plt.subplot(1,2,2, polar=True)
CS3 = ax[1].contour(pphi, rrho, h_y, colors='gray', linewidths=0.4)# 等高線表示
ax[1].clabel(CS3, fmt='%1.1f', inline=1, fontsize=9)# 等高線の値を表示
CS4 = ax[1].contourf(pphi, rrho, h_y, levels=v, cmap=mycolor2)
#ax = fig.colorbar(CS4, ax=ax[1], pad=0.1, shrink=1.0, orientation="horizontal") 
cbar = fig.colorbar(CS4, ax=ax[1], pad=0.1, shrink=1.0, orientation="vertical")
cbar.set_label(r"Relative amplitude $h_y$", fontname="Arial", fontsize=12)
[i.set_rgrids([0.2, 0.4, 0.6, 0.8, 1], angle=325., fontname="Arial", fontsize=9) for i in ax]
fig.tight_layout()
fig.savefig('p3_tlt_s13_5_'+s_mode+'.pdf')
plt.show()

rho2 = -rho[::-1]
rho2 = np.append(rho2, rho)
co_e, co_h, co_45, co_e_db, co_h_db, co_45_db = two_one_dim(e_x)
xx_e, xx_h, xx_45, xx_e_db, xx_h_db, xx_45_db = two_one_dim(e_y)

fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(12, 4)) # グラフ領域の作成，nrows=縦に並べる数，ncols=横に並べる数

ax[0].set_title("$E_x$ ("+t_mode+")")
ax[0].set_xlabel(r"Normalized radius $\rho/a$", fontsize=12) # x軸のラベル設定
[ax[j].set_ylim(-40.0, 10.0) for j in range(2)]
[ax[j].set_ylabel("Relative amplitude [dB]", fontsize=12) for j in range(2)]
ax[0].plot(rho2, co_e_db, label="E-plane")
ax[0].plot(rho2, co_h_db, label="H-plane")
ax[0].plot(rho2, co_45_db, label="45-plane")

ax[1].set_title("$E_y$ ("+t_mode+")")
ax[1].set_xlabel(r"Normalized radius $\rho/a$", fontsize=12) # x軸のラベル設定
ax[1].plot(rho2, xx_e_db, label="E-plane")
ax[1].plot(rho2, xx_h_db, label="H-plane")
ax[1].plot(rho2, xx_45_db, label="45-plane")

[ax[j].grid(color = "gray", linestyle="--") for j in range(2)]
[ax[j].minorticks_on() for j in range(2)]
[ax[j].set_xlim(-1.0, 1.0) for j in range(2)]
[ax[j].set_xlabel(r"Normalized radius $\rho/a$", fontsize=12) for j in range(2)]
[ax[j].legend(ncol=1, loc='lower right', fancybox=False, frameon = True, fontsize=12) for j in range(2)]

fig.tight_layout()
fig.savefig('p3_tlt_s13_7_'+s_mode+'.pdf')
plt.show()

# 直角座標系(x,y)
x_min, x_max, n_x = -1.0, 1.0, 101
y_min, y_max, n_y = -1.0, 1.0, 101
x = np.linspace(x_min, x_max, n_x)
y = np.linspace(y_min, y_max, n_y)
xx, yy = np.meshgrid(x,y, indexing='xy')# xy座標の並び (デフォルト）
rrrho = np.sqrt(xx**2+yy**2)
ppphi = np.arctan2(yy,xx)
e_rho, e_phi = circular_waveguide_mode(rrrho,ppphi, a,imode,m,n,xi,ic)
e_x, e_y = rhophi_xy(e_rho,e_phi, ppphi)
emax = np.array([e_x.max(), e_y.max(), e_rho.max(), e_phi.max()])
emaxx = emax.max()
e_x = e_x/emaxx
e_y = e_y/emaxx
x_c, y_c = np.cos(phi), np.sin(phi)

fig = plt.figure(figsize=(7, 7)) # グラフ領域の作成
v = np.linspace(0.0, 1.0, 21)
plt.title(t_mode)
e_amp = np.sqrt(e_x**2+e_y**2)
lw = 3.5*e_amp / e_amp.max()
plt.streamplot(xx, yy, e_x, e_y, color='orange', density=0.6, linewidth=lw,
               arrowsize=1.2,  # 矢印サイズ
               broken_streamlines=False)  # 線の切断を防ぐ
plt.contourf(x, y, e_amp, levels=v, cmap="Blues")# YlOrRd, OrRd
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.axis('scaled')
plt.colorbar(pad=0.1, shrink=0.77, orientation="vertical")
plt.plot(x_c, y_c, 'grey')

fig.tight_layout()
fig.savefig('p3_tlt_s13_9_'+s_mode+'.pdf')
plt.show()

円形導波管¶

モジュールのインポート¶

図のフォーマットの一括設定¶

単位ベクトルの計算（ユーザ関数）¶

円形導波管モードに対する特性方程式の根の計算（ユーザ関数）¶

円形導波管の伝搬モードの位相定数，遮断モードの減衰定数の計算（ユーザ関数）¶

円形導波管のモード関数（電界および磁界の$x$成分，$y$成分）の計算（ユーザ関数）¶

位置ベクトルの極座標$(\rho, \phi)$から直角座標$(x,y)$への変換（ユーザ関数）¶

電界のモード関数の極座標成分$e_\rho$, $e_\phi$から電界の直角座標成分$e_x$，$e_y$，磁界の直角座標成分$h_x$，$h_y$への変換（ユーザ関数）¶

2次元データからカット面データの切り取り（ユーザ関数）¶

TE-mode¶

TM-mode¶

円形導波管の断面寸法¶

遮断波数¶

遮断波長¶

遮断周波数¶

データを辞書としてまとめると，¶

pandasのDataFrameに変換¶

分散特性の計算¶

分散ダイアグラム(dispersion diagram)：$\beta$-$\omega$の関係¶

分散特性（dispersion characteristic）：正規化した位相定数 $\beta/k_0$ の周波数特性¶

モードの設定¶

モード関数の計算¶

カラーマップ名をリストに設定¶

電界のモード関数の極座標成分 $e_\rho$，$e_\phi$，電界の直角座標成分 $e_x$，$e_y$ のプロット¶

磁界の直角座標成分 $h_x$，$h_y$ のプロット¶

2次元データからカット面の1次元データ（0$^\circ$，45$^\circ$，90$^\circ$面）の切り取り¶

カット面での電界の直角座標成分 $e_x$，$e_y$ のデシベル値のプロット¶

電界のモード関数より電気力線と等高線図を重ねて描くと，¶

	No.	mode	m	n	chi	k_c	wL_c[mm]	f_c[GHz]
0	1	TE	1	1	1.841184	0.157366	39.927176	7.508420
1	2	TM	1	1	3.831706	0.327496	19.185519	15.625848
2	3	TE	1	2	5.331443	0.455679	13.788626	21.741833
3	4	TM	1	2	7.015587	0.599623	10.478563	28.609838
4	5	TE	1	3	8.536316	0.729600	8.611826	34.811434
5	6	TM	1	3	10.173468	0.869527	7.225979	41.487803
6	7	TE	1	4	11.706005	1.000513	6.279962	47.737549
7	8	TM	1	4	13.323692	1.138777	5.517485	54.334540
8	9	TE	1	5	14.863589	1.270392	4.945863	60.614299
9	10	TM	1	5	16.470630	1.407746	4.463294	67.167877