diff --git a/Matlab/Forces_Ashkin_Axial.m b/Matlab/Forces_Ashkin_Axial.m
new file mode 100644
index 0000000..3e1bf21
--- /dev/null
+++ b/Matlab/Forces_Ashkin_Axial.m
@@ -0,0 +1,112 @@
+%all distances in m
+clear
+close all
+clc
+format compact
+
+% These calculations are based on Ashkin's article "Forces of a single-beam
+% gradient laser trap on a dielectric sphere in the ray optics regime".
+% There are axial forces only
+
+n1 = 1.33; % index of refraction of the immersion medium
+n2 = 1.6; % index of refraction of the fused silica at wavelength 523 nm
+n = n2/n1; % n2/n1
+c0 = 3e8; % speed of light
+NA = 1.25; % numerical aperture
+th_max = asin(NA/n1); % maximum angle of incidence
+f = 100.0e-3; % objective lens focus or WD
+r_max = f*tan(th_max); % radius of a Gaussian beam (1:1 with input aperture condition)
+Rsp = 1.0e-6; % sphere radius
+P = 20.0e-3; % power of the laser
+
+thr = @(th) asin(n1/n2*sin(th)); % refraction angle
+
+%reflectivity
+R = @(th,psi) (tan(th-thr(th)).^2./tan(th+thr(th)).^2).*cos(psi).^2+...
+    (sin(th-thr(th)).^2./sin(th+thr(th)).^2).*sin(psi).^2;
+
+%transparency
+T = @(th,psi) 1-R(th,psi);
+
+% Factors
+Qs = @(th, psi) 1 + R(th, psi) .* cos(2*th) - T(th,psi).^2 .* (cos(2*th -...
+    2*thr(th)) + R(th, psi) .* cos(2*th)) ./ (1 + R(th,psi).^2 +...
+    2*R(th,psi) .* cos(2*thr(th)));
+
+Qg = @(th, psi) R(th, psi) .* sin(2*th) - T(th,psi).^2 .* (sin(2*th -...
+    2*thr(th)) + R(th, psi) .* sin(2*th)) ./ (1 + R(th,psi).^2 +...
+    2*R(th,psi) .* cos(2*thr(th)));
+
+Qmag = @(th, psi) sqrt(Qs(th, psi).^2 + Qg(th, psi).^2);
+
+% Average factors (circular polarization
+Qs_avg = @(th) 0.5*(Qs(th, 0) + Qs(th, pi/2));
+Qg_avg = @(th) 0.5*(Qg(th, 0) + Qg(th, pi/2));
+Qmag_avg = @(th) sqrt(Qs_avg(th).^2 + Qg_avg(th).^2);
+
+% Angles
+phi = @(r) atan(r/f); 
+thi = @(r,z) asin(z/Rsp.*sin(phi(r))); 
+
+Qgz = @(r,z) -Qg_avg(thi(r,z)).*sin(phi(r));
+Qsz = @(r,z) Qs_avg(thi(r,z)).*cos(phi(r));
+
+% Intensity profile
+a = 1.0;
+w0 = a*r_max;
+
+%I = @(r) P/(pi*r_max^2); % uniform distribution
+
+A = (1-exp(-2*r_max.^2/w0^2));
+I0 = P*2/(pi*w0^2)/A;
+I = @(r) I0*exp(-2*r.^2/w0^2); % Gaussian TEM00 beam
+
+%A = 2*pi*integral(@(r) r.*besselj(0,2.405/w0*r).^2,0,r_max)/P0;
+%w0_bb = 0.5*r_max;
+%I0 = P*2/(pi*w0^2);
+%I = @(r) I0*besselj(0,2.405/w0_bb*r).^2.*exp(-2*r.^2/w0^2); % Bessel beam
+
+% Intensity profile graphics
+rho = linspace(-r_max, r_max, 500);
+figure
+plot(rho, I(rho)/max(I(rho)),'k')
+grid
+xlabel('r, ì')
+ylabel('I(r)')
+sdf('my')
+
+% Integration
+Qres_g = @(z) 1/(pi*r_max^2)*2/(A*pi*w0^2)*integral2(@(beta,r) r.*I(r).*...
+    iscomplex(Qgz(r,z)),0,2*pi,0,r_max,...
+    'Method','iterated','AbsTol',1e-12,'RelTol',1e-6);
+
+Qres_s = @(z) 1/(pi*r_max^2)*2/(A*pi*w0^2)*integral2(@(beta,r) r.*I(r).*...
+    iscomplex(Qsz(r,z)),0,2*pi,0,r_max,...
+    'Method','iterated','AbsTol',1e-12,'RelTol',1e-6);
+
+% Calulation
+N = 200;
+z = linspace(-2*Rsp,2*Rsp,N);
+Axial_g = zeros(1,N);
+Axial_s = zeros(1,N);
+
+for ii = 1:N
+    Axial_g(ii) = Qres_g(z(ii));
+    Axial_s(ii) = Qres_s(z(ii));
+end
+
+F0 = n1*P/c0; % net force
+
+Axial_g = fliplr(Axial_g);
+Axial_s = fliplr(Axial_s);
+Axial = Axial_g + Axial_s;
+z = -fliplr(z);
+
+%Graphics
+figure
+plot(z,F0*Axial_g,'b-.',z,F0*Axial_s,'r--',z,F0*Axial,'k')
+legend('F_{g}','F_{s}','F_{t}')
+xlabel('r, ì')
+ylabel('F, Í')
+grid
+sdf('my')
\ No newline at end of file
diff --git a/Matlab/Forces_Ashkin_Ray_Efficiencies.m b/Matlab/Forces_Ashkin_Ray_Efficiencies.m
new file mode 100644
index 0000000..58300c5
--- /dev/null
+++ b/Matlab/Forces_Ashkin_Ray_Efficiencies.m
@@ -0,0 +1,48 @@
+close all
+clear
+format compact
+clc
+
+% These calculations are based on Ashkin's article "Forces of a single-beam
+% gradient laser trap on a dielectric sphere in the ray optics regime
+
+%all distances in mm
+a = 1.0e-6; % radius of the bead
+n1 = 1.0; % index of rafraction of the medium
+n = 1.4607; % n2/n1
+n2 = n*n1; % index of refraction of the fused silica
+c0 = 3e8; % speed of light
+
+%reflectivity
+R = @(th,psi) (tan(th-asin(n1/n2*sin(th))).^2./...
+    tan(th+asin(n1/n2*sin(th))).^2).*cos(psi).^2+...
+    (sin(th-asin(n1/n2*sin(th))).^2./...
+    sin(th+asin(n1/n2*sin(th))).^2).*sin(psi).^2;
+
+%transparency
+T = @(th,psi) 1-R(th,psi);
+
+r = @(th) asin(n1/n2*sin(th));
+
+% Factors
+Qs = @(th, psi) 1 + R(th, psi) .* cos(2*th) - T(th,psi).^2 .* (cos(2*th -...
+    2*r(th)) + R(th, psi) .* cos(2*th)) ./ (1 + R(th,psi).^2 +...
+    2*R(th,psi) .* cos(2*r(th)));
+
+Qg = @(th, psi) R(th, psi) .* sin(2*th) - T(th,psi).^2 .* (sin(2*th -...
+    2*r(th)) + R(th, psi) .* sin(2*th)) ./ (1 + R(th,psi).^2 +...
+    2*R(th,psi) .* cos(2*r(th)));
+
+Qmag = @(th, psi) sqrt(Qs(th, psi).^2 + Qg(th, psi).^2);
+
+t = linspace(0, pi/2, 1000);
+t_deg = t*180/pi;
+pol = pi/4;
+
+figure
+plot(t_deg, Qs(t, pol),'r--', t_deg, -Qg(t, pol),'b-.', t_deg, Qmag(t, pol),'k');
+grid
+xlabel('\theta, deg')
+ylabel('Q')
+legend('Q_s','Q_g','Q_t','location','northwest')
+sdf('my')
\ No newline at end of file
diff --git a/Matlab/Forces_Ashkin_Transverse.m b/Matlab/Forces_Ashkin_Transverse.m
new file mode 100644
index 0000000..d5ac37b
--- /dev/null
+++ b/Matlab/Forces_Ashkin_Transverse.m
@@ -0,0 +1,106 @@
+%all distances in m
+close all
+clear
+clc
+format compact
+
+% These calculations are based on Ashkin's article "Forces of a single-beam
+% gradient laser trap on a dielectric sphere in the ray optics regime".
+% There are transverse forces only
+
+n1 = 1.33; % index of refraction of the immersion medium
+n2 = 1.6; % index of refraction of the fused silica at wavelength 523 nm
+n = n2/n1; % n2/n1
+c0 = 3e8; % speed of light
+NA = 1.25; % numerical aperture
+th_max = asin(NA/n1); % maximum angle of incidence
+f = 100.0e-3; % objective lens focus or WD
+r_max = f*tan(th_max); % radius of a Gaussian beam (1:1 with input aperture condition)
+Rsp = 1.0e-6; % sphere radius
+P = 20.0e-3; % power of the laser
+
+thr = @(th) asin(n1/n2*sin(th)); % refraction angle
+
+%reflectivity
+R = @(th,psi) (tan(th-thr(th)).^2./tan(th+thr(th)).^2).*cos(psi).^2+...
+    (sin(th-thr(th)).^2./sin(th+thr(th)).^2).*sin(psi).^2;
+
+%transparency
+T = @(th,psi) 1-R(th,psi);
+
+% Factors
+Qs = @(th, psi) 1 + R(th, psi) .* cos(2*th) - T(th,psi).^2 .* (cos(2*th -...
+    2*thr(th)) + R(th, psi) .* cos(2*th)) ./ (1 + R(th,psi).^2 +...
+    2*R(th,psi) .* cos(2*thr(th)));
+
+Qg = @(th, psi) R(th, psi) .* sin(2*th) - T(th,psi).^2 .* (sin(2*th -...
+    2*thr(th)) + R(th, psi) .* sin(2*th)) ./ (1 + R(th,psi).^2 +...
+    2*R(th,psi) .* cos(2*thr(th)));
+
+% Average factors (circular polarization
+Qs_avg = @(th) 0.5*(Qs(th, 0) + Qs(th, pi/2));
+Qg_avg = @(th) 0.5*(Qg(th, 0) + Qg(th, pi/2));
+
+% Angles
+phi = @(r) atan(r/f);
+gamma = @(beta,r) acos(cos(pi/2-phi(r)).*cos(beta));
+thi = @(beta,r,y) asin(y/Rsp.*sin(gamma(beta,r))); 
+
+Qgy = @(beta,r,y) Qg_avg(thi(beta,r,y)).*cos(phi(r));
+Qsy = @(beta,r,y) Qs_avg(thi(beta,r,y)).*sin(gamma(beta,r));
+
+% Intensity profile
+a = 1.0;
+w0 = a*r_max;
+
+%I = @(r) P/(pi*r_max^2); % uniform distribution
+
+A = (1-exp(-2*r_max.^2/w0^2));
+I0 = 2*P/(pi*w0^2)*A;
+I = @(r) I0*exp(-2*r.^2/w0^2); % Gaussian TEM00 beam
+
+%P0 = exp(0.5)*w0*0.0025/4.81;
+%A = 2*pi*integral(@(r) r.*besselj(0,2.405/w0*r).^2,0,r_max)/P0;
+%I = @(r) 1/(A*P0)*besselj(0,2.405/w0*r).^2; % Bessel beam
+
+% Intensity profile graphics
+rho = linspace(-r_max, r_max, 500);
+figure
+plot(rho, I(rho)/max(I(rho)),'k')
+grid
+xlabel('r, m')
+ylabel('I(r)')
+sdf('my')
+
+% Integration
+Qres_g = @(y) 1/(pi*r_max^2)*integral2(@(beta,r) r.*I(r).*...
+    iscomplex(Qgy(beta,r,y)),0,2*pi,0,r_max,...
+    'Method','iterated','AbsTol',1e-6,'RelTol',1e-6);
+
+Qres_s = @(y) 1/(pi*r_max^2)*integral2(@(beta,r) r.*I(r).*...
+    iscomplex(Qsy(beta,r,y)),0,2*pi,0,r_max,...
+    'Method','iterated','AbsTol',1e-6,'RelTol',1e-6);
+
+% Calulation
+N = 150;
+y = linspace(-2*Rsp,2*Rsp,N);
+Transverse_g = zeros(1,N);
+Transverse_s = zeros(1,N);
+
+for ii = 1:N
+    Transverse_g(ii) = abs(Qres_g(y(ii)));
+    Transverse_s(ii) = Qres_s(y(ii));
+end
+
+Transverse = abs(Transverse_g) + Transverse_s;
+
+F0 = n1*P/c0; % net force;
+
+%Graphics
+figure
+plot(y,F0*Transverse_g,'r--',y,F0*Transverse_s,'b-.',y,F0*Transverse,'k')
+legend('F_{g}','F_{s}','F_{t}')
+xlabel('r, ì')
+ylabel('F, Í')
+grid
+sdf('my')
diff --git a/Matlab/iscomplex.m b/Matlab/iscomplex.m
new file mode 100644
index 0000000..152359f
--- /dev/null
+++ b/Matlab/iscomplex.m
@@ -0,0 +1,11 @@
+function S = iscomplex(A)
+[n,m] = size(A);
+S = zeros(n,m);
+
+for ii = 1:n
+    for jj = 1:m
+        S(ii,jj) = A(ii,jj)*double(isreal(A(ii,jj)));
+    end
+end
+
+end
\ No newline at end of file
diff --git a/Matlab/sdf.m b/Matlab/sdf.m
new file mode 100644
index 0000000..d7ada13
--- /dev/null
+++ b/Matlab/sdf.m
@@ -0,0 +1,85 @@
+function sdf(varargin)
+% SDF Set the line width and fonts of a figure
+% 
+% sdf(fig)
+% 
+% where fig is the figure number. If the figure number is omitted, the 
+% currently active figure is updated. Edit the file to set you own style 
+% settings.
+%
+% sdf(fig, 'stylename')
+% applies a pre-configured style from the File-->Export Setup menu of the
+% figure's window. The stylename should be one of the 'Export Styles'
+% section of the dialog.
+%
+% The function allows applying the same settings as through the 
+% File-->Export Setup-->Apply menu of the figure, but much faster and 
+% without the annoying clicking. 
+%
+% Example
+%   figure(1);      t=0:0.1:10;   plot(t, sin(t));
+%   sdf(1)
+%   pause
+%   sdf(1,'PowerPoint')
+
+% Andrey Popov, Hamburg, 2009
+
+%% Parse the input data
+default = true;
+if nargin == 0       % no input - take current fig and apply default style
+    fig = gcf();
+else                 % at least 1 input
+    if ischar(varargin{1})  % style name
+        default = false;
+        style_name = varargin{1};
+        fig = gcf();
+    else
+        fig = varargin{1};
+        figure(fig);        % just in case it does not exist
+        if nargin == 2
+            default = false;
+            style_name = varargin{2};
+        end
+    end
+end
+
+%% Apply a style
+if default      % Apply a default style
+    style = struct();
+    style.Version = '1';
+    style.Format = 'eps';
+    style.Preview = 'none';
+    style.Width = 'auto';
+    style.Height = 'auto';
+    style.Units = 'centimeters';
+    style.Color = 'rgb';
+    style.Background = 'w';          % '' = no change; 'w' = white background
+    style.FixedFontSize = '10';
+    style.ScaledFontSize = 'auto';
+    style.FontMode = 'fixed';
+    style.FontSizeMin = '8';
+    style.FixedLineWidth = '2';
+    style.ScaledLineWidth = 'auto';
+    style.LineMode = 'fixed';
+    style.LineWidthMin = '0.5';
+    style.FontName = 'auto';
+    style.FontWeight = 'auto';
+    style.FontAngle = 'auto';
+    style.FontEncoding = 'latin1';
+    style.PSLevel = '2';
+    style.Renderer = 'auto';
+    style.Resolution = 'auto';
+    style.LineStyleMap = 'none';
+    style.ApplyStyle = '0';
+    style.Bounds = 'loose';
+    style.LockAxes = 'on';
+    style.ShowUI = 'on';
+    style.SeparateText = 'off';
+
+    hgexport(fig,'temp_dummy',style,'applystyle', true);
+
+else    % Apply an existing style, defined as in the Export dialog
+    % The files are in folder   fullfile(prefdir(0),'ExportSetup');
+    style = hgexport('readstyle',style_name);
+    hgexport(fig,'temp_dummy',style,'applystyle', true);
+end
diff --git a/Python/trap_forces_axial.py b/Python/trap_forces_axial.py
new file mode 100644
index 0000000..20b0542
--- /dev/null
+++ b/Python/trap_forces_axial.py
@@ -0,0 +1,152 @@
+# These calculations are based on Ashkin's article "Forces of a single-beam
+# gradient laser trap on a dielectric sphere in the ray optics regime".
+# There are axial forces only
+
+import numpy as np
+import matplotlib.pyplot as plt
+import seaborn as sns
+from scipy import integrate
+from scipy import special
+from scipy import constants
+
+n1 = 1.3337  # index of refraction of the immersion medium
+n2 = 1.4607 # index of refraction of the fused silica at wavelength 523 nm
+n = n2 / n1 # n2/n1
+NA = 1.25  # numerical aperture
+th_max = np.arcsin(NA / n1)  # maximum angle of incidence
+f = 2.0e-3  # objective lens focus or WD
+r_max = f * np.tan(th_max)  # radius of a Gaussian beam (1:1 with input aperture condition)
+Rsp = 1.03e-6  # sphere radius
+P = 4.4e-3  # power of the laser
+
+
+# angle of refraction
+def r(th):
+    return np.arcsin(n1 / n2 * np.sin(th))
+
+
+# Fresnel reflectivity
+def r_f(th, psi):
+    return (np.tan(th - r(th)) ** 2 / np.tan(th + r(th)) ** 2) * np.cos(psi) ** 2 + \
+           (np.sin(th - r(th)) ** 2 / np.sin(th + r(th)) ** 2) * np.sin(psi) ** 2
+
+
+# Fresnel transparency
+def t_f(th, psi):
+    return 1 - r_f(th, psi)
+
+
+# force factors
+def q_s(th, psi):
+    return 1 + r_f(th, psi) * np.cos(2 * th) - t_f(th, psi) ** 2 * \
+           (np.cos(2 * th - 2 * r(th)) + r_f(th, psi) * np.cos(2*th)) / \
+           (1 + r_f(th, psi) ** 2 + 2 * r_f(th, psi) * np.cos(2*r(th)))
+
+
+def q_g(th, psi):
+    return r_f(th, psi) * np.sin(2 * th) - t_f(th, psi) ** 2 * \
+           (np.sin(2 * th - 2 * r(th)) + r_f(th, psi) * np.sin(2 * th)) / \
+           (1 + r_f(th, psi) ** 2 + 2 * r_f(th, psi) * np.cos(2 * r(th)))
+
+
+def q_mag(th, psi):
+    return np.sqrt(q_s(th, psi) ** 2 + q_g(th, psi) ** 2)
+
+
+# Average factors (circular polarization
+def q_s_avg(th):
+    return 0.5 * (q_s(th, 0) + q_s(th, np.pi/2))
+
+
+def q_g_avg(th):
+    return 0.5 * (q_g(th, 0) + q_g(th, np.pi/2))
+
+
+def q_mag_avg(th):
+    return np.sqrt(q_s_avg(th) ** 2 + q_g_avg(th) ** 2)
+
+
+# Angles
+def phi(dr):
+    return np.arctan(dr / f)
+
+
+def thi(dr, dz):
+    return np.arcsin(dz / Rsp * np.sin(phi(dr)), dtype=np.cfloat)
+
+
+def q_g_z(dr, dz):
+    return -q_g_avg(thi(dr, dz)) * np.sin(phi(dr))
+
+
+def q_s_z(dr, dz):
+    return q_s_avg(thi(dr, dz)) * np.cos(phi(dr))
+
+
+# Intensity profile
+a = 1.0
+w0 = a * r_max
+
+
+def intensity_uniform():
+    return P / (np.pi * r_max ** 2)
+
+
+def intensity_gaussian_tem00(dr):
+    i_0 = P * 2 / (np.pi*w0 ** 2)
+    return i_0 * np.exp(-2 * dr ** 2 / w0 ** 2)
+
+
+def intensity_bessel(dr):
+    w0_bb = 0.5 * r_max
+    i_0 = P * 2 / (np.pi * w0 ** 2)
+    return i_0 * special.jv(0, 2.405 / w0_bb * dr) ** 2 * np.exp(- 2 * dr ** 2 / w0 ** 2)
+
+
+# Intensity profile graphics
+sns.set()
+sns.set_style("darkgrid")
+
+rho = np.linspace(-r_max, r_max, 500)
+fig1 = plt.figure(1, figsize=(10, 6))
+plt.plot(rho, intensity_gaussian_tem00(rho), 'k')
+plt.xlabel('r, m', fontsize=18)
+plt.ylabel('I(r)', fontsize=18)
+
+
+# Integration
+def q_res_g(dz, func):
+    ans = integrate.quad(lambda x: x * func(x) * q_g_z(x, dz) * (~np.iscomplex(q_g_z(x, dz))).astype(float),
+                               0, r_max, epsabs=1e-12, epsrel=1e-6)
+    return 2 * np.pi * ans[0]
+
+
+def q_res_s(dz, func):
+    ans = integrate.quad(lambda x: x * func(x) * q_s_z(x, dz) * (~np.iscomplex(q_s_z(x, dz))).astype(float),
+                               0, r_max, epsabs=1e-12, epsrel=1e-6)
+    return 2 * np.pi * ans[0]
+
+
+# Calculation
+n = 200
+z = np.linspace(-2 * Rsp, 2 * Rsp, n)
+
+axial_g = [q_res_g(x, intensity_gaussian_tem00) for x in z]
+axial_s = [q_res_s(x, intensity_gaussian_tem00) for x in z]
+
+f_0 = n1 * P / constants.c  # net force
+
+axial_g = np.array(axial_g[::-1])
+axial_s = np.array(axial_s[::-1])
+axial = axial_g + axial_s
+z = -z[::-1]
+
+# Graphics
+fig2 = plt.figure(2, figsize=(10, 6))
+plt.plot(z, f_0*axial_g, 'b-.', lw=1, label='$F_{g}$')
+plt.plot(z, f_0*axial_s, 'r--', lw=1, label='$F_{s}$')
+plt.plot(z, f_0*axial, 'k', lw=1, label='$F_{t}$')
+plt.xlabel('r, m', fontsize=18)
+plt.ylabel('F, N', fontsize=18)
+plt.legend(fontsize=18)
+plt.show()
diff --git a/Python/trap_forces_efficiencies.py b/Python/trap_forces_efficiencies.py
new file mode 100644
index 0000000..0d5d521
--- /dev/null
+++ b/Python/trap_forces_efficiencies.py
@@ -0,0 +1,65 @@
+# These calculations are based on Ashkin's article "Forces of a single-beam
+# gradient laser trap on a dielectric sphere in the ray optics regime
+
+# all distances in mm
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+a = 1.0 * 1e-6  # radius of the bead
+n1 = 1.33  # index of refraction of the medium
+n = 1.8  # n2/n1
+n2 = n * n1  # index of refraction of the fused silica
+c0 = 3 * 1e8  # speed of light
+
+
+# Fresnel reflectivity
+def r_f(th, psi):
+    return (np.tan(th - np.arcsin(n1 / n2 * np.sin(th))) ** 2 /
+            np.tan(th + np.arcsin(n1 / n2 * np.sin(th))) ** 2) * np.cos(psi) ** 2 + \
+           (np.sin(th - np.arcsin(n1 / n2 * np.sin(th))) ** 2 /
+            np.sin(th + np.arcsin(n1 / n2 * np.sin(th))) ** 2) * np.sin(psi) ** 2
+
+
+# Fresnel transparency
+def t_f(th, psi):
+    return 1 - r_f(th, psi)
+
+
+# angle of refraction
+def r(th):
+    return np.arcsin(n1 / n2 * np.sin(th))
+
+
+# force factors
+def q_s(th, psi):
+    return 1 + r_f(th, psi) * np.cos(2 * th) - t_f(th, psi) ** 2 * \
+           (np.cos(2 * th - 2 * r(th)) + r_f(th, psi) * np.cos(2*th)) / \
+           (1 + r_f(th, psi) ** 2 + 2 * r_f(th, psi) * np.cos(2*r(th)))
+
+
+def q_g(th, psi):
+    return r_f(th, psi) * np.sin(2 * th) - t_f(th, psi) ** 2 * \
+           (np.sin(2 * th - 2 * r(th)) + r_f(th, psi) * np.sin(2 * th)) / \
+           (1 + r_f(th, psi) ** 2 + 2 * r_f(th, psi) * np.cos(2 * r(th)))
+
+
+def q_mag(th, psi):
+    return np.sqrt(q_s(th, psi) ** 2 + q_g(th, psi) ** 2)
+
+
+t = np.linspace(0, np.pi / 2, 1000)
+t_deg = t * 180 / np.pi
+pol = np.pi / 4
+
+plt.figure(figsize=(13, 8))
+plt.plot(t_deg, q_s(t, pol), 'r--', label='Q_s')
+plt.plot(t_deg, -q_g(t, pol), 'b-.', label='Q_g')
+plt.plot(t_deg, q_mag(t, pol), 'k', label='Q_t')
+plt.grid()
+plt.xlabel(r'$\theta$, deg', fontsize=18)
+plt.ylabel('Q', fontsize=18)
+plt.legend(fontsize=18)
+plt.title('Beam efficiencies', fontsize=20)
+plt.show()
diff --git a/Python/trap_forces_transverse.py b/Python/trap_forces_transverse.py
new file mode 100644
index 0000000..9d9cae2
--- /dev/null
+++ b/Python/trap_forces_transverse.py
@@ -0,0 +1,158 @@
+# These calculations are based on Ashkin's article "Forces of a single-beam
+# gradient laser trap on a dielectric sphere in the ray optics regime".
+# There are transverse forces only
+
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy import integrate
+from scipy import special
+from scipy import constants
+
+n1 = 1.3337  # index of refraction of the immersion medium
+n2 = 1.4607 # index of refraction of the fused silica at wavelength 523 nm
+n = n2 / n1 # n2/n1
+NA = 1.25  # numerical aperture
+th_max = np.arcsin(NA / n1)  # maximum angle of incidence
+f = 2.0e-3  # objective lens focus or WD
+r_max = f * np.tan(th_max)  # radius of a Gaussian beam (1:1 with input aperture condition)
+Rsp = 1.03e-6  # sphere radius
+P = 14e-3  # power of the laser
+
+
+# Angles
+def r(th):
+    return np.arcsin(n1 / n2 * np.sin(th, dtype=np.cfloat))
+
+
+def phi(dr):
+    return np.arctan(dr / f, dtype=np.cfloat)
+
+
+def gamma(db, dr):
+    return np.arccos(np.cos(np.pi / 2 - phi(dr)) * np.cos(db), dtype=np.cfloat)
+
+
+def thi(db, dr, dy):
+    return np.arcsin(dy / Rsp * np.sin(gamma(db, dr)), dtype=np.cfloat)
+
+
+# Fresnel reflectivity
+def r_f(th, psi):
+    return (np.tan(th - r(th)) ** 2 / np.tan(th + r(th)) ** 2) * np.cos(psi) ** 2 + \
+           (np.sin(th - r(th)) ** 2 / np.sin(th + r(th)) ** 2) * np.sin(psi) ** 2
+
+
+# Fresnel transparency
+def t_f(th, psi):
+    return 1 - r_f(th, psi)
+
+
+# force factors
+def q_s(th, psi):
+    return 1 + r_f(th, psi) * np.cos(2 * th) - t_f(th, psi) ** 2 * \
+           (np.cos(2 * th - 2 * r(th)) + r_f(th, psi) * np.cos(2*th)) / \
+           (1 + r_f(th, psi) ** 2 + 2 * r_f(th, psi) * np.cos(2*r(th)))
+
+
+def q_g(th, psi):
+    return r_f(th, psi) * np.sin(2 * th) - t_f(th, psi) ** 2 * \
+           (np.sin(2 * th - 2 * r(th)) + r_f(th, psi) * np.sin(2 * th)) / \
+           (1 + r_f(th, psi) ** 2 + 2 * r_f(th, psi) * np.cos(2 * r(th)))
+
+
+def q_mag(th, psi):
+    return np.sqrt(q_s(th, psi) ** 2 + q_g(th, psi) ** 2)
+
+
+# Average factors (circular polarization)
+def q_s_avg(th):
+    return 0.5 * (q_s(th, 0) + q_s(th, np.pi/2))
+
+
+def q_g_avg(th):
+    return 0.5 * (q_g(th, 0) + q_g(th, np.pi/2))
+
+
+def q_mag_avg(th):
+    return np.sqrt(q_s_avg(th) ** 2 + q_g_avg(th) ** 2)
+
+
+def q_g_z(db, dr, dy):
+    return q_g_avg(thi(db, dr, dy)) * np.cos(phi(dr), dtype=np.cfloat)
+
+
+def q_s_z(db, dr, dy):
+    return q_s_avg(thi(db, dr, dy)) * np.sin(gamma(db, dr), dtype=np.cfloat)
+
+
+# Intensity profile
+a = 1.0
+w0 = a * r_max
+
+
+def intensity_uniform(dr):
+    return 1 / (np.pi * r_max ** 2)
+
+
+def intensity_gaussian_tem00(dr):
+    amp = (1 - np.exp(-2 * r_max ** 2 / w0 ** 2))
+    p_0 = np.pi * w0 ** 2 / 2
+    return 1 / (amp * p_0) * np.exp(-2 * dr ** 2 / w0 ** 2)
+
+
+def intensity_bessel(dr):
+    p_0 = np.exp(0.5) * w0 * 0.0025 / 4.81
+
+    def temp_f(w):
+        return w * special.jv(0, 2.405 / w0 * w) ** 2
+    amp = integrate.quad(temp_f, 0, r_max)
+    return 1 / (2 * np.pi * amp[0]) * special.jv(0, 2.405 / w0 * dr) ** 2
+
+
+# Intensity profile graphics
+rho = np.linspace(-r_max, r_max, 500)
+fig1 = plt.figure(1, figsize=(10, 6))
+plt.plot(rho, intensity_gaussian_tem00(rho), 'k')
+plt.grid()
+plt.xlabel('r, m', fontsize=18)
+plt.ylabel('I(r)', fontsize=18)
+plt.show()
+
+
+# Integration
+def q_res_g(dy, func):
+    ans = integrate.dblquad(lambda dr, db, dy: dr * func(dr) * q_g_z(db, dr, dy) * (~np.iscomplex(q_g_z(db, dr, P))).astype(float),
+                            0, 2 * np.pi, 0, r_max, args=(dy, ),
+                            epsabs=1e-4, epsrel=1e-6)
+    return ans[0]
+
+
+def q_res_s(dy, func):
+    ans = integrate.dblquad(lambda dr, db: dr * func(dr) * q_s_z(db, dr, dy) * (~np.iscomplex(q_g_z(db, dr, P))).astype(float),
+                            0, 2 * np.pi, 0, r_max,
+                            epsabs=1e-4, epsrel=1e-6)
+    return ans[0]
+
+
+# Calculation
+n = 150
+y = np.linspace(-2 * Rsp, 2 * Rsp, n)
+
+transverse_g = np.abs(np.array([q_res_g(x, intensity_gaussian_tem00) for x in y]))
+transverse_s = np.array([q_res_s(x, intensity_gaussian_tem00) for x in y])
+
+f_0 = n1 * P / constants.c  # net force
+
+transverse = transverse_g + transverse_s
+
+
+# Graphics
+fig2 = plt.figure(2, figsize=(10, 6))
+plt.plot(y, transverse_g, 'b-.', lw=1, label='$F_{g}$')
+plt.plot(y, transverse_s, 'r--', lw=1, label='$F_{s}$')
+plt.plot(y, transverse, 'k', lw=1, label='$F_{t}$')
+plt.xlabel('r, m', fontsize=18)
+plt.ylabel('F, m', fontsize=18)
+plt.legend()
+plt.grid()
+plt.show()
\ No newline at end of file